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Binary pulsars: evolution and fundamental physics Ferdman, Robert Daniel 2008

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Binary pulsars Evolution and fundamental physics by Robert Daniel Ferdman B.Sc.(Physics), Trent University, 2000 M.Sc.(Astronomy), University of British Columbia, 2002 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Physics and Astronomy)  THE UNIVERSITY OF BRITISH COLUMBIA January 2008 C) Robert Daniel Ferdman, 2008  Abstract^  ii  Abstract In the standard theory of pulsar spin-up, a neutron star (NS) in a binary system accretes matter from its companion star; this serves to transfer angular momentum to the NS, increasing the spin frequency of the pulsar. Measurement of the orbital parameters and system geometry, and in particular the final system masses, thus provide important constraints for theories regarding binary evolution. We present results from an investigation of three binary pulsar systems. PSR J1802-2124 is in an intermediate-mass pulsar binary system with a massive white dwarf companion in a compact orbit with a period of 16.8 hours. We have performed timing analysis on almost five years of data in order to determine the amount of Shapiro delay experienced by the incoming pulsar signal as it traverses the potential well of the companion star on its way to Earth. We find the pulsar in this system to have a relatively low mass at 1.24 ± 0.11 M®, and the companion mass to be 0.79 ± 0.04111. . )  We argue that the full set of system properties indicates that the system underwent a common-envelope phase in its evolutionary history. The double pulsar system PSR 0737-3039A/B is a highly relativistic double neutron star (DNS) binary, with a 2.4-hour orbital period. The low mass of the second-formed NS, as well the low system eccentricity and proper motion, have suggested a different evolutionary scenario compared to other known DNS systems. We describe analysis of the pulse profile shape over six years of observations, and present the constraints this provides on the system geometry. We find the recycled pulsar in this system, PSR 0737-3039A, to have a low misalignment angle between its spin and orbital angular momentum axes, with a 95.4% upper limit of 14 °, assuming emission from both magnetic poles. This tight constraint lends credence to the idea that the supernova that formed the second pulsar  Abstract^  iii  was relatively symmetric, possibly involving electron captures onto an 0-Ne-Mg core. We have also conducted timing analysis of PSR J1756-2251 using four years of data, and have obtained tight constraints on the component masses and orbital parameters in this DNS system. We have measured four post-Keplerian timing parameters for this pulsar; the Shapiro delay s parameter, with a 5% measured uncertainty, is consistent at just above the la level with the predictions of general relativity. The pulsar in this system has a fairly typical NS mass of 1.312 ± O.017M ® , and the companion NS to be relatively light, with a mass of 1.2581017 Mo . This, together with the somewhat low orbital eccentricity of this system (e 0.18), suggests a similar evolution to that of the double pulsar. We investigate this further, through a similar pulse profile analysis to that performed with PSR J0737-3039A, with the goal of constraining the geometry of this system.  Contents^  iv  Contents Abstract  ^ii  Contents ^  iv  List of Tables ^  vii  List of Figures ^  viii  Acknowledgements ^  xi  1  Introduction: "A Brief History of Timing" 1.1  1.2  1.3  Pulsars as neutron stars  ^  ^  2  1.1.1^Pulsar spin-down ^  2  1.1.2^Magnetic field ^  3  1.1.3^Pulsar age estimation ^  4  Pulsar timing ^  4  1.2.1^Pulse profiles  5  ^  1.2.2^Pulse times-of-arrival ^  7  The timing model ^  9  1.3.1^Solar System corrections and astrometric parameters  ^  1.3.2^Orbital parameters ^ 1.3.3^Post-Keplerian parameters and relativistic effects  1.4  1  9 10  ^  11  1.3.4^Fitting procedure ^  14  Pulsars in binary systems  15  ^  Contents  2  1.4.1^Pulsar recycling ^  15  1.4.2^Binary evolution  16  ^  1.5^This thesis  22  Data acquisition and processing ^  23  2.1  Telescopes ^  23  2.2  Interstellar dispersion: causes and cures  24  2.2.1^Correcting for dispersive smearing ^  25  2.3  Coherent dedispersion in practice: GASP ^  28  2.4  Downstream data processing ^  30  2.4.1^Rejection of corrupted data  31  ^  2.4.2^Flux calibration ^  32  2.4.3^Profile combination ^  33  2.4.4^Work in progress: polarization calibration 3  34  PSR J1802-2124: how common is a common envelope? ^  36  3.1  Intermediate-mass binary pulsars ^  37  3.2  Observations  39  3.3  Timing Analysis ^  41  3.4  Results ^  47  3.4.1^Future measurements and studies ^  51  Evolution of the PSR J1802-2124 system  53  3.5  3.6 4  ^  ^  3.5.1^The question of common-envelope evolution for IMBPs ^  54  Conclusions ^  59  PSR J0737-3039A/B: the double pulsar ^  60  4.1  Formation and evolution of the double pulsar system  62  4.2  Geodetic precession and long-term profile changes ^  65  4.2.1^Past searches for geodetic precession effects in the double pulsar  66  Observations ^  67  4.3  ^  Contents^  vi  4.4 A new search for geodetic precession effects on PSR J0737-3039A .^69 4.4.1 Two-pole emission from PSR J0737-3039A ^ 90 4.5 Special relativistic aberration and short-term profile changes ^ 100 4.5.1 Prediction of aberration from long-term analysis ^ 104 4.5.2 Searching for aberration ^  106  4.5.3 Using multiple-epoch data simultaneously ^  118  4.6 Implications for evolution ^  120  5 PSR J1756-2251: a pulsar with a light neutron star companion ^123 5.1 Observations ^  124  5.2 Timing Analysis ^  125  5.3 Neutron star masses and a test of general relativity ^ 132 5.4 Geodetic precession in the PSR J1756-2251 system ^ 137 5.4.1 Pulse shape evolution ^  138  5.4.2 Constraints on the geometry of PSR J1756-2251 ^ 138 5.5 The evolution of PSR J1756-2251 ^  148  6 Concluding remarks ^  156  Bibliography ^  159  List of Tables^  vii  List of Tables 3.1  Observations of PSR J1802-2124 ^  40  3.2 Parameters for PSR J1802-2124 ^  46  3.3 Known intermediate-mass binary pulsars ^  56  4.1  Parameters for the PSR J0737-3039 system ^  61  4.2  Observations of PSR J0737-3039 ^  69  4.3 cu and S from long-term profile analysis of PSR J0737-3039A ^ 102 5.1  Observations of PSR J1756-2251 ^  5.2 Parameters for PSR J1756-2251  ^  126 131  5.3 Fit geometric parameters for PSR. J1756-2251 ^  148  5.4 Double neutron star properties ^  152  List of Figures^  viii  List of Figures 1.1 Example integrated profile for PSR J0737-3039A  ^6  3.1 PSR J1802-2124 template profile ^  42  3.2 Shapiro delay in PSR J1802-2124 ^  45  3.3 PSR J1802-2124 timing residuals ^  48  3.4 PSR J1802-2124 timing residual histograms ^  49  3.5 Joint (m 2 , Icos ij) probability density contours for PSR J1802-2124 ^50 3.6 Marginalized PDFs of m l , m 2 and !cos for PSR J1802-2124 ^ 51 4.1 Differences in the PSR. J0737-3039A pulse profile ^ 70 4.2 Pulse width measurements of PSR. J0737-3039A ^ 72 4.3 Diagram of pulsar spin geometry ^  75  4.4 Diagram of pulsar orbital geometry ^  76  4.5 Diagram of pulsar precession geometry ^  77  4.6 Joint probability contours for 6 and Ti  79  ^  4.7 Marginalized PDF for 6 from (6, TO grid search ^ 80 4.8 Marginalized PDF for  Ti ^  4.9 Joint probability contours for a and S ^ 4.10 Marginalized PDF for a ^ 4.11 Marginalized PDF for 6 from (a, 6) grid search ^  82 83 84 85  4.12 Histogram of best-fit a values from 6 and T1 grid search ^ 87 4.13 Histograms of best-fit p from one-pole scenario ^  89  4.14 Pulse width measurements of PSR J0737-3039A for two-pole scenario ^92  ix  List of Figures^  4.15 Joint probability contours for 6 and T1 in the two-pole model ^93 4.16 Marginalized PDF for S from (6, T1 ) grid search in the two-pole model^94 4.17 Marginalized PDF for T1 in the two-pole model ^ 95 4.18 Joint probability contours for a and S in the two-pole model ^ 96 4.19 Cleaned joint probability contours for a and S in the two-pole model^97 4.20 Marginalized PDF for a in the two-pole model ^  98  4.21 Marginalized PDF for S from (a, 5) grid search in the two-pole model ^99 4.22 Histograms of best-fit p from two-pole scenario ^  101  4.23 PSR J0737-3039A 820 MHz standard template profile ^ 105 4.24 Reference and orbital phase-binned profiles ^  108  4.25 Reference and orbital phase-binned profile residuals ^ 109 4.26 Profile shifts as a function of orbital period ^  110  4.27 Joint PDFs for single-epoch aberration fits ^  112  4.28 Joint PDFs for single-epoch aberration fits with values of p ^  113  4.29 Profile shifts as a function of orbital period for two-pole model ^ 115 4.30 Joint PDFs for single-epoch aberration fits ^  116  4.31 Joint PDFs for single-epoch aberration fits with p for two-pole model^117 4.32 Joint PDFs for multi-epoch aberration fits for one-pole model ^ 119 4.33 Joint PDFs for multi-epoch aberration fits for two-pole model ^ 121 5.1 PSR J1756-2251 standard profile ^  128  5.2 PSR. J1756-2251 best-fit timing residuals ^  129  5.3 PSR. J1756-2251 timing residual histograms ^  130  5.4 Joint (a12, mtotai) probability density contours for PSR J1756-2251 ^133 5.5 Marginalized PDFs for the PSR. J1756-2251 system masses^ 134 5.6 Mass-mass diagram for PSR J1756-2251 ^  136  5.7 Pulse width measurements of PSR J1756-2251 ^ 139 5.8 Joint probability contours for S and T1  ^  141  5.9 Marginalized PDF for S from (S, T1 ) grid search ^ 142  List of Figures  5.10 Marginalized PDF for T 1 ^  144  5.11 Joint probability contours for a and 6, i = 64.3° ^ 145 5.12 Joint probability contours for a and 6, i. = 115.7° ^ 146 5.13 Marginalized PDF for a ^  147  5.14 Marginalized PDF for 6 from (a, 5) grid search ^  149  5.15 Histograms of best-fit p ^  150  xi  Acknowledgements First and foremost, I would like to give most sincere thanks to my research advisor, Ingrid Stairs, without whom this dissertation would obviously not have been possible. Through her guidance and encouragement over the past five years, I have learned many more things not only about pulsar astronomy, but also about performing quality science in general, than I could possibly list here. It has been a real pleasure being her first graduate student. Thanks to Joeri van Leeuwen, from whom I've learned a great deal as well, and who no doubt helped me with my state of mind at crucial times. I would also like to thank fellow UBC pulsar group members past and present, and of course the graduate students of the UBC astronomy group, for the comradery and often useful discussions. Many thanks to the UBC Physics and Astronomy department secretaries and staff for all the help they have given me over the years. Many thanks as well to the members of my doctoral committee and university examiners for their guidance and very useful comments: Jaymie Matthews, Jeremy Heyl, Matthew Choptuik, Douglas Scott, and Philip Loewen. Additionally, I would like to thank my external examiner, Timothy Hankins, for his comments and thought-provoking questions. I have worked with many collaborators whom I would like to acknowledge and thank individually for their help and ideas along the way: Michael Kramer, David Nice, Don Backer, Paul Demorest, Maura McLaughlin, Duncan Lorimer, George Hobbs, Dick Manchester, Andrew Lyne, Andrew Faulkner, Fernando Camilo, Andrea Possenti, Rene Breton, Marta Burgay, Nichi D'Amico, Paulo Freire, Jason Hessels, and Vicky Kaspi. In addition, I would like to thank the Caltech, Swinburne University, and NRL pulsar groups for use of the CGSR2 cluster at Green Bank. I am grateful to Matthew Bailes  xii for providing flux density information on several pulsars, and to Joris Verbiest, Matthew Bailes, and Bryan Jacoby for helping in the understanding of the GBT clock history, which was very important for the timing performed in this work. I wish to express my gratitude to the University of British Columbia for generously funding a portion of my studies with a UBC University Graduate Fellowship award. Moreso than I can possibly express, I could not have arrived at this point without the encouragement and love of my parents, my sisters, and the rest of my family. The same is true for the great close friends I have made during my time in Vancouver, €i,8 well as my old friends in Ontario and abroad. I would like to thank the many coffee shops on Main Street for giving me a friendly place to work on the frequent occasions when I desperately needed a change from my home or my office. Finally, I would like in no small part to thank the City of Vancouver, for providing what could be the most beautiful setting possible within which to live during my seven-year run in graduate school; it is a place I will always remember and miss greatly.  1  Chapter 1  Introduction: "A Brief History of Timing" Jocelyn Bell discovered the first pulsar, PSR B1919+21, in 1967 at Cambridge University, an object which observations showed to be a source of rapid pulsation at highly regular intervals of 1.4 seconds (Hewish et al., 1968). It did not take long for those pulses to be associated with neutron stars (NS; Gold, 1968; Pacini, 1968). This was confirmed with the discovery of the pulsars in the Vela (89 ms; Large et al., 1968) and Crab nebulae (33 ms; Staelin & Reifenstein, 1968), which have spin periods that could only be achieved by a rotating object as compact as a NS. In addition, the association of these pulsars with supernova remnants corroborated the prediction of the existence of neutron stars, first proposed by Walter Baade and Fritz Zwicky in 1934, as being not only remnants of stars that have ended their lives as supernovae, but also extremely dense objects With small radii (Baade & Zwicky, 1934). Since then, many important discoveries in the field of pulsar astrophysics have been made. These include, for example: confirmation of the general relativistic prediction of orbital decay due to gravitational wave emission from the first-discovered radio pulsar in a binary system (Hulse & Taylor, 1975; Taylor & Weisberg, 1989); the first millisecond pulsar (Backer et al., 1982); the first pulsar in a globular cluster (Lyne et al., 1987), the first pulsar with planetary-sized companions (Wolszczan & Frail, 1992); and recently, the discovery of the first double neutron star system in which both objects are seen as pulsars (Burgay et al., 2003; Lyne et al., 2004), providing the most stringent test to date of general relativity in the strong field regime (Kramer et al., 2006). This (very abbreviated) list becomes significantly more extensive when one includes the eventual  Chapter 1. Introduction: "A Brief History of Timing" ^  2  discovery and study of neutron stars at X-ray and other wavelength ranges—Jocelyn Bell's discovery has indeed proved to be one of immense astrophysical significance. Exciting related topics such as the neutron star equation of state, its emission mechanism, the pulsar magnetosphere, globular cluster dynamics, and a myriad of others, are those for which the questions are many and the answers are few. Included in this list is binary pulsar evolution, a subject which itself has many open questions, and which will be the principal focus of this thesis. We first discuss the concepts and procedures that allow us to perform these studies.  1.1 Pulsars as neutron stars Radio pulsar emission is generally accepted to come from a region above the magnetic poles of a neutron star (Gold, 1968; Pacini, 1968; Goldreich & Julian, 1969; Sturrock, 1971). Every time this emission region passes by the observer's line of sight (should it ever cross the line of sight), we observe a pulse when that emission arrives at Earth. This phenomenon, known as the "lighthouse model", is the generally-accepted description of the relationship between the rotation of the NS and the pulses we observe. Detailed reviews of pulsars and pulsar astrophysics can be found in Manchester & Taylor (1977), Lyne & Smith (1998), and Lorimer & Kramer (2005).  1.1.1 Pulsar spin-down Pulsars are known to be remarkably stable timekeepers (e.g., Kaspi et al., 1994) In general, however, they do experience some slowing down of their rotation speeds. This is assumed to be caused by magnetic dipole radiation, most of which is released as highenergy radiation and a pulsar wind (as in the Crab pulsar, for example). It is also ultimately responsible for the emission we see at radio wavelengths.  Chapter I. Introduction: "A Brief History of Timing"^  3  Spin-down of the pulsar results in the release of energy due to the loss of rotational energy over time, or spin-down luminosity, given by (e.g., Lorimer & Kramer, 2005)  dE rot^d(I52212) =MO, ^ dt^dt  (1.1)  where I is the moment of inertia of the NS (typically assumed to be 10' g cm 2 ), Q = 27v is the angular rotational frequency, and 0 = 27/i its derivative with time. Spindown rates of the majority of pulsars with  ti  1-second spin periods are very small,  P 10 -15 s s -1 . Millisecond pulsar are even more stable rotators, with  P  10-20 ss-i  (see, e.g., Lorimer & Kramer, 2005).  1.1.2 Magnetic field If we do assume the pulsar to be a rotating magnetic dipole, we can equate the above expression for spin-down luminosity to that for the energy output of a rotating magnetic dipole. This allows us to solve for the surface magnetic field strength in terms of the pulsar spin period P and period derivative P (e.g., Lorimer Kramer, 2005): Bsurf  3.2 X 10 19 G ^PP ,^  (1.2)  assuming I = 10 45 g cm 2 , a NS radius of 10 km, and an angle between the spin and magnetic axes of 90°. An important caveat here is that the determination of the braking indices of several pulsars through measurements of their second spin-period derivatives have shown the dipole approximation not to be accurate in general (e.g., Manchester et  al., 1985;  Lyne et al., 1996; Livingstone et al., 2006). However, this expression represents a simple way to get an estimate for the field strength, and is useful in making quick comparisons within the pulsar population. For example, the approximate average surface magnetic field strength of regular pulsars is 10 12 G, while for millisecond pulsars, it is generally — 10 8 G. This decrease by — 4 orders of magnitude in magnetic field strength presumably occurs during the recycling process (e.g., Bisnovatyi-Kogan & Komberg, 1974). Pulsar recycling is discussed in Section 1.4.1.  Chapter 1. Introduction: "A Brief History of Timing" ^  4  1.1.3 Pulsar age estimation Another useful estimator is the characteristic age of the pulsar, an approximation of the time elapsed since the formation of the NS. This is based on the spin-down rate and the current spin period of the pulsar, assuming an initial period that is negligible compared to what is now observed, and that pulsar spin-down is due to magnetic dipole radiation. This gives (e.g., Lorimer & Kramer, 2005): T  P 216 •  (1.3)  This age is referred to as "characteristic" because, as with the estimation of the magnetic field strength above, it is based on assumptions that are likely not generally true. Observations of supernova remnant expansion rates and the positions and proper motions of pulsars likely associated with those remnants have revealed inconsistencies between these derived ages and the characteristic age of several pulsars (e.g., Gaensler Frail 2000 (cf. Thorsett et al. 2002); Kaspi et al. 2001). For the most part, however, it provides a handy way to compare the ages of pulsars within a population or between populations.  1.2 Pulsar timing Although pulsars are intrinsically very stable clocks, the travel time of the emitted pulses is affected by several factors, preventing the intervals between their arrival times as recorded at the telescope from maintaining the remarkable stability with which they are sent to us. By correcting for these factors, whether due to Solar System delays, propagation effects, or the Doppler shift of a binary pulsar, the observed pulses can be turned into a precision tool for studying a stunning variety of astrophysical phenomena in great detail. The fundamentals of pulsar timing have been extensively described elsewhere in great detail (e.g., Manchester & Taylor, 1977; Taylor & Weisberg, 1989; Taylor, 1992; Lorimer & Kramer, 2005; Edwards et al., 2006). We thus introduce and only briefly de-  Chapter I. Introduction: "A Brief History of Timing"^  5  scribe the basic principles involved in what follows, with additional attention given to those aspects most relevant to this thesis.  1.2.1 Pulse profiles As the pulsar emission beam cuts through the observer's line of sight with each rotation of the neutron star, it provides a flux that varies with location within the emission beam. This is recorded by the telescope as a pulse profile, the shape of which dependS on the details of the beam structure. Except in the cases of the highest-flux pulsars, for which single-pulse studies can be performed, the individual pulses received by the telescope are extremely weak. If we have a relatively accurate model predicting the pulse arrival times, we can stack the received signal according to the predicted pulse phase at a giVen time. This process is known as folding, which after a given time results in an integrated profile. Apart from providing an increase in signal to noise (S/N), folding is necessary for performing pulsar timing. It is a generally observed property of pulsar emission that the individual pulse-to-pulse shape varies substantially. However, folding over many pulses will normally produce a very stable profile shape that is a representative fingerprint for the given pulsar (Helfand et al., 1975). It is this profile stability that in part enables consistent and precise pulse arrival time measurements. Figure 1.1 shows an integrated profile for PSR J0737-3039A. This was constructed from data taken over five different observing sessions (3 May - 8 May 2006) lasting up to eight hours each, taken at 820 MHz with the Green Bank Telescope, using the Green Bank Astronomical Signal Processor pulsar backend. This includes data folded over more than — 5.2 x 10 7 individual pulses. It is usually the case, however, that pulse profile stability is achieved by integrating over many fewer pulsar rotations. The contribution of integrated profile stability to the overall arrival-time measurement uncertainty is in general very low compared to other factors (However, see the appendix of Hotan et al. (2005) for a discussion on the procedure used in the timing analysis of PSR J0737-3039A using low-S/N pulse profiles).  Chapter 1. Introduction: "A Brief History of Timing"^  6  0.12 0.10 ›, 0.08 0.) 0.06 0.04 0.02 0.00 ^ 0.0  .^I \*"•rw--"V"."1-.,-:  0.2^0.4^0.6^0.8^1.0  Pulse phase  Figure 1.1 Integrated pulse profile for PSR J0737-3039A, constructed using observations from 3 May - 8 May 2006 at 820 MHz using the Green Bank Astronomical Processor at the Green Bank Telescope.  Chapter 1. Introduction: "A Brief History of Timing" ^  7  1.2.2 Pulse times-of-arrival Each integrated profile has an associated time-stamp, initially derived from the observatory hydrogen maser clock, that represents the central reference time of the set of pulses contributing to the folded profile. Pulsar timing generally requires a large number of pulse time-of-arrival (TOA) measurements, in order to adequately sample binary orbits, for example. This need for frequent sampling normally comes at the expense of the S/N of the profiles used, affecting the accuracy of the measured arrival times. To remedy this, a very high S/N template profile is used as a reference with which an appropriate adjustment can be calculated. Once this is applied to the integrated profile time-stamps, high-accuracy TOA measurements can be obtained. Template profile A standard template profile for a given pulsar is constructed by averaging together many individual profiles, generally chosen for their high S/N and lack of contamination from radio frequency interference (a discussion of identification and exclusion of corrupted profiles is found in Section 2.4.1). This results in a very low-noise, highly stable profile'. It is also possible to create noise-free templates, by fitting multiple Gaussians to template profile data (Kramer et al., 1994; Kramer, 1994). Profile matching Accurate TOAs of incoming pulses can be measured through cross-correlation of observed profiles with the template profile. Following the notation of Taylor (1992), this is done by assuming that the observed profile p(t) is equivalent to the standard template s(t) having undergone a baseline shift a (which can be removed prior to cross-correlation), 'The stability of the template profile in time may break down if effects like geodetic precesSiOn, which causes a variation in the beam direction over time, are important. This would change the profile shape over time, as will be discussed in Section 4.4. In this case, one may wish to use separate template profiles for different observing epochs. Frequency dependence of the pulse profile shape may also require construction of a different template for each frequency observed.  Chapter 1. Introduction: "A Brief History of Timing" ^  multiplication by a scale factor b, a shift in pulse phase  T,  8  and an increase in the level of  random instrumental and other noise g(t). This gives p(t) = a + bs(t — T) + g(t).  Performing the cross-correlation gives the phase shift  T  (1.4)  which is then converted to a  time shift, and applied to the time-stamp of the observed profile, resulting in a TOA measurement. The accuracy of TOAs obtained by performing this cross-correlation in the time domain is limited by the sampling interval At of the data, with typical best accuracies of 0.1 At (Taylor, 1992). However, as shown by Taylor (1992), performing a  x 2 minimiza-  tion by comparing the Fourier transforms of p(t) and s(t) results in a measured shift, and TOAs, with accuracies limited only by the noise of the observed and template profiles. In addition, multiple and/or sharp features in the integrated pulse will result in significant higher harmonics in frequency space, and will thus contribute to providing a more precise fit to the template profile. TOA measurement accuracy is the most important factor affecting the accuracy of timing model parameter determination. Accounting for, and improving when possible, the various instrumental properties affecting measurement accuracy is therefore vitally important for making precision measurements. Template matching is also used to determine profile shifts when needed for other types of processing and analysis. For example, we use it for finding and excluding individual scans corrupted by radio frequency interference, as we discuss in Section 2.4.1. We also determine profile offsets as a function of orbital phase, as described in Section 4.5, in order to search for aberration effects in the profile shape of PSR J0737-3039A.  9  Chapter I. Introduction: "A Brief History of Tinting"^  1.3 The timing model In pulsar timing, the time evolution of the cumulative rotational phase 0 of the neutron star at a time T in the frame of the pulsar, is usually written as a Taylor expansion 3  . (T — Tref)2^-621 11 + 1 i%(T — Tref) ^,^(1.5) f) + — 0(T)^ref v(T T„^  where  ref  is the phase at reference time T = Tref , and v and its derivatives are among  the parameters to be fit. 0(T) can thus be seen as the number of rotations made by the neutron star since the time T„f. . A second spin derivative may be measured in young pulsars undergoing rapid spin-down, but is sometimes mimicked by phenomena such as timing noise (e.g., Arzoumanian et al., 1994). We believe this may be the case in PSR J1802-2124, discussed in Chapter 3. There are several factors that give rise to a set of delays A in the measured pulse arrival times, so that  ^ T — t o bs + A.  (1.6)  One factor comes from the fact that we measure these so-called topocentriC (i.e. the reference frame of the telescope) pulse times of arrival at an observatory on Earth, which is orbit around the Solar System barycentre. In addition, the pulsar may be in orbit itself in a binary system with another object, producing further time-varying changes in pulse arrival times. We must therefore work backward to account for all the effects causing these delays.  1.3.1 Solar System corrections and astrometric parameters The most significant Solar System delays include (e.g., Lorimer & Kramer, 2005): the Earth's motion around the Solar System barycentre (the so-called Romer delay A R, , ) ); the delay due to emission passing through the spacetirne near massive bodies (mainly significant in the case of the Sun), called the Shapiro delay As  ®,  as well as the Einstein  delay AE ® , which includes time dilation and gravitational redshift terms due to the velocity of the Earth and the varying proximity of Solar System bodies to Earth. From  Chapter 1. Introduction: "A Brief History of Timing"^  10  careful consideration of these effects, we can determine accurately the right ascension a and declination 6 of the pulsar. Solar System corrections are calculated in the timing analyses performed in this thesis using the DE405 Solar System ephemeris, published by the Jet Propulsion Laboratory (JPL; Standish, 1998). Deviations from the expected delay due to these effects can be caused by animal parallax 7 for nearby objects, and by relative motion between the pulsar and the Solar System barycentre, which can yield a measurement of the proper motion components it, and pg. We can thus summarize the barycentric corrections to the arrival times as (e.g., Lorimer & Kramer, 2005): AG(a, 11 a, 14, 7 ) = ARID ± Aso + AEo. (1.7) Here, the "0" in the above subscripts denotes that these delay terms are due to Solar System effects.  1.3.2 Orbital parameters Motion of the pulsar in its orbit around the system barycentre will cause a periodic variation in the pulse arrival times at Earth, due to Doppler shift and its varying position in spacetime relative to the Solar System barycentre. The binary properties are characterized by the five Keplerian parameters: the orbital period Pb, the projected semimajor axis of the pulsar's orbit x % sin i, the orbital eccentricity e, the longitude of periastron w, and the time of periastron passage To . These provide a means of translation from the pulsar reference frame to the binary centre-of-mass frame, through expressions that are similar to the Romer delay in the Solar System. If the binary is relativistic (discussed below), additional delays become important which are analogous to the Solar System Shapiro and Einstein delays, so that we have (e.g., Lorimer & Kramer, 2005):  AB — ORB (X, e, Pb, T0, w , (. L. '7 Pb1 ±' I e ) ASB (r, s) DEB (7) + DAB  ^  (1.8)  where the "B" in the above subscripts denotes that these delay terms are due to the presence of the pulsar in a binary system.  Chapter 1. Introduction: "A Brief History of Timing"^  11  The final term in equation 1.8 represents periodic changes in pulse arrival times due to the effects of aberration, which changes the portion of the pulsar emission region swept through the observer line of sight. This will be described further in Chapter 4 when we investigate aberration effects in the double pulsar system, PSR J0737-3039A/B. Briefly, however, the term in equation 1.8 corresponds to so-called "longitudinal" aberration, whereas our profile data are sensitive only to the "latitudinal" component, as will be discussed in that chapter. The Keplerian orbital parameters can be related to the pulsar mass m i and companion mass m 2 via Kepler's Third Law through the mass function, given by (e.g., Lorimer Kramer, 2005): (m2 sin i) 3 4712 x 3  , M® , f(rni, m2) = (ml + m2) 2 TE) Pb  (1.9)  where i is the orbital inclination, and the constant To = GM0 /c 3 = 4.925490947,as is the mass of the Sun expressed in units of time. These masses are not individually measurable through the Keplerian parameters alone. However, measurement of relativistic orbital parameters can help to break this degeneracy, as we now discuss.  1.3.3 Post-Keplerian parameters and relativistic effects If the pulsar observed is in a close orbit with another compact object, the orbital velocity can become a non-negligible fraction of the speed of light c. In addition, strong gravitational fields can cause measurable additional effects to the usual Keplerian paidmeters, for which general relativity (GR) is generally accepted as the best known description. However, it has been shown (Damour Deruelle, 1985, 1986) that these effects can be parametrized such that these departures from the Keplerian description are described in a theory-independent manner, allowing for tests of a variety of theories of gravity, including GR. This formulation is described via the so-called "post-Keplerian" (PK) parameters. For a given gravitational theory, the PK parameters are related to the system masses and the easily measured Keplerian parameters. For example, in the case of GR, if any two of these can be measured through timing, the pulsar and companion masses  12  Chapter 1. Introduction: "A Brief History of Timing"^  can be uniquely determined. Each additional measured PK parameter then giVes a consistency check on the theory, allowing it to be tested. In section 5.3 we will demonstrate such a self-consistency test for GR, for which the PK parameters are given by (e.g., Damour Deruelle, 1986; Taylor Sz Weisberg, 1989): 2/3 (  L .0 = 3Tr  Pb^5/3  1  1  —  e2  (mi + m2) 2/3 ;^(1.10)  1927r 5/3 ( Pb ) 5/3 mi m2 g(e) Pb = ^ To 27^ 5  (mi + m2)1/3'^  2/3 (Pb) 1/3 rn2 (M1 + 2rn2) e 27r^(mi + m2) 4/3  (1.11) (1.12)  r T®m2;^(1.13) -1/3 (Pb) -2/3 (m 1^+ mz)2/3 s T^— ^sin i. ^x^ 27  7n2  (1.14)  These are formulated for m 1 and m2 expressed in units of solar mass e . In equation 1.11 we have also defined  g(e)^  73^37 e 2 + e 4 ) (1 — e 2 ) -7/2 .^(1.15) 24 96 (1 + —  The first two of these relativistic parameters describes a change in the orbital configuration over time. The parameter Co is the advance of periastron, such that the longitude of periastron is now given by (e.g., Damour Deruelle, 1986; Taylor & Weisberg, 1989) w^+  b c;)  27r  '0;^  (1.16)  where wo is the longitude of periastron measured at the epoch To , and V) is the cumulative true anomaly since time To . Pb is the orbital decay that is caused by the release of energy 2 There  are four additional PK parameters: S r and  5o describe relativistic deformation to the orbit.  Sr is not separately measurable, but 60, though challenging, can in principle be measured in the long term with very high-precision data. There are also two aberration parameters A and B that are very difficult to determine; they can be absorbed into several of the other timing parameters, but in principle are expected to cause secular changes in the observed values of  x and e, in conjunction with geodetic  precession. However, as with the deformation parameters, very high-quality observations over a long time baseline would be needed to discern these effects, if such a measurement is at all possible (see, e.g., Damour & Taylor, 1992; Lorimer & Kramer, 2005).  Chapter I. Introduction: "A Brief History of Timing"^  13  from the system in the form of quadrupolar gravitational radiation. In some systems, the possibility also exists for measuring a change in projected semimajor axis x and change in eccentricity 6 due to various effects (e.g., Kopeikin, 1995; Damour Taylor, 1992); these will not be described here. The parameter -y characterizes the effect of gravitational redshift and time dilation due to the motion of the pulsar within the gravitational field of its companion, analogous to the Einstein delay in the case of the motion of Earth in the Solar System, described above. The r and s parameters are the so-called "range" and "shape", respectively, describing the extent of Shapiro delay experienced by the pulsar emission at it traverses the gravitational potential of the companion star. For the Shapiro delay to be pronounced, the companion must be sufficiently massive and the orbital inclination must be nearly edge-on to the observer line of sight. We find this to be an important effect in the case of PSR J1802-2124, as will be discussed in Chapter 3 of this thesis.  We now have an expression that describes the total delay on the pulse arrival times (e.g., Lorimer & Kramer, 2005):  A = A® + AB + Ac + AD (1.17) where A ® refers to the Solar System delays and AB to the delays present if the NS is in a binary system. These are summarized in equations 1.7 and 1.8, respectively. We have not yet discussed the last two of these terms. A c represents the corrections made to the clock time recorded at the observatory when compared to Coordinated Universal Time (UTC) or other time standards, carried out using data from the Global Positioning System (GPS) satellites. The term AD reflects the delay caused by the frequency-dependent refraction of the pulsar emission due to the interstellar medium along the line of sight. This effect, called interstellar dispersion, will be introduced and discussed in more detail in Chapter 2. The parameters that describe the above deviations in the pulse arrival times form a  timing model that characterizes the individual system being studied.  Chapter I. Introduction: "A Brief History of Timing"^  14  1.3.4 Fitting procedure In order to determine the relevant pulsar parameters, the timing model of a given pulsar is compared to the measured TOAs via a least-squares fit to the data, such that we minimize the expression  (0(Ti ) —  n,) 2  o-i  where n i is the closest integer to  (1.18)  o(T), and o f is the uncertainty of the TOA tobs,i as a  fraction of the pulse period. In pulsar timing the aim is to account for each rotation of the neutron star between any two TOAs. If this is achieved, the model is said to be phase connected, and residuals after performing the above least-squares fit will have a Gaussian distribution about zero and with scatter similar to the typical TOA uncertainties (barring other systematic effects on the measured arrival times, such as timing noise, for instance). This method of attaining phase coherence is what enables pulsar astronomers to obtain highly accurate parameter determination, often to an astounding number of significant figures. The precision of the resulting pulsar ephemeris improves with a set of TOAs that span a larger time baseline, and that more densely sample the orbit of a binary system of which the pulsar may be a member. Implementation of the timing model to observations is most widely performed, as in this thesis, with the tempo package 3 , FORTRAN-based software written and optimized over more than 30 years, primarily by researchers at Princeton University and the Australia Telescope National Facility (ATNF). A new, higher-precision, more flexible, C-based version has recently been released by ATNF, and is appropriately enough named tempo2 (Hobbs et al., 2006; Edwards et al., 2006). It will likely become the new standard pulsar timing package, as more members of the community adopt it. 3 http://www.atnf.csiro.au/research/pulsar/tempo  Chapter I. Introduction: "A Brief History of Timing"^  15  1.4 Pulsars in binary systems In the field of the Galaxy and in globular clusters, there are currently 130 pulsars known to be in binary systems, and a further 15 that are now-isolated recycled pulsars (Manchester et al., 2005a; McLaughlin et al., 2005), thought to have once had companions in order to achieve their fast spin periods. The research area of binary pulsars and how they have evolved is a very active one, and the details can become very involved. What follows is a brief description of the major concepts surrounding pulsar recycling and pulsar binary evolution. Excellent reviews are found in Bhattacharya & van den Heuvel (1991), Phinney & Kulkarni (1994), Tauris & van den Heuvel (2006), and Stairs (2004), for example.  1.4.1 Pulsar recycling An isolated pulsar will in principle continue to spin-down until magnetic dipole radiation can no longer sustain its radio emission, and it will eventually "turn off" (see, e.g., Chen & Ruderman, 1993). This situation can change if the pulsar is a member of a binary system with a main-sequence (MS) star, through interactions with the companion as it evolves to overfill its Roche lobe (the boundary equipotential surface where the gravitational influence on a particle is no longer solely due to the source star the Roche lobes of the two stars in a binary system are connected at the unstable point L 1 , the first Lagrangian point, where a particle will experience no net force). This happens either when the companion star evolves to meet the Roche lobe, or if the orbit decays due to angular momentum loss due to gravitational radiation or magnetic braking, causing the Roche lobe to shrink and meet the evolving companion (see, e.g., Tauris & van den Heuvel, 2006). At this point, mass transfer will ensue, from the companion star to the NS. The accreted matter will bring with it angular momentum that will causing the NS to "spin up" , frequently to millisecond periods (Smarr & Blandford, 1976; Alpar et al., 1982; Radhakrishnan Srinivasan, 1982; Srinivasan & van den Heuvel, 1982). There is a significant (up to — 4 orders of magnitude) drop in magnetic field strength (as well  Chapter I. Introduction: "A Brief History of Timing" ^  16  as a decrease in final spin-down rate), presumably due to the accretion process (e.g., Bisnovatyi-Kogan Komberg, 1974), thus making the recycled pulsar observable over a much longer timescale than normal isolated pulsars.  1.4.2 Binary evolution Although the concept of neutron star recycling as described above applies in general, observations of binary pulsars show that the final properties of these systems vary significantly, and are dependent on the particulars of their specific evolutionary histories. Pulsar binary systems found in the field of the Galaxy are usually sorted into four broad categories: • Low-mass binary pulsars (LMBPs) ^pulsars with millisecond spin periods, and low-mass (< 0.45 M® ) white-dwarf companions; • Intermediate-mass binary pulsars (IMBPs) ^pulsars with — 10 ms spin periods, and/or high-mass (> 0.45 MG ) carbon-oxygen (CO) or oxygen-neon-magnesium (0-Ne-Mg) white dwarfs; • Young eccentric pulsar-white dwarf systems ^unrecycled pulsars with very massive (> 0.9M0 ), probably 0-Ne-Mg, white dwarf companions; and • Double neutron star (DNS) binary systems. There are many other types of system, such as the pulsars found in globular clusters, those with planets, or those which contain young pulsars with main-sequence companions, that do not fit these molds. However, the groups listed above are those most relevant to this thesis, and are the systems that represent the majority of existing mass measurements (see, e.g., Nice, 2006), which are crucial to understanding their evolutions.  Chapter 1. Introduction: "A Brief History of Tinting" ^  17  Low-mass binary pulsars Here, when the two stars are on the main sequence, the primary star is above the critical mass for forming a NS through a supernova (> 8 Ak), and the secondary is an averagemass (' 1 AO MS star. The primary will eventually undergo a supernova explosion, leaving behind a neutron star-MS star binary. This remains the situation until the MS star evolves and expands, filling its Roche lobe, and channelling matter via an accretion disk onto the NS. It is during this phase of mass transfer that the system may be observed at X-ray wavelengths as a low-mass X-ray binary (LMXB). This phase also results in tidal circularization of the orbit. The end result is a spun-up millisecond pulsar and a low-mass He white dwarf (WD; see, e.g., Phinney & Kulkarni, 1994). Evidence supporting this scenario comes in part from the expected relationship between the core mass of the mass-losing secondary and the orbital period of the presupernova progenitors of LMBPs, for those with orbital periods Pb > 2 days (e.g., Rappaport et al., 1995). These undergo long, stable phases of mass transfer during which the Roche lobe of the secondary is filled. It is predicted that the size of the WD progenitor's envelope is directly related to the separation between the two stars, as well as the mass of the degenerate core of the giant secondary. Thus one would expect a correlation between the final WD mass and the orbital period of the resulting system (Savotiije, 1987; Rappaport et al., 1995; Tauris & Savonije, 1999). To date, observational determinations of the masses in such systems have been shown to agree well with the values predicted based on the orbital periods (see, e.g., Splaver et al., 2005). However, the statistics of the ensemble of these systems indicate some mismatch to theory, tending to overestimate the WD masses for long-orbital-period systems (e.g., Stairs et al., 2005). Mass transfer in these systems is very efficient at tidally circularizing the orbit. However, it is expected that the final eccentricity in these systems will be non-zero, due to the variable density of the convective cells within the red giant companion's envelope (Phinney, 1992). This leads to a prediction of an order-of-magnitude relationship be-  Chapter I. Introduction: "A Brief History of Timing" ^  18  tween the eccentricity and orbital period for wide-orbit (Pb > 2 d) NS-WD syStems. So far, this matches observation very well (e.g., Stairs et al., 2005). Double neutron stars  In the standard DNS evolutionary scenario, the initial MS stellar masses will both be > 8 .114. The primary star, being the more massive of the two, will proceed first in its nuclear evolution, filling its Roche lobe. Mass transfer will then proceed from its hydrogen envelope to the secondary, and the resulting He star will soon thereafter undergo a supernova event and form a neutron star. The secondary will then evolve and lose matter in a stellar wind, some of which is accreted by the neutron star. The resulting X-ray emission will cause the system to become observable as a high-mass X-ray binary (HMXB). The loss in angular momentum will bring about Roche lobe overflow (RLOF) in the secondary and inspiral of the NS, forming a common envelope (CE). After the CE is expelled, a NS and He star remain (e.g., Smarr & Blandford, 1976). The latter may undergo further RLOF and transfer more matter to the NS, typically spinning it up to periods of tens of milliseconds (e.g., Dewi & van den Heuvel, 2004). Finally, the He-star supernova then leaves behind the DNS system. Usually, it is the recycled NS that is visible as a pulsar. The companion NS, which has a much shorter observable lifetime due to its — 10, 000 x stronger magnetic field strength, and thus more rapid magnetic-dipole spin-down, is normally not seen'. Those DNS systems in compact orbits will spiral in over time due to gravitational radiation and eventually coalesce. This will produce great amounts of gravitational radiation that is hoped to be directly observable by instruments such as LIGO, based on the predicted merger rates (e.g., Kalogera et al., 2004). There exists a second channel by which evolution involving two neutron stars of similar initial mass can proceed, often referred to as the double-core scenario (Brown, 4  two notable exceptions are the younger pulsar in the double pulsar system, PSR J07 3 7-3039B  (Lyne et al., 2004), and PSR J1906+0746 (Lorimer et al., 2006), in which the non-recycled pulsar is seen, and in the case of the latter, not the spun-up NS  Chapter 1. Introduction: "A Brief History of Timing"^  19  1995). This scheme was formulated to avoid the hypercritical accretion of the first-formed NS in a DNS system, possibly causing it to collapse into a black hole (Chevalier, 1993). In the scenario proposed by Brown (1995), the CE phase occurs after both stars have finished burning hydrogen. After the envelope has been ejected, two He stars remain, and the more massive of these will soon explode in the first supernova. From this point on, evolution proceeds as described above. Although CE evolution seems to be a natural way to bring two neutron stars into a closer orbit than the original stellar radius of either NS progenitor, it is still an open question as to whether a CE phase is necessarily required in this type of evolution (Dewi et al., 2006). This debate also has implications in the case of short-period IMBPs, as we further discuss in Chapter 3. Among the known recycled pulsars in DNS systems, there is a strong observed correlation between spin period and orbital eccentricity (McLaughlin et al., 2005; Faulkner et al., 2005). It has been conjectured that this may be due to longer phases of mass transfer, and hence more recycling, in systems with lower-mass He companions. This would result in less mass-loss during the He-star supernova explosion, producing a lower-eccentricity orbit in the case of symmetrical supernovae (Faulkner et al., 2005). It has also been suggested that the lack of high-eccentricity, low spin-period DNS systems may be the result of a selection effect, in which compact, high-eccentricity systems will coalesce at a faster rate, rendering them unobservable (Chaurasia Bailes, 2005). Another explanation put forward by Dewi et al. (2005) points out that supernova kicks (so-called "natal" kicks) will in general impart a random distribution of eccentricities to the resulting DNS system. However, if a low-enough velocity natal kick is applied to these systems, a spin period-eccentricity trend similar to that observed can be reproduced. Thus, they argue that the observed correlation may constrain the kick velocity distribution for DNS binaries, and that the He star-NS phase is the dominant factor in determining the final orbital parameters (see also Willems et, al., 2007). Dewi et al. (2005) also note that the observed misalignment angles between the recycled pulsar spin axis and the orbital angular momentum in PSR B1913+16 (22 O; Kramer, 1998) and PSR B1534+12 (25'; Stairs et al., 2004), and their derived natal kick veloci-  Chapter 1. Introduction: "A Brief History of Timing" ^  20  ties, may be somewhat at odds with their argument. After a supernova, this misalignment angle is expected to equal the difference in angles between the pre- and post-supernova orbital planes (e.g., Wex et al., 2000). Indeed, the kick velocities derived from these angles are predicted to be large: > 250 km s -1 and 190 — 600 km s -1 have been calculated for PSR B1913+16 (Wex et al., 2000; Willems et al., 2004); for PSR B1534+12, 15 — 1350 km s -1 and > 170 km s -1 are derived for the natal kick (Willems et al., 2004; Thorsett et al., 2005, respectively). However, Dewi et al. (2005) notes that it is still an open question whether the axes are aligned in the matter accretion process prior to the second supernova, and hence whether the supernova kick is solely responsible for the subsequent misalignment. This debate will clearly benefit from a larger sample of DNS systems and measurements of their properties. In Chapters 4 and 5, we determine constraints on the PSR J0737-3039A/B and PSR J1756-2251 system geometries, respectively, and discuss the resulting implications for possible evolutionary scenarios. IMBPs and young eccentric systems These will be discussed at greater length in Chapter 3. Briefly, the evolutionary histories of IMBPs are somewhat of a mystery (Camilo et al., 1996). However, it is believed that the NSs in these systems did not undergo as long-duration a mass transfer phase as those in the LMBPs, evidenced by the order-of-magnitude greater spin periods seen in the pulsars within these systems. Some IMBPs are thought to have evolved from a shortlived phase of CE evolution, leaving behind a CO or 0-Ne-Mg WD companion after the envelope is expelled (see, e.g., van den Heuvel, 1994). As we discuss in Chapter 3, this is a subject of debate. The young eccentric NS-WD binary systems are rare, with only two having been found to date. Like the IMBPs, they have a massive WD companion, but are observed to have much longer spin periods 0.394 s for PSR J1141-6545 (Kaspi et al., 2000b; Bailes et al., 2003) and 1.066 s for PSR B2303+46 (van Kerkwijk Kulkarni, 1999) — indicative that they have not been spun-up in a mass-transfer phase. These systems are thought to have been created in a correspondingly rare process, in which the WD  Chapter 1. Introduction: "A Brief History of Timing" ^  21  was formed before the NS (Dewey & Cordes, 1987; Portegies Zwart & Yungelson, 1999; Tauris & Sennels, 2000). This would be possible if the initially more massive MS primary transfers enough matter to the secondary that it pushes the latter above the mass needed to form a NS. The primary has now become a white dwarf, which eventually spirals into the common envelope of the now-massive secondary. Once the envelope is expelled, a He star-WD binary remains. The details of how the He star loses its envelope before the supernova phase are thought to differ between the two known young eccentric binaries (Davies et al., 2002). However, it is clear that the resulting NS will not be recycled, and the binary orbit will retain the eccentricity induced by the supernova. Some evidence and more questions Direct observational evidence of pulsar recycling came with the first X-ray detection of an accreting millisecond X-ray pulsar, SAX J1808.4-3658 (Wijnands & van der Klis 1998; Chakrabarty & Morgan 1998), and several have since been identified (see, e.g. Chakrabarty, 2005, for a review on this topic). Many of these seem to be very shortperiod systems with very low-mass companions. The exact evolutionary history and future of these objects is a subject of active work (e.g., Bildsten & Chakrabarty, 2001; Deloye & Bildsten, 2003; Nelson & Rappaport, 2003). As with every successful theory, there remain several exceptions and unanswered questions regarding recycled pulsars. One of the longest-standing mysteries is that regarding the origin of isolated millisecond pulsars. They probably do not result from complete ablation of the companion star by the pulsar wind in "black widow"-type systems (Ruderman et al., 1989), since the rate at which this is estimated to occur is likely too slow to evaporate the WD on similar timescales to the characteristic ages of these pulsars (e.g., Stappers et al., 1998). There are also many "oddball" systems that cannot be simply explained by a standard evolutionary scenario. Among these are the pulsars in globular clusters that fall victim to the complex dynamics within those dense systems, pulsar-planet systems, and several other individual systems that present interesting excursions into rarely-observed physical  Chapter 1. Introduction: "A Brief History of Timing"^  22  circumstances. One thing is certain: there exists a large variety of system typeS, and in order to disentangle the specific processes involved in their formation and evolution, more observational constraints of binary properties are required. This will in turn constrain the theories that strive to make sense of what has often been referred to as the pulsar "zoo".  1.5 This thesis Following Chapter 2, in which we discuss the observing systems and data processing, we describe the observations and analysis of three binary pulsar systems: PSR J1802 - 2124 (Chapter 3) is an IMBP system for which we have measured the component masses with pulsar timing, through detection of the effects of Shapiro delay. We find these measurements to provide constraints on the formation history of this class of system.  PSR J0737 - 3039A is the recycled pulsar in the double pulsar system (Chapter 4). We search for the effects of geodetic precession in this pulsar, expected over time to change the direction of the emission beam relative to the observer's line of sight. This in turn should change the observed shape of its integrated pulse profile, which we measure and use to set constraints on the geometry of the system. PSR J1756 - 2251 (Chapter 5) is a DNS system for which we precisely measure the pulsar and companion neutron star masses through determination of three relativistic orbital parameters, providing a test of GR.. As with the analysis of PSR J0737-3039A, we also attempt to determine the system geometry in this system by constraining the effect of geodetic precession on the pulse profile shape over time. In all these systems, the combination of orbital properties, system masses, and geometries provide the best clues we have toward uncovering their evolutionary histories. Through this work, we hope to contribute some small amount of increased understanding of the processes that govern binary evolution in systems containing stars that, after ending their main sequence lives, have begun their new lives as pulsars.  23  Chapter 2  Data acquisition and processing 2.1 Telescopes The observational data obtained for the studies performed in this thesis were taken with the 64-m Parkes radio telescope in Australia and the 105-m Robert C. Byrd Green Bank Telescope (GBT) in West Virginia, USA. The telescope receivers have dipole feeds that accept the electromagnetic (EM) radiation at orthogonal polarizations for a given frequency band, usually in either X-Y linear or left-right circular polarization bases. The data used in this thesis were taken exclusively with linear polarization feeds. Data received by the telescope are down-converted by a series of local oscillators, amplifiers, and filters, through an intermediate-frequency phase, collectively referred to as the telescope IF/LO chain. The precise IF/LO settings are determined before every observing session in tandem with the telescope operator. The signal is then fed to specialized instruments, or backends, that perform further conversions, digitization, and data manipulation that is required by the astronomer for the given project that is undertaken. The effects of interstellar dispersion can severely degrade the incoming signal. Perhaps the most important task of a pulsar backend is that of correcting for this impediment before the data can be analysed for various studies. We thus first describe dispersion, its effect on pulsar emission, and the methods of its removal.  ^  24  Chapter 2. Data acquisition and processing^  2.2 Interstellar dispersion: causes and cures A full treatment of dispersion of pulsar emission and its removal can be found elsewhere (e.g., Hankins Sz Rickett, 1975; Manchester & Taylor, 1977; Lorimer & Kramer, 2005). Here, we present a brief overview of the principles involved. The interstellar medium (ISM) can be modeled as an ionized plasma; EM radiation passing through it will thus experience some measure of refraction. The group velocity of an EM wave travelling through the ISM is thus given by: Vg = C  1  —(  f 112 )2  (2.1)  where f is the frequency of the EM wave, and fp is the plasma frequency, given by: fp=  e 2 ne  (2.2)  nin e  where e is the electron charge, m e is the electron mass, and 74 is the electron number density of the plasma. The extra time taken for a wave travelling a distance L, compared to the travel time in the absence of an ISM (or equivalently, compared to a signal of infinite frequency) is thus  foL ne (1) dl dl L ^ e2^ ^I t =--^— — ^ti 0^ vg^c^27rm e c^f 2  ^L  (2.3)  where the approximation above assumes fp, < f, which holds in the case of the ISM and typical observing frequencies. We can now express the dispersive delay between two observing frequencies fi and 12 , as: t2 —t i =  e  2^i 1^1^  L  ^ne(1)d1 ,^(2.4) 27rm e e f? f? 10  where fi > 12 . For a given pulsar at distance L, the dispersion constant D is defined (e.g., Manchester & Taylor, 1977):  t2—ti D=^ f2-2 f1-2 •  (2.5)  If we collect data from a given pulsar at multiple frequencies, we can directly measure the delay in the observed pulse arrival times, and thus determine the constant D. In  Chapter 2. Data acquisition and processing ^  25  practice, tempo replaces the term e 2 /27rm e e with the constant 2.41x110 -16 CM -3 pc's, which is very close in value'. We then define the dispersion 'measure DM as: DM = 2.41 x 10 -16 D cm -3 pc.^  (2.6)  The dispersion measure is thus a (very good) approximation to the electron column density  f L n e (1)dl, but is defined based on a constant and the observed time delay in  arrival times of data taken at separate frequencies. In general, a given pulsar's DM is observed to vary slightly over time (e.g., Kaspi et al., 1994) due to changes in the intervening ISM.  2.2.1 Correcting for dispersive smearing The effect of dispersion on the pulse profile, and correcting for it, is of particular importance in performing high-precision timing. As the pulsar emission propagates through the ISM, it experiences the delays discussed above, which serve to smear the profile when observing across even a modest bandwidth. Using equation 2.4 we find that over a bandwidth Af centred at a frequency f , the smearing in time will be 2 DM Af  tDM —  2.410 x 10 -16 f3  seconds,  (2.7)  for frequencies expressed in Hz, and under the assumption that Af < f. As an example, for a bandwidth Af =- 64 MHz at an observing frequency f = 820 MHz, similar to what we have used at the GBT to perform observations of PSR J0737-3039A (DM = 48.9 pc cm -3 ), this corresponds to a delay of approximately 1 ms across the band used. This is a sizable fraction of the spin period of the pulsar (22.7 ms). Clearly this presents a problem for pulsar observations, especially those of recycled pulsars, a great many of which have spin periods that are an order of magnitude shorter than this. There are two main methods that are employed by pulsar astronomers in the effort to reconstruct as faithfully as possible the pulse profile as emitted from the neutron star. 1  e2/27T.Tnee = (4.148808 ± 0.000003) x 10 15 cm 3 pc -1 s, whereas the constant used in practice is  1/(2.410 x 10 -16 ) = 4.149 x 10 15 cm 3 pc -1 s.  Chapter 2. Data acquisition and processing^  26  We now briefly discuss each of these, as they were used in obtaining the data sets for the work carried out in this thesis. Filterbank (incoherent) dedispersion The principle behind this method is a relatively simple one: Although the dispersive delay across the entire observing bandwidth is sizable compared with the pulsar spin period, if that bandwidth can be divided into many narrow frequency channels, then the pulse broadening within each of these channels becomes much smaller compared to the pulsar spin period. This is typically done with a spectrometer using narrow-band filters that accept the incoming signal within small frequency ranges. Each channel is separately digitized, and the appropriate delay, given by equation 2.4 (relative to a reference frequency at the centre of the band) is then applied to each subset of the signal. The resulting data from all channels can then be summed, producing a pulse profile that is significantly less smeared and higher in signal-to-noise than it would be without this "channelization" of the frequency band. Data acquired from the Parkes Telescope that was used in this thesis were taken with a filterbank dedispersion backend. Coherent dedispersion While filterbank systems result in an immense improvement in pulsar timing Precision, the drawback to this method of dispersion removal is that there remains residual smearing due to the finite-size bandwidth of each frequency channel. This has the result of washing out features in the pulse profile; in the case of millisecond pulsars, the broadening across a frequency channel can be of the order of the expected feature size, thus hiding the true pulse shape. This presents a crucial limitation when performing studies of millisecond pulsar emission, for example, which requires precise knowledge of the pulse structure. It is also a disadvantage for timing studies that aim to measure subtle effects on the pulse arrival times, such as the post-Keplerian orbital parameters, necessary for obtaining tight constraints on the system masses and performing ultra-precise tests of general relativity. The retrieval of intricate pulse structure can greatly increase the precision  27  Chapter 2. Data acquisition and processing^  of pulse TOA measurements, as described in Section 1.2.2. This is the aim of coherent dedispersion (Hankins Rickett, 1975), which attempts to fully remove the effect of interstellar dispersion on the incoming pulsar signal. The power of coherent dedispersion comes in viewing the delay in the pulse arrival time as equivalent to a phase shift caused by the ISM, which acts as a filter that is characterized by a transfer function H. This function, when convolved with the signal as emitted by the pulsar, results in the delay that is observed. To undo the dispersion, we use the measured amplitude and phase of the complex voltage  vineasured(t)  generated  in the telescope feed, directly related to the original EM signal arriving at the telescope. By convolving the incoming signal with the inverse of the ISM transfer function, we recover the intrinsic voltage emitted by the pulsar, and complete removal of dispersion can be achieved. This is most easily done in frequency space, in which we define the Fourier transforms Vmeasured of Vmeasurech and TINS of the recovered signal originating at the neutron star vNs. We then have VNS(fo + f) = Vmeasured(f0 f)11 -1 (f0 + f), (2.8)  for fo — 0f/2 < f < fo Af/2, where Af is the observing bandwidth centred at frequency fo . This assumes that the incoming signal is well-filtered and Nyquist sampled so that there is no signal outside this frequency range. The transfer function is given by (e.g., Hankins Rickett, 1975; Lorimer & Kramer, 2005)  H(fo + 1)—  e  ±i DM ^2r , f)jdf 2  2.4,0-16 (fo  (2.9)  where the negative sign applies to lower sideband 2 data. Applying the operation in equation 2.8 has the effect of "unwinding" the phase shift that has been applied by the ISM to the incoming pulsar signal. 2  "Lower sideband" refers to the band frequency order being reversed due to the choice of local  oscillator frequencies applied to the signal during the down-conversion process.  Chapter 2. Data acquisition and processing^  28  2.3 Coherent dedispersion in practice: GASP Coherent dispersion removal is computationally expensive; it entails computing the Fourier transforms of the observed voltage time series, multiplication by the inverse transfer function, inverse transforming back to the time domain, squaring the resulting signal for detection, then folding the time-series into pulse profiles. For a frequency band with size Af that has been mixed to baseband in quadrature to two bands of width 0f/2, a data stream will be digitized at evenly spaced intervals tramp = (Of ) -1 in order to be complex-sampled at the Nyquist rate. The minimum number of samples to be Fourier transformed must be greater than the corresponding smearing in time due to dispersion. In addition to this, one needs to account for the fact that for a dispersive smearing time corresponding to n samples, accurate dedispersion of the samples at the ends of a set of data of length N to be Fourier transformed (FT block) requires information from an additional n/2 points on either side of that block. As a result, an overlap is required such that for a given FT block, the last n/2 samples of the previous block are appended to the start of the current one, and an additional n/2 samples are included at the end (see, e.g., Press et al., 1986). FT blocks must then be a total of N + n samples long, with only the central N points providing useful data after dedispersion (see, e.g. Lorimer r Kramer, 2005; Demorest, 2007). With this in mind, and using equation 2.7, we find that the minimum required number of samples required for a data block to undergo this process is  trim  NFT > 2 a DM (0f) 2 . tramp  (2.10)  Thus, the situation worsens as pulsars with larger DM are observed. Until relatively recently, this method could only be applied practically with specialized hardware over relatively small bandwidths. In recent years, however, larger computations have been made possible, owing to the great increase in speed, and lower cost, of PC processors. This has allowed for the use of large computer clusters to perform coherent dedispersion in software, which allows for very flexible implementation. Examples of such systems include the Princeton Mark IV system, which has until recently been used at the Arecibo  Chapter 2. Data acquisition and processing^  29  telescope (Stairs et al., 2000), and the CPSR/CPSR2 systems at the Parkes telescope (van Straten, 2003). This type of coherent dedispersion system has now become the standard in pulsar timing instrumentation. In this thesis, the majority of the data-taking for the described analyses has been performed with the Green Bank Astronomical Signal Processor (GASP) backend, which has been developed over the past five years in a collaboration between the University of British Columbia, the University of California at Berkeley, and Bryn Mawr College. GASP (as well as its sister backend ASP, the Arecibo Signal Processor) is a system that performs coherent dedispersion in real time on the Nyquist-sampled data stream in software. It can Nyquist-sample an observing bandwidth of up to 128 MHz. The signal is then divided into 32 4-MHz frequency channels, so that the complex sample rate per channel is 0.25µs. In addition to this, GASP folds the dedispersed signal into integrated pulse profiles, using predictions based on the current best pulsar ephemerides, also in real time. This is done on a "Beowulf" cluster which is composed of the following components: • a master PC node, which is responsible for ensuring all data has consistent timestamps throughout the observing session, as well as storage of the real-tiMe folded pulse profile data; • four dataserver nodes, which retrieve the incoming sampled and channelized data stream from onboard DMA cards that are directly connected to the spectrometer, and distribute the data to the slave PCs; and • 16 slave processor nodes, which perform the coherent dedispersion on the data stream, as well as the folding of pulse profiles, which are then sent back to, and saved on, the master node hard disk in the Flexible Image Transport Systeth (FITS) data file format. In practice, however, the number of samples required to be Fourier transformed are too large for most pulsars, making it difficult to keep pace with the large data rate obtained  Chapter 2. Data acquisition and processing ^  30  from observing over the full band. Observations are usually performed over 64 MHz of bandwidth, though we are often able to increase this to up to 96 MHz, when we are able to add computing nodes from the CGSR2 system 3 , increasing the data processing capabilities. Further detailed information on the GASP spectrometer hardware and data acquisition software can be found in Demorest (2007). The author's particular contribution to the data acquisition system software were as follows: • calculation and implementation of the inverse transfer (or "chirp") function within the ASP Real Time Software (ARTS) data package, which performs data acquisition, coherent dedispersion, folding, and storing of data; • implementation of real-time profile folding routines, which use separate sets of polynomial coefficients for each frequency channel to calculate the predicted pulse phase of each data sample. The latter is necessary in the GASP system, since the DM shifts between adjacent 4-MHz channels can become a significant fraction of a short-period orbit, especially in lower-frequency observations; and • contribution to the development of the data file format and disk-writing routines for GASP data products.  2.4 Downstream data processing Once the pulse profiles have been folded and stored, they must then be processed further before performing subsequent analysis. This requires several steps, which are now outlined. These have been implemented, or are in the process of being implemented, by the author. 3  Another coherent dedispersion backend at the GBT; computing nodes are used courtesy of the  Swinburne/Caltech/NRL pulsar collaboration.  Chapter 2. Data acquisition and processing^  31  2.4.1 Rejection of corrupted data It is often the case that some amount of the data obtained within an observing session is unsatisfactory for further use. These are occasionally readily identified as pulse profiles that have been folded using an incorrect time-stamp, due to poor synchronization between dataservers, or faulty IF/LO settings, and can be excluded from further processing. More frequently, however, the incoming signal is corrupted by radio frequency interference (RFI) that affects the data across the entire band (broadband interference) and/or within specific frequency channels (narrowband interference), and which operates on varying timescales. The signatures of RFI can be highly unpredictable, and as such, the specific data scans that are affected are often difficult to pinpoint, and are almost always tedious to track down and remove. It is thus unavoidable that there will remain several scans corrupted by RFI, which will at best be reflected in the data as an extra level of noise. At the present time, real-time excision of RFI-contaminated data is unavailable on the GASP system, but is a project on which work is being done by other members of our group. Currently, in order to minimize the effect of RFI on the analysis of data collected by GASP, we apply a procedure that identifies individual folded profiles which are found to be spuriously offset in phase with respect to the whole distribution. This is done using the fftf it routine (Taylor, 1992), which cross-correlates a high signal-to-noise template profile (assembled from known uncontaminated data taken within the same session, or else one that was previously constructed) to a given pulse profile, and returns the amount of phase offset between the two (see Section 1.2.2). This cross-correlation is normally used to adjust pulse profile time-stamps for the purposes of pulsar timing, but has proven useful in this application. The calculated phase shifts is expected to follow a Gaussian distribution, so outliers to this distribution are identified as corrupted profiles, and are left out of further processing. Data which are contaminated by RFI are usually immediately identifiable by eye, so this method is believed to be fairly robust for rejection of corrupt data. More importantly, a small fraction of the data which are not affected by the effects of RFI is rejected by this process.  Chapter 2. Data acquisition and processing ^  32  2.4.2 Flux calibration Correct determination of the pulse flux serves two main purposes. The most obvious of these is to gain accurate profile flux information for studies that require it. More importantly, however, flux calibration ensures that the relative contributions from each orthogonal polarization component to the overall total power signal are appropriately scaled, in order to obtain as faithfully as possible the true pulse profile shape. Flux calibration as performed in this thesis uses a phase-correlated pulsed signal from a noise diode, injected at the receiver. At the GBT, the standard noise diode signal is set up to be periodic at 25 Hz. The pulsar is observed with the pulsed diode signal activated, and the data are folded at the noise source frequency to obtain a high signalto-noise "profile", which is at an "on" level for half of the signal period, and at an "off" level for the remainder of that period. The height of the calibration signal corresponds to its flux density, characterized by a temperature T caj, measured in Kelvin. There are two principal methods for calibrating the pulsar signal. One of these uses an unpolarized catalogue continuum source of known flux, such as a radio galaxy or quasar, against which calibration can be performed. This is done by observing the source with the noise diode signal turned on, then moving off-source, again observing with the noise diode signal activated. We can then calculate a calibration factor to be applied to the pulsar signal count to obtain a measurement in flux units. This is given by F(Boff-source Aoff—source) 1 Cal factor = , A Jy count 0-on-source — Aoff—source) Beal Acal  1,  (2.11)  where F is the continuum source flux in Jy, and A and B correspond to the average instrumental signal count units (referred to in equation 2.11, and hereafter, as "counts") measured for the "off" and "on" phases of the calibration pulse, respectively. The subscripts "off/on-source" refer to pointings off and on the continuum source with the noise source pulsing, and the subscript "cal" corresponds to the noise diode source being activated with the telescope pointed at the pulsar. The term in square brackets gives the flux per calibration signal height, obtained from observing the continuum source, and the second factor divides by the height of the pulsed cal when pointing on the pulsar.  Chapter 2. Data acquisition and processing^  33  This is done to avoid the effects of gain and background noise variations at different telescope elevations. The result obtained from equation 2.11 is then multiplied by the pulsar signal data to obtain a flux-calibrated pulse profile. The pulse profiles are calibrated separately for data observed in each orthogonal polarization, as well as within each frequency channel, prior to averaging. When continuum source calibration is not possible (usually due to observing time constraints), we perform the following operation: Cal factor = where G is the telescope gain in K Jy  -1  Tca l  . Jy count -1 , G(B — A) •  (2.12)  ; in the case of the GBT 820 MHz and 1400 MHz  receivers, G = 2.0 K Jy -1 (Minter, 2007). This calibration factor is calculated and applied for each polarization component (which in general have different Tcal values) of the pulse profile, and at each frequency, before they are combined to give a total power signal. A disadvantage to this method is that the value of Tcal must be monitored regularly, which is not always practical. When Tca l value measurements are not made close enough in time to the observing session, we use results from continuum source observations taken as near as possible to the current session. On the infrequent occasions when the calibration signal was not used, we scale the profile in each polarization by the inverse of the RMS of their respective off-pulse signals. In any case, the relative scale factors between data taken for each of the two hands of polarization is most important for timing analysis; small corrections to the nominal value of the telescope gain present a comparatively minimal effect for this purpose.  2.4.3 Profile combination Frequently, we wish to combine many integrated profiles to obtain higher signal-to-noise data with which to perform our analysis. This can be done across a range of frequencies by averaging sets of profiles from contiguous channels, where each resulting profile is then labelled with a frequency that corresponds to the average of each set; the repreSentative pulse phase and period for that profile is taken from the value at the midpoint of the  Chapter 2. Data acquisition and processing ^  34  profile that originally was labelled with that average frequency. We can then combine data to obtain profiles that represent longer integration times. This is done by simply averaging together neighbouring sets of profiles in time. The representative time-stamp of the resulting profile and spin-period phase is taken from the central integration of the combined data set. The resulting averaged pulse profiles can then be used for timing and profile analysis, which we describe in the following chapters.  2.4.4 Work in progress: polarization calibration An additional concern is so-called "leakage" of signal from one handedness of polarization into the other. This is symptomatic of the telescope receiver feeds deviating from exact orthogonality with respect to each other, or from exact linearity or circularity, for ex-  ample. For several endeavours, this becomes a significant hindrance; analyses which are affected include studies of the pulsar emission mechanism, investigations of the Galactic magnetic field using the effects of Faraday rotation on the linear polarizations on a collection of pulsar signals, and magnetospheric studies in pulsar system environments, among others. Although proper polarization calibration can generally overcome this obstacle, the benefit of its application to pulse profile data is usually most beneficial for those pulsars from which analysis can yield timing residuals of sub-microsecond precision (see, e.g., van Straten, 2006). This is not the case for those pulsars studied in this thesis. However, for several pulsars that have proven to be excellent precision timers and/or which are highly polarized sources, Demorest (2007) has shown that polarization calibration problems can be a non-trivial effect in GASP data. An example of this is the millisecond pulsar PSR B1937+21, for which Demorest (2007) demonstrates a low-level (sub-µs) dependence of uncorrected timing residuals on frequency and parallactic (or hour) angle. He has developed a method of "self-calibration" that involves an adaptation of the cross-correlation procedure developed by Taylor (1992), but also includes polarization and relative gain parameters to achieve better self-consistent template pro-  Chapter^Data acquisition and processing^  35  file matching. This reduces the dependence of the timing residuals on frequency and parallactic angle. A similar reduction in systematics should be possible if the total intensity is first corrected for polarization "leakage", following well-established procedures (Stinebring, 1982; Johnston, 2002; van Straten, 2004). These use observations of a pulsar with known polarization properties (e.g., PSR B1929+10, a highly linearly-polarized source), and consist of performing a fit to the pulse profile data to obtain absolute parameters, thus characterizing the effect of the telescope system on the polarization properties of the pulse profile. These telescope parameters can then be applied to any pulsar data that have been taken with an identical observing setup. Calibration software for data taken with GASP (and ASP) that uses this latter method is currently in advanced development, primarily by the author.  36  Chapter 3  PSR J1802-2124: how common is a common envelope? The millisecond periods observed in the majority of pulsars with WD companions indicate that they have undergone a relatively long, stable period of accretion of material from the outer envelope of the companion progenitor, during which the system is seen as a low-mass X-ray binary (Bhattacharya van den Heuvel, 1991; Wijnands & van der Klis, 1998). In the process, the matter-donating star has lost an appreciable amount of mass. This conclusion is supported by the relatively low masses of the WDs found in these binaries, referred to as low-mass binary pulsar (LMBP) systems (see, e.g., Tauris & van den Heuvel, 2006). PSR J1802-2124 (Faulkner et al., 2004) differs in many key ways from most other pulsars in known NS-WD binaries: it has a longer spin period, a significantly more compact orbit, and a heavier companion than are typically found. This points to a separate evolutionary path taken by this system. Specifically, it belongs to the class of  intermediate-mass binary pulsars (IMBPs; see, e.g., Camilo et al., 1996). Our observations of this system have led to measurements of the component masses—an exciting prospect, since this makes PSR J1802-2124 one of only two IMBPs with a mass determination. This has allowed us to study its evolution, and other systems like it, in more detail than afforded by previous observations of IMBPs.  Chapter 3. PSR J1802-2124: how common is a common envelope? ^37  3.1 Intermediate-mass binary pulsars The intermediate-mass binary pulsars (Camilo et al., 1996; Edwards Bailes, 2001a) are a class of relatively unstudied NS-WD systems. They contain NSs with relatively long spin periods (tens of milliseconds), and/or relatively massive carbon-oxygen (CO) or oxygen-neon-magnesium (0-Ne-Mg) WD companions (> 0.4 M o ), in contrast to their LMBP counterparts. In addition, many of those IMBPs with measured eccentricities have values that, while near-circular, are generally at least 1 or 2 orders of magnitude larger than for most LMBP systems (although PSR J1802-2124 is found to be at the lower end of the IMBP eccentricity range). The exact origins of IMBPs remain a puzzle, and several proposed formation scenarios have been suggested for these systems (e.g., Li, 2002). A widely accepted idea is that, as with double neutron star (DNS) binaries, the NS spirals into the envelope of its companion to form a common envelope (CE), which is then promptly ejected from the system (e.g., van den Heuvel, 1994). This is supported by the short orbital periods (Pb ) seen in many of the IMBP systems. It has also been proposed, however, that a neutron star within the envelope of its companion will be forced to undergo hypercritical accretion, becoming a black hole and rendering the system unobservable (see, e.g., Chevalier, 1993; Brown, 1995; Brown et al., 2001, hereafter B01). Tauris et al. (2000) have argued that systems with heavy CO WD companions and orbits with 3 < Pb < 70 days can undergo a short-lived phase of highly super-Eddington mass transfer to the NS. This occurs when the mass transfer rate from the donating star The is very much larger than the Eddington rate (the approximate maximum rate of accretion onto the neutron star, Th —Edd = 1.5 x 10-8 M® yr'). In this case, infalling material will be ejected from the system due to radiation pressure from the accreted material (see, e.g., Tauris et al., 2000). Here, the inspiral that results in a CE is avoided if the re-radiated accretion energy is great enough to evaporate most of the transferred material before it approaches the NS too closely (see also Taam et al., 2000). Still, this scheme does not work for IMBPs with Pb < 3 days, suggesting the need to invoke CE  Chapter 3. PSR J1802-2124: how common is a common envelope?^38 evolution to explain their existence. B01 suggests a possible alternate formation scenario in which the two progenitors are main sequence stars of similar mass, which evolve to form two helium cores. This is similar to a related scenario for the evolution of close DNS binaries (Brown, 1995), the difference being that to form an IMBP, one of the stars would be just below the mass threshold for NS formation, becoming a WD instead. It is clear that the evolution of IMBPs remains an open question. There are now sixteen known IMBP systems, and only one of these, PSR J0621+1002, has measured masses (m 1 = 1.701g Mo , m 2 = 0.971 .. 2157 MG; Splaver et al:, 2002). Here we present results from timing analysis of PSR J1802-2124, discovered in the Parkes Multibeam Pulsar Survey (Manchester et al., 2001; Faulkner et al., 2004). The measured Keplerian orbital parameters from the initial timing of this pulsar show that it can be classified as an IMBP: the minimum companion mass is 0.8 M o , based on an assumed pulsar mass of 1.35 Mo . The orbit is very circular, with e = 2.47 ± 0.05 x 10  -6  (even more circular than most other known IMBP systems), supporting the notion that there was no second supernova explosion, and that the companion is thus a white dwarf. The orbit is also relatively compact (16.8 hours), and the pulsar is only mildly spun up, with a 12.65-ms spin period. The measured DM of this system is 149.6 pc cm -3 , which places it at an estimated distance of 2.9 kpc, assuming the NE2001 Galactic free electron distribution model (Cordes & Lazio, 2002). In the case of PSR J1802-2124, its heavy companion led us to believe that the system would be a good candidate in which to look for the Shapiro delay of the pulses in gravitational potential of the white dwarf. Thanks in part to the high sensitivity of the GBT, we were in fact able to measure such an effect, enabling us to determine the individual masses of each member of the binary system. In what follows, we discuss these measurements, as well as their implications for reconstructing the formation and evolutionary histories of this system and others like it.  Chapter 3. PSR J1802-2124: how common is a common envelope?^39  3.2 Observations We have extended the data set presented by Faulkner et al. (2004), using the 64-m Parkes telescope in Australia. Observations have been carried out by the author's collaborators at regular intervals with the Parkes telescope using a 2 x 512 x 0.5-MHz filterbank centered at 1390 MHz. These were usually 20 minutes in duration. The data from each channel were detected and the two polarizations summed in hardware before 1-bit digitization every 80-250,us. The data were recorded to tape and subsequently folded off-line. Each observing session typically produced five TOA measurements. The nearly five-year timing baseline of the Parkes telescope observations has helped determine effects that are measurable in the longer term, such as the astrometric parameters. We have also used the 100-m Green Bank Telescope in West Virginia. Data-taking at the GBT was performed with the Green Bank Astronomical Signal Processor (GASP; Demorest, 2007), discussed in Section 2.3. The signal was divided into 16 or 24 x 4MHz channels', which were then coherently dedispersed (Hankins & Rickett, 1975) in software. After this, the signal was detected, and folded using the current best ephemeris for the pulsar. The resulting pulse profiles were each built up over typically 3 minutes of integration time. These were usually flux-calibrated in each polarization using the signal from a noise diode source that was injected at the receiver. Finally, the data were summed together across all frequency channels to give the total power signal. A summary of the observing details are found in Table 3.1. Using the GBT, we have obtained a total of 15 epochs of data. Six of these observing sessions consisted of two 8-hour paired sessions in order to gain full orbital coverage. This is of particular importance for the detection of Shapiro delay. The rest consisted of stand-alone days of observation; apart from two short 3-hour observation sessions, each of these epochs consisted of approximately 8 hours of continuous data-taking. One of these days, MJD (Modified Julian Date) 53917 (2006 July 1), showed time-stamp jumps 'The number of channels used occasionally varied, due to radio frequency interference and computing resources.  Table 3.1 Summary of observations of PSR J1802-2124. Telescope  Instrument  Centre  Gain  Tsys  Sampling  Effective no.  Total effective  Integration  frequency (MHz)  (K Jy -1 )  (K)  (As)  of channels  bandwidth (MHz)  time (s)  20  0.25  16-24'  64-96  180  22/28b  80-250  512  256  typically 240  GBT  GASP  1400  2.0  Parkes  Filterbank  1390  0.74  a The number of channels that were used varied depending on the availability of the CGSR2 computing nodes at the GBT, as well as on the removal of channels that are contaminated with radio frequency interference (RFI). b Tsys  values given for the Parkes telescope are for the Multibeam (centre beam) and H-OH receivers, respectively.  Chapter 3. PSR 11802-214: how common is a common envelope?^41 within the same observation, due to sampler clock problems for that day, and so we excluded this epoch entirely from our subsequent analysis.  3.3 Timing Analysis In order to determine the pulse times-of-arrival (TOAs), we first constructed a high signalto-noise profile by aligning many individual pulse profiles in phase and averaging them together. We then performed a multiple-Gaussian fit to this integrated profile (using eight components) obtaining a zero-noise reference template profile (Kramer et al., 1994; Kramer, 1994), shown in Figure 3.1. This was used to calculate TOAs from the GASPderived PSR J1802-2124 pulse profile data. When multiple integrated GBT pulse profiles were combined to derive a TOA, a phase offset was first imposed on each integrated profile before summation, to reflect the updating of the ephemeris for this pulsar since those observations were taken. Pulse TOAs were then calculated by cross-correlating each pulse profile with the reference template profile in the frequency domain (Taylor, 1992). For Parkes data, using a reference profile that was derived from one day of observation, this was done using the psrchive software (Hotan et al., 2004b), which was also used to sum the data. The time offset corresponding to each of the phase shifts was then added to the time-stamp recorded for each profile, resulting in a TOA that represents the midpoint in time of each particular integration. In total, we measured 2332 individual pulse TOAs: 456 from Parkes data, and 1876 from GBT data. A model ephemeris for the pulsar was then fitted to the topocentric TOAs, using the tempo software package. Included in this model is the motion of the Earth, calculated using the JPL DE405 Solar System model (Standish, 1998). Additionally, we fit for arbitrary time offsets between the Parkes and GBT-derived TOAs, to account for any instrumental and standard template profile differences. Corrections were also made to account for offsets between the clock readings from each observatory and UTC time, obtained using data from the Global Positioning System satellites.  Chapter 3. PSR J1802-2124: how common is a common envelope?^42  1.0 +.)  • •••4  0.8 0.6 •  )›.1  •r,  0.4 0.2 0 .0 ^ ^ 0.0^0.2 0.4^0.6 0.8^1.0 Pulse phase  Figure 3.1 Standard template profile for PSR J1802-2124, created by fitting multiple Gaussians to a high signal-to-noise profile. This was used to calculate pulse times-ofarrival for data taken with the GBT.  Chapter 3. PSR J1802-2124: how common is a common envelope?^43 In order to obtain a best-fit value for dispersion measure, we averaged the GASPderived pulse profiles into four frequency bins (1352, 1376, 1400, and 1424 MHz). We performed timing on this subset of the total data set, arriving at a value for DM that we then held fixed for the timing analysis on the entire data set (149.6264+0.0006 pc cm -3 ). During one epoch, however (13 December 2006, 1\4.1D 54082), we did expect a slight change in DM, due to the pulsar passing behind the Sun relative to our line of sight, causing a temporary increase in electron column density (see, e.g., Splaver et al., 2005). To account for this, we included an arbitrary time offset as a parameter to be fit in the timing analysis during this day of observation. The effects of orbital motion on the pulse arrival times were taken into account using the ELL1 timing model (Lange et al., 2001). In addition to the basic Keplerian parameters, we fitted for the Shapiro delay of the pulsed emission as it traversed the gravitational potential well of the companion star. This effect is described in the timing model in terms of the so-called "range" (r) and "shape" (s) parameters; the delay in the pulse arrival times for small-eccentricity orbits is given by (see, e.g., Lange et al., 2001; Lorimer & Kramer, 2005):  At = ln {1 — s sin [— (t — t„,)]} , (3.1) Pb where t is the pulse TOA and t is the epoch of ascending node. Unless the orbit is -asc -S close to edge-on, the Shapiro delay cannot be disentangled from the arrival time delay due to orbital motion (see Lange et al., 2001, appendix). Figure 3.2 shows the timing residuals resulting from various fits to the TOAs. The effect of Shapiro delay is still very evident when fitting for the Keplerian orbital parameters, which absorbed some, but not all, of the Shapiro delay signal. Once the r and s parameters are measured, they can be converted into the companion mass m 2 and inclination angle i. This is done through the following relations (Damour Deruelle, 1986):  r = G 8  ^  C3  = sin i,^  (3.2) (3.3)  Chapter 3. PSR J1802-124: how common is a common envelope? ^44 where the relation for r assumes that general theory of relativity is the correct description of gravity. Figure 3.3 shows plots of the timing residuals from each instrument over time, and histograms of those residuals are shown in Figure 3.4. In obtaining a best-fit model using these values, the scatter in the resulting residuals, while very close to having a random Gaussian distribution about zero, was greater than most of the errors on the individual data points, which were derived from the standard profile cross-correlations (discussed in Section 1.2.2). This was especially the case for the Parkes data, resulting in a value of y2 per degree of freedom v that is greater than one (x 2 = 1.5 and 1.2 for Parkes and GBT data, respectively). This was almost certainly due to an underestimation of the TOA uncertainties that resulted from the profile cross-correlation process, or from lower-quality profiles that arose because of signal contamination by radio frequency interference, or coarse signal quantization as the data were sampled. To compensate, we have calculated a scaling factor to multiply with (and for Parkes data, an additional amount to add in quadrature to) the original uncertainties in the TOAs, so that x 2 /v 1 for each data set. The GBT TOAs had errors that required very little correction, and dominated the data set; we thus report the uncertainties directly output by tempo as 68.3% confidence limits on the fit parameters, shown in Table 3.2. It should be pointed out that we obtain a significant measurement of a frequency second derivative from our timing analysis. This may be due to one or more causes. There may be long-term dispersion-measure changes that can affect the data in this manner, although after searching for a DM derivative in the frequency-separated GASP data set, we found no evidence for such an effect. Perhaps the most likely explanation is that we could be observing timing noise in the pulsar. Collection of more data over time will enable us to better characterize and account more precisely for the inclusion of a second frequency derivative in our timing model. In any case, this long-term trend had no effect on our measurement of the orbital parameters, which is our focus for the time being. The typical weighted RMS of the timing residuals from Parkes data were 12.3 ps for  Chapter 3. PSR J1802-2124: how common is a common envelope?^45 40 30 20 10 0 —10 —20 30 20 •  10 r 7d^0 7,1 —10 a) 1=4 —20 —30 30 20 10 0 —10 —20 —30 0.0  ^  0.2  ^  0.4^0.6 Orbital phase  ^  0.8  ^  10  Figure 3.2 GBT-derived timing residuals for the PSR J1802-2124 system, plotted against orbital phase relative to ascending node passage. Top: The full effect of Shapiro delay. Here, the Shapiro delay r and s parameters were excluded from the fit, with the best-fit orbital and other parameters held fixed. Middle: Once again, the Shapiro delay terms were left out of the fit, but in this case the Keplerian orbital parameters were left to vary as free parameters. Some of the Shapiro delay signal was absorbed into these parameters, however, the effect of Shapiro delay is still very evident in these residuals. Bottom: All parameters, including Shapiro delay, were included in the timing model fit.  Chapter 3. PSR J1802-212.4: how common is a common envelope? ^46  Table 3.2 Parameters for PSR J1802-2124, measured and derived from timing observations and analysis. Timing parameter^  Parameter value  Data span (MJD)  ^52605.2 — 54301.4  Right Ascension, a (J2000)  ^18h02m05'335558(6)  Declination, S (J2000)  ^—21024'03'.'6527(9)  Proper motion in a,^(mas yr -1 )  ^—0.83(9) 79.0664242299630(7)  Rotation frequency, v (s -1 ) ^ Frequency derivative, f, (10 -16 S -2 )  —4.5587(4)  Frequency second derivative, V (10 —^s  —3.36(14) 53453.0  Reference Epoch (MJD) ^ Dispersion measure, DM (pc cm -3 )  149.6264(6)  Projected semimajor axis, x^a p sin i (lt-s)  3.7188532(5)  Orbital Period, Pb (days) ^  0.698889243385(11)  Epoch of ascending node,^(MJD) ^  53452.633290843(6)  esinw  ^0.00000087(9)  e cos w  ^0.00000231(4)  Cosine of inclination angle, 'cos it ^  0.178(-11, +12)  Companion mass, m2 (M0) ^  0.79(4)  Derived parameters Eccentricity, e ^  0.00000247(5)  Longitude of periastron, w (°) ^  21(2)  Epoch of periastron passage, To (MJD) ^  53452.673(4)  Orbital inclination, i (°) ^  79.7(-6, +7) or 100.3(-7, +6)  Mass function, f (M0) ^  0.11305587(4)  Pulsar mass, m1 ( M0) ^  1.24(11)  NOTE.—Parentheses indicate the la uncertainties on the last digit (or last two digits, if two digits are given). Two  numbers separated by a comma indicate the lower and upper uncertainties, respectively.  Chapter 3. PSR 11802-2124: how common is a common envelope? ^47 this pulsar, while for the GBT data, the RMS was 2.0 ,us. The high timing quality of the GBT data was partly due to an increase in observing bandwidth beginning MJD 53693 (19 November 2005), made possible by expanding the data processing power to include computing nodes normally used by the CGSR2 (Caltech-Green Bank-SWinburneRecorder) backend, in addition to the usual GASP nodes. This allowed the widening of the bandwidth from 64 MHz to 96 MHz. It is certain that the use of the GASP instrument has allowed us to discern the Shapiro delay signal in this system more convincingly, and on a much shorter timescale, than would have been possible with the Parkes data alone.  3.4 Results In order to ensure that the measured system masses represent the best model fit, we probed the x 2 over a fine grid of values, evenly distributed in (cos - m 2 space (we use the absolute value of cos i since we cannot distinguish whether i < 90 ° or i > 90 0 ), allowing the rest of the parameters to vary. We then used the computed  x 2 values to  obtain a Bayesian joint posterior probability density by following a similar procedure to Splaver et al. (2002), as follows. We first map the  x 2 grid of values into a Bayesian  likelihood function: 1  , cos i) - e-Ax2l2, (3.4) 2  where {ti } represents the data set, and 0x 2 = )( 2 Vnin is the difference betWeen each value of  x 2 in the (m 2 , cos i) grid and the overall minimum  x 2 value in that grid. Thus,  the joint posterior probability density of m 2 and cos il is given by: p(m2 p(m 2 , cos illti })  , cos i)p(ft cos i) (3.5) P({tj})  Here, p(m 2 , cos i) represents the prior probability for values of m 2 and Icos and the denominator p({ti l) = p(m9 , cos i)p({t i lim 2 , cos i) is a normalization factor that ensures the total probability is equal to one. We choose uniform priors for the companion WD mass in the range 0 < m 2 < 1.4 M® , based on the maximum expected WD mass.  Chapter 3. PSR 11802-21,24: how common is a common envelope? ^48  100 50 0 -50 -100 52500^53000^53500^54000  MJD Figure 3.3 Timing residuals for the PSR, J1802-2124 system plotted against MJD. Parkes-derived residuals are plotted in red, and GBT-derived residuals are plotted in black. The Parkes data were taken regularly over time, to aid in measurement of astrometric parameters. The data represented here do not include those from the actual discovery and initial timing, which were taken with 3, rather than 0.5 MHz, channels. The spacing of GBT data was, as discussed earlier, chosen to sample as fully as possible the orbit of the system.  Chapter 3. PSR 11802-2124: how common is a common envelope?^49 Parkes  GBT/GASP 800  600  0  400  200  —60 —40 —20 0 20 40 60 Residuals (As)  0 —15 —10 —5 0^5^10 Residuals (p.^)  15  Figure 3.4 Histograms of timing residuals for PSR J1802-2124, for Parkes (left) and GASP data taken on the GBT (right). Both data sets are consistent with a roughly Gaussian distribution.  Our prior for the cosine of the inclination angle is uniform in the range 0 < !cos < 1. Thus we have p(m9, cos i) =  m2,max — m2,min 1COS i max — I COS i min  (3.6)  as our prior distribution. We further refined our search, once a coarse grid search demonstrated the area of largest probability density. The resulting confidence contours are shown in Figure 3.5, along with curves of constant pulsar mass m 1 calculated through the Keplerian mass function, given by equa,  tion 1.9. The most probable values for the pulsar mass, companion mass, and Icos i l were found by calculating their respective marginalized probability density functions (PDFs). Details can be found in Splaver et al. (2002, appendix). Figure 3.6 shows these PDFs, as well as the interval enclosing 68.3% of the area under the functions. The bounds of these regions were calculated by determining the parameter values at which the tails  Chapter 3. PSR, J1802-2124: how common is a common envelope? ^50  Orbital inclination ^ 82°^80°^78° 76° 1.0 0  (,)  0.9  cn  0.8 as 0.7 0  0.6 0.12 0.14 0.16 0.18 0.20 0.22 0.24 'cos Figure 3.5 68.3%, 95.4%, and 99.73% confidence contours for PSR J1802-2124 in orbital inclination—companion mass space. Curves of constant pulsar mass are plotted over the contours.  ▪  Chapter 3. PSR 11802-2124: how common is a common envelope?  ^  51  0.20 0.015  0.010 •  0  0.10 0.005  0.05  0.000  0.00 0.8^1.0^1.2^1.4^1.6^1.8 Pulsar mass (Me ) .^ • 0.04 •  0.6^0.8^1.0 Companion mass (M 0 )  ' ^•  4->  •  0.03 0.02  as O 0.01 0.00 0.12 0.14 0.16 0.18 0.20 0.22 0.24 'cos  Figure 3.6 Bayesian marginalized probability density functions for pulsar mass, companion mass, and icos ij. 68.3% confidence intervals are shown by the hashed regions.  on either side of each PDF covers 15.85% of the total area. We find that the best, fit median pulsar and companion masses are 1.24+0.11 MG and 0.79 + 0.041c70 , respectively (68.3% uncertainties). This represents the second-most precise pulsar mass measurement to date in a NS-WD system obtained through pulsar timing, after PSR J1909-3744 (Jacoby et al., 2005).  3.4.1 Future measurements and studies We have also measured the right-ascension component of the system's proper motion to be p a -0.83 + 0.09 Inas yr' (68.3% uncertainty). The pulsar's small ecliptic latitude has made it difficult to measure its proper motion in declination with the current data set.  Chapter 3. PSR J1802-124: how common is a common envelope? ^52 However, within five years, we expect to obtain a significant measurement of /1 6 . These measurements will help us to constrain the space velocity of this system, furthering our understanding of IMBP formation history, by giving us insight into the nature of the natal kick imparted to the system after the NS progenitor underwent a supernova explosion, for instance. We have conducted simulations of future expected data spacing, and have found that, owing to the compactness of its orbit, five more years of observing PSR J1802-2124 will deliver a — 15% determination of orbital decay, with a  ti  6% measurement to come in ten  years. This will be very exciting, as it would allow us to test GR in two different ways: firstly, we would have a third PK parameter measured, allowing us to perform a test of GR,, by determining whether the constraints it sets on pulsar and companion masses are consistent with those found from the Shapiro delay measurement; secondly and more uniquely, the fact that the PSR J1802-2124 system is a NS-WD binary makes it ideal for setting limits on the existence of dipolar gravitational radiation. This is predicted in some scalar-tensor theories of gravity, due to the difference in the self-gravities between the two stars (see, e.g., Esposito-Farese, 2004). Measurement of the orbital decay, and any deviation from that predicted by GR (which does not predict the existence of dipolar gravitational radiation) would allow us to set an upper limit to this effect. Such a measurement has thus far only been possible in two NS-WD systems: PSR J1141-6545 (Kaspi et al., 2000b; Bailes et al., 2003) and PSR J0751+1807 (Nice et al., 2005). Longer-term measurement of the PSR, J1802-2124 may help to further constrain the existence of this effect. In addition, the measurement of orbital decay could help to constrain the system masses, since it will eventually be measured to higher precision than the Shapiro delay r parameter (though kinematic corrections (Damour & Taylor, 1991; Nice & Taylor, 1995) may affect our ability to use this measurement for either of these purposes).  Chapter 3. PSR J1802-2124: how common is a common envelope?^53  3.5 Evolution of the PSR J1802-2124 system The timing results from observations of PSR J1802-2124 over the past five years show that it is a light pulsar possibly the lightest known NS with a WD companion with a relatively small spin period in a binary system with a massive WD. These mass measurements represent the first made for what we refer to as short-period IMBPs (Pb < 3 days; see Table 3.3). We find that several NS-WD binary formation scenarios cannot explain the observed parameters of the PSR J1802-2124 system. The usual LMBP mass transfer scenario, which would invoke an extended, stable period of accretion of matter onto the NS surface, is difficult to reconcile with our measurements of the pulsar and WD companion masses. The highly super-Eddington accretion scenario outlined earlier (Tauris et al., 2000) also does not appear to be able to produce the PSR J1802-2124 system. While the companion is likely to be a CO WD (0.4 < m2 < 0.9 M® ), the 16.8-hour orbital period is significantly less than the — 3-day minimum period produced in this scenario. The double-He core progenitor scheme of B01, used to explain the formation of PSR B0655+64, assumes that the progenitors of the NS and WD have similar masses. However, the NS mass in the PSR. J1802-2124 system differs significantly from that of the WD companion. This probably indicates a corresponding disparity in mass for their progenitors, making this theory difficult to apply in this case. The compactness of the orbit, the large WD mass, and moderately slow pulsar spin period of the PSR J1802-2124 system, support the idea that it underwent CE evolution. Our mass measurements indicate that the pulsar probably had little time to accrete matter from the white dwarf before the envelope was ejected, similar to the modest recycling of pulsars in DNS systems such as PSR B1913+16 (Taylor & Weisberg, 1989) or PSR, B1534+12 (Stairs et al., 2002). Although the evolution of the PSR J1802-2124 system is generally understood, the precise history of this system and other short-period IMBPs can only be elucidated through detailed binary stellar evolution simulations, which is well beyond the scope  Chapter 3. PSR J1802-2124: how common is a common envelope?^54 of this thesis. In the following section, we attempt to gain a better understanding of the populations of PSR J1802-2124 and related systems through further comparison, without performing full-fledged evolution calculations.  3.5.1 The question of common-envelope evolution for IMBPs Using the population synthesis results of Portegies Zwart Yungelson (1998), as well as evolution analysis by Beale & Brown (1998), B01 argues that, within a factor of two, the ratio of the birthrate of short-period IMBPs (i.e. those which have passed through a CE phase in their evolution) to that for the young eccentric NS-massive WD binaries is expected to be 13 1; only two of the latter class have been observed (Thorsett et al., 1993; van Kerkwijk Kulkarni, 1999; Kaspi et al., 2000a; Bailes et al., 2003). However, the surface magnetic field is generally two orders of magnitude weaker in the IMBPs, presumed to be brought down from — 10 12 G during the accretion process. Pulsars with weaker magnetic fields are observable for a longer time, since the spin-down due to dipole radiation proceeds at a slower rate. This is quantified by an "observability premium" H = 10 12 G/B (Wettig & Brown, 1996), a relative measure of the observable lifetime of the pulsar. Given all this, B01 estimates that we should see at least R. 50 — 100 times as many IMBPs that are products of CE evolution as we do eccentric NS-WD binaries; including PSR J1802-2124, only four or five such systems have so far been found. According to this argument, hypercritical accretion-induced collapse of most CEembedded NSs into black holes is responsible for this observational discrepancy. We also note that through evolutionary model analysis, Belczynski et al. (2002) find that roughly two-thirds of NS systems can survive hypercritical accretion for a maximum NS mass greater than 2 M c) . However, we find a relatively low mass for PSR J1802-2124, indicating that this pulsar (as well as those in the precisely-measured pulsars in DNS systems) has not accreted a significant amount of mass, regardless of the specific formation mechanism undergone by these systems.  Chapter 3. PSR J1802-2124: how common is a common envelope?^55 We now revisit the assumptions made by B01 and recalculate the expected ratio R. of short, period IMBPs observed to eccentric NS-WD systems. Table 3.3 lists all known IMBPs and the two known eccentric NS-WD binaries, along with various parameters for comparison. As stated above, the disparity between observed IMBP and eccentric NS-WD systems is contingent on the result from population synthesis modelling that short, period circular and eccentric NS-heavy WD systems should form at approximately the same rate (Portegies Zwart Yungelson, 1998; Brown et al., 2001). Approximately two-thirds of the known IMBP systems have orbital periods above — 3 days, and thus are possibly explained by the Tauris et al. (2000) scheme involving a short-lived highly superEddington accretion phase. Therefore, we will follow B01 and restrict our comparison to short-period IMBPs in what follows. B01 explores the possible contribution of observational selection effects in order to explain at least part of the perceived lack of observed IMBPs, by comparing the 430-MHz luminosity densities of three known IMBP systems to DNS and eccentric binary systems. They found that the IMBPs had luminosity densities about an order of magnitude less than the other types of pulsar systems, but argued that their much-larger observability premiums more than compensate for possible selection effects based on relative ltithinosity densities. We believe this comparison to be inadequate, since the majority of the known IMBPs were discovered—and only have known flux densities—at  ti  1400 MHz. We therefore  re-examine the issue of selection effects by comparing the pulsars at this freqtiency, at which most of the IMBPs are seen. A quick glance at Table 3.3 shows that on average the luminosity densities (calculated as L = 4ird 2 F, where d is the distance to the pulsar and F is the 1400-MHz flux density) of the two classes differ by less than an order of magnitude. The quantity in the second-to-last column is the product of the luminosity density and the observability premium H, which we denote as LH. This is a more representative measure of observability; for a luminosity-limited survey, the factor L must be also taken into account when determining the overall observability for a diskdistributed population, which is the case for the majority of pulsars (see Camilo et al.,  Table 3.3 Known intermediate-mass binary pulsars. PSR  Spin  Orbital  period (ms)  Eccentricity  Surface  Flux density  Distance'  Luminosity density  L140oll  period  magnetic field  (1400 MHz)  (kpc)  (1400 MHz)  (103 inJy kpc 2 )  (days)  (101°G)  (mJy)  References  (rnJy kpc 2 )  Short-period IMBPs (Pb < 3 days) B0655+64  195.7  1.03  0.0000075  1.17  0.3  0.49  0.9  0.077  1,2,3  J1232-6501  88.2  1.86  0.00011  0.856  0.34  6.2  160  19  4,5  J1435-6100  9.34  1.35  0.0000105  0.0484  0.25  2.2  15  31  4,5  J1757-5322  8.87  0.453  0.0000040  0.0489  2.3  0.96  27  55  6,7  J1802-2124  12.6  0.699  0.0000025  0.0966  0.77  2.9  84  87  8, this work  9,10  Long-period IMBPs (Pb > 3 days) J0621+1002  28.8  8.32  0.0025  0.118  1.9  1.4  44  37  J0900 -3144  11.1  18.7  0.0000103  0.0748  3.8  0.54  14  19  11  J1022+1001  16.4  7.80  0.000097  0.0854  3.0  0.45  7.6  9  9,12  J1157-5112  43.6  3.51  0.000402  0.253  0.2-3.5  1.3  4.2 - 7.4  1.7 - 2.9  6,7  J1420-5625  34.1  40.3  0.003500  0.154  0.13  1.5  3.7  2.4  13  J1454-5846  45.2  12.4  0.001898  0.615  0.24  2.2  15  2.4  4,5  J1603-7202  14.8  6.31  0.0000092  0.0488  3.0  1.2  51  105  9,14  J1745-0952  19.4  4.94  0.000018  0.137  0.7  1.8  29  21  6,7  J1810-2005  32.8  15.0  0.000025  0.225  2.0  4.0  402  180  4,15  J1904+0412  71.1  14.9  0.00022  0.283  0.23  4.7  65  23  4,15  J2145-0750  16.0  6.84  0.000019  0.0699  8  0.57  30  43  9,16  Eccentric NS-CO WD binaries J1141-6545  394  0.198  0.17  132  3.3  > 3.7 b  > 570  > 0.43  17,18,19  B2303+46  1066  12  0.66  78.8  0.38'  2.9740  42  0.053  20  REPERENCES.-1.-Jones  & Lyne (1988); 2.-Lorimer et al. (1995); 3.-Hobbs et al. (2004); 4.-Camilo et al. (2001); 5.-Manchester et al. (2001);  6.-Edwards & Bailes (2001b); 7-Bailes, private communication; 8.-Faulkner et al. (2004); 9.-Kramer et al. (1998); 10.-Splaver et al. (2002); 11.-Burgay et al. (2006); 12.-Hotan et al. (2004a); 13.-Hobbs et al. (2004); 14.-Toscano et al. (1999); 15.-Morris et al. (2002); 16.-Loehmer et al. (2004); 17.-Ord et al. (2002); 18.-Kaspi et al. (2000a); 19.-Bailes et al. (2003); 20.-Thorsett et al. (1993). NcrrE.-Most of the values for these parameters were obtained, or derived from values obtained from Manchester et al. (2005a);  http://www.atnf.csiro.au/research/pulsar/psrcat/. 'For all pulsars, except where noted, we have used the NE2001 model (Cordes Lazio, 2002) to derive the distances, based on the dispersion measures of the objects. b  For PSR J1141-6545, we have used the distance published in Ord et al. (2002), derived from the neutral hydrogen absorption spectrum along the pulsar's line of sight. PSR B2303+46 does not have a published 1400 MHz flux density. In this case we estimate it using published spectral index for this pulsar, from Maron et al. (2000).  C5t  Chapter 3. PSR J180:2-2124: how common is a common envelope? ^57 2001, for a discussion of IMBP scale heights). As stated above, we restrict our comparison to the short-period IMBPs, and exclude PSR B0655+64, which may have formed through double He-core evolution, as proposed by B01. The ratio e between the average value of LII for the remaining short-period IMBPs and the eccentric NS-WD systems has the range e — 110 — 905. The limits of this range come from using the LII value for each eccentric NS-WD system separately; these values differ by two orders of magnitude, and so taking an average of the two would have proven valueless. Here, we assume that the fraction of pulsars that have emission beams that sweep past Earth is the same for each class. The actual so-called "beaming" fractions for these two pulsar types is in fact not well-understood (see Kramer et al., 1998, for a discussion of the beaming fraction of recycled pulsars). A full population synthesis comparison between short-period IMBPs and young, eccentric NS-WD systems, including such parameters, and accounting for survey selection effects, is needed to determine the true discrepancy. We thus arrive at an estimate 7?, N )3e 110 — 905, and Table 3.3 shows that the observed ratio 'R o bs 2. We are thus left with a factor of — 55 — 450 inconsistency between the population of short-period IMBPs we expect and those we obserVe. This line of reasoning alone thus does not settle the question of the viability of CE evolution in IMBP formation. However, as we now briefly discuss, additional selection effects associated with searching for and finding new IMBP systems (neglected by B01) need to be accounted for, and would scale down the discrepancy. For a given luminosity and DM, a shorter spin period will render the putSar more prone to the observational effects of dispersive smearing. This is because, in fasterrotating pulsars, the pulse will become smeared to a greater extent as a fraction of the spin period. This applies here, since IMBPs show an overall spin period distribution that is substantially shorter than in the eccentric NS-WD binaries. To illustrate this pOint, we have calculated the observed fractional pulse width as a function of DM for two pulsars at 1400 MHz, using 3-MHz channels. This is similar to the search observation setup for the Parkes Multibeam Pulsar Survey (e.g., Manchester et al., 2001). An eccentric NS-WD binary pulsar like PSR J1141-6545 (Pspin = 394 ms) has a fractional pulse  Chapter 3. PSR J1802-21,24: how common is a common envelope?^58 width that would never be observed to be greater than 2% of the pulse period, out to a DM > 1200 pc cm -3 , near the limit of the known pulsar population. An IMBP like PSR. J1802-2124 (Pspir, = 12.6 ms), however, has a fractional pulse width that grows to more than one-eighth of a pulse period at DM — 170 pc cm  -3 .  This indicates that the  eccentric binaries can be discovered to much larger volumes than the IMBPs; indeed, the largest DM to which an IMBP has thus far been discovered is PSR J1810-2005, at 240.2 pc cm -3 (Camilo et al., 2001), which has a spin period about 3 times that of PSR J1802-2124. We have calculated the maximum distances out to which one would expect to detect the two classes of pulsar discussed here; these are based on the maximum observable DMs estimated for PSR J1802-2124 and PSR J1141-6545, which we have used to represent the IMBPs and eccentric NS-WD binaries, respectively. Tä do this, we have selected 15,000 random points within the range of celestial coordinates observed in the Parkes Multibeam Survey. Distances were calculated using the NE2001 Galactic free electron distribution model (Cordes & Lazio, 2002), and truncated at the edge of the Galaxy where appropriate. Each distance was converted to a maximum observable volume V a d 2 (for a disk population) for the given line of sight, assuming that the pulsar luminosities would permit detection out to these distances. Under theSe crude assumptions, the ratio of the average volumes out to which each pulsar type can be probed is proportional to the ratio of each type of object that one would expect to find in the Parkes Multibeam Survey (a more thorough comparison would need to take into account the sensitivity limit of the survey). From this we find a ratio Vii4i/Vig62 — 3.6; this estimate would then reduce the disparity between the predicted and obserVed ratio of short-period IMBPs to the eccentric NS-massive WDs by a factor of — 3.6 ; down to 'R./R,,,b, — 15 — 130. Future surveys that use narrower-channel instruments should thus expect to find a larger fraction of higher-DM IMBPs compared to eccentric binaries, adding to the current sample of this class of binary system. We also note that pulsar acceleration would cause further signal spread in the Fourier search domain, to a larger extent for IMBPs than for young pulsars in similar orbits (e.g., Hessels et al., 2007). Although difficult to quantify, this is an important additional  Chapter 3. PSR J1802-214: how common is a common envelope? ^59 selection effect against discovery of IMBPs relative to the eccentric NS-WD binaries. While the discrepancy in the observed ratio of these two system types pointed out by B01 may still be supported by the available data on IMBPs, we emphasize again that a more precise estimation of observable numbers of short-period IMBPs will come with further population synthesis studies, as well as accounting carefully for survey selection effects.  3.6 Conclusions The mass measurements of the PSR J1802-2124 system highlight the dependenCe of the final system configuration on the precise mass transfer histories and specific evolution of the system in question. As discussed earlier, the similarity between the properties of this system and those of recycled DNS pulsars hints that the recent evolutionary paths of these two system types may have been the same, probably involving a CE/inspiral phase. It is clear, however, that to arrive at a definitive picture of IMBP evolution, and more generally, the evolution of the many observed binary system types ATe must ;  discover more systems with measurable masses.  60  Chapter 4  PSR J0737-3039A/B: the double pulsar PSR, J0737-3039A/B has provided pulsar astronomers and neutron-star theorists with an abundance of astrophysical phenomena to study in more detail, and with more precision, than ever before. Most spectacular of these is surely the timing study that has led to the confirmation of the predictions of general relativity in the strong-field regime to within 0.05%, based on the measurement of Shapiro delay in this system (Kramer et al., 2006). The measured system parameters resulting from this timing analysis are shown in Table 4.1. Another topic of study that observations of the double pulsar has allowed is that of how this system, and perhaps others like it, has formed and evolved to arrive at its current configuration. Our analysis confirms that the channel of binary evolution undergone by this system may be somewhat different than that of most other DNS systems for which orbital parameters and component masses have been measured. The remainder of this chapter will focus on describing the direct observational constraints on its evolution that we have gained through study of this system. A portion of this chapter has been submitted to appear in the proceedings of the conference "40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More", held at McGill University, Montreal, Canada, 12 - 17 August, 2007 (Ferdman et al., 2007).  Chapter .4. PSR J0737-3039A/B: the double pulsar ^  61  Table 4.1 Parameters for the PS11. J0737-3039 system, measured and derived from timing observations and analysis. Timing parameter  ^  PSR J0737-3039A PSR J0737-3039B"  Right ascension, a (J2000) ^  07 h 37m51'24927(3)  Declination, 6 (J2000) ^  —30 ° 39'40'.'7195(5) —3.3(4)  Proper motion in right ascension, ua (mas yr -1 ) ^ Proper motion in declination, Parallax,  7i  pd  2.6(5)  (mas yr -1 ) ^  3(2)  (mas) ^  Rotation frequency, 1/ (Hz) ^  44.054069392744(2)  0.36056035506(1)  —3.4156(1)  —0.116(1)  Frequency derivaive, i (10 -15 5 -2 ) ^  53156.0  Reference timing epoch (MJD) ^ Dispersion measure, DM (pc cm -3 ) ^  48.920(5) 0.10225156248(5)  Orbital period, PE, (days) ^  0.0877775(9)  Eccentricity, e ^ Projected semimajor axis, x a p sin i (lt-s) ^ Longitude of periastron, w (°) ^  1.415032(1)  1.5161(16)  87.0331(8)  87.0331 + 180.0  Epoch of periastron passage, To (MJD) ^  53155.9074280(2)  Advance of periastron, w (° yr -1 ) ^  16.89947(68)  Gravitational redhsift/time dilation parameter, -y (ms)  0.3856(26)  16.96(5)b  6.21(33)  Shapiro delay r parameter (ps) ^  0.99974(-39, +16)  Shapiro delay s parameter ^ Orbital period derivative, Pb (10 -12 ) ^  —1.252(17)  Derived parameters Total proper motion, p (mas yr -1 )  ^  4.2(4) — 500  Distance from DM, dDM (pc)  ^  Distance from parallax, d o (pc)  ^200 to 1000  Transverse velocity, vi r (d 500 pc) (km s -1 )  ^  Orbital inclination angle, i (°)  ^88.69( —76, +50)  Total system mass,  ^2.58708(16)  mtot  (MG)  Neutron star mass, mi (M®)  10(1)  ^1.3381(7)^1.2489(7)  REFERENCES. — Data taken from Kramer et al. (2006). NOTE.—Parentheses indicate the lo- uncertainties on the last digit (or last two digits, if two digits are given). Two  numbers separated by a comma indicate the lower and upper uncertainties, respectively. a Measured parameters which are common to both pulsars are shown only in the PSR J0737-3039A column. b Although this separate value of periastron advance was found for PSR J0737-3039B, the more precise value for PSR J0737-3039A (with which it is consistent at the 2cr level) was adopted in the final analysis.  Chapter 4. PST? J0737-3039A/B: the double pulsar ^  62  4.1 Formation and evolution of the double pulsar system In the PSR J0737-3039A/B system, we identify the first-formed, and recycled neutron ;  star as the "A" pulsar, having a spin period of 22.7 ms. The "B" pulsar, formed in the aftermath of the second supernova, has not been not spun up, rotating once every 2.77 s. It is specifically the evolution of the progenitor of PSR J0737-3039B that is believed to have caused the difference in current system properties between the PSR J0737-3039A/B system and the PSR B1913+16 and PSR B1534+12 binaries as we now observe them (e.g., Podsiadlowski et al., 2005). The latter two systems are believed to be the products of core-collapse supernovae, described in more detail in Section 1.4.2. The key outcomes of this catastrophic event are a large amount of mass lost, and a substantial kick given to the system owing to significant asymmetry in the supernova explosion. These leave behind distinct signatures, in both the orbital properties and the system velocity of the daughter DNS system, if it can avoid being disrupted in the process (see, e.g., Wex et al., 2000). The ejection of a large amount of matter from a binary system, along with a significant natal kick, will normally be expected to cause an increase in the system eccentricity. The effect of tidal drag on the neutron star are very small, with gravitational radiation being the only other known circularization process in the DNS system. Thus, knowing the age of the post-supernova system, we can determine the eccentricity left behind by tho second supernova. The properties of the PSR B1913+16 and PSR B1534+12 systemS suggest that the companion neutron stars formed via core-collapse supernovae (Wex et al., 2000; Willems et al., 2004; Thorsett et al., 2005). These studies are based on their large respective eccentricities e --- 0.617 and 0.274, as well as their high transverse velocities, Vtr  88 and 107 km/s (Taylor & Weisberg, 1989; Stairs et al., 2002, respectively).  The observed parameters of the PSR J0737-3039A/B system, shown in Table 4.1, appear to be somewhat different. This system has an order-of-magnitude smaller eccentricity and transverse velocity than the PSR B1913+16 and PSR B1534+12 systems. These values are much lower than typically expected if the second supernova effected a  Chapter 4. PSR J0737-3039A/13: the double pulsar^  63  large natal kick to the system, though are not by themselves conclusive evidence against a core-collapse supernova event having occurred. However, the mass of the second-formed neutron star, PSR J0737-3039B, is significantly lower. Taken together, theSe properties present important clues that suggest a different evolutionary path may have been taken by the B pulsar progenitor in forming the neutron star. It has been suggested that this may best be explained by the progenitor to pulsar B having gone thrOugh an electron-capture supernova (Podsiadlowski et al., 2005). This occurs when an 0-Ne-Mg core passes a threshold density that allows electrons to be captured on 'Mg. This decreases the electron degeneracy pressure, which in turn lowers the Chandrasekhar mass of the core, inducing its collapse (Miyaji et al., 1980; Nomoto, 1984; Podsiadlowski et al., 2005). This may avoid large supernova kicks, due to the hypothesized short timescale over which this type of event proceeds, which is much shorter than the timescale needed for instabilities that produce large kicks to develop. The binding energy of the neutron star for many equations of state is given by EB 0.084 ( MN S MO ) 2  Mo (Lattimer & Yahil, 1989; Lattimer Prakash, 2001), corre-  sponding to MB 0.13 Af® for PSR J0737-3039B (see also Stairs et al., 2006). Through independent modelling of the pre-supernova mass of the B pulsar based on a collapsing 0-Ne-Mg core, Podsiadlowski et al. (2005) have found that the critical mass for collapse should range from 1.366 to 1.375 Al , consistent with the above estimate for MB; this would mean that almost no baryonic matter has been lost during the supernoVa event. Any remaining energy would have gone into changing the orbital properties of the system, or contributing to a kick at the time of the supernova. The measured mass of PSR, J0737-3039B, as well as the low transverse velocity of the system, thus present tantalizing clues that the progenitor of the B pulsar may have ended its life in this manner. In addition, it is expected from accretion theory that the the spin axis of the A pulsar will become aligned with the total angular momentum of the binary system (wellapproximated by the orbital angular momentum) as it accreted matter donated by the B pulsar progenitor. If the supernova undergone by the B pulsar is close to symmet-  Chapter 4. PSR J0737-3039A/B: the double pulsar^  64  ric, this alignment will not be disturbed (Podsiadlowski et al., 2004). By contrast. if there is a large kick to the system, the resulting misalignment will equal the angle between the orbital planes of the system before and after the supernova event (e.g., Wex et al., 2000). Several studies (e.g., Dewi & van den Heuvel, 2004; Piran Shaviv, 2005; Willems et al., 2006; Stairs et al., 2006), have examined the explosion of the B progenitor. Using the timing-derived proper motion (Kramer et al., 2006), Stairs et al. (2006) predict a post-supernova misalignment angle 6 for PSR J0737-3039A of < 11 °. Willems et al. (2005) predict compatible values under different kinematic and progenitormass assumptions. If the above studies are correct (see Kalogera et al. 2007 for a discussion and criticism of the assumption of a small radial velocity used in Piran Shaviv 2005 and Stairs et al. 2006), the measurement a low spin-orbit misalignment angle for PSR J0737-3039A, in conjunction with the low system eccentricity and transverse velocity, would provide crucial evidence in explaining the observed properties of thiS system. There are however, several caveats that one must take into account before accepting this channel of evolution. First, it is possible that a low-mass iron core can produce the low-mass B pulsar, and proceed with little asymmetry due to the promptness of the event (Pfahl et al., 2002; Podsiadlowski et al., 2004); it is thus difficult to distinguish between certain types of supernova based on mass and kick velocity alone. In addition, it has been suggested that this fast timescale, in both types of progenitors, is still long compared to that of an inspiral of the NS when the helium star overflows its Roche Lobe (DeVvi. & Pols, 2003). The resulting CE phase could rapidly end in a merger, either preventing the formation of the DNS, or dramatically reducing the DNS observable lifetime. To avoid forming a CE, it has been thought that the He star should have a minimum mass of — 2.4 Al® (Dewi et al., 2002; Dewi Pols, 2003, cf. Ivanova et al. 2003). A similar lower mass limit was also considered to be necessary for the He-burning core to form a NS (see Nomoto, 1984; Habets, 1986; Willems et al., 2006). In this case, a large kick velocity to the system (> 70 km s ') would be needed in order to offset the large eccentricity created -  from the mass loss alone (Podsiadlowski et al., 2005). However, as Podsiadlowski et al. (2005) have pointed out, it may not be necessary for a low-mass He star-NS system to  Chapter  4. PSR J0737-3039A/B: the double pulsar ^  65  pass through a CE phase (see also Ivanova et al., 2003). If this is not required, then the mass of the pre-supernova He star can be as low as 1.4 M® , resulting in little to no kick. This is in better agreement with the analyses of Stairs et al. (2006), Piran Shaviv (2005), and Willems et al. (2006), who find small natal kick velocities to be associated with low-mass progenitors for the B pulsar. Although the electron-capture scenario does well to explain the observed properties of the double pulsar, there clearly exist several details in these models that must be resolved before we can definitively attribute this scenario to the the formation of this system, and others like it. A clear discuSSion and review of the advantages and disadvantages of the electron-capture scenario can be found in Kalogera et al. (2007). We thus aim to determine the orbital geometry of PSR J0737-3039A/B system, and in particular, constrain the misalignment between the A pulsar spin and orbital angular momentum axes. One way to accomplish this is through investigation of the effects of  geodetic precession on the observed properties of the pulsar over time.  4.2 Geodetic precession and long-term profile changes According to GR., the spin axis of a pulsar in a binary system will precess about the total angular momentum vector of the system (Damour & Ruffini, 1974). This occurs at a rate given by (Barker & O'Connell, 1975): ,-, 5/3  c21sRL T2/3 M2 (4Mi + 3m2) 1 (  Pb ® 2(Mi + n12) 4 / 3 1 — e 2 '  (4.1)  where in this formulation, m 1 and m 2 are respectively the pulsar and companioh masses, expressed in solar masses, e is the orbital eccentricity, Pb is the orbital period, and T,,, = GMT,/c3 = 4.925490947ms is the mass of the Sun expressed in units of time. The effect of geodetic precession on the spin axis orientation of this pulSar serves to change our line of sight through the pulsar emission region over time. Apart from the time baseline over which the pulsar data are analysed, the extent to whieh these  Chapter 4. PST? J0737-3039A/B: the double pulsar ^  66  effects can be observed depends on the spin and orbital geometries of the pulsar system. This is particularly the case for the angle of misalignment 6 between the pulsar spin and orbital angular momentum (which, as stated before, approximates well the total angular momentum vector of the binary system), which forms the opening angle of the cone that is swept out by the spin axis over the course of a precession period. These geometric parameters can be modeled and determined through long-term analysis of the pulse profile. It has been shown that for PSR B1913+16, the relative amplitudes of the two major pulse components are changing significantly over time, as is the separation between these components (Taylor .Sz Weisberg, 1989; Weisberg et al., 1989; Kramer, 1998). It has also been demonstrated that the PSR B1534+12 profile displays a change in shape over time that is consistent with the rate of precession predicted by GR (Stairs et al., 2004). The precession periods for the other relativistic DNS binaries mentioned earlier, PSR B1913+16 and PSR B1534+12, are approximately 298 and 706 years, respectively (Weisberg et al., 1989; Stairs et al., 2004). By comparison, the PSR J0737-3039A/B system has a precession period of 75 years for the A pulsar and 71 years for the B pulsar (Lyne et al., 2004). The effects of geodetic precession on the pulse profile in this system should thus be more readily observable on a shorter timescale than for PSR B1913+16 and PSR B1534+12, provided that 6 is non-negligible.  4.2.1 Past searches for geodetic precession effects in the double pulsar Since the PSR J0737-3039A and B pulsars have already been observed for a larger fraction of their precession periods compared to the two other DNS systems mentioned above, we should, given a moderate spin-orbit axis misalignment, expect an observable change in the pulse profile shape over a shorter timescale in these pulsars. This does not, however, seem to be the case for PSR J0737-3039A. Using a data set that spans almost three years, Manchester et al. (2005b) found no evidence that the profile width of PSR J0737-3039A was changing with time. They  Chapter 4. PSR J0737-3039A/B: the double pulsar^  67  argued that this may be attributed to the pulsar being at or near a precessional phase of 0 ° or 180 °, rather than the pulsar spin axis being aligned, or nearly aligned, with the orbital angular momentum axis. Although the position of the pulsar at a "special" precessional phase is statistically improbable, they have argued that having 6 0 ° would require a beam radius p> 90 °. Since they assume in their analysis that the pulSar emits from a single magnetic pole, this would correspond to a broad beam structure that wraps around the neutron star, which seems rather unlikely. To further investigate, we have performed a similar analysis with GBT data, taken between June 2005 and April 2007. Almost two years long, this time baseline, added to that of the Parkes data from the Manchester et al. (2005b) study, would help to clarify whether the previous analysis was indeed performed during a special precessiOn phase in which the pulse profile, as seen from Earth, would not undergo any signific4lit shape change. What follows is a description of the observations and analysis performed to this end'.  4.3 Observations For the studies described in this section, we have used data taken at the 64-m Parkes and 100-m Green Bank radio telescopes. Data used from Parkes spans from the initial epoch of observations that led to the discovery of PSR J0737-3039A/B on 13 August 2001 (MJD 52134) to 8 August 2004 (MJD 53225). These were taken using the centre beam of the Parkes multibeam and H-OH receivers using a filterbank system with 2 x 512 x 0.5 MHz channels centred at 1390 MHz. Further details about the observing setup for obtaining these data can be found in Manchester et al. (2005b). Folded data and full-pulse width measurements were provided by R. N. Manchester (private communication). 'Geodetic precession effects on PSR J0737-3039B will be studied and reported by other members of our research team; long-term changes in its pulse profile have, however, already been observed (Burgay et al., 2005).  Chapter 4. PSR J0737-3039A/B: the double pulsar^  68  Observations of the double pulsar at the GBT were taken using the GASP backend, and span from June 2005 to April 2007. The observing strategy at the GBT has been decided upon such that it would benefit the timing analysis that has produced the most recent stringent test of GR (Kramer et al., 2006). We have been taking data in monthly observing sessions, each consisting of a 5 to 8-hour track of the object at 820 and 1400 MHz in alternate months. This was done in order to effectively constrain astrometric parameters such as position and proper motion, as well as possible changes in the measured DM of the pulsar. We have also conducted biannual concentrated observing campaigns that span approximately 1-2 weeks each, and which typically contain 5-6 obserVing sessions that each last 6-8 hours. The purpose of these was to better constrain orbital parameters and to investigate the effects of special relativistic aberration on the pulse shape over an orbital period, the latter of which will be discussed in Section 4.5. These campaign observations were taken exclusively using the 820-MHz receiver. In general, up to 16 x 4 MHz frequency channels were used, observing at a single frequency band during each observation in order to maximize the collection of data. See Table 4.2 for a summary of the observations performed for the work described in this chapter: Time-series data were folded using the predicted topocentric pulse period, over typical integration times of approximately 30 seconds for the A pulsar. This choice of integration time reflects a compromise between ensuring a fully-sampled orbit, which was critical for the very precise Shapiro delay measurement obtained for the timing studies of thiS pulsar, and obtaining pulse profiles with adequate signal-to-noise ratio to effectively carry out that analysis. We have solely used the concentrated campaign observations to perform the studies that follow. They have allowed us to use a significant amount of data within a short time at each of these five epochs, without having to be concerned with non-negligible long-term profile shape changes that might otherwise contaminate our results.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  69  Table 4.2 Observations of the double pulsar system PS13. J0737-3039 for performing pulse profile shape analysis. Telescope  Instrument  Centre  Gain  frequency (MHz)  (K Jy -1 )  (K)  Sampling  Effective no.  Total effective  (As)  of channels  bandwidth (MHz)  GBT  GASP  820  2.0  25  0.25  16a  64  Parkes  Filterbank  1390  0.74  22/28b  80/125  512  256  a The number of channels that were used varied occasionally within a given session due to the removal of those channels contaminated with radio frequency interference (RFI). b Ts y s  values given for the Parkes telescope are for the Multibeam (centre beam) and H-OH receivers, respectively.  4.4 A new search for geodetic precession effects on PSR J0737-3039A To obtain a high signal-to-noise profile that represents the pulse profile shape at each epoch, we have calculated an average pulse profile for each set of the concentrated campaign observations. In doing this, we leave out, any scans that are found to be contaminated by radio frequency interference. This is done as described in Section 2.4: We then aligned each of the averaged profiles to that constructed from the most recent epoch in April 2007 to look for residual signal that could be due to pulse shape change. Figure 4.1 shows the aligned and subtracted profiles for each epoch. While there seem to be subtle changes in the profile shape over the almost 2 years of observations, it is certainly not as apparent as one would expect if the spin-orbital misalignment is significantly non-zero, as is the case with PSR B1913+16 and PSR B1534+12. As shown in Table 4.1, the orbital inclination of the PSR J0737-3039A/B system is i = 88.6911 ° (or 91.311:50 °)—nearly edge-on to our line of sight. If indeed the spin axis of the A pulsar is aligned, or nearly aligned, with that of the orbital angular momentum, then it follows that the spin axis should be nearly 90 ° from the region of emission. This presents the possibility that we are viewing emission from both magnetic poles of an orthogonal rotator. In investigating the geometry of the PSR J0737-3039A/B system, we performed analysis assuming both one- and two-pole emission models. We  ▪  Chapter 4. PSR J0737-3039A/B: the double pulsar^  70  0.10 0.08 0.06 0.04  g  0.02  0.00 0.10 3.1 0.08  2006.11  g 0.06 cl 0.04  o 0.02  1111  • 0.00 %,51  -0 004  0.10 ›.; :Z' 0.08  2006.05  2 0.06 0  0.04  O 0.02 ▪ 0.00  r, 8 :8  4 48  0.10 .1g 0.08 g 0.06 1"1 0.04  O 0.02 r7. 0.00  •1 m  ›; an  0.10 0.08  g 0.06 c=1 0.04  o 0.02  EL" %.1  0.00  1 .884 00  0.2^0.4^0.6 Pulse Phase  0.8  ^  1.0  Figure 4.1 Pulse profiles and difference residuals over nearly two years of GBT observations. High signal-to-noise, aligned profiles are shown from each of five concentrated observing campaigns. The most recent of these, taken in April 2007, is shown in the top panel. Each subsequent (shifted and scaled) profile and its difference from the April 2007 profile are shown and labelled in arbitrary flux units. One cannot see signifiCant pulse  shape changes over time.  Chapter  4. PSR J0737— 3039A/B: the double pulsar^  71  have conducted a similar analysis to Manchester et al. (2005b), performing a fit to the the pulse width data to arrive at likely parameters that describe the geometry of the system. Now that we have extended our data set to include nearly 3 years of additional observations of this system, the constraints on the system geometry are more rigid. As with the Manchester et al. (2005b) work, we measured pulse widths at 10% of the peak pulse height. The top panel of Figure 4.2 shows the widths obtained by Manchester et al. (2005b) and in this work. One can see that within each set of data there is no evidence for pulse shape change. The systematic offset between the two data sets is principally due to two factors. The first comes as a result of the fact that we have used two separate telescopes and instruments for each of the two data sets. The Manchester et al. (2005b) data were taken using a filterbank backend, whereas our set was taken using GASP, a coherent dedispersion backend, which generally results in sharper profiles with less residual smearing. A more significant factor is that the two data sets were taken at different observing frequencies. Most pulsars show some evolution in pulse shape with observing frequency (see, e.g., Lorimer k. Kramer, 2005), possibly caused by emission from different heights above the neutron star surface within the emission cone (see, e.g., Rankin, 1983). The pulse shape evolution with observing frequency in the PSR J0737-3039A profile is described in Manchester et al. (2005b). In order to be able to use all the data in a single fit, we adjust the measured Parkes widths by subtracting from each of those measurements the difference between the weighted means of the GBT and Parkes data sets. To obtain the errors on the adjusted Parkes data, the original Parkes data uncertainties are added in quadrature to that of the difference in the two means. This subtraction is of course not physically  correct, but  it does allow the study of pulse shape evolution over time, since it retains the principle that there is zero pulse change within each data set. The result, which we use for the fitting analysis, is shown in the bottom panel of Figure 4.2. Here we plot (1) 0 , the quantity we used for the fit, equal to half the full width of the pulse. These measurements presume that the emission that produced the observed pulse profiles is from a single magnetic pole, an assumption made by Manchester et al. (2005b) based on the observed  Chapter PSR J0737-3039A/B: the double pulsar^  72  239.0 a) c.  238.0  237.0 U)  a.  236.0  52500  53000^53500 MJD (days)  54000  52500  53000^53500 MJD (days)  54000  119.0 118.5  117.5 117.0  Figure 4.2 Top: Full-profile widths at 10% of the peak amplitude for PSR J0737-3039A as a function of MJD for data taken by Manchester et al. (2005b) at 1390 MHz at the Parkes telescope (open circles) and those taken at 820 MHz at GBT by our group (filled circles). The systematic offset between the two data sets is mainly due to profile shape differences between observing frequencies and instruments used. Bottom: HAlf-profile widths 4) 0 for PSR J0737-3039A as a function of MJD. The Parkes data set was adjusted by subtracting the difference of the (weighted) average widths of the Parkes and GBT data sets.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  73  symmetry in the leading and trailing edges of the pulse profile. This represents nearly 6 years of data, or — 7.5% of its precession period; the hypothesis that the pulsar exists in a special phase of precession thus seems to be an unlikely explanation for the observed lack of profile variation. The dependence of the observed pulse width on the system geometry can be expressed by the following: cos p — cos cos a cos Do -= sin sin a (  (4.2)  where 4)0 is half the full pulse width, the angle a is that between the spin and magnetic axes, is the angle between the spin axis and the observer line of sight, and p is the opening angle of the emission cone (Rafikov & Lai, 2006). In using this eqUation, we are assuming a circular emission beam (i.e. no variation in p with latitude on the pulsar surface). In their work, Manchester et al. (2005b) investigated the effect of using a noncircular beam on their analysis, and found that the results were only marginally affected. We thus believe that a circular emission beam is a reasonable assumption for this analysis. See Figures 4.3 and 4.4 for schematic diagrams that show the angles involYed in the above expressions. Because of geodetic precession, the angle describing our line of sight relative to the pulsar spin axis, varies over time. In order to express equation 4.2 in terms of pAtameters that do not vary with time, we make use of the fact that the direction of the spin axis vector gi can not only be described by the polar angles ((, 7i) (where  n is the angle  between ascending node and the projection of the spin axis on the plane of the sky), but alternatively by (6, Os o ), assuming that precession occurs as predicted by GR. 6 is the spin-orbit misalignment angle, and O so(t) is the longitude, or phase, of Wl in its precession around the orbital angular momentum vector  k, as measured from the — J  axis (Damour & Taylor, 1992). The transformation ((, 7)^(6, Cbso) is given by Damour & Taylor (1992): cos A = cos 6 cos i — sin 6 sin i cos cbs o  (4.3)  sin 6 sin Os° cos 7/ =_ ^ sin A  (4.4)  Chapter 4. PSR J0737— 3039A : the double pulsar^  74  where A =- 71 - (, and so sin A = sin ( and cos A = — cos (. We thus have: cos ( = — cos 6 cos i + sin 6 sin i cos Os°^(4.5) cos 71 =-  sin 6 sin Os° ^ sin (  (4.6)  We can also recast Os° as: oso Qson(t — To,  ^  (4.7)  where S27 Pin is the angular precession frequency, t is the epoch, and T1 is the reference crossing time of the spin axis through precession phase O s o = 0 °, analogouS to the reference epoch To for periastron precession. This analysis was performed separately for the cases of cos i > 0 (i = 88.69 ± gi70 °) and cos i < 0 (i = 91.311 5706 ) We use a single value for the inclination in our analysis for each of these two cases; the fractional uncertainty in these values is small enough that doing so would not significantly effect our results. We then added together the resulting probability densities prior to calculating the marginalized PDFs for each parameter. Finally, ((, /7) are now given by: cos = — cos 6 cos i + sin 6 sin i cos [CriPin (t — T1)] cowl  =  sin 6 sin [C21 Pin (t — TO] sin (  (4.8) (4.9)  See Figure 4.5 for a diagram demonstrating the precession geometry described here. We then substitute equation 4.8 into equation 4.2. This gives us an expression for the pulse width (D o that is time-varying, and that depends on the three angles a; 6, and p, as well as the epoch of zero precession phase T1 . These parameters can be determined through a least-squares fitting of our pulse width data to the model given by eqtlAtion 4.2. Here we perform two grid search fits. The first pair of values we search are 6 and T1 , with 0 < 6 < 180 ° and with T1 running over one precession period centred at MJD 53000; both grid parameters are sampled with 250 bins. We performed a fit to the data using a Levenberg-Marquardt algorithm (e.g., Press et al., 1986), holding 6 and T1 fixed at each grid point, allowing a and p to vary as free parameters, arriving at a best-fit y 2 value for each (6, T1 ) combination. The reduced x 2 we obtained is somewhat less than  Chapter 4. PSR J0737-3039A/B: the double pulsar^  75  Observer line of sight Figure 4.3 Pulsar spin geometry. Here, g i is the pulsar spin axis and 74 is the line of-sight -  axis. m(t) is the magnetic axis, along which the emission beam lies. The magnetic axis sweeps out a cone over the pulsar spin period, during which the emission beam crosses the observer line of sight. a is the angle between the spin and magnetic axes; ( is the angle between the spin axis and the observer line of sight. The complementary angle A = 7r — ( is often used as well. p is the half-opening angle of the emission beain. This diagram is based on Figure 1 in Damour & Taylor (1992).  Chapter PSR J0737-3039A/B: the double pulsar^  76  K  Ascending node  Orbital plane  Plane of the sky  Pulsar direction of motion Observer line of sight  Figure 4.4 Orbital geometry for a binary pulsar system. Here, of the sky, so the  I and f  define the plane  K points in the direction away from the observer. The vectors i and  -/ define the plane of the pulsar orbit, so that  k" points in the direction of the orbital  angular momentum. i is the orbital inclination relative to the observer line of sight. w is the longitude of periastron. This is measured from the ascending node, the most positive point along the line of intersection of the plane of the sky with the orbital plane. A is the angle complementary to (", the angle between the pulsar spin axis Wl and the observer line of sight. 6 is the angle between Wi and k. n is the angle between the ascending node and the projection of the pulsar spin axis on the plane of the sky. This diagram is based on Figure 1 in Damour & Taylor (1992).  Chapter 4. PSR J0737-3039A/B: the double pulsar^  77  Orbital plane  Plane of the sky Observer line of sight  and f define the plane of the sky, points in the direction away from the observer. z and 3* define the plane of the  Figure 4.5 Pulsar precession geometry. The vectors so the  K  f  pulsar orbit, so that k points in the direction of the orbital angular momentum. i. is the orbital inclination relative to the observer line of sight. Due to geodetic preceSSion, the pulsar spin axis gi will trace out a cone with opening angle 6, the misalignment angle between the pulsar spin axis and the orbital angular momentum.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  78  1.0. We then used these values to obtain a Bayesian joint posterior probability density for S and T1 by following a similar procedure as in Section 3.4. There is no reason for us to prefer a given spin-orbit misalignment angle, so We choose a uniform prior distribution for 6 within our constraints. Nor do we have infOrmation that causes us to prefer a specific epoch of precession phase zero over any other. In this case, a uniform distribution of zero precession phase times is the most reasonable prior distribution for T1 which we incorporate to arrive at a joint probability density function ,  for 6 and T1 . The resulting probability contours are shown in Figure 4.6. In this and subsequent joint probability contour plots derived from geodetic precession fits, we only show the result for the case of cos i > 0. The inclination is sufficiently close to 90 ° that the contribution from the first term in equation 4.5 does not change by a significant amount by replacing i by 180° — i, and hence gives very similar results to those we have obtained for the case of i < 90 °. This demonstrates that T1 is almost completely unconstrained for S < 10 ° and 6 170 °, and that regions of high probability density for the epoch of zero precesSion phase are those within which 6 is less constrained. Since a priori we do not expect the spin axis of the pulsar to be at a special phase of precession (i.e. where Oso — 0 0, 90 0 , 180 0 , and 270 °), we tend to prefer small values of 6 (and 6 — 180 0 ). To make this more quantitative, we have calculated marginalized probability densities for each of these parameters, in which we consider the total probability densitieS obtained from using both positive and negative values of cos i. The marginalized PDF for S is shown in Figure 4.7. We focus on the region between 0 and 90 ° because the prObability densities are mirrored by those between 90 and 180 0 , and it has been shown that having  S < 90 ° is more physically likely, unless the supernova kick is extremely large, based on models of the misalignment angle in PSR B1913+16 (Bailes, 1988). We thus qtiote upper limits S < 37° (95.4% confidence) and S < 69 ° (99.73% confidence). Figure 4:8 shows the marginalized PDF for T1 . While there are clear peaks denoting the best-fit T1 value, one can see that a significant fraction of the total probability resides outside these peak  Chapter 4. PSR J0737-3039A/B: the double pulsar^  79  65000 60000 -z 55000 E:  50000 45000 40000  ^ 50^100 150 6 (degrees)  Figure 4.6 Joint probability contours for the angle 6 between the spin and orbital angular momentum axes, and the epoch T1 of zero precession phase, assuming one-pole emission. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours. T i is not well constrained for d < 10° and 6 > 170 0 , while 6 is less constrained near regions corresponding to current precession phases near 0, 90, 180, and 270 °. Here we display the result for the cos i > 0 case.  Chapter 4. PSI? 10737-3039A/B: the double pulsar ^  80  0.015 a.) 0.010  Q, 0.005  0.000 20^40^60 6 (degrees)  ^  80  Figure 4.7 Marginalized probability density function for 6, the angle between the spin axis of PSR J0737-3039A and the angular momentum axis of the double pulsar system. This is derived from the (6, T1 ) joint probability distribution, and we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% upper limit confidence regions, corresponding to 15 °, 37°, and 69 °, respectively.  Chapter 4. PSR. J0737-3039A/B: the double pulsar ^  81  regions. However, if we presume that the value of T 1 with the highest probability density corresponds to the epoch of zero precession phase, then the span of our data set would be centred at a precession phase of — 180 0 . This would produce little or no change in the measured pulse widths, but is essentially a form of fine-tuning, so we are inclined to discount this scenario. We then performed a series of fits over a grid of a and 6 values, with 0° < a < 180 ° and 0 ° < S < 180 °, again with 250 grid points for each parameter. We choose uniform distributions as our prior probabilities for these angles within our constraints, as we do not have information that would convince us to expect otherwise. The best-fit reduced  X 2 we obtained is somewhat less than 1.0. The joint posterior probability distribution for a and 6 resulting from this fit is shown in Figure 4.9. It favours a fairly narrow range of a around 90°. The range of probable 6 is less narrow, however most of the probability density is at values close to 0 ° and 180 °, with the latter being less physically likely (Banes, 1988). One can notice that when 6 = 0 0 , a is completely unconstrained. Physically this means that regardless of the angle between the spin and magnetic axes, perfect alignment between the pulsar spin and orbital angular momentum axes will cause no change in the pulse profile shape, rendering other parameters (except p, which sets the width of the beam) completely degenerate. As with the (6, T1 ) grid search; we find that the majority of the probability density is near to 6 — 0 0 . Figure 4.10 shows the marginalized PDF for the a parameter. The 68.3% confidence interval (shaded region) encloses a region a = 89.61 9-4.4 °, and for the 95.4% interval we find 89.6+ 45 2 ° (89.614 s ° at 99.73% confidence), where the quoted value is the median of the distribution. Figure 4.11 shows the marginalized PDF for the 6 parameter as derived from this grid fit, where as before we show 0 ° < 6 < 90 °. We obtain a 95.4% confidence upper limit to the misalignment S < 51 ° (82 ° at 99.73% confidence), favouring a low value for this angle. We prefer the constraints set on S by marginalizing over the (6, T1 ) joint PDF, on the following grounds: there is no reason to prefer a specific epoch of zero precesSion over another. This is a quantity that is determined by our line of sight to the pulsar, which  chapter 4. PSR J0737-3039A/B: the double pulsar ^  0.012  82  Precession Phase (degrees) —315 —270 —225 —180 —135 —90 —45  0.010 6; 0 0.008  -  a)  0.006 4 0  0.004 0.002 0.000 40000 45000 50000 55000 60000 65000 T 1 (MJD)  Figure 4.8 Marginalized probability density function for T 1 , the epoch of zero precession phase, in which we combine the results from both the cos i > 0 and cos i < 0 analyses. The epochs corresponding to the peaks of the distribution are MJDs 53505 and 67192, corresponding to a current precession phase O so = 0 and 180 °, respectively. These represent a small fraction of the total probability, leading us to believe that T 1 is relatively unconstrained. The top axis labels the precession phase assuming that the peak of the PDF corresponds to Oso = 0°. The blue and red dashed lines show the span covered by the Parkes and GBT observations, respectively, under this assumption. ThiS puts our data around cb so — 180 (-= 180 ° in this plot), which corresponds to a special precession 0  phase, and requires fine-tuning of the parameters.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  83  150  50  ^ 150 50^100 a (degrees) Figure 4.9 Joint probability contours for the angle a between the pulsar spin axis and magnetic axis, and the angle 6 between the spin and orbital angular momentiiin axes. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours. For most values of 6, a is constrained within a fairly narrow region around 90°. a becomes progressively less constrained as 6 reaches 0 and 180°. 6, while relatively less constrained than a, has most of its probability density near its lowest and highest values: Here we display the result for the cos i > 0 case.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  84  0.04 .0a) 0.03 1■1 •1■1  xis 0.02 0  0.01 0.00  ^ 50^100 150 a (degrees)  Figure 4.10 Marginalized probability density function for a, the angle between the spin and magnetic axes of PSR J0737-3039A, under the assumption of one-pole emission. Here, we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% confidence regions, corresponding to a = 89.6+919.44 0 , 89.6 + 5456 .1 0, and 89.61: 81 0 respectively. This leads us to believe that PSR J0737-3039A may be an orthogonal rotator.  Chapter .4. PSR J0737-3039A/B: the double pulsar^  ›.1  85  0.08  ,t 0.06  0.04 0 ;.4  0.02 0.00 20^40^60 (degrees)  ^  80  Figure 4.11 Marginalized probability density function for 6, the angle between the spin axis of PSR. J0737-3039A and the orbital angular momentum axis. This is derived from the (a, 6) joint probability distribution, where we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% upper limit confidence regions, corresponding to 9.7°, 51°, and 82°, respectively. Although not extremely well-constrained, it favours a low value of 6.  Chapter 4. PSIS J0737-3039A/B: the double pulsar^  86  we expect to be uniformly distributed. In the case of a, however, we are forced to use a uniform prior, since we do not have any prior knowledge about the distribution of a in pulsars, specifically in recycled pulsars (see, e.g., Xilouris et al., 1998; Kramer et, al., 1999). We thus adopt 8 < 37 ° (95.4% confidence) as our upper limit. We note that values of a we found at each (8, T1 ) grid point are consistent with the marginalized PDF for a, found from the (a, 8) grid analysis. Figure 4.12 shows a histogram of best-fit values of a found at all (6,T1 ) grid points. From this histogram we obtain a tight distribution around a median value of 89.2 °. We compare this to Figure 4.10 and are reasonably confident that our quoted value of a is consistent with this. Based on our results for this one-pole emission case, we believe that the most likely geometry of this pulsar is that of a near-orthogonal rotator, with the spin axis closely aligned with the orbital angular momentum vector. The epoch of zero precession phase is not well-constrained; a peak in marginalized probability density is found at T 1 = MJD 67192, but contains a small fraction of the total T1 probability density. The constraints we obtain in the one-pole scenario are not tight enough to be conclusive; of course;  a longer  time baseline will place further restrictions on these parameters. This result is at odds with previous work. While the analysis by Manchester et al. (2005b) favours 8 < 60 °, consistent with our value, they conclude that although they arrive at a somewhat low best-fit solution for a, a wide variety of geometrical configurations is possible. They enforce p < 90 ° in their fits to the pulse width data, reasoning that a beam with p > 90 ° is unphysical, or else means that the beam centre has been misidentified. They also concede that the system being near a phase of special precession is statistically unlikely. Through position angle variation analysis, Demorest et al. (2004) prefer solutions with a — 5 ° or a — 90 °. They choose the former low-a solution; in order to avoid an emission beam opening angle 2p ' 180 °. Our results virtually exclude low-a solutions (as well as those near 180 0 ). The only cases where a can adopt low values occur when 8 — 0 ° (and — 180 °). We further note that the Demorest et al. (2004) result is based on a fit of the rotating vector model (RVM; R.adhakrishnan Sz Cooke, 1969) to the data, which may not be applicable to this pulsar.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  87  0.25 0.20 0.15 0.10 0.05 0.00 ^  0  50^100^150^200 a (degrees)  Figure 4.12 Histogram of best-fit values for a from grid search analysis over (d, TO-space, weighted by the probability density at the given grid point. This combines the results from both the cos i > 0 and cos i < 0 analyses. We find a median value of 89.2 0 , with 99.73% interval 82 ° < a < 97°. This agrees well with the results found from the (a, 8) grid analysis. The dashed line corresponds to the median value of the distributiOn.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  88  In all cases, however, we find that it is nearly impossible to avoid best-fit solutions with p > 90 °. Figure 4.13 shows histograms of best-fit values found for p at all grid points for the two grid searches we performed. For that obtained through the (5, T1 ) search we extract a 99.73% interval 109° < p < 119 0 , and from the (a, (5) grid we find slightly wider range, 94° < p < 142°. It seems to be the case that if we constrain PSR. J0737-3039A to be emitting from a single magnetic pole, that it would have to do so from a beam structure extending beyond a single hemisphere of the neutron star, so that the beam centre is actually on the opposite side of the pulsar to where we expect, based on the profile symmetry. This unusual emission scenario is one of the reasons that Manchester et al. (2005b) do not favour a S — 0° geometry, which they justify by further commenting that it is probable that a significant natal kick was imparted to PSR J0737-3039B ; making a low value of S unlikely. The timing analysis by Kramer et al. (2006) has shown the transverse velocity of the double pulsar system to be relatively low compared to other DNS systems. This and the studies conducted by Piran & Shaviv (2005), Willeins et al. (2006), and Stairs et al. (2006) suggest that a large natal kick is actually unlikely for the PSR: J0737-3039A/B system, assuming the system has a small radial velocity: This in turn predicts a low value for S. Our analysis now also indicates that this may indeed be the case: the lack of profile variation is in fact due to a low spin-orbit misalignment angle. Another way to reconcile this small value of S with the observed pulse profile shape is mentioned, but dismissed, by both Manchester et al. (2005b) and Demorest et al. (2004): if PSR J0737-3039A is an orthogonal rotator as favoured by our analysis, then the possibility arises that the profile we observe from this pulsar represents contributions from the two magnetic poles. On a superficial level, the profile shape lends itself to such a postulation: The two pulse components are roughly separated by 180 °, and there is a region of what seems to be a lack of emission between these two components. Qualitative arguments such as these are not particularly valuable, however, as the pulse shape depends on the details of the emission beam structure, about which much is still  • Chapter 4. PSR J0737-3039A/B: the double pulsar ^  89  0.8 0.6 0.4 0.2 00 0^50^100^150 p (degrees)  ^  200  0.5  O0.4 •  N  0.3  ••-■  4 0.1 0.0 0^50^100^150^200 p (degrees)  Figure 4.13 Histograms of best-fit values of emission beam radius p from each point in our grid fits, and weighted by the probability density at the given grid point. These combine the results from both the cos i > 0 and cos i < 0 analyses. Top: Result from the (6, T1 ) grid, where we find a 99.73% confidence interval of 109 ° < p < 119 °. Botto rt: Result -  from the (a,6) grid fit, where we arrive at a 99.73% interval of 94 ° < p < 142 °. Such a large beam indicates that its centroid is on the opposite hemisphere of the neutron star compared to what is expected. The dashed lines indicate the median values of each distribution.  Chapter 4. PSR ,10737-303924/13: the double pulsar ^  90  not understood. Since the pulse polarization analysis presented in Demorest et al. (2004) does not appear to be in good agreement with the WM (a common trait among the profiles of many recycled pulsars; see Xilouris et. al. 1998), we cannot, use the polarization position angle measurements to resolve the question of the number of emitting poles in PSR. J0737-3039A. Another, more straightforward, analysis would be to compare the spin period and component widths of the PSR J0737-3039A profile to the empirical relationship observed between those two quantities (e.g., Rankin, 1993). As with the polarization study, however, the precise relationship between the rotation period and pulse shape of recycled pulsars is not yet well-understood (Kramer et al., 1998). We now describe a re-analysis of the data under the assumption that we observe emission from both magnetic poles of the double pulsar.  4.4.1 Two-pole emission from PSR J0737-3039A We have explored the possibility of two-beam emission from PSR J0737-3039A by recalculating pulse widths for both the Parkes and GBT data sets, with each pulse component treated as being due to emission from a different magnetic pole. We thus determined the width of each pulse component separately, opting to use the 25% peak flux Width for these measurements. Below this fractional pulse height, there are features in the profile that, when noise is added, negatively affect our measurements, making them unreliable. For instance, the first of the two components has a near-horizontal "ledge" in its leading edge that lies at approximately 10% of its peak amplitude. A similar featurO, though not as pronounced, is also found at around the same fractional pulse height in the trailing edge of the second component. We arrive at better-defined width measurements in regions where the profile is steep. We chose to leave out the initial data point from this analysis, since the extremely low signal-to-noise in that profile makes it difficult to obtain a reliable width measurement. As in the one-pole case, we shift the Parkes-derived widths  Chapter 4. PSR 10737-3039A/B: the double pulsar^  91  to match those measured from the GASP data. The measured widths and half-widths (13 0 of each pulse component after shifting the Parkes data are found in Figure 4.14. We then performed an identical analysis on both sets of pulse widths to that done for the single-width case. The results we find for the system geometry agree with those obtained from the single-pole emission model, and also produced reduced x 2 values that are somewhat less than 1.0. The joint probability density distributions for S and T1 that we find for each pulse component are found in Figure 4.15. The marginalized PDFs for 6 and T1 are shown in Figures 4.16 and 4.17, respectively. We find these have similar behaviour to those found in the one-pole scenario. In this case, however, even tighter upper limits to the spin-orbit misalignment angle 6 are favoured. There is significant probability density at most epochs of T1 , indicating that, especially at low 6,  T1 is unconstrained. In Figure 4.18 we present the joint probability distribution for a and 6. These are also consistent with what we found in the one-pole case, favouring a near 90 ° along with low (and near-180 °) values of 6. There is, however, a noticeable spike in the probability density at a — 45° and 6 — 50 °. This corresponds to a special case in which cos p sin S cos O s° = cos a, which causes the rate of profile width change dlid/dt — 0 (Manchester et al., 2005b). The best-fit values for the parameters T1 and p in this region of the (a, 6) grid correspond to values that would indeed give this equality. Physically speaking, we believe this is an unlikely fine-tuning of the parameters and so do not view this solution as being credible. In any case, solutions with a — 90 ° and small 6 have much larger probability densities than these solutions. Figure 4.19 shows the same joint (a, 6) PDFs, with this region removed. We use these "cleaned" distributions to derive the marginalized PDFs for a and 6, shown in Figures 4.20 and Figures 4.21, respectively. As in the one-pole case, we give more credence to the values for S obtained in the (6, T1 ) grid fit, since we are more confident in the prior we attribute to T 1 than we are in that for a. Finally, we look at the distribution of best-fit values of p found in each grid fit. In Figure 4.22 we plot the histograms of these solutions found from analysis of the pulse  Chapter  4. PSR J0737-3039A/B: the double pulsar ^  37.0 L .7,  m  92  28.0 -  36.5 -  a)  be^  27.0 -  <I ,  1^f f  O 36.0 -^I 1:$^ 1 '', 35.5 's' a.,  f  26.0  25.0  i 35.0 a  53000  •  24.0  34.5 - ... 53500 MJD (days)  54000  18.5  53000  53500^54000 MJD (days)  53000  53500 MJD (days)  13.0  18.0  a •  17.5  •  17.0  11.5  16.5  11.0 53000  53500 MJD (days)  54000  54000  Figure 4.14 Width data for the first and second pulse components, shown on the left and right columns, respectively. Top: Full-profile widths at 25% of the peak amplitude for PSR J0737-3039A as a function of MJD are shown for Parkes filterbank data (open circles) and GASP data (filled circles). Bottom: Half-profile widths (1) 0 for PSR J0737-3039A as a function of MJD. As in the single-width case, the Parkes data set was adjusted by subtracting off the difference of the average widths of the two data sets. As before, errors in the adjusted Parkes data come from adding in quadrature the uncertainty in the difference in the mean to the original width uncertainties.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  93  65000 60000 55000 E:  50000 45000 40000  ^ 50^100 150 (degrees) 6  65000 60000 55000 E:  50000 45000 40000  ^ 50^100 150 6 (degrees)  Figure 4.15 Joint probability contours for the angle 8 between the spin and orbital angular momentum axes, and the epoch T1 of zero precession phase, assuming two-pole emission, for the first (top) and second (bottom) pulse components. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours. T 1 is not well constrained, particularly for 6 < 10 ° and 6 > 170 °. Here we display the results for the cos i > 0 ease.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  94  0.04  2") 0.02 0  c.  a..  0.01 0.00 20^40^60^80 6 (degrees)  0.05 o• 0.04 a) >1 0.03 0.02 0  0.01 0.00 20^40^60 6 (degrees)  ^  80  Figure 4.16 Marginalized probability density function for 6, the angle between the spin axis of PSR. J0737-3039A and the angular momentum axis. This is derived from the  (6, T1 ) joint probability distribution in the two-pole emission scenario, for the first (top) and second (bottom) pulse components. Here, we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% upper limit confidence regions, correspOnding to 6.1°, 14°, and 21 °, respectively, for the first pulse component, and 4.7°, 11 °: and 17° for the second pulse component. This favours an even lower upper limit to 6 than we obtained for the one-pole scenario.  ^  Chapter 4. PSR J0737-3039A/B: the double pulsar^  95  Precession Phase (degrees) —180 —135 —90 —45^0^45^90 135 0.012  0.010 U)  a) 0.008 ›)  0.006  as -2 0.004 c.  0.002 0.000 40000 45000 50000 55000 60000 65000 T 1 (MJD) Precession Phase (degrees) —180 —135 —90 —45^0^45^90 135 0.012  0.010 0 0.008 a.) 0.006 as  4  0.004  a. 0.002 0.000 40000 45000 50000 55000 60000 65000 T 1 (MJD)  Figure 4.17 Marginalized probability density function for T1 , the epoch of zero precession phase under a two-pole emission scenario, for the first (top) and second (bottom) pulse components. Here, we combine the results from both the cos i > 0 and cos i < 0 analyses. The top axis shows precession phase, and is labelled assuming that the peak  of the PDF  corresponds to Oso = 0 °. The blue and red dashed lines show the span covered by the Parkes and GBT observations, respectively, under this assumption.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  96  150 41?  (1) a) 100 ea) a) 50  ^ 50^100 150 a (degrees)  150  6.0  100  50  ^ 50^100 150 a (degrees)  Figure 4.18 Joint probability contours for the angle a between the A pulsar Spin and magnetic axes, and the angle 6 between the spin and orbital angular momenttim axes, assuming two-pole emission, for the first (top) and second (bottom) pulse components. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours. As in the one-pole case, a is constrained within a fairly narrow region around 90°, and 6 has most of its probability density near 0° and 180°. Here we display the results for the cos i > 0 case.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  150  97  ••• •  tzt  100  a)  50  cz•  ...jE •  ^ 50^100 150 a (degrees)  150  a) an  100  "c3  50  ^ 150 50^100 a (degrees)  Figure 4.19 Joint probability distribution as in Figure 4.18 for the angle a betWeen the spin and magnetic pulsar axes, and 6 the spin-orbit misalignment angle. Here We have removed the portion of the PDF that contains the region of parameter space Where an unlikely combination of specially fine-tuned parameters gives d(D o /dt — 0. As in Figure 4.18 we show the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours. Here we display the results for the cos i > 0 case.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  98  0.06 0.05 0.04 0.03 cci  a.,  0.02 0.01 0.00 50^100  ^  a (degrees)  150  0.06 a.)  it  0.02  0.00  .  .^.  50  100 a (degrees)  150  Figure 4.20 Marginalized probability density function for a, the angle between the spin and magnetic axes of PSR J0737-3039A, under a two-pole emission scenario, for the first (top) and second (bottom) pulse components. Here, we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% confidence regions, corresponding to a = 89.6 + 2:2°, 89.6+,42°, and 89.612: 31 °, respectively, for the first pulse component, and a = 91.1 +410.10, 91.1 + 2 7j2°, and 91.11i7 ° for the second pulse component. As in the single-pole emission analysis, this leads us to believe that PSR, J0737-3039A is a near-orthogomd rotator, but with results that are more constraining in the two-pole emission scenario.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  99  0.14  L 0.08 0.06 0  a.$~ 0.04 0.02 0.00 20^40^60^80 6 (degrees)  0.15  os  2  a.  0.05  0.00 20^40^60^80 6 (degrees)  Figure 4.21 Marginalized probability density function for S, the angle between the spin axis of PSR J0737-3039A and the angular momentum axis of the double pulsar system. This is derived from the (a, 6) joint probability distribution under the two-pole emission scenario, for the first (top) and second (bottom) pulse components. Here, we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% upper limit confidence regions, corresponding to 6.1°, 19°, and 58 °, respectively, for the first pulse component, and 4.7°, 15 °, and 36 ° for the second pulse component.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  100  profile from each pole, and for both grids. In general, we see that p < 90 ° is clearly favoured, with high occurrences of small values of p within that range. Allowing emission to come from both magnetic poles in this pulsar thus avoids the need for exotically large beams, or else a reinterpretation of the the location of the emission beam centre. A summary of results for the one- and two-pole emission models for a and d is found in Table 4.3. We find the results from assuming two-pole emission to be consistent with those found for the one-pole case, and provide even tighter constraints on 6. In .  addition, having two emission beams naturally gives p significantly lower than 90 °, which seems to be a more reasonable configuration. We thus favour a configuration in which PSR J0737-3039A is an orthogonal rotator with a spin axis that is nearly aligned with the orbital angular momentum of the system, and in which the pulse profile that we observe is due to emission from both magnetic poles.  4.5 Special relativistic aberration and short-term profile changes Another method for determining the orbital geometry of this system takes advantage of the high orbital velocities of the neutron stars in the PSR J0737-3039A/B system, approximately 0.001c for both pulsars A and B on average. This will cause non-negligible special relativistic aberration to affect the emission direction with respect to our line of sight. Such a variation will in turn produce a periodic change in both the position of the observed pulse profile centroid, as well as distortion in its shape; over the PSR. J0737-3039A orbital timescale (Domani & Taylor, 1992; Rafikov & Lai, 2006). -  A shift in the pulse centroid position, or so-called "longitudinal" aberration, is very difficult to detect. The resulting arrival time delay shifts the entire pulse profile without causing any distortion in its shape. Furthermore, detecting the variations due to this effect with pulsar timing is extremely challenging to do on the timescale of the pulsar orbit, as it will mostly be absorbed into the Romer delay, described in section 1.3. Indeed,  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  101  0.8 0.6  r i  0  0  0.5  g  0  0.4  0  0.6  N 0.4 ts: 7t;  0.3 0.2  o 0.2  z  0.1 00  0.0 0^50^100^150^200 p (degrees)  .^.^.  0  .^.  50^100^150^200 p (degrees)  0.6 0.5 0  ti 0.4  — 0.3 -^ cr:1 0.2  z 0  0.1 0.0  ^ ^ 0^50^100^150 200 ^ p (degrees)  50^100^150 p (degrees)  ^  200  Figure 4.22 Histograms of best-fit values of emission beam radius p from each point in our grid fits, assuming two-pole emission, and weighted by the probability density at the given grid point. These combine the results from both the cos i > 0 and cos i < 0 analyses. Results for the first and second pulse components are shown in the left and right columns, respectively. Top: Results from the (J, T1 ) grid, where we find 99.73% confidence intervals of 17° < p < 26 ° and 12 ° < p < 20 °. Bottom: Results from the (a, 8) grid fit, where we arrive at a 99.73% interval of 11 ° < p < 55 ° and 10 ° < p < 46 °. The solid lines indicate the location of the median values of each distribution. We find that the two-pole model clearly favours p < 90  Table 4.3 Summary of results for parameter estimation of a and 6 from long-term profile evolution analysis of PSR J0737-3039A. a and 6 values are derived from the (a, 6) and (6, T1 ) joint probability density functions, respectively. Parameter  One-pole model Median  68.3% interval^95.4% interval  99.73% interval  89.6  70 — 99^34 — 136  16 — 159  < 15^< 37  < 69  a (0 ) 6  (°)  Two-pole model Parameter  Pole 2  Pole 1 Median  68.3% interval  95.4% interval  99.73% interval  Median  68.3% interval  95.4% interval  99.73% interval  44 — 148  91.1  87 — 101  69 — 121  54 — 135  < 21  • ^• ^•  < 4.7  < 11  < 17  a (1  89.6  84 — 98  60 — 124  4 (0 )  ".  < 6.1  < 14  Chapter 4. PSR, J0737-3039A/B: the double pulsar^  103  it is estimated that it will take tens of years of timing observations to single out the effect of longitudinal aberration at the 2u level (Rafikov & Lai, 2006; Damour & Taylor, 1992; Kramer et al., 2006). The aberration in the "latitudinal" direction should, however, be detectable. Unlike the longitudinal component, it affects components of the pulse at different spin phases by varying amounts, causing the stretching and compressing of the observed pulse profile. The magnitude of this distortion will change over an orbital period (Rafikov & Lai 2006; see also Damon' . & Taylor 1992). The latitudinal aberration at a given orbital phase causes a delay in pulse arrival times, given in Rafikov & Lai (2006) by (At)lr = C(sin  + e sin w) + D(cos q5 + e cos w),^(4.10)  where  C=  Qbap^1  ^ cos 77 Qp eV1 — e 2 sin ( tan x o 1 Qbap D = ^cos i sin ri, O p cV1 — e 2 sin ( tan X o  (4.11) (4.12)  and where tan Xo =  sin a sin (1) 0 ^(4.13) cos a sin ( — cos 1.o sin a cos (  is the position angle of linear polarization at pulse phase 4) 0 . This analysis thus implicitly assumes the rotating vector model (Radhakrishnan & Cooke, 1969). For this analysis we take (1) 0 to be the pulse phase at the leading edge, which we approximate to be half the measured pulse width. Any offsets that arise from this approximation can be ignored, as the change in X o at these pulse longitudes is very small. 'ti) is the true anomaly as measured from the ascending node of the orbit, e is the orbital eccentricity, i is its inclination, Qb = 27/Pb is the orbital angular frequency in radians per second,  Qp = 27f0  is the angular spin frequency of the A pulsar, % -= al c/ sin i is  the semimajor axis of the A pulsar orbit, and w is the longitude of periastron. Since the orbit of the PSR J0737-3039A/B system is processing, the value of w at the epoch t  Chapter 4. PSI? 10737-3039A/B: the double pulsar ^  104  representing a given observing campaign (which we have taken to be the middle of the given epoch) is w = wo +  t —T0 365.25  w  '^  (4.14)  with w o being the value at epoch To in MJD, advancing at a rate The angle a is that between the spin and magnetic axes of the pulsar, (" is the angle between the spin axis and our line of sight, and 77 is the angle between the ascending node and the projection of the spin axis on the plane of the sky (see Figure 4.4). Equation 4.10 predicts the shift in units of time, but we can easily convert it to an angular pulse phase shift since (At)A t = AcD o /Q p . Thus, we now have: A 1 0 Qp [C(sin //) + e sin w) + D(cos + e cos w)]. ^(4.15) ( )  For each observational epoch, we calculate the orbital phase of each 30-second integrated pulse profile within each frequency channel and average all pulse profiles belonging to a given orbital phase bin, producing a representative high signal-to-noise profile for each orbital phase. We have chosen 10 orbital bins for this analysis, so that we Can adequately sample the orbital period of the pulsar while still maintaining a reasonable level of signal-to-noise for each averaged profile. We also constructed a standard reference profile for each epoch, by averaging all profiles at all orbital phases. We have left, out from this analysis the data taken during the June 2005 observing campaign. This was due to several corrupted scans that could not be identified through the regular RFI searches we perform. These affected certain orbital-phase binned profiles, which contain on average a tenth of the data included in the reference profile for that epoch. In Figure 4.23 we show the reference template profile we used for the data taken in May 2006, and demonstrate the meaning of the (I), and A ,1, 0 parameters.  4.5.1 Prediction of aberration from long-term analysis From equations 4.11, 4.12, and 4.15, we can bring out the factor Qbap^1 A=^ C2 p cV1 — e 2 sin ( tan x o '  (4.16)  ^  Chapter 4. PSR J0737-3039A/B: the double pulsar^  105  1  0.12  ^043 0^li 11 0.10 ^1 1 -;; II I1 0.08 1 AA^iv'i \ ^1I :1) 0.06 I 1^ ^1^ I I I^ ^1^ 0.04 I i •■■1  (  1  0.02 0.00 —180  +.  ^  nry  ^ ^ 90 180 —90^0 Pulse Phase (degrees)  (Do Figure 4.23 May 2006 standard template profile for PSR, J0737-3039A, composed by averaging data taken during the May 2006 campaign observations at 820 MI D, With the -  GASP backend at the GBT. Drawn on this profile are labels demonstrating the potential Pulse contraction by an amount 0(1)0 at pulse longitude (1o.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  106  which represents the amplitude of the periodic aberration signal that, would be observed. Here, C(8, T1 ) is given by equation 4.8, and tan x o is calculated using equation 4.13. We use the results we obtain from the long-term profile analysis in Section 4.4, shown in Table 4.3, to predict an upper limit to the aberration signal we expect, to find in PSR J0737-3039A. Since ( depends on the precession phase, which we find to be unconstrained, we adopt a precession phase of Os o (Ti ) = 45'; this corresponds to the median value of Icos Osol under a uniform distribution. Estimating 77 from our our long-term profile analysis results, we find from equation 4.9 that 'cos < 0.18, 0.075, and 0.058, for the one-pole analysis and the first and second pulse components in the two-pole analysis, respectively (the sign of cos  n is not known due to the ambiguity in the sign of cos i, and  these are upper limits since our measurement of 8 is restricted to an upper limit): This is an order of magnitude larger than the factor !cos i sin n i in equation 4.12 (— 0.023 for all three analyses; due to the near edge-on orbital inclination of the system). We therefore multiply equation 4.16 by the calculated value of cos I iII. These upper limits on Icos are consistent with 77 — 90 or 270 °, i.e. the spin axis appears aligned with the orbital angular momentum axis, projected onto the plane of the sky. We thus estimate an amplitude A cos 7/ I to the aberration signal of 0.00099 °, 0.00063 °, and 0.00086 ° for the one-pole scenario, and the first and second pole in the two-pole emission model, respectively. We will see in subsequent sections that these calculated amplitudes are smaller than our measured upper limits to the profile shift. We nevertheless proceed, to verify consistency between the results between the long-term profile analysis of Section 4.4 and short-term analyses that follow.  4.5.2 Searching for aberration Figure 4.24 again shows the standard profile, along with the folded data binned according to orbital phase for the April 2007 campaign observations, used to determine profile shifts. The binned profiles have been aligned and scaled to match the reference profile through cross-correlation with the standard profile in the frequency domain. This reduces the  chapter 4. PSR ,10737-3039A/B: the double pulsar ^  107  effect that possible flux changes caused by effects such as interstellar scintillation (which is not related to pulse shape variation due to aberration) have on our analysis. In addition, data obtained with GASP are particularly beneficial for this analysis; unlike filterbank data (such as that taken with the Parkes telescope for this pulsar) those obtained by GASP do not yield varying weights for different parts of the pulse profile, again due to scintillation effects (see Stairs et al. 2002, cf. Arzoumanian 1995, for a discussion of such filterbank effects on the timing of PSR B1534+12). Figure 4.25 has the same format, but shows the difference profiles obtained by subtracting each orbitally-binned profile from the reference profile. In both cases it is difficult to discern any differences in the profiles or profile residuals between orbital bins, apart from noise features of low signifiCance. As suggested by Rafikov & Lai (2006), if there is a periodic fluctuation in the pulse shape, we would expect to measure a sinusoidal variation in the shift between the separate pulse components over an orbital period. To investigate this, we perform timing on each half of each orbitally-binned profile against its corresponding half in the reference profile, through cross-correlation as described earlier. We then note the difference in pulse phase shift we obtain between each half-profile as a function of orbital phase. This measured shift difference in pulse phase is shift = 204) 0 , where 0(1) 0 is given by 4.15. This timing analysis is performed for each observational epoch. The resulting angular shift differences are shown in Figure 4.26. It demonstrates neither any clear periodic behaviour ; nor any obvious trend common to all epochs; in fact virtually all the measurements are consistent with zero phase shift within 2a. We thus use the phase shifts found to obtain absolute  upper limits to those experienced by the observed profile at each orbital phase, so that for each epoch we have: 04" 0 (0) < !Alio (P) !measured + 2604) 0 Mmeasured, (4.17) for its 2a upper limit, where SA43 0 (0) is the measured uncertainty on 0(I) 0 . It can be seen that the aberration amplitude prediction, indicated on Figure 4.26 by daShed lines, is much smaller than these limits. However, in principle, we can still use them to derive  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  108  0.1 ti  0.10 0.08 cn 0.06 7.7-  , 0.04 'E0 m 0.02 E.— .7 x 0.00 ^  W.  0.0  0.2^0.4  0.6  0.8  1.0  Pulse Phase  phase = 0.95  0.85  0.45  0.25  0.15  0.05  Figure 4.24 Reference template profile (top) and profiles binned according to orbital phase, constructed from campaign observations taken in April 2007 at the Green Bank Telescope at 820 MHz. No significant differences are noticeable.  ▪  Chapter  1. PSI? J0737-3039A/B: the double pulsar^  109  ti  P, 0.08 oi 0.06 ;35 0.04 A 0.02 x 0 00 3 00  0.2^0.4^0.6 Pulse Phase  phase = 0.95  0.005 V  •  1 0  0.8  0.000 -0.005  0.85  0.75  0.65  0.55  0.45  0.35  mo* 0.15  4)60441/4446sonoi 0.05  Figure 4.25 The reference template profile for the April 2007 data set is plotted at the top of the figure, followed by differences between each orbital phase-binned profile shown in Figure 4.24 and the standard profile for that epoch. Red dashed lines indicate the zero points in these plots. Once again, it is difficult to discern any significant features in the residual profiles.  Chapter 4. PSI? J0737-3039A/B: the double pulsar^  • • • •  0.04  110  Nov 2d05 May 2006 Nov 2006 Apr 2007  0.02 a) a) ao a)  0  0.00  —0.02 —0.04 —0.06 — 0.0  .  0.2  0.4^0.6 Orbital phase  0.8  1 .0  Figure 4.26 Pulse profile angular phase shifts as a function of orbital phase. These were obtained through timing each half of the PSII, .10737-3039A profile against the corresponding half of the standard template profile. This was done separately for each epoch to avoid long-term effects on the profile shape. It can be seen that there is no obvious trend in the resulting shifts, and no common behaviour between epochs. Dashed lines indicate the predicted aberration amplitude from long-term profile analysis.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  111  constraints on the system geometry. In particular, as mentioned above, this will be useful as a consistency check for the analysis performed on the pulse profile in Section 4.4. As in Section 4.4, we performed a Levenberg-Marquardt least-squares fit to the data using equation 4.15. This was done over a grid of values for a (the angle between the pulsar spin and magnetic axes) and ( (the angle between the pulsar spin axis and the observer's line of sight) with the constraints 0 < a < 180 ° and 0 < < 180 , and 0  allowing 7) to vary in the fit at each grid point. The result is a best-fit y2 value at each point in (a, C)-space. We converted these X 2 values to arrive at a joint posterior probability density function as described in Section 4.4. As before, we have no reason to expect a preferred orientation for these angles within the constraints imposed, so we choose a uniform prior distribution for each parameter within 0 < a < 180 ° and 0< < 180 °. Figure 4.27 shows joint probability density contours for each epoch. One can immediately see that the parameter space is virtually unconstrained for both parameters; the best conclusion we can extract from this analysis is that values of a and ( near 0 or 180 ° are not favoured. Using equation 4.2 for (N, we can compute values of constant emission beam radius at p onto each (a, () grid point. Figure 4.28 shows the probability contours for a and ( for the May 2006 epoch, with contours of constant p overlaid. It is clear that regardless of the favoured value of a, the opening angle of the emission cone is likely greater than 90 °, as was found for the long-term profile evolution analysis in Section 4.4. This implies that the true centroid of emission is on the opposite hemisphere of the neutron star from what is normally assumed. As stated in section 4.4, a second explanation exists, in which the emission from the pulsar comes from both magnetic poles, with two p < 90 ° emission beams each producing a separate pulse for every neutron star rotation. To investigate the possibility of twopole emission and the constraints this model gives, we again treat each profile component separately. Since it is unclear in this case where to divide each pulse component, we did not perform a timing comparison as was done in the one-pole case. Instead, we measured  Chapter 4. PSR J0737-3039A/B: the double pulsar  ^  November 2005  112  May 2006 150  150  a)  00  ta0 a)  100  ke,  50  50  50^100 a (degrees)  50  150  November 2006  an  150  April 2007 150  150  a)  100  a (degrees)  100  100 a)  50  50  50^100  ^ 150 ^  ^  a (degrees)  50^100  ^  150  a (degrees)  Figure 4.27 Joint posterior probability distributions for a and ( at each epoch of concentrated campaign observations. Here we have used uniform prior distributions for < a < 180° and 0 < < 180°. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours.  Chapter 4. PSR J0737-3039A/B: the double pulsar^  113  150  a)  a) 100  av  a) Pci  50  ^ 50^100 150 a (degrees) Figure 4.28 Joint posterior probability distributions for a and (, shown for the May 2006 observing epoch. Overlaid are contours of constant beam opening angle p. This suggests that if we restrict the observed pulse profile to be due to emission from one pole, values of p > 90 ° are more likely.  Chapter 4. PSI? J0737-3039A/B: the double pulsar^  114  the pulse width of each half-profile in each orbital phase bin, and compare it to its corresponding half-standard profile. As in Section 4.4.1, we used widths measured at 25% of the peak flux to avoid shallow and noisy features that could corrupt the accuracy of the measurement. As before, this difference in width between each orbitally-binned and corresponding standard template profiles corresponds to 20(I) 0 , where in this case (1) 0 is the distance from the centre of the pulse, well-approximated by half the width measurement. In Figure 4.29 we plot these phase shifts as a function of orbital phase for both pulse profile components (i.e. the profile observed from each magnetic pole). We again see no discernible periodic trend to the behaviour in the phase shift over an orbital period for either pulse component. As with the one-pole case, we proceed by converting these measurements to absolute shift limits, determined as described in equation 4.17. We then perform a fit to these data using the predicted shifts given by equation 4.15. The resulting (a, C) joint probability distributions for both profile components are shown in Figure 4.30 for the November 2005 epoch. This is representative of the results from all epochs, which provide very little constraint, as with the single-pole case. Figure 4.31 shows the resulting distributions for each profile component for the May 2006 epoch observations, with contours of constant p overlaid. Here, the difference between the one and two-pole models becomes especially distinct. As in the long-term profile analysis, we find that the two-pole model naturally allows for p < 90 °, an opening angle range that seems more reasonable based on what is known about pulsar emission characteristics. We have thus far performed fits to each epoch separately, since without assuming anything about the extent of the effects of geodetic precession on the pulsar and system geometry, the quantities and 7/ could potentially vary from epoch to epoch. However, we would ideally like to include data from all epochs in a single fit.  Chapter 4. PSR, J0737-3039A/B: the double pulsar^  0.6 -0.4 a) a)  115  • Nov 2005 — • May 2006 • Nov 2008 • Apr 2007 —  —  0.2 7  4 a)  0.0  —0.2 — a —0.4 -0.6 .  0.0  ^  0.2  ^  ^ ^ 0.4^0.6 0.8 1.0 Orbital phase  0.6  Nov 2005 • May 2006 • Nov 2008 • Apr 2007 •  0.4 "VT 0.2 a) •  0.0 —0.2  IIPP  '4IP  '  —0.4 —0.6 .^.  0.0^0.2  0.4^0.6 Orbital phase  0.8  ^  1.0  Figure 4.29 Pulse profile angular phase shifts for the first (top) and second(bottotn) profile components as a function of orbital phase. These are obtained by taking the width at 25% peak amplitude. As in the one-pole width measurements, there is no obvious trend in the resulting shifts, and no common behaviour between epochs. Dashed lines indicate the predicted aberration amplitude from long-term profile analysis, which overlaps with the solid zero phase-shift line, since it is very small compared with the scale plotted here.  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  116  November 2005 150  (12  a)  an  100  a.) 1:1  50  50^100  ^  150  a (degrees)  November 2005 150  l)  50  50^100  150  a (degrees)  Figure 4.30 Joint posterior probability distributions for a and  c at the November 2005  epoch of concentrated campaign observations, assuming the emission comes from both magnetic poles of the pulsar. Here we have used uniform prior distributions for 0 < cr < 180° and 0 < ( < 180°. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours, for the first (top) and second (bottom) profile components.  ▪  Chapter 4. PSR J0737-3039A/B: the double pulsar ^  117  150  a)  •  bi)  100  50  ^ 50^100 150 a (degrees)  150  a)  E 100 ao a)  -c)  50  ^ 50^100 150 a (degrees)  Figure 4.31 Joint posterior probability distributions for a and in the two-pole scenario, for the first (top) and second (bottom) profile components. Data are shown for the May 2006 observing epoch. Overlaid are contours of constant beam opening angle p. This suggests that restricting the emission as coming from one magnetic pole likely favours values of p < 90 °.  Chapter 4. PSI? J0737-3039A/B: the double pulsar^  118  4.5.3 Using multiple-epoch data simultaneously Because of the effects of geodetic precession, the spin axis of the pulsar should precess around the orbital angular momentum axis of the system (Damour Ruffini, 1974; Barker O'Connell, 1975), causing and 77 to vary with time, since these quantities depend on the direction of our line of sight to the pulsar. We could thus perform a fit that allows a different ( and n at each epoch t so that now c(t) and 17 n(t). Therefore, if we have n epochs of data, then A(1) 0 depends on the free parameters (a, (o, • • , (72-1 1 ri0)  • •  Tin - i) so that there are 2n + 1 free parameters in our fit.  Another approach (as discussed in section 4.4) takes advantage of the fact that and r vary with time. We perform the same transformation given by equations 4.8 and 4.9, parametrizing ( and 71 in terms of 6 and T1 , which we then substitute into equation 4.15. We are then left with a description of the expected change in profile phase Oh o that depends on only the three free parameters (a, 6, T1), rather than the 2n + 1 parameters discussed above. In principle, observation of aberration can thus give a direct determination of the spin-orbit misalignment and precession phase, helping us to directly constrain the orbital geometry. We performed a least-squares fit to the data using equation 4.15, this time over a grid of values for a and 6, constraining these parameters to be within 0 < a < 180 ° and 0 < 6 < 180 °, leaving T1 as a free parameter in the fit at each grid point. We again computed a. Bayesian likelihood function and joint, probability density as described in the case for the single-epoch fitting of a and (. We used uniform distributions for a and S to construct our priors. As before, we performed our analysis assuming both one- and two-pole emission. The resulting joint posterior probability density functions for the one-pole case is shown in Figure 4.32. We find a more constraining result in this case, with a near 90 ° being favoured, as are low values of 6 (and those near 180 °). In general, we see that a and  6 are not very constrained, which is unsurprising given that our pulse shift upper limits are large compared to what we have predicted in Section 4.5.1.  Chapter 4. PSI? J0737-3039A/B: the double pulsar^  119  150  50  ^ 50^100 150 a (degrees) Figure 4.32 Joint posterior probability density distributions for a and S under the one-pole emission scenario, found using data from all epochs. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours. Values of a near 90 ° have the highest probability densities. The high densities of contour boundaries reflect the flatness of the  X 2 space.  Chapter  4. PSR J0737-3039A/B: the double pulsar ^  120  The results for the joint (a, 6) probability density function, assuming emission from both magnetic poles, are shown in Figure 4.33. The constraints derived from the twopole scenario are not as tight as those from assuming one-pole emission. Compared to the single-epoch analysis however, a is better constrained. On the whole, we find that analysis of the upper limits to the aberration signal yields much weaker limits on the system geometry than precession alone, although they are still consistent with low misalignment angle, as well as with our results from the long-term profile analysis.  4.6 Implications for evolution Our results imply that the misalignment angle between the spin axis of PSR J0737-3039A and the orbital angular momentum axis of the PSR, J0737-3039A/B system 6 is small, whether we believe that the emission from the pulsar is from one or both magnetic poles. We find that modeling the effect of geodetic precession on the measured pulse widths of PSR, .10737-3039A over two years results in 95.4% upper limits to the misalignment angle 6 of 37° in the single-pole case, and 14° and 11 ° in the two-pole case (for the first and second profile components, respectively). We also find that for this low value of misalignment angle that the epoch of zero precession T1 is not well-constrained. This supports the expectation that it has become difficult to ascribe this lack of change to special precession phase width, considering that our data span approximately 7.5% of the precession period for PSR, J0737-3039A. This is a much larger fraction than for PSR B1913+16 and PSR, B1534+12, in which long-term profile evolution has been observed. A low misalignment angle means that it is likely that a very small kick was imparted to the system due to the supernova of the pulsar B progenitor. This agrees with the low-kick hypothesis that is favoured by measurements finding a low transverse velocity and eccentricity of the double pulsar, as well as the low mass of the B pulsar, all found from timing measurements of the double pulsar (Kramer et al., 2006). It also lends credence to the studies performed by Piran Shaviv (2005), Willems et al. (2006), and Stairs et al. (2006), which favour a low-mass (< 2 /11,-,) progenitor, and a low natal kick  Chapter  4. PSR J0737-3039A/B: the double pulsar ^  121  150  a)  an  100  a)  50  50  ^  ^ 100 150 a (degrees)  150  50  ^ 50^100 150 a (degrees)  Figure 4.33 Multi-epoch joint posterior probability density distributions for a and ö under the two-pole emission scenario, from analysis done on the first (top) and second (bottom) pulse components. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours. In both plots, values of a near 90 ° have the highest probability densities.  Chapter 4. PSI? ,I07,37-3089A/B: the double pulsar ^  122  (< 100 km s') given the constraints of low space velocity. In the case of the last study, our constraints also agree with their estimate of the misalignment angle, which they predict to be 0.5 < b < 11 ° (95.4% confidence). This analysis thus supports a scenario in which the PSR, J0737-3039B underwent a low mass-loss, relatively symmetric supernova event. The prominent, candidates for such an event are an electron capture supernova, or the collapse of a low-mass iron core (Podsiadlowski et, al., 2005, 2004), and we therefore favour one of these scenarios as the one that, produced the double pulsar system as we now observe it. Discovery and observations of an increasing number of DNS binary systems will help to determine how prevalent is this type of system, and could provide further insight into this alternate channel of double neutron star formation.  123  Chapter 5  PSR J1756-2251: a pulsar with a light neutron star companion PSR. J1756-2251 is a double neutron star binary system, discovered in the Parkes Multibeam Survey (Manchester et al., 2001; Faulkner et al., 2005). Initial timing of this pulsar showed it to have a similar orbital period to the binary pulsar PSR B1913+16 (Hulse k Taylor, 1975) of — 8 hours. However, it was also found to be more spunup (Psph, = 28.4 ins), in a somewhat less eccentric orbit (e — 0.18), with a companion neutron star apparently having a relatively low mass m 2 = 1.18112 M® (Faulkner et al., 2005, see Table 5.4 for properties of other DNS systems, including PSR B1913+16). This showed it to have more characteristics in common with PSR .10737-3039A, the recycled pulsar in the double pulsar system (Burgay et al., 2003; Lyne et al., 2004; Kramer et al., 2006). As discussed in the previous chapter (and references therein), it can be argued that the B pulsar in that system had a low-mass progenitor (< 2 AI® ) that underwent an electron-capture supernova. Its low orbital eccentricity could be caused by the low amount of mass lost from this supernova, along with the relative symmetry of the event. The latter would results in a small natal kick to the B pulsar, and explain the current small transverse velocity observed in the PSR J0737-3039A/B system (Piran Shaviv, 2005; Willems et al., 2006; Stairs et al., 2006). The resemblance of PSR, J1756-2251 to the double pulsar in its orbital eccentricity and low mass companion neutron star thus may present a new opportunity to investigate this channel of DNS evolution  (e.g.,  van den Heuvel, 2004). We have extended the existing observational data of PSR J1756-2251 to gain more significant constraints on the system parameters through timing of this pulsar. We also  Chapter 5. PSI? 1756-2251: a pulsar with a light neutron star companion ^124  used this new data set to perform an analysis of the pulse shape evolution to study the effects of geodetic precession on the observed pulse profile. This helps to constrain the pulsar and orbital geometry, providing further clues as to how this system formed and evolved.  5.1 Observations Observations at the Parkes telescope have been performed for PSR J1756-2251 by the author's collaborators since its initial discovery in the Parkes Multibeam Survey (Manchester et al., 2001). The initial search observations are not included in the timing analysis performed here. However, we do incorporate the data obtained from Parkes that were used in the initial timing study of this pulsar (Faulkner et al., 2005). These observations have been (and continue to be) carried out regularly at 1374 MHz over 288 MHz bandwidth divided into 3-MHz channels, and at 1390 MHz over 256 MHz bandwidth divided into 0.5 MHz channels. The data from each channel were detected and the two polarizations summed in hardware before 1-bit digitization every 250 and 80250 its, respectively. The data were recorded to tape and subsequently folded offline in typically 10-minute subintegrations. Further details of the Parkes observations can be found in Faulkner et al. (2005). Observations with GASP at the GBT were performed at 1400 MHz. These were generally taken over a total bandwidth of 64 MHz until January 2006, when we began to include, when available, computing nodes from the CGSR2 pulsar backend. This increased our processing power, which allowed us to increase the observing bandwidth to 96 MHz. As with the pulsar observations described in previous chapters, the data were coherently dedispersed (Hankins & Rickett, 1975) in software, then detected, and folded using the current best ephemeris for the pulsar every 180 sec-  onds. This was done in order to minimize the amount of pulse phase drifting within an integration, while still maintaining adequate signal to noise ratio in each pulse profile. The data were flux-calibrated in each polarization using the signal from a noise diode source that is injected at the receiver. The calibrated data were then summed together  Chapter 5. PS17. J1756-2251: a pulsar with a light neutron star companion ^125 across all frequency channels to give the total power signal. Each observing session lasted — 8 hours, in order to fully sample the orbit of PSR. J1756-2251. A summary of the observing details are found in Table 5.1.  5.2 Timing Analysis We first constructed a standard template pulse profile for PSR.11756-2251 by averaging the data from all scans that did not show RFI contamination or other unusual features. The latter of these exclusion criteria was the case for data taken on 21 Mar 2005 (MJD 53450), winch showed an unexplained overall phase offset from the rest of the data set. It was also found that the channels processed by CGSR nodes on 27 Feb 2006 (MJD 53793) had a feature in the profile that was offset from the main pulse by approximately half a pulse phase, due to an unidentifiable cause. Those data were also left out of the timing fit. Pulse TOAs were then calculated by cross-correlation of each integrated pulse profile with the standard profile in the frequency domain (see Section 1.2.1). This was done with the GASP data using the fftfit routine (Taylor, 1992). For Parkes data this was done, using a template profile derived from one high signal-to-noise day of observation, with the psrchive software (Hotan et al., 2004b) (which uses fftfit), which was also used to sum the data. The time stamp for each integrated profile was then shifted by the time offset corresponding to the phase shifts calculated by the cross-correlation. The uncertainties on the shifts were adopted as the TOA uncertainties. Each TOA was taken to represent the mid-point arrival time for each integration. In total, we measured 2608 individual pulse TOAs: 333 from Parkes data, and 2275 from GBT data with GASP. We then fit a model describing the expected pulse arrival times to the topocentric TOAs, using the tempo software package. As usual, this model takes into account the effects of the Earth's motion on the measured pulse TOAs using the the JPL DE405 Solar System ephemeris (Standish, 1998). Differences in instrumentation and reference template profiles between Parkes and GBT observations cause an overall offset in measured pulse arrival times, and such a shift was included as a parameter in the fit. Clock  Table 5.1 Summary of observations of PSR J1756-2251. Telescope  Instrument  GBT  GASP  Parkes  Filterbank  Centre  Cain  Zys  Sampling  Effective no.  Total effective  Integration  frequency (MHz)  (K Jy -1 )  (K)  (Ps)  of channels  bandwidth (MHz)  time (s)  1400  2.0  20  0.25  16-24'  64-96  180  1374  0.74  28  250  96  288  600  1390  0.74  22/28b  80-250  512  256  600  a The number of channels that were used varied depending on the availability of the CGSR2 computing nodes at. the GBT, as well as on the removal of channels that. are contaminated with radio frequency interference (RFI). b Z ys  values given for the Parkes telescope are for the Multibeam (centre beam) and H-OH receivers. respectively.  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion^127 corrections between each observatory and UTC time were obtained using data from the Global Positioning System satellites. The effects of orbital motion on the pulse arrival times were taken into account using the Damour-Deruelle (DD) timing model (Damour Deruelle, 1985, 1986) implemented within the tempo software. The basic formulation of this model is discussed in Section 1.3. In addition to the basic Keplerian parameters, this model describes the post-Keplerian orbital parameters in a theory-independent manner. After obtaining a best-fit set of parameters, we re-processed the data, shifting each integration in time by the difference in phase between the original profile and that predicted by the new ephemeris. This resulted in better-aligned pulse profiles, with which we also re-constructed the standard reference profile (shown in Figure 5.1), which was used to then re-perform the timing analysis. As with the PSR, J1802-2124 timing analysis discussed in Section 3.3, we then obtained a best-fit value for dispersion measure by subdividing the GASP-derived pulse profile data into separate frequency bins. In this case, we obtained TOAs for integrated profiles within each of six frequency bins (1348, 1364, 1389, 1396, 1412, and 1428 MHz). We performed a timing fit to this data set, and arrived at a best-fit value for DM (121.198 + 0.005 pc cm -3 ). This value was held fixed for the subsequent timing analysis performed on the entire data set, the results from which are presented in this section. Figure 5.2 shows timing residual plots from each instrument against MJD and orbital phase. The weighted RMS of the timing residuals from Parkes data were 18:6 /is for this pulsar, while for the GBT data, the RMS was 16.5 ps. The only slight increase in quality of data that we see in the GBT data is due to the larger bandwidth and longer integration times (10 minutes versus 3 minutes for GASP) used in the Parkes observations. Also, because the PSR J1756-2251 pulse profile is essentially featureless, coherent dedispersion, as implemented in GASP, only provides a modest advantage in observing this pulsar. However, we resolve the orbit better with GASP TOAs than we could with Parkes because of the high signal-to-noise ratio we obtain with GBT data in just 3 minutes of integration.  Chapter 5. PSI? J1756-251: a pulsar with a light neutron star companion ^128  0.04 0.03 g cl) 0.02 ra 0.01 0.00 0.0  ^  0.2  ^  0.4^0.6 Pulse Phase  ^  0.8  ^  1.0  Figure 5.1 Standard template profile for PSR, J1756-2251, created with, and used to calculate pulse times-of-arrival for, data taken with the GBT using GASP.  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion^129  200 100  11 11  ^I ill  —200  53000  53500 MJD  54000  54500  200 100  —200  0.0  0.2  ^ ^ 1.0 0.4^0.6 0.8 Orbital phase  Figure 5.2 Timing residuals for PSR .J1756-2251, after including best-fit parameters in  the timing model. Parkes-derived residuals are shown in red, and those obtained with GASP data taken at the GBT are shown in black. Top: Residuals as a function of MJD.  Bottom: Residuals as a function of orbital phase.  Chapter 5. PSR 11756-2251: a pulsar with a light neutron star companion ^130 Parkes  GBT/GASP 1500  80  60  1000 0  0  40  500 20  0  —50^0^50 Residuals (As)  0 —200 —100^0^100 Residuals (As)  200  Figure 5.3 Histograms of timing residuals for PS13, J1756-2251, for Parkes (left) and GASP data taken on the GBT (right). Both data sets are consistent with a roughly Gaussian distribution.  Figure 5.3 plots histograms of the timing residuals for each instrument used. These are Gaussian-distributed, however there was an underestimation of the TOA uncertainties due to unmitigated RFI and coarse quantization of the analog signal as it was Sampled. This resulted in a reduced  x 2 for the fit of 2.3 for the Parkes-derived data and 1.16  for the GASP-derived data. To account for these effects, we have scaled and; in the case of the Parkes-derived TOAs, added an amount in quadrature to, the nominal TOA uncertainties obtained from each instrument by an amount that gives  x 2 = 1 for each  data set. The scaling factor employed toward the GASP-derived data set was very small (— 1.08), indicating that the original calculated uncertainties are well-understood. These data comprise the great majority of the entire set (89%), and so we directly quote the timing parameter uncertainties produced by the tempo software. We list the measured and derived parameters from our fit in Table 5.2.  Chapter 5. PSR 11756-2251: a pulsar with a light neutron star companion^131  Table 5.2 Parameters for PSR J1756-2251, measured and derived from timing observations and analysis. Timing parameter  Parameter value  Data span (MJD) ^ Right Ascension, a (J2000) ^ Declination, b (J2000) ^ Proper motion in right ascension,^(mas yr -1 ) ^ Rotation frequency, v (Hz) ^ Frequency derivative, 1' (10 -15 S -2 ) ^ Reference timing epoch (MJD) ^ Dispersion measure, DM (pc cm  -3 )  Orbital Period, Pb (days) ^ Eccentricity, e ^ Projected semimajor axis, x^a p sin i (lt-s) ^ Longitude of periastron, w (°) ^  52826.6 — 54388.1 17h56m46M3365(2) —22°51'591.144(2) —0.7(2) 35.1350732593154(16) —1.25590(2) 53563.0 121.196(5) 0.31963389656(9) 0.1805694(3) 2.75644(2) 327.8247(4)  Epoch of periastron passage, T0 (MJD) ^  53562.7807749(3)  Advance of periastron, w (' yr — I) ^  2.58254(12)  Gravitational redhsift/time dilation parameter, -y (ms)  0.00118(2)  Shapiro delay r parameter (Me)" ^  < 1.9  Shapiro delay s parameter ^  0.95(5)  Orbital period derivative, Pb (10 -13 ) ^  —2.1(3)  Derived parameters Mass function, f^111®  ^  Orbital inclination angle, i (°) b Pulsar mass, ml ( AT(9) b  ^  ^  Companion mass, m2 (11 ,10) b  ^  0.220102(4) 64.3 or 115.7(1.7) 1.312(17) 1.258( —17, +18)  NOTE.—Parentheses indicate the la uncertainties on the last digit (or last two digits, if two digits are given). Two numbers separated by a comma indicate the lower and upper uncertainties, respectively. '2a upper limit. b  Derived using the Damour-Duruelle General Relativity timing model (DDGR; Taylor & Weisberg, 1989), which  assumes General Relativity to be the correct theory of gravity.  Chapter 5. PSR 11756-2251: a pulsar with a light neutron star companion ^132  5.3 Neutron star masses and a test of general relativity In order to measure the masses of the pulsar and its companion neutron star, we employed the Damour-Deruelle General Relativity (DDGR.) timing model (Taylor & Weisberg, 1989). This model assumes that GR is the correct theory of gravity, and directly models the timing in terms of the total system and companion masses, along with the usual Keplerian orbital parameters. We performed a maximum likelihood analysis similar to that done in the case of PSR J1802-2124, described in Section 3.4. Here, We probe companion and total system mass in our grid, and derive a joint probability diStribution through performing a timing fit at each grid point, holding each (rn2, mtotai) pOint fixed. From this, we obtain marginalized PDFs for each of these parameters. We then derive a PDF for the pulsar mass m 1 , in the same manner as we have done in Section 3.4. The resulting joint PDF for m 2 and 7T/total is shown in Figure 5.4, and the marginaliZed PDFs for the system masses are shown in Figure 5.5. From this analysis, we derive a pulsar mass m 1 = 1.312 + 0.017 4.) , companion mass m 2 = 1.2581t 87 /110 , and total system mass m taaj = 2.5702+0.0002 M. Our value for the companion mass is somewhat higher than that determined by Faulkner et al. (2005), although they are in agreement at the 2a level. Our analysis represents a larger time span of data, and much better orbitalphase sampling using GASP data we thus trust this result as being more robust than the previously reported mass measurement. Among the fitted post-Keplerian parameters, we were able to significantly measure four of these, using the DD model: advance of periastron w = 2.58254 + 0.00012 ° yr -1 , the gravitational redshift/time dilation parameter 7 0.00118 + 0.00002 ms, the Shapiro delay "shape" parameter s = 0.95+ 0.05 (interpreted as sin i), and the rate of orbital period decay' Pb = —2.1+0.3 x 10' 3 . We have also measured an upper limit to the Shapiro  'The measurement, of the orbital period derivative is in general corrupted by kinematic effects (Damon' Taylor, 1991; Nice Taylor, 1995) associated with the different accelerations experienced .  by the Solar System and pulsar system in the Galactic potential (e.g., Kuijken & Gilmore, 1989), as well  Chapter 5. PSR J1756-2'251: a pulsar with a light neutron star companion^133  " 73 -.  2.5710  E  2.5705 2.5700 2.5695  E-4  2.5690 1.20 1.22 1.24 1.26 1.28 1.30 1.32 Companion mass (M® )  Figure 5.4 Joint probability contours derived from a maximum likelihood analysis of the companion and total system mass of PSR J1756-2251, using the DDGR timing model. Shown are 68.3% (blue), 95.4% (green), and 99.73% (red) confidence contours:  ^  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion^134  In  a  0.08  0.020  ,d 0.015  0  0.010  ;45 0.04 a  2  ;-■ 0.02 a. 0.00  0.005  0.000 ^ 1.20^1.25^1.30^1.35^1.40 1.15^1.20^1.25^1.30^1.35 ^ Pulsar mass (M0 ) Companion mass (M 0 )  0.14 t" 0.12  g  0.10 0.08  .o 0.06 4 0  0.04 0.02 0.00 2.569^2.570^2.571 Total system mass (M® )  Figure 5.5 Marginalized probability density functions for the pulsar mass, companion mass, and total system mass in the PSR J1756-2251 system. The shaded regions correspond to the 68.3% confidence intervals for each distribution.  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion^135 delay "range" parameter (interpreted under GR as the companion mass) r < 1.9 itic, (2o  -  upper limit), which is currently not very well-constrained. As explained in Section 1.3.3, measurement of any two PK parameters results in a unique determination of the component masses of the system in GR. Each additionally-measured PK parameter therefore provides an independent test of that theory. Figure 5.6 plots the GR-derived mass constraints determined from each measured PK parameter. All four of these parameters intersect at the same point on the diagram, within the measured uncertainties of those parameters. They also agree extremely well with the DDGR model determination of the system masses. We thus have a verification of the predictions of GR at the 5% level. This limit is based on the significance of our measurement of the Shapiro delay s pAI'ameter, which agrees with the value of sin i obtained with the DDGR model at just over the la level. This is likely due to the relatively low inclination angle of the orbit of this system relative to our line of sight, making a measurement of s more difficult than in the case of more edge-on systems. With five more years of observational data, we expect to better the determination of s to 3%. However, the stringency of the GR test by that time is expected to be as low as 2%; this estimate results from simulations in which we predict a measurement of orbital decay on that timescale, to 2% precision. Of course, the quality of such a GR test will depend on the kinematic corrections involved (Damour & Taylor, 1991; Nice & Taylor, 1995), which may become significant. Our derived value for the companion mass makes it one of the lowest-maSS neutron stars known (along with PSR J1802-2124 and PSR J0737-3039B), which may have interesting implications. The similarity in mass and other parameters to PSR J0737-3039B may imply that these two double neutron star systems have proceeded through comparable evolutionary histories. We have investigated this similarity further by searching for possible effects of geodetic precession on this pulsar, in order to constrain the geometry of this system. as acceleration due to the NS proper motion (Shklovskii, 1970). The size of these effects is au order of magnitude lower than the measurement uncertainty we can currently attain for Pb, and is thus not a major concern in our present determination of this parameter.  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion ^136  2.5 cf)  2.0  E  1.5 1.0  ra  E  0.5  0  L.)  0.0 1^2^3  Pulsar mass (M ® ) Figure 5.6 Pulsar mass/companion mass diagram for PSR J1756-2251. Shown are the general-relativistic mass constraints (la) for the four post-Keplerian parameterS we have significantly measured: advance of periastron (W), the gravitational redshift/time dilation parameter (7), the Shapiro delay s parameter, and the orbital period decay rate (Pb; no kinematic corrections have been applied). The s parameter, with a measurement uncertainty of 5%, agrees with the intersection of the other parameter constraints at just over the la level. The black dot (which encompasses the measured error bars) represents the DDGR model-derived component masses of the neutron stars in this systetri, which assumes GR to be the correct description of gravity.  Chapter 5. PSI? J1756-2251: a pulsar with a light neutron star companion ^137  5.4 Geodetic precession in the PSR J1756-2251 system Based on the measured system masses, along with the orbital period and eccentricity, the predicted geodetic precession period of the PSR J1756-2251 spin axis is 487 years, from equation 4.1. This falls between those of PSR B1913+16 and PSR B1534+12, two systems for which the effects of geodetic precession have have been clearly observed, even within the small fraction of their respective precession cycles that have thus far been observed in these systems (Weisberg et al., 1989; Stairs et al., 2004). We now have a long enough time baseline to warrant a search for the effects of geodetic precession on the observations of PSR J1756-2251 in the form of pulse shape changes. We use the high signal-to-noise GASP data taken at the GBT to perform thiS analysis. These data span nearly 2 years, corresponding to 0.4% of the pulsar precession period. Although this seems at first glance to be a relatively small data span with Which to perform this study, it must be noted that pulse shape changes at the 1% level per year are observed in the PSR B1534+12 system, which has a much longer 706-year precession period (Arzoumanian, 1995; Stairs et al., 2004). Our motivation for searching for these effects is to characterize the spin and orbital geometries of this system. In light of the similarity in masses, eccentricity, and proper motion to the double pulsar binary, we wish to compare these system parameters to the PSR J0737-3039A/B system as well. Along with the spin and orbital pAtameters mentioned above, measurement of the system geometry, and in particular the spin-orbit misalignment angle ö, can shed light on the evolutionary history of this system: As discussed in Section 4.6 (and references therein), a lack of spin-orbit misalignment in the pulsar may be caused by a low-mass loss, relatively symmetric supernova event occurring in the progenitor of the companion neutron star. In what follows, we diScuss the measurements and results from analysis of the pulse shape of PSR J1756-2251 over two years, aiming to constrain the effects of geodetic precession on the observed width of the pulse profile.  Chapter 5. PSR 11756-2251: a pulsar with a light neutron star companion ^138  5.4.1 Pulse shape evolution All of the approximately 8-hour observing epochs are spaced at roughly two-month intervals, with the exception of those between 20 and 30 August 2006, which we averaged together to obtain a single width measurement for that 10-day period. We calculated an average pulse profile from the data taken within each of these epochs, obtaining high signal-to-noise representative profiles. In this analysis, our noise level is larger than for the PSR J0737-3039A cumulative profiles. For this reason, we chose to measure pulse widths at 50% of the maximum pulse flux density, where the profile slope is relatively smooth. Figure 5.7 shows the pulse width measurements obtained as a function of time. There is no overall visible trend seen in the pulse widths over time, hinting at one of two possibilities: the misalignment of spin axis of the pulsar and the orbital angular Momentum has a small value, or that the pulsar is currently at a special phase of precession (e.g. Oso = 0 or 180 0 ). However, given the size of the precession period, this latter suggestion seems like a somewhat unlikely explanation.  5.4.2 Constraints on the geometry of PSR J1756-2251 We determined geometrical parameters for this system in the same way as in our analysis of PSR. J0737-3039A, described in Chapter 4. Equation 4.2, together with eqUation 4.8, expresses the half-pulse width (I) 0 as a function of time. 43 0 depends on the angle a between the pulsar spin and magnetic axes, the spin-orbit misalignment angle 6, the emission beam opening angle p, and T1 , the epoch of zero precession phase. The data were then fit to this model, allowing us to determine these 4 parameters. In the case of all fits to the PSR, J1756-2251 pulse widths, we obtained values of reduced y2 that are in the range — 7 — 8; this indicates that the best-fit model does not pass through all of the (relatively small) error bars on the measured pulse widths. As in the PSR .J0737-3039A analysis, we perform two sets of fits, which respectively probe the x2 for grids of (6, T1 ) and (a, 6) values. For each grid, the parameter's at each grid point, are held fixed, and the remaining two parameters are left free to vary in the  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion^139  10.0 cf)  a)  tto  a)  9.5 4  9.0  a) 8.5 0 a..  8.0  53600  ^  53800^54000 MJD (days)  ^  54200  Figure 5.7 Profile widths at 50% of the peak amplitude for PSR J1756-2251 as a function of MJD.  Chapter 5. PSR 11756-2251: a pulsar with a light neutron star companion ^140 fit. We use the same constraints and number of grid points for these parameters as in Section 4.4, except for T 1 , which in this case runs over the full 487-year precession period, starting at zero MJD and sampled with 1000 grid points. More detail on the fitting procedure is discussed in Section 4.4. We then calculate a Bayesian joint posterior probability density for each set of fits, using uniform prior distributions for each grid parameter, between the range of values within which we define our grid, and zero outside this range. We then calculate marginalized probability densities for each grid parameter. Refer to Section 4.4 for details and explanation of the determination of prdbability density functions from this analysis. As with PSR J0737-3039A, this analysis was performed separately assuming cos i > 0 (i = 64.3 °) and cos i < 0 (i -= 115.7'). The fractional uncertainty in these values is small enough (see Table 5.2) that we believe it would not factor significantly in our results; we thus use a single value of the inclination in our analysis for each of these two cases. The resulting probability densities from each of these cases were added together before calculating the marginalized PDFs for each parameter. The resulting joint probability density distributions are shown in Figure 5.8 for the  (6, T1 ) grid. It can be seen that regions near 6 — 0 and 180 °, as well as 6 30 ° and 150 ° are favoured in these fits. The total marginalized probability density for 6 is shown in Figure 5.9. As in the analysis of PSR J0737-3039A, we show 0° < b < 90 ° since the marginalized PDF for 6 is essentially mirrored about 6 = 90 °, and since 6 < 90 ° is favoured by modeling of DNS binaries (Banes, 1988). One can see a second peak at  S — 30 '; this increase in probability density corresponds to the peak values of T1 that are related to the special precession phases of 0 ° and 180°. From this we find a 95.4% confidence upper limit 6 < 76 ° (89 ° at 99.73% confidence), which is more conservative than would be the case if we were to discount the solutions at those special phases of precession. The total marginalized PDF for T 1 is shown in Figure 5.10. We find two main peaks in this distribution, at MJD 53800 and MJD 142690, which are separated by 180 ° in precession phase. The first of these two dates corresponds to March 2006, which falls within the GASP data span (bordered in the figure by blue dashed lines assuming  Chapter 5. PSR i1756—P  ^a pulsar with a light neutron star companion^141  150000  100000 E4-  50000  50^100  ^  150  6 (degrees)  150000  100000 E-:  50000  ^ 50^100 150 6 (degrees) Figure 5.8 Joint probability contours for the angle 6 between the spin and orbital angular momentum axes, and the epoch T 1 of zero precession phase, in the PSR J1756-2251 system. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence regions.  Top: PDF calculated for i = 64.3 °. Bottom: PDF calculated for i = 115.7°. In both cases, values of 6 near 0 ° and 180 ° have the highest probability densities.  Chapter 5. PSR J1756-251: a pulsar with a light neutron star companion^142  0.020  0.005  0.000 20^40^60 6 (degrees)  ^  80  Figure 5.9 Marginalized probability density function for 6, the angle between the spin axis of PSR. J1756-2251 and the angular momentum axis of the double pulsar system. This is derived from the (6, T1 ) joint probability distribution, where we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% upper limit confidence regions, corresponding to 33 °, 76 °, and 89 °, respectively.  Chapter 5. PSR J1956-51: a pulsar with a light neutron star companion ^143 the best-fit T1 value is indeed zero precession phase). This is not surprising—if our data set happened to coincide with a precession phase near zero, this would naturally explain the lack of change seen in the measured profile widths. However, a question that. must be asked is whether there are significant alternatives to this scenario. From viewing the PDF plot for T1 , we see that the majority of the total probability corresponds to epochs other than that found to have the highest probability density. We conclude that T 1 remains relatively unconstrained; this is in fact expected to be the case for low values of 8, as can be seen in the joint probability density in Figure 5.8. We show the joint PDFs for each inclination value for the (a, 8) grid fit in Figures 5.11 and 5.12. In general, one can see that a is not very tightly constrained, although values near a '0 ° and 180 ° are clearly not favoured. Most of the probability density also seems to fall near the values 6 — 0 and 180 °. Similarly to that found in our long-term profile analysis of PSR J0737-3039A, we see an island of probability density within 60 ° < a < 90 ° and 90 ° < 8 < 140 ° for the i = 64.3 ° fit, and 60 ° < a < 90 ° and 40 ° < 8 < 90 ° for the i = 115.7° fit. As described Section 4.4.1, these correspond to a special case of fine-tuned parameter values that result in d4) 0 dt — 0 (Manchester et al., 2005b). As argued in that section, this is  an unlikely  combination of parameters that form an unreliable solution. We thus recalculated the (a, 8) joint probability density functions, excluding this range of parameter space, before deriving the individual marginalized probability density functions. Figure 5.13 shows the resulting summed marginalized PDF for a. As surmised from the joint probability distribution, a is not particularly well-constrained. We find  a median  value 831 67 °, where the error bars reflect the 68.3% confidence region for this parameter (83+ 674° and 83 + 95 ° at 95.4% and 99.73% confidence, respectively). As mentioned above, the analysis does, however, disfavour PSR J1756-2251 from being very close to an aligned or anti-aligned rotator. Figure 5.14 shows the total marginalized PDF for 6. This agrees with our qualitative evaluation of the (a, 6) joint probability density that low Values are favoured: We find a 95.4% upper limit 6 < 67 ° for the misalignment angle (88 ° at 99.73% confidence). Unlike the result from the PDF obtained from the (6, T1 ) grid analysis, this  Chapter 5. PSI? J1756-2251: a pulsar with a light neutron star companion ^144  Precession Phase (degrees) —90 —45^0^45^90 135 180 225  0.005 •-. 61) 0.004 a) 0.003 as  0.002 0.001 0.000 50000  ^  100000 T 1 (MJD)  ^  150000  Figure 5.10 Marginalized probability density function for T 1 , the epoch of zero precession phase, in the PSR J1756-2251 system, obtained by combining the results from both the cos i > 0 and cos i < 0 analyses. The epochs found to be the peaks in the diStribution are MJD 53800 and MJD 142690, corresponding to current precession phases (/)0 = 0 ° and 180 0 , respectively. The top axis labels precession phase, assuming that the peak of the PDF corresponds to dso = 0 °. The blue dashed lines show the span covered by our observations under this assumption, and nearly overlap here since the region they enclose is very small on this scale.  ▪  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion ^145  150  4.0  50  50^100 a (degrees)  150  150  a) 0)  en  100  a) -e  50  ^ 50^100 150 a (degrees)  Figure 5.11 Top: Joint probability contours for the angle a between the pulsar spin axis and magnetic axis, and the angle S between the spin and orbital angular moinentum axes, for the PSR. J1756-2251 system. Shown are the 68.3% (blue), 95.4% (green), and 99.73% (red) confidence regions. While not as constraining as that found from analysis of PSR .J0737-3039A, we find most of the probability density to be contained around — 90 ° and S — 0 and 180°. Bottom: Joint PDF after excising the region of parameter space where a specially fine-tuned combination of parameters yields cl(1) 0 dt ti 0. We note that the asymmetry of the PDF is due to the fact that the orbital inclination is significantly different from 90'; here i = 64.3 ° has been assumed.  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion ^146  150  a)  P. 100 be a) 4  .0  50  ^ 50^100 150 a (degrees)  150  100  50  ^ 50^100 150 a (degrees)  Figure 5.12 Top: Joint probability contours for the angle a between the pulsar spin axis and magnetic axis, and the angle S between the spin and orbital angular momentum axes, for the PSR 11756-2251 system. This is a similar plot to Figure 5.11, but here we assume i = 115.7°.  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion ^147  0.008  a)  0.006  0.004 0  c.  I:1" 0.002  0.000  ^ 50^100 150 a (degrees)  Figure 5.13 Marginalized probability density function for a, the angle between the spin axis of PSR, J1756-2251 and its magnetic axis. This was derived from the cleaned joint PDFs shown in Figures 5.11 and 5.12, where we combine the results from both the cos i > 0 and cos i < 0 analyses.. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% confidence regions, corresponding to a = 831 67 °, 83 4- 64 °, and 831 6°, 3 respectively. Although not very constraining, this hints that PSR J1756-2251, like PSR J0737-3039A, may be close to an orthogonal rotator.  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion^148 Table 5.3 Summary of results for geometric parameter estimation from long-term profile evolution analysis of PSR J1756-2251, from (T1 , (5) and (a, 8) grids, respectively. Parameter  Peak value  68.3% interval  95.4% interval  99.73% interval  < 33  < 76  < 89  6 (°) T1  MJD 53800  -^-^•  Parameter  Median  68.3% interval  95.4% interval  99.73% interval  a (°)  83  47 — 120  19 — 154  8.3 — 174  6 (° )  •^•  < 21  < 67  < 88  is a monotonically-varying distribution. Table 5.3 summarizes the geometric parameter estimates for PSR J1756-2251 from this analysis. This is not as constraining as the results from profile width analysis of PSR J0737-3039A, and significantly less so than those obtained from assuming two-pole emission in the double pulsar. The range of misalignment angles we find also overlaps with the values reported for PSR B1913+16 and PSR. B1534+12 (Kramer, 1998; Stairs et al., 2004). Our results from this part of the analysis are thus not conclusive enough to categorize the geometry of PSR, J1756-2251 as being similar to or different from the pulsar systems mentioned above. Continued observation of this system is thus crucial toward alleviating this ambiguity, as well as whether the pulsar is at a special phase of spin precession. Figure 5.15 shows the histograms of best-fit values of the emission beam halfLopening angle p obtained over all points in each grid analysis. It can be seen in both cases that p < 90 ° is favoured, with 99.73% confidence intervals of 4.8 ° < p < 67° and 2.0 ° < p < 108 ° from the (8, T1 ) and (a, 6) grid fits, respectively.  5.5 The evolution of PSR J1756-2251 We now discuss the clues that the above analysis may give toward understanding the evolutionary history of the PSR J1756-2251 system, and use the existing census of  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion^149  0.030 0.025 0.020 •.., I' 0.015 :75 0.010 0.005 0.000 20^40^60 6 (degrees)  ^  80  Figure 5.14 Marginalized probability density function for 6, the angle between the spin axis of PSR J1756-2251 and the angular momentum axis of the double pulsar system. This is derived from the cleaned (a, 6) joint probability distribution shown in Figures 5.11 and 5.12, in which we combine the results from both the cos i > 0 and cos i < 0 analyses. The hashed, vertical, and diagonal shaded regions enclose the 68.3%, 95.4%, and 99.73% upper limit confidence regions, corresponding to 21 °, 67°, and 88 °, respectively. We arrive at slightly tighter constraint than we find from the (6, Ti ) grid analysis.  Chapter 5. PSR J1756-251: a pulsar with a light neutron star companion ^150  0.25 0.20 0.15  0.10 0.05 0.00 ^ 0  50^100^150  p (degrees)  0.12 0.10 0.08 0.06  iI I  0.04 0.02 0.00 0  50^100^150^200 p (degrees)  Figure 5.15 Histograms of best-fit values of emission beam radius p from each point in our grid fits, weighted by the probability density of the fit at the corresponding grid point. Top: result from the (S, T1 ) grid, where we find a 99.73% confidence interval of 4.8 ° < p < 67°. Bottom: result from the (a,6) grid fit, where we arrive at a wider 99.73% interval of 2.0 ° < p < 108 °. In both cases, however, p < 90 ° is favoured:  Chapter 5. PSR J1756-2251: a pulsar with a light 'neutron star companion ^151 double neutron star binary parameters as a context within which to do so. Table 5.4 lists all DNS binaries for which masses of both neutron stars have been measured. One can see similarities between certain systems. PSR B1913+16 and PSR B1534+12 have massive companions, large eccentricities, and high transverse velocities. It is believed that these systems have undergone a core-collapse supernova in forming the second neutron star. Such high eccentricities and space velocities are indicative of a high massloss, asymmetric supernova from a massive progenitor, that imparted a significant natal kick to the system (e.g., Wex et al., 2000). PSR B2127+11C has similar masses, eccentricity, and space motion to PSR B1913+16 and PSR B1534+12. However, it resides in the globular cluster M15. The evolutionary history that gave this pulsar its current orbital parameters and proper motion has likely involved the unique dynamics present in the dense cluster environment, including events such as exchange interactions that are extremely rare even in the densest areas of the field. It is thus reasonable to assume that the evolution of this pulsar differs substantially from the others in Table 5.4. Taken alone, the relatively low eccentricity of PSR J1756-2251 is not necessarily revealing, as many evolutionary scenarios can produce a small value such as we find. However, the resemblance between the low NS masses in this and the PSR J0737-3039A/B systems is intriguing, suggesting that these binary systems have likely proceeded through similar evolutions. Van den Heuvel (2004, 2007) argues for the evolutions of these, and possibly other DNS systems, as having possibly undergone electron capture supernova events. In addition, the spin periods of PSR J1756-2251 and PSR J0737-3039A are a factor of — 2 lower than those of PSR B1913+16 and PSR B1534+12, indicating different amounts and durations of mass transfer in recycling the pulsars to their current rotational speeds. Based on the observed correlation between spin period and eccentricity in most known DNS systems (McLaughlin et al., 2005; Faulkner et al., 2005), it has been suggested by, e.g., Dewi et al. (2005) that systems which have experienced a small amount of mass loss during the second supernova are those which had lower-mass helium stars  (*)  ti  Table 5.4 Properties of double neutron star systems for which component masses have been measured. Spin  Orbital  Period (ins)  Period (hours)  Transverse  Pulsar  Companion  Precession  velocity (km/s)  mass ( M0)  mass ( M0)  period (years)  J0737-3039A  22.70  2.45  0.0878  10  1.34  1.25  75.2  1  J0737-3039Ba  2773  2.45  0.0878  10  1.25  1.34  70.9  1  B1534+12  37.90  10.1  0.274  107  1.33  1.34  706  2,3  J1756-2251  28.46  7.67  0.181  1.31  1.26  487  4,this work  J1906+0746'  144.1  3.98  0.0853  1.25  1.37  157  5,6  B1913+16  59.03  7.75  0.617  88  1.44  1.39  296  7  c-.... ,.  B2127+11C  30.53  8.05  0.681  168  1.36  1.35  278  8  sl..  PSR  Eccentricity  References  ti  " s..., '"  ,.' i:?:, -3 z' ,--=,• .,,...,,.,  REFEHENCES.-L-Kramer et al. (2006); 2.-Stairs et al. (2002); 3.-Stairs et al. (2004); 4.-Faulkner et al. (2005); 5.-Lorimer et al. (2006); 6.-Kasian (2007); ^co 7.-Weisberg & Taylor (2003); 8.-Jacoby et al. (2006). ^  NOTE.-Most of the values for these parameters were obtained, or derived from values obtained, from Manchester et al. (2005a);  http://www.atnf .csiro.au/research/pulsar/psrcat .^ a  Young, unrecycled pulsar.^  -3 0 Cr. ',...4 Q  ('0 Q N.  Chapter 5. PSR J1756-251: a pulsar with a light neutron star companion^153 prior to that event and thus a longer timescale within which mass transfer could occur. This, they argue, could explain the shorter spin periods as well as the low eccentricities in these systems. Section 4.6 outlines our reasons for believing that the observed properties of the PSR. J0737-3039A/B system imply a scenario in which the B pulsar progenitor underwent an electron capture, as opposed to core collapse, supernova explosion. There is mounting evidence that a similar evolutionary scheme may also apply to PSR J1756-2251. The only published analysis on the natal kick velocity of PSR, J1756-2251 (as well as PSR J1906+0746) is by Wang et al. (2006). The results they obtain are not very constraining for this system, since they rely only on the orbital parameters for these system, and do not include kinematic information when deriving the kick velocities. In addition to the companion mass to this pulsar, which is one important clue, we have measured a low proper motion (albeit at low precision) in the right ascension direction, = —0.7 + 0.2 mas yr -1 . The distance to PSR J1756-2251 based on its dispersion measure is — 2.5 kpc (Cordes & Lazio, 2002; Faulkner et al., 2005). This corresponds to a velocity in the direction of right ascension v a — 8.3 km s -1 . We compare this to the transverse velocity of the PSR, J0737-3039A/B system, v t , — 10km If the proper motion in declination of PSR J1756-2251 is also small, this would present another tantalizing clue that perhaps the PSR J1756-2251 system may also have both suffered a relatively small natal kick from the supernova of the second-born neutron star, as was likely the case for the double pulsar. However, this is still very speculative: we have not yet determined a transverse velocity for PSR J1756-2251, and it is furthermore argued by Kalogera et al. (2007) that a small transverse velocity does not necessarily imply a small velocity in the radial direction. Proper motion in declination has been difficult to measure since, similarly to the PSR J1802-2124 system, this pulsar is located very near to the ecliptic equator (i3 — 0.6 °), making detection of proper motion in this direction a challenging task. We do, however, expect to obtain an upper limit to this quantity in the next 5 years, within which time we will further reduce the uncertainty on the proper motion in right ascension of PSR J1756-2251.  Chapter 5. PSR J1756-251: a pulsar with a light neutron star companion ^154 In an electron-capture supernova, there should be little or no change in the orientation of the spin axis of the recycled pulsar. Since it is be expected to have become aligned with the total angular momentum of the system (well-approximated by the orbital angular momentum) during the mass-transfer process, the first-formed NS should retain this near-alignment after this low-kick event (e.g., Podsiadlowski et al., 2005). This seems to be the case for PSR J0737-3039A, as found in the previous chapter. However, our constraints on the misalignment angle in PSR J1756-2251 still allow for the range of estimates found by Bailes (1988), and encompass the values found for PSR B1913+16 and PSR B1534+12. We thus require further observations to better constrain this parameter, and its evolutionary history. One major difference between PSR J1756-2251 and PSR J0737-3039A/B is the factor of 3 longer orbital period in the former system. If indeed the second supernova in the PSR J1756-2251 system was relatively symmetric with little mass loss, there would perhaps be little change in the orbital period in the resulting double neutron star binary, which was likely set by the evolution of this system prior to the second supernova under this scheme (e.g., Dewi & Pols, 2003; Ivanova et al., 2003). PSR J1906+0746 (Lorimer et al., 2006) presents an interesting case. Its spin period is considerably higher than the other pulsars in Table 5.4, and its companion neutron star is substantially more massive (Kasian, 2007). At first glance, this seems like a system unique unto itself. However, it is thought that the observed pulsar is actually the result of the second supernova, and that the (as yet) unseen companion is the recycled neutron star in the system. If this is the case, then the parameters describing this system start to appear similar to those of the PSR J0737-3039A/B and PSR J1756-2251 systems: a low eccentricity, and a low mass for the non-recycled neutron star (van den Heuvel, 2007). The low mass loss and weak kick suffered by a star proceeding through an electroncapture supernova (Podsiadlowski et al., 2004) might suggest a relatively high survival rate for DNS systems in which this is the mechanism for the second supernova. It may thus be the case that DNS systems that have experienced this type of supernova  Chapter 5. PSR J1756-2251: a pulsar with a light neutron star companion ^155 are as common, or more common, than those formed in the aftermath of core collapse supernovae, which typically suffer a relatively large amount of mass loss and a large kick. Although the sample is currently low, it is beginning to seem that there may be (if the speculations on the histories of PSR. J1756-2251 and PSR J1906+0746 turn out to be correct) approximately equal representation by each type of system evolution. One question begs asking, however: if electron capture supernovae are expected to leave behind more binary systems intact, why have we not found a greater proportion of these systems? The answer is likely comprised of a combination of several possible factors: Firstly, survey selection effects can make some of these systems difficult to uncover. For example, those like the double pulsar would have enhanced pulse smearing due to their small orbital period and thus large acceleration (see, e.g., Lorimer, 2005, Section 3:1, for a review on this topic); this is less of a problem for systems like PSR J1756-2251 with larger orbits, although both systems may have formed in the same way. In addition, perhaps core-collapse SNe are substantially more common than electron-capture SNe. It is conceivable that a system containing a low-enough mass star to eventually undergo electron capture is more likely to become unbound in the initial supernova event, resulting in fewer candidate NS-MS star systems to produce systems like PSR J1756-2251 and PSR J0737-3039A/B. Although much analysis has been done in this area (see, e.g., Chaurasia Bailes, 2005; Dewi et al., 2005; Ihm et al., 2006; Willems et al., 2007, for studies addressing systems with low eccentricities and/or low-velocity kicks), more work in population synthesis and binary evolutionary modeling will clearly be need to help to address these possibilities, and would give predictions of relative numbers of each type of system expected to be observed.  156  Chapter 6  Concluding remarks Binary star systems form via a diverse number of possible evolutionary scenarios (e.g., Bhattacharya & van den Heuvel, 1991; Tauris van den Heuvel, 2006); those binaries that contain one or more neutron stars are no exception. This is evidenced by the very different properties that we observe in such systems. We are fortunate on the one hand to be able to determine those properties through highly precise pulsar tinning analysis. On the other hand, the limited amount of observed binary pulsars, and the even smaller number of those with measurable masses (see, e.g., Nice, 2006)—a crucial piece in solving the evolutionary history puzzle of each system studied--constitute thus far a relatively meager statistical sample from which we would like to make broad generalizations about the overall picture of the so-called pulsar "zoo". Thus, studies of these systems potentially provide benefits toward achieving several goals of varying scopes. One of these is the discovery and increasingly accurate descriptions of very specific classes of systems. An example of this is the case of the IMBPs, through observations and timing analysis of PSR J1802-2124 (Chapter 3). This the second such system in which the masses of both components have been measured, and so provides an important clue about the nature of this category of system. As new systems are discovered, subdivision of existing classes sometimes proves necessary. This appears to be the case for the double pulsar system PSR J0737-3039A/B, as discussed in Chapter 4. We believe that we have added to the evidence that the younger pulsar in this system was formed in the aftermath of an electron-capture (or other low mass-loss) supernova event (Podsiadlowski et al., 2005). As fascinating as these systems are to study in their own right, it is also of great  Chapter 6. Concluding remarks^  157  importance to carry out this research with the goal of describing binary evolution as a  whole. This is necessary for making predictions of, for example, NS merger rates and thus the possibility of gravitational wave detection from instruments such as LIGO (e.g., Kalogera et al., 2004). Accurate population synthesis studies are required for characterizing these rates, as well as for other endeavours, such as gaining a better understanding of massive star formation rates, and the connection between various observed populations (e.g. binary radio pulsars and X-ray binaries; e.g., Portegies Zwart Yungelson 1998; Willems & Kolb 2002, 2003; Pfahl et al. 2003). Although it is always exciting to discover a new variety of astrophysical object, increasing the known members of an existing class is vital toward making strides in understanding the overall population. In Chapter 5, we have described evidence suggesting that the PSR J1756-2251 system may have formed in a similar way to that of the double pulsar (see also van den Heuvel, 2004, 2007). If further study of this pulsar provides significant evidence of this similarity, it will provide important constraints concerning the formation and evolutionary processes of this recently-emerged sub-class of DNS binary systems. The wide (and constantly widening) array of existing system types only highlights the need to uncover as many new binary pulsars as possible, so that we can hope to make meaningful classifications based on physical properties and evolutionary histories. Powerful search techniques have been, and continue to be, very helpful toward this end. In particular, those that take into account the high accelerations experienced by NSs within close binary systems have been very successful in finding many new pulsars (e.g., Anderson et al., 1990; Ransom et al., 2001). This method has been especially crucial in the discovery of many compact binary pulsar systems residing in several globular clusters (e.g., Cannlo et al., 2000; Hessels et al., 2007). Other properties of recent pulsar searches have proven very helpful for finding new millisecond and recycled pulsars. These include much narrower frequency channels and faster time sampling than was technologically possible in the past. Some surveys, such as the Parkes Multibeam Pulsar Survey (PMPS; Manchester et al., 2001) and modern globular cluster surveys (e.g., Camilo et al., 2000; Hessels et al., 2007; Ransom et al., 2005),  Chapter 6. Concluding remarks^  158  also use high observing frequencies, minimizing the the amount of dispersive smearing and scattering, and sky background from the Galactic Plane. Large-scale pulsar surveys provide an obvious way to discover large numbers of systems. The PMPS (Manchester et al., 2001) is a very successful example, having approximately doubled the previously known pulsar population, and significantly increased the observed binary population (including PSR J1802-2124 and PSR J1756-2251, two of the pulsars studied in this thesis; Faulkner et al. 2004). As stated above, however, many discoveries are still needed. New undertakings such as the ALFA pulsar survey, currently being conducted using the Arecibo telescope (Cordes et al., 2006; Lorimer et al., 2006), and the upcoming LOFAR low-frequency array survey (van Leeuwen & Stappers, 2004) are expected to uncover many more systems of various types for study. In the further future, the Square-Kilometre Array will be sensitive enough to discover many more pulsars. This will include completely new types of binary systems, as well as those outside the Milky Way (Cordes et al., 2004; Kramer et al., 2004). This will no doubt provoke unprecedentedly large advances in the field. Pulsar binary evolution is a thriving field of study, and is still very much in the exploratory stage. Many significant developments have been made thus far, but a great deal of progress lies ahead before we can gain an accurate picture of the binary pulsar population as a whole. As stated in the first chapter of this work, it is hoped that this thesis has made some contributions toward this end.  159  Bibliography Alpar, M. A., Cheng, A. F., Ruderman, M. A., & Shahan', J. 1982, Nature, 300, 728 Anderson, S. B., Gorham, P. W., Kulkarni, S. R., ^Prince, T. A. 1990, Nature, 346, 42 Arzoumanian, Z. 1995, PhD thesis, Princeton University Arzoumanian, Z., Nice, D. J., Taylor, J. H., & Thorsett, S. E. 1994, ApJ, 422, 671 Baade, W. & Zwicky, F. 1934, Proc. Nat. Acad. Sci., 20, 254 Backer, D. C., Kulkarni, S. R., Heiles, C., Davis, M. M., ^Goss, W. M. 1982, Nature, 300, 615 Bailes, M. 1988, A&A, 202, 109 Bailes, M., Ord, S. M., Knight, H. S., & Hotan, A. W. 2003, ApJ, 595, L49 Barker, B. M. & O'Connell, R. F. 1975, ApJ, 199, L25 Belczynski, K., Kalogera, V., & Bulik, T. 2002, ApJ, 572, 407 Bethe, H. A. & Brown, G. E. 1998, ApJ, 506, 780 Bhattacharya, D. & van den Heuvel, E. P. J. 1991, Phys. Rep., 203, 1 Bildsten, L. & Chakrabarty, D. 2001, ApJ, 557, 292 Bisnovatyi-Kogan, G. S. & Komberg, B. V. 1974, Sov. Astron., 18, 217 Brown, G. E. 1995, ApJ, 440, 270  Bibliography^  160  Brown, G. E., Lee, C.-H., Portegies Zwart, S. F., & Bethe, H. A. 2001, ApJ, 547, 345 Burgay, M., D'Amico, N., Possenti, A., Manchester, R. N., Lyne, A. G., Joshi, B. C., McLaughlin, M. A., Kramer, M., Sarkissian, J. M., Camilo, F., Kalogera, V., Kim, C., & Lorimer, D. R. 2003, Nature, 426, 531 Burgay, M., Joshi, B. C., D'Amico, N Possenti, A., Lyne, A. G., Manchester, R. N., McLaughlin, M. A., Kramer, M., Camilo, F., & Freire, P. C. C. 2006, MNRAS, 368, 283 Burgay, M., Possenti, A., Manchester, R. N., Kramer, M., McLaughlin, 1\4. A., Lorimer, D. R., Stairs, I. H., Joshi, B. C., Lyne, A. G., Camilo, F., D'Amico, N., Freire, P. C. C., Sarkissian, J. 1\4., Hotan, A. W., & Hobbs, G. B. 2005, ApJ, 624, L113 Camilo, F., Lorimer, D. R., Freire, P., Lyne, A. G., & Manchester, R. N. 2000, ApJ, 535, 975 Camilo, F., Lyne, A. G., Manchester, R. N., Bell, J. F., Stairs, I. H., D'Amico, N., Kaspi, V. M., Possenti, I., Crawford, F., & McKay, N. P. F. 2001, ApJ, 548, L187 Camilo, F., Nice, D. J., Shrauner, J. A., & Taylor, J. H. 1996, ApJ, 469, 819 Chakrabarty, D. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 328, Binary Radio Pulsars, ed. F. A. Rasio & I. H. Stairs, 279 Chakrabarty, D. & Morgan, E. H. 1998, Nature, 394, 346 Chaurasia, H. K. & Bailes, M. 2005, ApJ, 632, 1054 Chen, K. & Ruderman, M. 1993, ApJ, 402, 264 Chevalier, R. A. 1993, ApJ, 411, L33 Cordes, J. 1\4., Freire, P. C. C., Lorimer, D. R., Camilo, F., Champion, D: J., Nice, D. J., Ramachandran, R., Hessels, J. W. T., Vlemmings, W., van Leeuwen, J., Ransom,  Bibliography^  161  S. M., Bhat, N. D. R., Arzotnnanian, Z., McLaughlin, M. A., Kaspi, V. M., Kasian, L., Deneva, J. S., Reid, B., Chatterjee, S., Han, J. L., Backer, D. C., Stairs, I. H., Deshpande, A. A., & Faucher-Giguere, C.-A. 2006, ApJ, 637, 446 Cordes, J. M., Kramer, M Lazio, T. J. W., Stappers, B. W., Backer, D. C., & Johnston, S. 2004, 48, 1413 Cordes, J. M. & Lazio, T. J. W. 2002, astro-ph/0207156 Damour, T. & Deruelle, N. 1985, Ann. Inst. H. Poincare (Physique Theorique), 43, 107 ---. 1986, Arm. Inst. H. Poincare (Physique Theorique), 44, 263 Damour, T.^Ruffini, R. 1974, Cornptes Rendus, Serie A — Sciences Mathematiques, 279, 971 Damour, T. & Taylor, J. H. 1991, ApJ, 366, 501 ---. 1992, Phys. Rev. D, 45, 1840 Davies, M. B., Ritter, H., & King, A. 2002, MNRAS, 335, 369 Deloye, C. J. & Bildsten, L. 2003, ApJ, 598, 1217 Demorest, P., Ramachandran, R., Backer, D. C., Ransom, S. M., Kaspi, V., Arons, J., Spitkovsky, A. 2004, ApJ, 615, L137 Demorest, P. B. 2007, PhD thesis, University of California, Berkeley Dewey, R. J. & Cordes, J. M. 1987, ApJ, 321, 780 Dewi, J. D. M., Podsiadlowski, P., Pols, 0. R. 2005, MNRAS, 363, L71 Dewi, J. D. M., Podsiadlowski, P., Sena, A. 2006, MNRAS, 368, 1742 Dewi, J. D. M. & Pols, 0. R. 2003, MNRAS, 344, 629  Bibliography^  162  Dewi, J. D. M., Pols, 0. R., Savonije, G. J., & van den Heuvel, E. P. J. 2002, MNRAS, 331, 1027 Dewi, J. D. M. van den Heuvel, E. P. J. 2004, MNRAS, 349, 169 Edwards, R. T. & Bailes, M. 2001a, ApJ, 547, L37 2001b, ApJ, 553, 801 Edwards, R. T., Hobbs, G. B., & Manchester, R. N. 2006, MNRAS, 372, 1549 Esposito-Farese, G. 2004, contribution to 10th Marcel Grossmann meeting, gr qc/0402007 Faulkner, A. J., Kramer, M., Lyne, A. G., Manchester, R. N., McLaughlin, M. A., Stairs, I. H., Hobbs, G., Possenti, A., Lorimer, D. R., D'Amico, N., Camilo, F., & Burgay, M. 2005, ApJ, 618, L119 Faulkner, A. J., Stairs, I. H., Kramer, M., Lyne, A. G., Hobbs, G., Possenti, A., Lorimer, D. R., Manchester, R. N., McLaughlin, M. A., D'Amico, N., Camilo, F., & Burgay, M. 2004, MNR,AS, 355, 147 Ferdman, R. D., Stairs, I. H., Kramer, 1\4., Manchester, R. N., Lyne, A. G. Breton, R. P., McLaughlin, M. A., Possenti, A., & Burgay, M. 2007, in 40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More (New York: American Institute of Physics), in press, arXiv:0711.4927v2 [astro-ph] Gaensler, B. M. & Frail, D. A. 2000, Nature, 406, 158 Gold, T. 1968, Nature, 218, 731 Goldreich, P. & Julian, W. H. 1969, ApJ, 157, 869 Habets, G. H. M. J. 1986, A&A, 167, 61  Bibliography^  163  Hankins, T. H. & Rickett, B. J. 1975, in Methods in Computational Physics Volume 14 ---- Radio Astronomy (New York: Academic Press), 55 Helfand, D. J., Manchester, R. N., & Taylor, J. H. 1975, ApJ, 198, 661 Hessels, J. W. T., Ransom, S. M., Stairs, I. H., Kaspi, V. M., & Freire, P. C. C. 2007, ApJ, 670, 363 Hewish, A., Bell, S. J., Pilkington, J. D. H., Scott, P. F., ^Collins, R. A. 1968, Nature, 217, 709 Hobbs, G., Faulkner, A., Stairs, I. H., Camilo, F., Manchester, R. N., Lyne, A. G., Kramer, M., D'Arnico, N., Kaspi, V. M., Possenti, A., McLaughlin, M. A., Lorimer, D. R., Burgay, M., Joshi, B. C., & Crawford, F. 2004, MNRAS, 352, 1439 Hobbs, G., Lyne, A. G., Kramer, M., Martin, C. E., & Jordan, C. 2004, MNRAS, 353, 1311 Hobbs, G. B., Edwards, R. T., Manchester, R. N. 2006, MNRAS, 369, 655 Hotan, A. W., Bailes, M., & Ord, S. M. 2004a, MNRAS, 355, 941 -. 2005, MNRAS, 362, 1267 Hotan, A. W., van Straten, W., & Manchester, R. N. 2004b, Proc. Astr. Soc. Aust., 21, 302 Hulse, R. A. & Taylor, J. H. 1975, ApJ, 195, L51 Ihm, C. M., Kalogera, V., & Belczynski, K. 2006, ApJ, 652, 540 Ivanova, N., Belczynski, K., Kalogera, V., Rasio, F. A., & Taam, R. E. 2003, ApJ, 592, 475 Jacoby, B. A., Cameron, P. B., Jenet, F. A., Anderson, S. B., Murty, R. N., & Kulkarni, S. R. 2006, ApJ, 644, L113  Bibliography^  164  Jacoby, B. A., Hotan, A., Bailes, M., Ord, S., & Kuklarni, S. R. 2005, ApJ, 629, L113 Johnston, S. 2002, Pub. of the ASA, 19, 277 Jones, A. W. & Lyne, A. G. 1988, MNRAS, 232, 473 Kalogera, V., Kim, C., Lorimer, D. R., Burgay, M., D'Amico, N., Possenti, A., Manchester, R. N., Lyne, A. G., Joshi, B. C., McLaughlin, M. A., Kramer, M., Sarkissian, J. M., & Camilo, F. 2004, ApJ, 601, L179 Kalogera, V., Valsecchi, F., Sr, Willems, B. 2007, in 40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More (New York: American Institute of Physics), in press, arXiv:0712.2540v1 [astro-ph] Kasian, L. 2007, in 40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More (New York: American Institute of Physics), in press, arXiv:0711.2690v1 [astro-ph] Kaspi, V. M., Lackey, J. R., Mattox, J., Manchester, R. N., Bailes, M., & Pace, R. 2000a, ApJ, 528, 445 Kaspi, V. M., Lyne, A. G., Manchester, R. N., Crawford, F., Camilo, F., Bell, J. F., D'Amico, N., Stairs, I. H. McKay, N. P. F., Morris, D. J., & Possenti, A. 2000b, ApJ, 543, 321 Kaspi, V. M., Roberts, M. S. E., Vasisht, G., Gotthelf, E. V., Pivovaroff, M., & Kawai, N. 2001, ApJ, 560, 371 Kaspi, V. M., Taylor, J. H., & Ryba, M. 1994, ApJ, 428, 713 Kopeikin, S. M. 1995, ApJ, 439, L5 Kramer, NI. 1994, A&AS, 107, 527 Kramer, NI. 1998, ApJ, 509, 856  Bibliography^  165  Kramer, M., Backer, D. C., Cordes, J. M., Lazio, T. J. W., Stappers, B. W., & Johnston, S. . 2004, 48, 993 Kramer, NI., Lange, C., Lorimer, D. R., Backer, D. C., Xilouris, K. M., Jessner, A., & Wielebinski, R. 1999, ApJ, 526, 957 Kramer, M., Stairs, I. H., Manchester, R. N., McLaughlin, M. A., Lyne, A. G., Ferdman, R. D., Burgay, M., Lorimer, D. R., Possenti, A., D'Amico, N., Sarkissian, J. M., Hobbs, G. B., Reynolds, J. E., Freire, P. C. C., & Camilo, F. 2006, Science, 314, 97 Kramer, M., Wielebinski, R., Jessner, A., Gil, J. A., & Seiradakis, J. H. 1994, A&AS, 107, 515 Kramer, M., Xilouris, K. M., Lorimer, D. R., Doroshenko, 0., Jessner, A., Wielebinski, R., Wolszczan, A., & Camilo, F. 1998, ApJ, 501, 270 Kuijken, K. & Gilmore, G. 1989, MNRAS, 239, 571 Lange, C., Camilo, F., Wex, N., Kramer, M., Backer, D., Lyne, A., & Doroshenko, 0. 2001, MNRAS, 326, 274 Large, M. I., Vaughan, A. E., & Mills, B. Y. 1968, Nature, 220, 340 Lattimer, J. M. & Prakash, M. 2001, ApJ, 550, 426 Lattimer, J. M. & Yahil, A. 1989, ApJ, 340, 426 Li, X. 2002, ApJ, 564, 930 Livingstone, M. A., Kaspi, V. M., Gotthelf, E. V., & Kuiper, L. 2006, ApJ, 647, 1286 Loehmer, 0., Kramer, M., Driebe, T., Jessner, A., Mitra, D., Lyne, A. G. 2004, A&A, 426, 631 Lorimer,^D.^R.^2005,^Living^Reviews^in^Relativity, http://relativity.livingreviews.org/Articles/lrr-2005-7/  Bibliography^  166  Lorimer, D. R. & Kramer, M. 2005, Handbook of Pulsar Astronomy (Cambridge University Press) Lorimer, D. R., Stairs, I. H., Freire, P. C., Cordes, J. M., Camilo, F., Faulkner, A. J., Lyne, A. G., Nice, D. J., Ransom, S. M., Arzoumanian, Z., Manchester, R. N., Champion, D. J., van Leeuwen, J., Mclaughlin, M. A., Ramachandran, R., Hessels, J. W., Vlemmings, W., Deshpande, A. A., Bhat, N. D., Chatterjee, S., Han, J. L., Gaensler, B. M., Kasian, L., Deneva, J. S., Reid, B., Lazio, T. J., Kaspi, V. M., Crawford, F., Locomen, A. N., Backer, D. C., Kramer, M., Stappers, B. W., Hobbs, G. B., Possenti, A., D'Amico, N., Burgay, M. 2006, ApJ, 640, 428 Lorimer, D. R., Yates, J. A., Lyne, A. G., & Gould, D. M. 1995, MNRAS, 273, 411 Lyne, A. G., Brinklow, A., Middleditch, J., Kulkarni, S. R., Backer, D. C., & Clifton, T. R. 1987, Nature, 328, 399 Lyne, A. G., Burgay, M., Kramer, M., Possenti, A., Manchester, R. N., Camilo, F., McLaughlin, M. A., Lorimer, D. R., D'Amico, N., Joshi, B. C., Reynolds, J., & Freire, P. C. C. 2004, Science, 303, 1153 Lyne, A. G., Pritchard, R. S., Graham-Smith, F., & Camilo, F. 1996, Nature, 381, 497 Lyne, A. G. & Smith, F. G. 1998, Pulsar Astronomy, 2nd ed. (Cambridge: Cambridge University Press) Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005a, Astron. J., 129, 1993 Manchester, R. N., Kramer, M., Possenti, A., Lyne, A. G., Burgay, M., Stairs, I. H., Hotan, A. W., McLaughlin, M. A., Lorimer, D. R., Hobbs, G. B., Sarkissian, J. M., D'Amico, N., Camilo, F., Joshi, B. C., & Freire, P. C. C. 2005b, ApJ, 621, L49 Manchester, R. N., Lyne, A. G., Camilo, F., Bell, J. F., Kaspi, V. M., D'Amico, N., McKay, N. P. F., Crawford, F., Stairs, I. H., Possenti, A., Morris, D. J., & Sheppard, D. C. 2001, MNRAS, 328, 17  Bibliography  ^  167  Manchester, R. N., Newton, L. M Durdin, J. M. 1985, Nature, 313, 374 Manchester, R. N. & Taylor, J. H. 1977, Pulsars (San Francisco: Freeman) Maron, 0., Kijak, J., Kramer, M Wielebinski, R. 2000, A&AS, 147, 195 McLaughlin, M. A., Lorimer, D. R., Champion, D. J., Arzoumanian, Z., Backer, D. C., Cordes, J. M., Fruchter, A. Sand Lommen, A. N., & Xilouris, K. M. 2005, in Aspen Center for Physics Conference on Binary Radio Pulsars, ed. F. Rasio & I. Stairs Minter, T. 2007, The Proposer's Guide for the Green Bank Telescope,  http://www.gb.nrao.edu/gbtprops/man/GBTpg/GBTpg_tf.html Miyaji, S., Nomoto, K., Yokoi, K., & Sugimoto, D. 1980, PASJ, 32, 303 Morris, D. J., Hobbs, G., Lyne, A. G., Stairs, I. H., Camilo, F., Manchester, R. N., Possenti, A., Bell, J. F., Kaspi, V. M., Amico, N. D., McKay, N. P. F., Crawford, F., Kramer, M. 2002, MNRAS, 335, 275 Nelson, L. A. & Rappaport, S. 2003, ApJ, 598, 431 Nice, D. J. 2006, Adv. Space Res., 38, 2721 Nice, D. J., Splaver, E. M., Stairs, I. H., Lamer, 0., Jessner, A., Kramer, M., & Cordes, J. M. 2005, ApJ, 634, 1242 Nice, D. J. & Taylor, J. H. 1995, AO, 441, 429 Nomoto, K. 1984, ApJ, 277, 791 Ord, S. M., Bailes, M., van Straten, W. 2002, MNRAS, 337, 409 Pacini, F. 1968, Nature, 219, 145 Pfahl, E., Rappaport, S.,^Podsiadlowski, P. 2003, ApJ, 597, 1036 Pfahl, E., Rappaport, S., Podsiadlowski, P.,^Spruit, H. 2002, ApJ, 574, 364  Bibliography^  168  Phinney, E. S. 1992, Philos. Trans. Roy. Soc. London A, 341, 39 Phinney, E. S. & Kulkarni, S. R. 1994, ARAA, 32, 591 Piran, T. & Shaviv, N. J. 2005, Phys. Rev. Lett., 94, 051102 Podsiadlowski, P., Dewi, J. D. M., Lesaffre, P., Miller, J. C., Newton, W. G., ^Stone, J. R. 2005, MNRAS, 361, 1243 Podsiadlowski, P., Langer, N., Poelarends, A. J. T., Rappaport, S., Heger, A., ^Pfahl, E. 2004, ApJ, 612, 1044 Portegies Zwart, S. F. & Yungelson, L. R. 1998, A&A, 332, 173 - -. 1999, MNR AS, 309, 26 Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. 1986, Numerical Recipes: The Art of Scientific Computing (Cambridge: Cambridge University Press) R,adhakrishnan, V. & Cooke, D. J. 1969, Astrophys. Lett., 3, 225 Radhakrishnan, V. & Srinivasan, G. 1982, Curr. Sci., 51, 1096 Rafikov, R. R. & Lai, D. 2006, ApJ, 641, 438 Rankin, J. M. 1983, ApJ, 274, 333 . 1993, ApJ, 405, 285 Ransom, S. M., Greenhill, L. J., Herrnstein, J. R., Manchester, R.. N., Camilo, F., Eikenberry, S. S., & Lyne, A. G. 2001, ApJ, 546, L25 Ransom, S. M., Hessels, J. W. T., Stairs, I. H., Freire, P. C. C., Camilo, F., Kaspi, V. M., & Kaplan, D. L. 2005, Science, 307, 892 R.appaport, S., Podsiadlowski, P., Joss, P. C., DiStefano, R., & Han, Z. 1995, MNRAS, 273, 731  Bibliography^  169  Ruderman, M., Shaham, J. & Tavani, NI. 1989, ApJ, 336, 507 Savonije, G. J. 1987, Nature, 325, 416 Shklovskii, I. S. 1970, Sov. Astron., 13, 562 Smarr, L. L. & Blandford, R. 1976, ApJ, 207, 574 Splaver, E. M., Nice, D. J., Arzoumanian, Z., Camilo, F Lyne, A. G., & Stairs, I. H. 2002, ApJ, 581, 509 Splaver, E. M., Nice, D. J., Stairs, I. H., Locomen, A. N., & Backer, D. C. 2005, ApJ, 620, 405 Srinivasan, G. & van den Heuvel, E. P. J. 1982, A&A, 108, 143 Staelin, D. H. & Reifenstein, III, E. C. 1968, Science, 162, 1481 Stairs, I. H. 2004, Science, 304, 547 Stairs, I. H., Faulkner, A. J., Lyne, A. G., Kramer, M., Lorimer, D. R., McLaughlin, M. A., Manchester, R. N., Hobbs, G. B., Camilo, F., Possenti, A., Burgay, M., D'Amico, N., Freire, P. C. C., Gregory, P. C., k Wex, N. 2005, ApJ, 632, 1060 Stairs, I. H., Splaver, E. M., Thorsett, S. E., Nice, D. J., & Taylor, J. H. 2000, MNRAS, 314, 459 Stairs, I. H., Thorsett, S. E., & Arzoumanian, Z. 2004, Phys. Rev. Lett., 93, 141101 Stairs, I. H., Thorsett, S. E., Dewey, R. J., Kramer, M., McPhee, C. A. 2006, MNRAS, 373, L50 Stairs, I. H., Thorsett, S. E., Taylor, J. H., & Wolszczan, A. 2002, ApJ, 581, 501 Standish,^E.^M.^1998,^JPL^Planetary and^Lunar Ephemerides, DE405/LE405,^Memo^IOM^312.F-98-048^(Pasadena:^JPL), http://ssd.jpl.nasa.gov/iau-comm4/de405iom/de405iom.pdf  Bibliography^  170  Stappers, B. W., Bailes, M., Manchester, R. N., Sandhu, J. S., & Toscano, M. 1998, ApJ, 499, L183 Stinebring, D. R.. 1982, PhD thesis, Cornell University Sturrock, P. A. 1971, ApJ, 164, 529 Taam, R. E., King, A. R.., & Ritter, H. 2000, ApJ, 541, 329 Tauris, T. M. & Savonije, G. J. 1999, A&A, 350, 928 Tauris, T. M. & Sennels, T. 2000, A&A, 355, 236 Tauris, T. M. & van den Heuvel, E. P. J. 2006, Formation and Evolution of Compact Stellar X-ray Sources, 623-665 Tauris, T. M., van den Heuvel, E. P. J., & Savonije, G. J. 2000, ApJ, 530, L93 TaylOr, J. H. 1992, Philos. Trans. Roy. Soc. London A, 341, 117 Taylor, J. H. & Weisberg, J. M. 1989, ApJ, 345, 434 Thorsett, S. E., Arzoumanian, Z., McKinnon, M. M., & Taylor, J. H. 1993, ApJ, 405, L29 Thorsett, S. E., Brisken, W. F., & Goss, W. M. 2002, ApJ, 573, L111 Thorsett, S. E., Dewey, R. J., & Stairs, I. H. 2005, ApJ, 619, 1036 Toscano, M., Sandhi', J. S., Bailes, M., Manchester, R. N., Britton, M. C., Kulkarni, S. R., Anderson, S. B., & Stappers, B. W. 1999, MNR.AS, 307, 925 van den Heuvel, E. P. J. 1994, A&A, 291, L39 van den Heuvel, E. P. J. 2004, in Fifth Integral Science Workshop, arXiv:astroph/0407451v1  Bibliography^  171  van den Heuvel, E. P. J. 2007, in The Multicoloured Landscape of Compact Objects and their Explosive Origins, AIP Conference Proceedings (New York: American Institute of Physics), in press, arXiv:0704.1215v2 [astro-ph] van Kerkwijk, M. k: Kulkarni, S. R. 1999, ApJ, 516, L25 van Leeuwen, J.^Stappers, B. 2004, astro-ph/0406522 van Stroten, W. 2003, PhD thesis, Swinburne University of Technology van Straten, W. 2004, ApJS, 152, 129 . 2006, ApJ, 642, 1004 Wang, C., Lai, D., & Han, J. L. 2006, ApJ, 639, 1007 Weisberg, J. M., Romani, R. W., k Taylor, J. H. 1989, ApJ, 347, 1030 Weisberg, J. M. Sz Taylor, J. H. 2003, in Radio Pulsars, ed. M. Bailes, D. J. Nice, & S. Thorsett (San Francisco: Astronomical Society of the Pacific), 93 Wettig, T. Brown, G. E. 1996, New Astronomy, 1, 17 Wex, N., Kalogera, V., Kramer, M. 2000, ApJ, 528, 401 Wijnands, R. & van der Klis, M. 1998, Nature, 394, 344 Willems, B., Andrews, J., Kalogera, V., & Belczynski, K. 2007, in 40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More (New York: American Institute of Physics), in press, arXiv:0710.0345v1 [astro-ph] Willems, B., Kalogera, V., & Henninger, M. 2004, ApJ, 616, 414 Willents, B., Kalogera, V., & Henninger, M. 2005, in Binary Radio Pulsars, ed. F. Rasio I. H. Stairs (San Francisco: Astronomical Society of the Pacific), 123 Willems, B., Kaplan, J., Fragos, T., Kalogera, V., & Belczynski, K. 2006, Phys. Rev. D, 74, 043003  Bibliography  ^  Willems, B. k Kolb, U. 2002, MNRAS, 337, 1004 -  ----. 2003, MNRAS, 343, 949 Wolszezan, A. & Frail, D. A. 1992, Nature, 355, 145 Xilouris, K. M., Kramer, M., Jessner, A., von Hoensbroech, A., Lorimer, D., Wie ski, R., Wolszczan, A., & Caniilo, F. 1998, ApJ, 501, 286  172  

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