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Radio observations of two binary pulsars Kasian, Laura Elizabeth 2012

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Radio Observations of Two Binary Pulsars by Laura Elizabeth Kasian  B.Sc. Physics, University of Winnipeg, 2003 M.Sc. Astronomy, University of British Columbia, 2005  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in The Faculty of Graduate Studies (Astronomy)  The University of British Columbia (Vancouver) March 2012 c Laura Elizabeth Kasian 2012  Abstract The study of pulsars in binary systems produces a wide variety of scientific results, including unique tests of general relativity and constraints on the equation of state of matter at extremely high densities. Through pulsar timing (which utilizes the fact that pulsars are precise clocks), it is possible to precisely measure the orbital parameters and masses of some binary pulsars, which can place constraints on their mass transfer histories. We present timing results for two binary pulsars. The intermediate-mass binary pulsar (IMBP) PSR J0621+1002 is a mildly recycled pulsar in an 8.3-day orbit around a massive white dwarf (WD) companion. It is one of only two known IMBPs with a precise mass measurement. We collected 9 days’ worth of data using the 305-metre Arecibo telescope (allowing for full orbital coverage), which we used to improve constraints on the advance of periastron, and in turn, the pulsar and companion masses (to 1.53+0.10 −0.20 M  +0.28 and 0.76−0.07 M , respectively) and inclination angle of the system. These results, combined  with the relatively long orbital period, suggest a disk accretion evolutionary scenario involving short-lived periods of hyper-accretion, in which a moderate amount of mass has been transferred to the neutron star (NS). PSR J1906+0746 is a young pulsar in a compact ∼4-hour orbit around a companion that was discovered in the early stages of the PALFA survey using the 305-metre Arecibo telescope. We present the timing results using data collected between 2005 to 2009 using the Green Bank, Arecibo, and Nanc¸ay telescopes. We have measured the advance of periastron, the time dilation ii  and gravitational redshift parameter, and the orbital decay, and we find the pulsar and companion +0.011 masses to be 1.323+0.011 −0.011 M and 1.290−0.011 M , respectively. Although the companion may be  a second NS, it is more likely to be a massive WD. The system’s evolution probably involved a substantial transfer of mass from the WD progenitor onto the NS progenitor through Roche-lobe overflow accretion, followed by the formation of the WD, and a short common envelope phase, and finally the ejection of the envelope and the pulsar-forming supernova.  iii  Preface The work presented in this thesis was done as a part of several collaborations. The work described in Chapters 2 and 4 was in collaboration with the members of the PALFA consortium, whose Tier I membership at the time of this writing consists of Bruce Allen, Ramesh Bhat, Slavko Bogdanov, Adam Brazier, Fernando Camilo, Shami Chatterjee, Jim Cordes, Fronefield Crawford, Julia Deneva, Gregory Desvignes, Jason Hessels, Fredrick Jenet, Victoria Kaspi, Benjamin Knispel, Patrick Lazarus, Andrew Lyne, Maura McLaughlin, David Nice, Scott Ransom, Paul Scholz, Ingrid Stairs, Benjamin Stappers, Kevin Stovall, Mark Tan, Joeri van Leeuwen, and Weiwei Zhu. There have been other collaborators who have participated in PALFA in the past, and/or those who have contributed to PALFA as Tier II members. The major publications that have resulted from the PALFA consortium, in chronological order, are: Cordes et al. 2006, Lorimer et al. 2006, Champion et al. 2008, Hessels et al. 2008, Deneva et al. 2009, and Knispel et al. 2010. Though the student was a co-author on these publications, she did not contribute to the writing. Her contributions to the PALFA survey are described in Chapter 2, and in addition to her work on the pulsar J1906+0746 described in Chapter 4, she has made general contributions to the operation of the survey such as collecting data with the Arecibo telescope, running the search pipeline on a computer cluster at UBC, and ranking pulsar candidates that resulted from the search procedure. The work described in Chapter 4 on PSR J1906+0746 was done by the student as a member of the PALFA consortium. The student collected a large portion of the data for this pulsar iv  using the Green Bank and Arecibo telescopes; her advisor I. H. Stairs and other collaborators in the PALFA consortium also collected much of the J1906+0746 data used in this thesis. All J1906+0746 data from the Green Bank and Arecibo telescopes were reduced by the student for this thesis using the ASPFitsReader code (Demorest 2007; Ferdman 2008), SIGPROC (D. R. Lorimer) and SIGFOLDMSP (I. H. Stairs; see Appendix for a brief description of these and other software packages). The data from the Nanc¸ay telescope were reduced by collaborators Gregory Desvignes and Ismael Cognard. All times of arrival (TOAs) for all data used in this thesis were created by the student, with the exception of the WAPP TOAs for J0621+1002, which were created by collaborator D. J. Nice, as well as the pre-2005 data used in the timing analysis of J0621+1002 (which is the data and timing solution presented in Splaver et al. 2002). The analysis presented in Chapter 4 was done by the student under the direction of her advisor. Two pieces of software were provided by M. Kramer: BFIT, which fits multiple gaussian components to a pulse profile (see §4.5); and MAKEBEAM, which creates a two-dimensional map of the emission beam using a series of gaussian decompositions of pulse profiles (see §4.6). A subset of the data presented in this thesis was used produce preliminary results that were published in a conference proceedings (Kasian et al. 2008). Though the reduction and analysis of the data subset were similar to the results presented in this thesis, the final timing solution for the conference proceedings resulted in pulsar and companion mass measurements that were different from the values presented in this thesis, with the companion being more massive than the pulsar. Our present results indicate that the pulsar is the more massive object in the system, indicating a new set of implications for the system’s evolutionary history. The work described in Chapter 3 on PSR J0621+1002 was also done by the student as part of a collaboration with I. H. Stairs and D. J. Nice and building on a data set produced by E. M. Splaver, D. J. Nice, Z. Arzoumanian, F. Camilo, A. G. Lyne, and I. H. Stairs (Splaver et al. 2002). She collected much of the data over the nine-day observing campaign in 2006, and reduced the v  resulting ASP data (collaborator D. J. Nice reduced the corresponding WAPP data). She also performed the timing analysis presented in Chapter 3, including the grid to determine probability contours for the masses of the pulsar and companion, and created probability density functions for the masses and inclination of the pulsar system. Preliminary results from an independent timing analysis were presented by D. J. Nice, I. H. Stairs and L. E. Kasian in a conference proceedings (Nice et al. 2008), though those results did not sufficiently take into account variations in the dispersion measure over the data from 2006 (as discussed in Section 3.2.1). The results in this thesis therefore supersede that conference proceedings. Finally, all text in this thesis is original and was written by Laura Kasian. This thesis does not contain any excerpts or reproductions from any of the above co-authored publications that were written by others.  vi  Table of contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv  Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vii  List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ix  List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  x  List of acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xii  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xiv  1  Introduction . . . . . . . . . . . . . . . . . . . . . . . 1.1 A brief history of radio pulsars . . . . . . . . . . . 1.2 Radio pulsars: basic physics . . . . . . . . . . . . 1.3 Signal propagation through the interstellar medium 1.3.1 Dedispersion . . . . . . . . . . . . . . . . 1.4 Pulsar timing . . . . . . . . . . . . . . . . . . . . 1.4.1 Times of arrival . . . . . . . . . . . . . . . Standard profiles . . . . . . . . . Pulse profiles and times of arrival 1.4.2 Timing model . . . . . . . . . . . . . . . . 1.4.3 Timing pulsars in binary systems . . . . . . 1.5 Binary pulsars . . . . . . . . . . . . . . . . . . . . 1.5.1 Pulsar mass measurements . . . . . . . . . 1.6 This thesis . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  1 1 8 12 14 17 18 18 19 21 23 26 28 29  2  PALFA: searching for pulsars using the Arecibo L-band Feed Array . . . . . . . 2.1 Brief description of the Pulsar Arecibo L-band Feed Array (PALFA) survey . . 2.2 The author’s contributions to the PALFA survey . . . . . . . . . . . . . . . . .  31 32 34  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  . . . . . . . . . . . . . .  vii  3  The intermediate-mass binary pulsar J0621+1002 3.1 Data and analysis . . . . . . . . . . . . . . . . 3.1.1 Times of arrival . . . . . . . . . . . . . 3.2 Timing . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Dispersion measure changes . . . . . . 3.2.2 Measuring the periastron advance, ω˙ . 3.2.3 Calculating the total mass . . . . . . . 3.3 Pulsar and companion masses . . . . . . . . . 3.4 Results and implications . . . . . . . . . . . .  4  The young, relativistic binary pulsar J1906+0746 . . . . . . . . . . . . . . . . . . 61 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2 Observations and data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.4 Profile evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5 Gaussian fitting and template evolution . . . . . . . . . . . . . . . . . . . . . . 70 4.6 2-dimensional beam model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.7 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.7.1 Times of arrival . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.7.2 TEMPO pulsar timing software package . . . . . . . . . . . . . . . . . 79 4.7.3 Measurement of post-Keplerian parameters . . . . . . . . . . . . . . . 79 Estimating the measurability of γ, the time dilation/gravitational redshift parameter . . . . . . . . . . . . . . . . . . . . . . . 82 Measuring P˙b , the orbital period derivative . . . . . . . . . . 84 4.7.4 Mass measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.8 Dispersion measure variations . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.8.1 Secular DM variation . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.8.2 Orbital DM variation . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.9 Orbital aberration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.9.1 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.9.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.10 Nature of the companion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.11 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105  5  Conclusions and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . 108  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  . . . . . . . . .  36 41 42 43 45 53 54 55 59  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 viii  List of tables 3.1 3.2 3.3 3.4  J0621+1002 timing parameters . . . . . . . . . . . . . . . . . . . . . . . . . . J0621+1002: models for dispersion measure and corresponding ω˙ and M values J0621+1002: models for dispersion measure and corresponding ω˙ and M values J0621+1002 estimated parameters (68% confidence) . . . . . . . . . . . . . .  46 51 52 59  4.1 4.2  Known pulsars in relativistic and/or double neutron star binary systems . . . . J1906+0746 timing parameters . . . . . . . . . . . . . . . . . . . . . . . . . .  64 81  ix  List of figures 1.1 1.2 1.3 1.4 1.5 1.6 3.1 3.2 3.4 3.5 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15  Lighthouse model for radio pulsar emission. . . . . . . . . . . . . . . . . . P − P˙ diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The effect of dispersion on pulsar signals. . . . . . . . . . . . . . . . . . . An illustration of how the combination of beaming and rotation causes us observe a radio pulsar’s pulsed signal . . . . . . . . . . . . . . . . . . . . J0621+1002 ASP standard profiles at 1400 MHz and 430 MHz. . . . . . . Binary orbit geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . to . . . . . .  9 11 15 18 20 24  Illustration of a more eccentric orbit facilitating a better detection of ω˙ . . . . . J0621+1002 ASP standard profiles at 1400 MHz and 430 MHz. . . . . . . . . J0621+1002 residuals from the 2006 Arecibo campaign using four different models for the DM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J0621+1002 mass-mass contour plot . . . . . . . . . . . . . . . . . . . . . . .  40 44  Example of a GASP summed profile decomposition . . . . . . . . . . . . . . . 1906+0746: illustration of alignment of ASP and GASP gaussian components . 1906+0746: Full collection of gaussian components . . . . . . . . . . . . . . . 1906+0746: ASP and GASP gaussian components . . . . . . . . . . . . . . . 1906+0746: WAPP Gaussian components . . . . . . . . . . . . . . . . . . . . Flux density of the main peak of the J1906+0746 pulse profile versus MJD for GASP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beam map for J1906+0746 . . . . . . . . . . . . . . . . . . . . . . . . . . . . J1906+0746 Timing residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . 1906+0746: Values of γ for different subsets of MJD. . . . . . . . . . . . . . . 1906+0746: variation of ’measured’ γ values for simulated data . . . . . . . . Gamma versus Omega (reproduction of Figure 5 from Damour and Taylor [1992]) 1906+0746: variation of ’measured’ γ values for simulated data at different points in the orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1906 mass-mass diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DM vs MJD for all epochs where WAPP data was available for J1906+0746. . . DM versus orbital phase for all epochs where WAPP data was available for J1906+0746. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71 72 73 74 75  50 56  76 78 80 85 86 87 88 91 93 95 x  4.16 DM versus orbital phase for the two epochs that exhibit the largest DM variation 96 4.17 J1906+0746 - orbital aberration search over 8 orbital bins - October 2006 campaign101 4.18 J1906+0746 - orbital aberration search over 8 orbital bins - March 2008 campaign102  xi  List of acronyms ALFA Arecibo L-band Feed Array ASKAP Australian Square Kilometre Array Pathfinder ASP Arecibo Signal Processor ATNF Australia Telescope National Facility AXP anomalous X-ray pulsar BON Berkeley-Orl´eans-Nanc¸ay CE common envelope DM dispersion measure DNS double neutron star FFT fast Fourier transform FT Fourier transform GASP Green Bank Astronomical Signal Processor GBT Green Bank Telescope GC globular cluster GR general relativity IMBP intermediate-mass binary pulsar ISM interstellar medium LMBP low-mass binary pulsar LMXB low-mass X-ray binary LOFAR Low Frequency Array MeerKAT Karoo Array Telescope MJD modified Julian day MSP millisecond pulsar  xii  NRAO National Radio Astronomy Observatory NS neutron star PALFA Pulsar Arecibo L-band Feed Array PMPS Parkes Multibeam Pulsar Survey PDF probability density function RFI radiofrequency interference RMS root mean square RRAT rotating radio transient RVM rotating vector model SEP Strong Equivalence Principle SGR soft gamma repeater SKA Square Kilometre Array SNR signal-to-noise ratio SSB Solar System Barycentre TOA time of arrival WAPP Wideband Arecibo Pulsar Processor WD white dwarf  xiii  Acknowledgements There are many people that have helped in the work presented in this thesis. I would first like to thank my advisor, Ingrid Stairs, for her guidance and support throughout my time at UBC. This thesis would not exist without her expertise and patience, and I appreciate having been encouraged to attend conferences and visit telescopes where I was able to meet collaborators and other students. I am grateful to the other members of my doctoral committee, Mark Halpern, Jeremy Heyl, Harvey Richer, Joerg Rottler, for their thoughtful guidance over the years, to my university examiners Jaymie Matthews and Matthew Yedlin, and my external examiner Jocelyn Bell Burnell (University of Oxford) for their helpful comments on the thesis. There are many collaborators I would like to acknowledge here, including David Nice, Duncan Lorimer, Maura McLaughlin, Scott Ransom, Michael Kramer, Paulo Freire, Don Backer, Jim Cordes, Jason Hessels, Julia Deneva, Vicky Kaspi, Zaven Arzoumanian, Fernando Camilo, Andrew Lyne, Gregory Desvignes and Ismael Cognard. I am grateful for the past and present members of the UBC pulsar group, particularly Joeri van Leeuwen and Rob Ferdman, from whom I learned much during my early years in graduate school, and Aaron Bernsden, Marjorie Gonzalez, and Cindy Tam for their encouragement later on. I would also like to acknowledge the support of my fellow graduate students, as well as the postdocs and faculty all of whom have played a large role in my education throughout the years. I wish to thank my parents, sister, family and friends for their encouragement throughout graduate school, and for being so supportive of my completing this thesis, particularly once I had xiv  begun law school. This work was generously supported by external funding from the Natural Sciences and Engineering Research Council of Canada through a Canada Graduate Scholarship. I also wish to acknowledge the University of British Columbia for funding a portion of my graduate work with a partial UBC University Graduate Fellowship. L AURA E LIZABETH K ASIAN Vancouver, B.C. 2012  xv  Chapter 1  Introduction 1.1  A brief history of radio pulsars  A new field of radio astronomy was born when Jocelyn Bell discovered the first pulsar in 1967. The first pulsar, PSR B1919+21, and others that were found soon after, were determined to be of galactic origin (Hewish et al. 1968). It was not long before the connection was made between the pulsating radio signal of the first pulsars and the concept of rotating neutron stars (Pacini 1968; Gold 1968). In 1934, Baade and Zwicky had proposed that neutron stars may be created during the supernova explosions of massive stars, in which the dense cores of the dying stars would collapse even further to very small radii. This, among others, seemed a plausible explanation for the first pulsars, since the repetition rate of the signal from B1919+21 was only 1.33 seconds, too short a timescale to be produced by most astronomical objects that were known at the time. The first solid observational evidence that would verifiably link the observed pulsars to neutron stars came when a pulsar was found near the centre of the Crab nebula (Staelin and Reifenstein 1968), the remnant of a supernova documented by the Chinese in 1054 AD. This serendipitous discovery opened the doors to a fascinating new realm of physics and astronomy, one which continues to yield important discoveries and which promises to bring exciting results in the future. The four decades following the first pulsar discovery have seen many extreme pulsar systems, including the first binary pulsar (Hulse and Taylor 1975), the first  1  millisecond pulsar (Backer et al. 1982), the planet pulsar (Wolszczan and Frail 1992), and the double pulsar system (Burgay et al. 2003; Lyne et al. 2004) in which both objects in a binary orbit are seen as pulsars. The first known binary pulsar, B1913+16 (Hulse and Taylor 1975), a relativistic double neutron star system with a 7.75-hour orbital period, not only provided new evidence about the evolution of pulsars in binaries, but also acted as a rare laboratory for observing the effects of strong-field gravity. The system had spin properties distinct from the then-known population of isolated pulsars, having a higher spin rate, at 59 ms, high characteristic age, and a magnetic field significantly lower than the isolated pulsars. Smarr and Blandford (1976) explained the evolution of the binary pulsar with a model in which the pulsar was spun up through the transfer of mass and angular momentum from its companion before it became a second neutron star, which has since formed the basis for models explaining most currently-known binary pulsars. Further, several years of observing B1913+16 led to unprecedented tests of general relativity (GR) (Taylor and Weisberg 1982; Taylor and Weisberg 1989), discussed below. When the first millisecond pulsar (MSP), which spins at a rate of 641 Hz, was discovered by Backer et al. (1982), it was immediately thought to be an old pulsar that was spun up by a companion, in accordance with the spin-up model suggested to explain the double neutron star (Alpar et al. 1982). There have since been around 90 MSPs discovered in the galactic field (Lorimer 2008), with another ∼110 being discovered in globular clusters (GCs) (eg, Camilo et al. 2000, Ransom et al. 2005, and Freire et al. 2008). Due to the extremely high spin frequencies and the fact that a striking majority of MSPs are in binary systems, it is believed that they are formed through extended mass-transfer interactions with low-mass companions, which has caused them to gain angular momentum and spin up to the millisecond periods that we observe (Alpar et al. 1982). This is in contrast to the double neutron star systems, where the more massive companion (and thus shorter period of mass transfer) leads to less mass being transferred to the pulsar, and 2  ultimately results in pulsars that are only mildly recycled pulsars (∼20-100 ms for double neutron stars, as opposed to ∼1-10 ms for MSPs). Formation scenarios for binary pulsars are discussed in further detail in §1.5 and in Chapters 4 and 3.  Below is a list of some of the past science contributions and future goals of pulsar astronomy: Tests of general relativity Binary pulsar systems provide a unique opportunity to test the predictions of general relativity (GR) against observations, and to compare it to other theories of gravity (see Stairs 2003, 2010). The discovery of the first binary pulsar B1913+16 prompted the development of such tests, taking advantage of an extremely precise clock in a strong gravitational potential (Wagoner 1975; Eardley 1975; Damour and Ruffini 1974; Barker and O’Connell 1975). A highly relativistic system, B1913+16 was observed through high-precision timing and was found to have an orbital decay (i.e., change in binary period over time) that was consistent with the predictions of GR, establishing the existence of gravitational radiation (Taylor and Weisberg 1982, 1989). Binary pulsars in tight orbits with periods less than a day are particularly suited to make high-precision measurements of deviations from Newtonian physics, and a handful have since been discovered and have demonstrated a self-consistency within the GR framework: B1534+12 (Stairs et al. 2002); J0737-3039A/B (Kramer et al. 2006); J1756-2251 (Ferdman 2008); J1141-6545 (Bhat et al. 2008), B2127+11C (Jacoby et al. 2006), and J1906+0746 (Kasian et al. 2008, and Chapter 4 of this thesis). To date, the most stringent test of GR has been made with the double pulsar system J0737-3039A/B, which measured the Shapiro delay shape parameter to within 0.05% of the value predicted by GR. Though the double pulsar has the shortest orbital period of any known pulsar binary, the high precision of the test is due in large part to the unique ability to accurately measure the mass ratio of pulsars A  3  and B in the system (Kramer et al. 2006). Additionally, the general relativistic effect of geodetic precession (the precession of the pulsar’s spin axis about its total angular momentum vector; Damour and Ruffini 1974; Barker and O’Connell 1975) has been observed in several binary pulsars as secular changes in the pulse profiles (Weisberg et al. 1989; Arzoumanian 1995; Stairs et al. 2004; Hotan et al. 2005; Manchester et al. 2010; Lorimer et al. 2006). Variations in the eclipse properties of the double pulsar (Breton et al. 2008) have also provided a good test of geodetic precession. In addition to the above tests made possible through the timing of individual relativistic binary pulsars, it has also been possible to use pulsars to test the Strong Equivalence Principle (SEP), both through searches for the polarization of pulsar-white dwarf orbits in preferred directions manifested as an extra acceleration in the direction of the acceleration of the system by the galaxy (Damour and Sch¨afer 1991; Wex 2000; Stairs et al. 2005, Gonzalez et al. 2011), and through tests for dipolar orbital decay in pulsar-white-dwarf binaries, an effect not present in GR but which is predicted for some other theories of gravity (Will 1993; Damour and Esposito-Farese 1996; Lazaridis et al. 2009). In addition to these tests available for individual systems, there are currently large international collaborations (the North American Nanohertz Gravitational Wave Observatory1 , the Parkes Pulsar Timing Array2 and the European Pulsar Timing Array3 ) dedicated to setting limits on − with the goal of eventually measuring − the stochastic gravitational wave background using an ensemble of ultra-stable millisecond pulsars (e.g., Sazhin 1978; Detweiler 1979; Foster and Backer 1990; Hobbs et al. 2010).  1 http://nanograv.org/ 2 http://www.atnf.csiro.au/research/pulsar/ppta/ 3 http://www.epta.eu.org/  4  Probing the equation of state of matter at extremely high densities Studies of neutron stars, which have masses of ∼ 1.4M and radii of ∼ 10 km, allow us a unique opportunity to study matter at densities higher than we can ever achieve in a laboratory. There are many models to explain the neutron star (NS) interior (see Lattimer and Prakash 2007; Lattimer 2010). Observers have been able to put constraints on the neutron star equation of state. Measurements of the most massive pulsars (e.g. J1614-2230, whose mass of 1.97 ± 0.04M is the highest precisely measured NS to date; Demorest et al. 2010) place limits on the value of the maximum density and pressure at the centre of NSs (Lattimer and Prakash 2005), while the detection of pulsars with extremely fast spin rates (e.g. the fastest-known pulsar spin rate of 716 Hz; Hessels et al. 2006) constrain models for the composition of neutron stars (Lattimer and Prakash 2004). A Bayesian analysis of the masses of radio pulsars in white dwarf binaries (Kiziltan et al. 2010) found an upper limit of a 2 M neutron star with no signs of truncation in the underlying neutron star population, suggesting that the upper limit is due to evolutionary constraints and is not tied to GR or the physics of the NS interior; i.e., it is possible that NSs with masses higher than the cutoff exist. Additionally, observations of phenomena such as pulsar glitches (e.g. Radhakrishnan and Manchester 1969) can tell us about properties of the inner and outer structure of neutron stars, e.g. models involving superfluids (Anderson and Itoh 1975; Alpar et al. 1984) or starquakes (Ruderman 1969; Baym and Pines 1971). The discovery of new exotic pulsar systems with extreme masses and spin rates, and improving our measurements of currently-known pulsars, are essential to further understanding the interiors of these objects.  5  Studies of globular clusters Since the first pulsar was found in the M4 globular cluster (GC) (Lyne et al. 1987), many more GCs have been found to contain pulsars, with a current total of 127 known pulsars in 27 GCs4 . The majority are millisecond and/or binary pulsars, a finding that is consistent with the overabundance of low-mass X-ray binarys (LMXBs) − MSPs progenitors − in GCs as compared to the Galactic disk (Katz 1975; Clark 1975). There are many scientific advantages to studying the pulsars in GCs (see Ransom 2008; Camilo and Rasio 2005 for summaries). The high stellar density provides for proportionally higher probabilities of interactions between star systems, allowing for some very unique systems (e.g., the fastest-spinning pulsar known, found in Terzan 5, Hessels et al. 2006, and highly massive pulsars in several GCs, e.g. Freire et al. 2011). Searches for pulsars in GCs demand high time resolution (in order to be sensitive to the extremely short spin periods of the MSPs that are populous in GCs) and long integration times (since MSPs are intrinsically faint). Additionally, computationally expensive search algorithms (e.g., acceleration searches for binary pulsars, whose observed periods shift over the course of their orbits Johnston and Kulkarni 1991; Ransom 2001) are required for GCs. However, there are clear logistical advantages to searching for pulsars in GCs, namely that a globular cluster fits well within the beam of a radio telescope and thus requires a single pointing which can yield many pulsars (e.g. Terzan 5 (Lyne et al. 1990, 2000; Ransom et al. 2005), 47 Tucanae (Manchester et al. 1991; Camilo et al. 2000), and M28 (Lyne et al. 1987; B´egin 2006)); and also, the GC is at a known dispersion measure (DM), thus greatly reducing the range of DM values that needs to be searched as compared to that normally required in pulsar searching.  4 See  http://www.naic.edu/∼pfreire.html for an up-to-date list of pulsars in globular clusters (maintained by Paulo  Freire).  6  Understanding stellar evolution Studies of pulsars offer remarkable insights into the late stages of stellar evolution. Though we have a reasonably thorough understanding of the main sequence, the details of the later stages and ultimate fates of stars are not well understood. Supernovae themselves are complex events, being very difficult to model satisfactorily, and although the resulting neutron stars emit thermal high-energy radiation while they are young, this emission fades as the object begins to cool, and is no longer a source of information about the object (e.g., Lattimer and Prakash 2004). Pulsar emission allows us to probe neutron stars well after the supernova stage, giving observers the opportunity to learn about the final stage of stellar evolution (e.g., the study of pulsar populations, leading to information such as natal kicks and birthrates: Hobbs et al. 2005; Vranesevic et al. 2004; Faucher-Gigu`ere and Kaspi 2006, Keane and Kramer 2008). Additionally, pulsars that are in binary systems provide yet another source of information about stellar evolution. The binary pulsar systems are like a fossil record of the progenitor system, containing clues about the binary pair’s mass transfer history (see Stairs 2004).  7  1.2  Radio pulsars: basic physics  Perhaps the most useful characterization of a pulsar comes from a measurement of its spin period ˙ Using high-sensitivity radio telescopes with fast time resolution, (P) and period derivative (P). we can determine the period of a pulsar to extremely high precision (often to one part in 1015 ), and its period derivative to a correspondingly high precision (roughly one part in 106 for many pulsars)5 . The basic emission model for radio pulsars is that of a spinning, radiating magnetic dipole, whose spin and magnetic axes are misaligned, and which radiates beams of radio emission from its polar regions (often called the lighthouse model; see Figure 1.1). Measurements of the period and period derivative of a pulsar are particularly useful for comparing it against the general pulsar population: the assumptions that 1) the neutron star has a dipolar magnetic field and that the observed energy loss is dominated by magnetic dipole radiation, and 2) the pulsar had a negligible period at the time of its birth, allow for P and P˙ to be related to the neutron star’s surface magnetic field strength BS and characteristic age τc (e.g., Lorimer and Kramer 2005):  BS = 3.2 × 1019 G τc =  PP˙  (1.1)  P 2P˙  (1.2)  Although the above assumptions are not thought to adequately describe most pulsars, the simple spinning magnetic dipole model remains an useful framework for characterizing the known population of radio pulsars. The characteristic ages for some young pulsars in supernova remnants have been found to be inconsistent with other age estimates (e.g., from measurement of 5 ATNF  Pulsar Catalogue: http://www.atnf.csiro.au/people/pulsar/psrcat (Manchester et al. 2005)  8  Ra  dio  be  am  Magnetic Axis  Outer Gap Polar Gap  os  ed  fiel d  lines  Neutron Star  Cl  Light cylinder  Rotation Axis  Open field lines  9 Figure 1.1: Lighthouse model for radio pulsar emission.  proper motions, as in Migliazzo et al. 2002); however, the characteristic age and surface magnetic field calculations can be an effective tool for the comparison of pulsars against one another. While we do not currently have a model of pulsar radio emission that truly describes all observations, one common feature of all current models is that they all involve coherent radiation originating in the pulsar’s magnetosphere. The first and most basic model of pulsar emission was put forth by Goldreich and Julian (1969), and despite many attempts to develop more realistic treatments which have not been successful, the Goldreich-Julian model is often used to illustrate basic concepts of pulsar emission. This model defines the light cylinder as a boundary within which the plasma corotates rigidly with the pulsar, and which is defined by the radius RLC where the plasma speed equals the speed of light (e.g. Lorimer and Kramer 2005):  RLC =  c ∼ 4.77 × 104 (2π/P)  P s  (1.3)  The lighthouse model is useful in describing the regions where the radio emission may occur. Figure 1.1 shows two potential regions of origin for radio emission. The two regions where acceleration gaps may occur and thus provide the conditions necessary to produce the observed coherent pulsar emission are the polar cap and outer gap regions. The polar cap region is defined by the region between the open field lines above the magnetic polar cap, and the outer acceleration gap is the region near the light cylinder between the open and closed field lines (e.g. Lorimer and Kramer 2005). Higher-energy (X-ray, γ-ray) emission seen from pulsars are generally believed to have broader beaming fractions and to originate in the outer gaps (e.g. Abdo et al. 2009). Although it is generally believed that radio pulsar emission originates above the polar cap, recent evidence suggests that young pulsars with high spin-down luminosities may produce radio emission at higher altitudes above the neutron surface (Ravi et al. 2010), transitioning to lower emission heights for older pulsars.  10  Figure 1.2: P − P˙ diagram for the known ∼ 1800 radio-loud pulsars (excluding those in globular clusters). The pulsars studied in this thesis are labelled as large seven-point stars. Normal, isolated pulsars are green filled circles; binaries are blue double circles; those observed as X-ray and γ-ray sources are filled cyan triangles and circles, respectively; those with SNR associations are marked with red open stars; and AXPs and SGRs are marked by red skeletal stars. Data were obtained from the ATNF Pulsar Catalogue (http://www.atnf.csiro.au/people/pulsar/psrcat/; Manchester et al. 2005.)  11  We can make observations about the pulsar population by plotting the periods versus period derivatives on what is commonly called the P − P˙ diagram. Figure 1.2, which shows the ∼1800 known pulsars in the Galactic disk, shows that the vast majority of pulsars have periods between ∼ 100 ms and 3 s and period derivatives between ∼10−17 and 10−12 s/s, and are largely isolated pulsars (with no binary companion). The corresponding magnetic fields are roughly ∼1011 − 1012 G, and their characteristic ages τc are ∼10 kyr − 100 Myr. However, there are several subpopulations that have emerged as more exotic pulsars have been discovered over the years. Perhaps the most striking sub-class of pulsars are the millisecond pulsars, which sit at the lower left-hand corner of the P − P˙ diagram, which have extremely fast periods between 1.4ms and ∼30 ms, and low period derivatives between 10−21 and 10−19 s/s. Their magnetic fields are thus comparatively low (∼108 G), and they have comparatively long characteristic ages (τc ∼10 Gyr) relative to the vast majority of pulsars. Also, the millisecond pulsars are much more likely to have a binary companion than the normal pulsars (∼75% vs 2% for normal pulsars, according to the ATNF catalogue, Manchester et al. 2005), which is consistent with the spin-up model which is used to explain the recycled systems, and requires the pulsar to have had a companion from which to have accreted mass.  1.3  Signal propagation through the interstellar medium  The pulsed signal emitted along a pulsar’s radio beam must travel through the interstellar medium (ISM) to reach an observer on Earth. The photons that form the signal experience a delay due to electromagnetic interactions with charged particles (namely, free electrons) in the ISM, which results in a refractive index µ that depends on the observing frequency f as follows (e.g., Lorimer and Kramer 2005):  12  µ=  fp f  1−  2  (1.4)  which also depends on the plasma frequency f p of the charged particle: e2 ne πme  fp =  (1.5)  where e is the charge on an electron, n is the electron plasma number density, and me is the electron mass. Although free protons are also abundant in the ISM, they have a much smaller plasma frequency than the electrons due to their much larger mass, and do not contribute substantially to the refractive index of the ISM. Thus, the ISM acts as a dispersive medium through which the pulsar signal propagates, introducing a frequency-dependent delay in the pulsars signal. We can calculate the relative delay between two frequencies if we make the following set of assumptions: a cold, isotropic distribution of electrons, a low electron density, low amplitude of oscillation, and that we can ignore the effects of the small magnetic field. For two frequencies ν1 and ν2 in MHz, the relative delay is given by: ∆t =  1 × ν1−2 − ν2−2 · DM s 2.41 × 10−4  (1.6)  d  DM = 0  ne dz  where ne is the number density of free electrons along the propagation path z between the Earth and the pulsar at distance d (e.g. Hankins and Rickett 1975) and DM is the dispersion measure. Although dispersion affects observing at all frequencies to some degree, we can see from the 1/ν 2 dependence of its induced time delay that its effect is more pronounced at lower wavelengths. Thus, correcting for dispersive effects is particularly important for pulsar observing at radio 13  wavelengths (as compared to X-ray, gamma-ray, and optical observations). Because pulsars are generally such weak radio sources, they are observed using relatively wide bandwidths (up to several hundred MHz) in order to maximize the amount of signal collected in a given interval of time. However, dispersion through the ISM has a significant effect on pulsar observations at radio wavelengths. Within a given channel of bandwidth ∆ν, the observed pulse will represent a sum of all frequencies within that frequency range. Because the pulses at all frequencies will not be aligned to the same reference phase, the frequency-averaged pulse will be broadened (see Figure 1.3) over a time interval τDM , which can be approximated as (eg, Lyne and Graham-Smith 1998):  τDM ∼ 8.3 × 103  1.3.1  DM ∆ν sec 3 νMHz  (1.7)  Dedispersion  In order to correct for the dispersive effect of the ISM, we must apply a frequency-dependent correction (according to Equation 1.6) to the signal collected from a radio telescope. This can be done using two different methods, both of which were used for different data sets collected for this thesis. Using the first method, incoherent dedispersion, the data are collected in many frequency channels, each channel having a bandwidth ∆ν, split over a total bandwidth B. After the data are collected and stored, the appropriate time delay is computed for each channel according to Equation 1.6 (relative to some reference channel) before summing over the whole bandwidth (see Figure 1.3 for the effect of incoherent dedispersion). This method does not, however, account for dispersive smearing across each individual channel (though the amount of smearing can be reduced significantly by increasing the number of channels used over a given total bandwidth, reducing the bandwidth of each channel). The amount of dispersive smearing that remains is 14  determined by τDM ∼ 8.3 × 103 νDM ∆ν (i.e. Equation 1.7). 3 MHz  (a) No dedispersion  (b) Filterbank Dedispersion  Δν  ν₂  Individual frequency channels  B  ....  ν₃  νn  νn Apply frequency-dependent shift for each channel  Summed without dedispersing  ∆tn =  DM B sec 3 νM Hz  Summed profile  τDM ∼ 8.3 × 103  1 × (ν1−2 − νn−2 ) · DM sec 2.41 × 10−4  Summed after filterbank dedispersion  summed pulse is boadened by amount  Summed profile  Channel bandwidth Δν  ....  B  ....  ν₃  ....  Individual frequency channels  ν₂  ν₁  Δν  Channel bandwidth Δν  ν₁  Figure 1.3: The effect of dispersion on pulsar signals.  The second method is called coherent dedispersion, and is performed at the data collection stage. The advantage of this method over filterbank dedispersion is that it removes the effect of dispersive smearing within individual channels as well as between them. Coherent dedispersion recovers the intrinsic shape of the profile modulo scattering, which is preferred for studies of the pulse structure (as the pulse shape is related to the geometry of the pulsar emission). Also, since  15  the profiles are completely corrected for dispersive delays caused by the ISM, they have a higher SNR which leads to better precision on the time of arrivals (TOAs) that are produced from those profiles (described in § Sharp profile features that are recovered also increase the TOA precision. The idea behind coherent dedispersion is that the frequency-dependent phase shift of the pulsed signal caused by the ISM can be viewed as a filter described by transfer function H (Hankins and Rickett 1975). The pulsar’s intrinsic signal (complex voltage vint (t)) is convolved with H as it travels through the ISM, producing the complex voltage vmeas (t) measured by the telescope (for f within a finite bandwidth ∆ f centred on f0 ): Vmeas ( f0 + f ) = Vint ( f0 + f )H( f0 + f )  (1.8)  where Vmeas and Vint , defined for −∆ f /2 < f < ∆ f /2, are the Fourier transforms (FTs) of vmeas and vint . The transfer function for the ISM is given by:  H( f0 + f ) = e where D =  e2 2πme c  +i  2πD DM f 2 ( f0 + f ) f02  (1.9)  is the dispersion constant and DM is the dispersion measure of the pulsar.  It is then possible to recover the intrinsic complex voltage emitted by the pulsar by applying the inverse transfer function H −1 to the measured signal, which is typically done by Nyquist sampling the data stream and using FTs to allow multiplication by H −1 in the frequency domain. For this thesis, data were collected using both filterbank and coherent dedispersion machines. The two machines that provided filterbank data6 are the Wideband Arecibo Pulsar Processors (WAPPs) (Dowd et al. 2000) at the Arecibo observatory in Puerto Rico and the pulsar Spigot 6 The  WAPPs and the Spigot are autocorrelation spectrometers which, for the purposes of our analysis, provided filterbank data.  16  (Kaplan et al. 2005) at the Green Bank Telescope (GBT) in West Virginia, USA. The three coherent dedispersion machines used to collect the data in this thesis are the Arecibo Signal Processor (ASP) (Demorest 2007; Ferdman 2008) at Arecibo, the Green Bank Astronomical Signal Processor (GASP) (Demorest 2007; Ferdman 2008) at the GBT, and the Berkeley-Orl´eansNanc¸ay (BON) (a clone of ASP/GASP; Theureau et al. 2005; Cognard and Theureau 2006) at the Nanc¸ay Observatory in France.  1.4  Pulsar timing  We see a pulsar’s flux density change as its emission beam moves through our line of sight, which produces a periodic pulsed signal (as in Figure 1.4). Because the flux density of an individual pulse is so faint for most pulsars, each rotation cannot normally be distinguished (with several exceptions, e.g. B0809+74 and B0329+54, Taylor et al. 1975). Due to the periodic nature of the signal, we can usually obtain a precise enough estimate of the pulse period to fold the signal at that rate, stacking the signal over many rotations. When we add several hundred to several thousand pulses together, this allows us to obtain a pulse profile with a high enough signal-to-noise ratio to compute a TOA for that set of folded pulses (which is discussed in more detail in § below). Once we obtain a list of TOAs, we convert them to the Solar System Barycentre (SSB), and then use a timing model (using standard pulsar timing packages TEMPO7 and TEMPO2 (Hobbs et al. 2006); § 1.4.2) to assign each TOA a number that corresponds to an integer number of neutron star rotations since an arbitrary reference time. We then compare the arrival times predicted by the timing model to the actual arrival times computed from the profiles, and subtract the predicted values from the actual TOAs, yielding residuals. The timing model used in these packages (see Edwards et al. 2006) includes the effects of spin and astrometric 7 http://tempo.sourceforge.net/  17  parameters, dispersion, propagation through the earth’s troposphere (TEMPO2 only), and the doppler motion and, if the pulsar is in a binary system, relativistic effects caused by its orbital  Intensity  Intensity  motion as it moves around its companion.  Pulse Phase Pulse Phase  (a) On-pulse  (b) Off-pulse  Figure 1.4: An illustration of how a pulsar’s rotation, in combination with its beamed emission along an axis different from its rotation axis, can allow us to see pulsed signal. In the illustration, the pulsar is tilted towards us and therefore see only the uppermost emission beam once per rotation. Figure a) shows the pulsar with its emission beam partially aligned with our line of sight. At this phase, we see an increase in observed flux density. In Figure b) each emission cone points away from us, and we observe no flux from the pulsar emission.  1.4.1  Times of arrival Standard profiles  When we integrate the pulsed signal over many observations or years, we obtain a profile shape that is generally stable over time (Helfand et al. 1975), and which is unique to each pulsar for a given observing frequency. A particular profile shape is thought to be physically linked to  18  the geometry of that pulsar’s emission beam (Lyne and Rickett 1968, Lyne and Smith 1968, Gold 1969). Some pulsars exhibit changes in their pulse profiles over time. These changes have been found to be a result of two types of pheomena: either as a result of secular changes in the viewing geometry or of the system due to geodetic precession, or temporal ’mode changing’ of the emission itself. The profile evolution due to changing system geometry was first seen in B1913+16 (Weisberg et al. 1989), and is also seen, for example, in J1906+0746 (see §4.4). Some pulsars that exhibit mode changing − in which the pulse profile has two or more distinct shapes that switch continuously between each other (e.g., Backer 1970; Lyne 1971) − have been found to have their individual ’modes’ correlated with distinct spin-down rates (Lyne et al. 2010). It is common for standard profiles to vary significantly in shape from one frequency band to another. As an example, Figure 1.5 shows the standard profile for 0621+1002 at two frequencies, 430 MHz and 1400 MHz (using data were acquired with the coherent dedispersion machine ASP on the Arecibo telescope; see §3). As we believe that pulsar profile shapes are determined by the pulsar emission, this supports a generally frequency-dependent emission geometry.  Pulse profiles and times of arrival  A dedispersed time series from a long observation of a pulsar is split into several-minute integrations, each of which is folded and summed at the pulsar’s spin frequency. Each of these pulse profiles is then cross-correlated with a standard template unique for each pulsar and each observing frequency (as in § This is done with a matching algorithm (Taylor 1992) that uses FFTs to measure a phase shift between the fiducial points (usually determined by the phase of the fundamental frequency) of the profile and the template, yielding a time of arrival (TOA) for that set of stacked pulses. The result is a set of TOAs, which lists information about each profile, namely the TOA itself (the time associated with the pulse as measured by the observatory’s clock), the uncertainty on the TOA measurement, and other information such as the frequency 19  Figure 1.5: Standard profiles for J0621+1002 at 1400 MHz and 430 MHz, using the ASP coherent dedispersion machine on the Arecibo telescope. Flux density is plotted versus pulse phase (where one neutron star rotation is 28.3ms for J0621+1002, Splaver et al. 2002).  20  and observatory where the data was collected, which are required by the timing model.  1.4.2  Timing model  The motion of the Earth around the sun, along with the motion of telescopes around the Earth, places us in a non-inertial reference frame. The pulsar timing software packages TEMPO and TEMPO2 read a list of topocentric (as measured at the observatory) TOAs, which must first be converted to the SSB - which is a nearly inertial reference frame - to remove the effect of the Earth’s orbital motion about the sun. The barycentric correction of the TOAs is as follows:  tb = t − D/ f 2 + ∆R + ∆E − ∆S  (1.10)  (e.g. Lorimer and Kramer 2005), where D is the dispersion constant (measured in Hz and given by D = DM/(2.41 × 10−16 ), f is the observing frequency, ∆R , ∆E  and ∆S are the Rømer,  Einstein and Shapiro delays respectively, explained below (Taylor and Weisberg 1989). The Rømer delay ∆R accounts for the delay between the SSB and the observatory as projected along the vector from the SSB to the pulsar. It is given by ∆R = (r · n)/c, ˆ where r is the distance vector from the SSB to the reference location of the telescope, and nˆ is the unit vector from the observatory to the pulsar. The Rømer delay varies smoothly over the course of one year, with a maximum value of roughly 500 seconds for a pulsar on the ecliptic. The Einstein delay ∆E accounts for the gravitational redshift due to the masses present in the solar system and the time dilation caused by the relative motion of the Earth around the Sun. For all significant masses mi (each located at a distance ri from the Earth) present in the solar system, the Einstein delay is given by the integral of  d∆E dt  v2  i + 2c⊕2 , where v⊕ is the velocity of the = ∑ Gm c2 ri  Earth with respect to the SSB. While the Einstein delay does vary over the course of a single year, the fact that the bodies in the solar system are continually changing with respect to one  21  another (and hence, with respect to the Earth) results in this delay averaging to a constant over a long amount of time. Ignoring all but the sun’s contribution to the summation term, a typical value of the Einstein delay over the course of one year is of order 0.5 seconds (e.g., Edwards et al. 2006). The actual value of the delay will be longer than this due to the inclusion of the effects of Jupiter and other masses in the solar system. The Shapiro delay ∆S arises from the curvature of space-time due to the Sun. The Shapiro delay is given by ∆S = − 2GM log (1 + cos θ ), where θ is the angle between the pulsar, the Sun, c3 and the Earth at the time of the observation, . The magnitude of the Shapiro delay will vary consistently over the course of one year (although it will not vary regularly as does the Rømer delay, as the Shapiro delay is maximized when the pulsar is directly in the direction of the Sun, and is negligible elsewhere). The magnitude of the Shapiro delay at its maximum is roughly 120 µs at the limb of the sun. Good approximations for converting TOAs to the SSB are the Jet Propulsion Laboratory’s DE200 and DE405 ephemerides (Standish 1982, 1998). In this thesis, DE405 is used. Two further corrections are made to the TOA: a correction to account for the drift in pulse arrival time at different observing frequencies due to the DM; and also clock corrections which compensate for drift of the observatory’s local clock relative to time standards such as TT(BIPM). Once the TOAs have been transformed to the SSB and corrected for other effects, we are able to enumerate the pulsar’s rotations by determining precisely how many integer-numbered rotations the neutron star has undergone between a reference time and the time with which each profile is associated. The basic pulsar timing model accounts for spin and astrometric parameters, ˙ the dispersion measure, position, and including the pulse period, P, and period derivative, P, proper motion. In order to obtain a good measurement of the pulsar’s position, a year’s worth of data is required so that we can measure the variation in the delay caused by the Earth’s motion around the sun throughout its orbit (i.e. the variation of the Rømer and Shapiro delays over the 22  course of a year). Measurement of a pulsar’s proper motion requires multiple years of data, and it is also possible to measure parallax for some pulsars.  1.4.3  Timing pulsars in binary systems  When a pulsar is in an orbit around a binary companion, the orbital motion of the pulsar around the centre of mass of the system introduces a time-dependent delay to the pulsar’s signal. These delays can be predicted using various models of binary motion, the most basic of which is a classical system involving the Keplerian orbital parameters (Figure 1.6). The pulsar timing packages TEMPO and TEMPO2 provide several binary models which use different parametrizations to describe the orbits of the binary systems. Observers are thus provided with an opportunity to compare the observed pulse arrival times with the predictions from different models of binary orbital motion. Although a Keplerian model is sufficient for many binary pulsars, we often require additional corrections to the standard binary orbital parameters, when relativistic effects are present. A good measure of of whether or not relativistic effects can be ignored is a calculation of the velocity of the pulsar at periastron, given by (e.g. Lorimer and Kramer 2005): vp 1/3 =T c  2π Pb  1/3  1+e 1−e  1/2  m2 M 2/3  (1.11)  where m1 is the pulsar mass, m2 is the companion mass, M = m1 + m2 is the total system mass, e is the eccentricity, Pb is the orbital period of the system, and the constant T = GM /c3 = 4.925490947µs. When v p is some non-negligible fraction of the speed of light c (e.g., v p ∼0.001c for J1906+0746), additional post-Keplerian parameters are required. The post-Keplerian parameters include (see, eg, Damour and Deruelle 1986, Taylor and Weisberg 1989) the advance of ˙ the time dilation and gravitational redshift (or Einstein) parameter γ, the rate of periastron ω,  23  des f no  o line  n  tro s a ri pe  ν )  ω  e 1-  ( centre ap of mass  i  described through the longitude of the a i is marked by . The axis, and thetrue anomaly to Earth Figure 1.6: Above is a diagram of the geometry describing a Keplerian orbit. The ellipse in the plane of the orbit is defined by the eccentricity e and the semimajor axis a p (which we observe projected onto our line of sight as a p sin i). The + symbol represents the centre of mass of the binary system, which marks one of the focii of the elliptical orbit. The relative positioning between the orbital plane and the plane of the sky are described through the longitude of the ascending node (marked by ) and the inclination angle i. The argument of periapsis, ω, is the angle between the line of nodes and the semimajor axis, and the true anomaly ν is the angle between periastron and the position of the orbiting object (as measured from the centre of mass). This figure is based on Figure 8.3(b) of Lorimer and Kramer 2005.  24  orbital decay P˙b , and the range and shape parameters r and s that result from the Shapiro delay if the orbit is sufficiently edge-on. These post-Keplerian parameters can be used to describe the following delays that arise due to the binary motion of the pulsar about its companion (which are analogous to those delays described above due to the presence of masses in our solar system): the Rømer delay ∆BR , Einstein delay ∆BE , and Shapiro delay ∆BS . The Rømer delay ∆BR is the delay due to the propagation across the binary orbit, and is given by: ∆BR = x sin ω[cos u − e(1 + δr )] + x[1 − e2 (1 + δθ )2 ]1/2 cos ω sin u  (1.12)  where u is the eccentric anomaly of the orbit, and δr and δθ are the relativistic deformations of the orbit (such that we can define new eccentricities er ≡ e(1 + δr ) and eθ ≡ e(1 + δθ ); Lorimer and Kramer 2005). The orbital Einstein delay ∆BE is the combined effect of gravitational redshift and time dilation resulting from relative motions of the Earth and the pulsar, and is given by: ∆BE = γ sin u  (1.13)  The orbital Shapiro delay ∆BS is the delay induced by the pulsar’s signal due to its propagation through the curved spacetime near the pulsar’s companion. This delay, which is strong only at the orbital phase where the pulsar is behind its companion (and thus does not vary regularly throughout its orbit), is given by: ∆BS = −2r log {1 − e cos u − s[sin ω(cos u − e) + (1 − e2 )1/2 cos ω sin u]}  (1.14)  If we assume that general relativity is the correct theory of gravity, the relations between the post-Keplerian parameters and the masses are (approximated to the first post-Newtonian order): 25  ω˙ = 3  Pb 2π  γ = e  Pb 2π  192π P˙b = − 5  −5/3  1/3  T  (T M)2/3 (1 − e2 )−1  (1.15)  2/3  (1.16)  M −4/3 m2 (m1 + m2 )  −5/3  Pb 2π  1+  73 2 37 4 5/3 e + e (1 − e2 )−7/2 T m1 m2 M −1/3 24 96  r = T m2 s = x  Pb 2π  (1.17) (1.18)  −2/3  T  −1/3  M 2/3 m−1 2  (1.19)  (e.g., Taylor and Weisberg 1989) where x = a1 sin i is the projected semimajor axis of the orbit, and the other parameters are the same as in Equation 1.11, above. We note that the above relations describe only the contributions due to GR, and that there are may also be systematic contributions to ω˙ and P˙b .  1.5  Binary pulsars  Although the majority of the ∼ 2000 known pulsars are isolated, roughly 5 − 10 percent are in binary orbits around companions8 . When we use a binary model to fit a pulsar’s orbit over time, we are given a unique opportunity to learn important properties of the system, which can be used to understand its evolutionary history and to probe GR and the equation of state of matter at extremely high densities. Observers and theorists have combined the information from the collection of systems with well-constrained orbital parameters to assess likely formation channels for different classes of binary pulsars (e.g. Stairs 2004 for a review). Pulsars are broadly categorized as either young or 8 ATNF  Pulsar Catalogue: http://www.atnf.csiro.au/people/pulsar/psrcat (Manchester et al. 2005)  26  recycled, depending on whether or not they are thought to have been spun up by a companion. Pulsars in binary systems are further categorized into several major classes, and those most relevant to this thesis are outlined here: Low mass binary pulsars (LMBPs) The most populous class is the LMBPs, which consists of (recycled) millisecond pulsars orbiting low-mass white dwarfs, with spin periods between 1 and 15 ms, extremely low eccentricities, and low companion masses between ∼0.15 and 0.4 solar masses (Camilo et al. 2001), likely He white dwarfs (WDs). These binary pulsars are explained nicely by long periods of accretion from a low-mass companion (Alpar et al. 1982), and are generally well-understood. Intermediate-mass binary pulsars (IMBPs) Another class of binary pulsar, the IMBPs, consisting of moderately-recycled pulsars with periods between ∼15 and 200 ms, with massive (likely CO, with  0.5 solar masses) WD companions, are less common among the known  binary pulsars. Their properties are not easily explained by one overall evolutionary model, and there are few observational constraints in the form of intermediate-mass binary pulsars (IMBPs) with precise mass estimates with which to further distinguish between different models (Camilo et al. 2001; Splaver et al. 2002; Ferdman et al. 2010). The binary J0621+1002 is one of the two known IMBPs with precise mass measurements, and is discussed in detail in Chapter 3. Double neutron stars (DNSs) The class of DNSs contains a handful of mildly-recycled pulsars (with spin periods between ∼20 and 105 ms; see Table 4.1) which orbit a second neutron star with orbital periods between 2 hours and 20 days. Having survived two supernovae, these systems are thought to have evolved either through wind accretion or common envelope (CE) evolution, during which the pulsar has accreted mass from its companion, but with a shorter mass transfer phase than the low-mass binary pulsars (LMBPs), consistent 27  with the higher spin periods of the double neutron stars (DNSs). Young binary pulsars While the recycled pulsars in binary systems are very rotationally stable, having undergone a spin-up process, and thus represent the majority of the known binary pulsar population, a small number of young pulsars in binary systems have also been discovered. In addition to the examples of young pulsars in relativistic binaries around compact objects listed in Table 4.1, there are also young pulsars in binaries around main sequence stars, (e.g., Johnston et al. 1992; Kaspi et al. 1994; Stairs et al. 2001). Studying binaries from the unique perspective of a young pulsar can lead to interesting constraints on formation mechanisms for such systems. This is discussed further in the context of the young, relativistic pulsar J1906+0746 in Chapter 4.  1.5.1  Pulsar mass measurements  For pulsars in binary systems, the pulsar and companion masses are related to each other and the orbital inclination of the system with respect to the plane of the sky through the mass function, f (m1 , m2 ), which comes from Kepler’s third law and can be written as: f (m1 , m2 ) =  4π 2 x3 (m2 sin i)3 = M (m1 + m2 )2 T Pb2  (1.20)  where i is the inclination angle of the system. The mass function is determined by measurements of Pb and x, and can in turn be used through the above relation to constrain the unknown parameters (m1 , m2 , and i). If we assume a pulsar mass of 1.35M (Thorsett and Chakrabarty 1999) it is possible, through measurement of the Keplerian parameters, to obtain a lower limit on the mass of the companion, m2 , (as sin i ≤ 1, and the resulting inequality m2 ≥ f 1/3 (m1 + m2 )2/3 can be solved for m2 ). However, in binary systems where relativistic effects are measurable through post-Keplerian parameters, further mass constraints are possible. 28  When one post-Keplerian parameter is measured, this allows for a constraint on the masses of the system (as with J0621+1002 in Chapter 3). When two post-Keplerian parameters are measured, this allows us to distinguish between the masses of the two objects in the system (e.g. with J1906+0746 in Chapter 4). When three or more such parameters are measurable, it is possible to over-constrain the masses of the system, providing a consistency check within the GR framework or other theory of gravity. If the inclination angle of the system is known, or if other information is available (e.g. if the the companion is observable as a main sequence star or a white dwarf), it may be possible to place further constraints on the masses of the pulsar and companion. If the system is nearly edge-on (i.e. has an inclination angle of nearly 90◦ ), the Shapiro delay r and s parameters may be measured. If the orbit is sufficiently eccentric (i.e. if e is sufficiently large), we can accurately measure the value of ω at any time, which can lead to a ˙ Measurements of ω˙ can be obtained on short timescales for relativistic precise measurement of ω. binaries with periods less than ∼1 day, and on longer timescales for mildly relativistic systems. Similarly, for relativistic binaries with short orbital periods (on the order of several hours), it is possible to measure the orbital period decay, P˙b on a reasonable timescale of several years.  1.6  This thesis  The focus of this thesis is the observation and analysis of two binary pulsar systems. After a brief description of the PALFA survey (Chapter 2) which yielded J1906+0746 as an early result, we describe the observations and timing results of the two binary pulsars: J0621+1002 (Chapter 3), a mildly recycled pulsar in an 8.3-day orbit about a relatively massive white dwarf companion, is one of only two known IMBP systems with a precise mass measurement. Through an observing campaign using the Arecibo telescope that spanned nine consecutive days (allowing for full 29  orbital coverage), we have determined the advance of periastron to better precision, thus more stringently constraining the masses of the pulsar and white dwarf. J1906+0746 (Chapter 4) is a young pulsar in a ∼ 4-hour orbit around a binary companion which may be either a white dwarf or neutron star, and has been observed using timing data from the Arecibo and Green Bank telescopes for this thesis. The timing results include a precise measurement of the advance ˙ and estimates of the time dilation and gravitational redshift parameter γ and of periastron ω, the orbital decay P˙b . The pulsar exhibits a significant profile evolution, which is attributed to geodetic precession. In both systems, the orbital parameters and corresponding mass estimates are assessed in light of other similar pulsar systems, to better understand their evolutionary histories. The goal of this thesis is to contribute through these high-precision measurements to the overall understanding of stellar evolution and to confirm self-consistency within GR.  30  Chapter 2  PALFA: searching for pulsars using the Arecibo L-band Feed Array High-precision studies of pulsars offer a rich variety of scientific payoffs; however, this would not be possible without the search efforts of the surveys that discovered these pulsars. Searching for pulsars is not trivial; large-scale pulsar surveys require many hours of telescope time and computationally intensive search algorithms, which calls for state-of-the-art hardware, extensive data storage facilities, and ample computing power. However, the scientific benefits of pulsar surveys are manifold. The full collection of known pulsars allows for models of the Galactic pulsar distribution (e.g., Lorimer 2011) and models of the interstellar medium (ISM) (e.g., Cordes and Lazio 2002). Increasing the sample of known pulsars improves our understanding of the underlying pulsar population and leads to better models of the Galactic ISM. Likewise, surveys targeted at detecting rare and physically interesting objects, particularly millisecond pulsars (MSPs) and binary pulsars in short-period orbits, have an ability to discover exotic systems such as a neutron star-black hole binary or a second double pulsar which could present an exciting opportunity to probe general relativity (Kramer et al. 2006) or the neutron star equation-of-state (e.g., Lattimer and Prakash 2007; see §1.1), while the most stable MSPs can be used in an ensemble to put constraints on a background of gravitational waves (e.g., Hobbs et al. 2010).  31  2.1  Brief description of the PALFA survey  The PALFA survey (Cordes et al. 2006), operating through a roughly thirty-person consortium1 , has been searching for pulsars using the Arecibo L-band Feed Array (ALFA) receiver on the 305-metre Arecibo telescope in Puerto Rico since August 2004. ALFA is a seven-beam receiver that improves efficiency by allowing search data to be collected from seven different directions simultaneously. It was modelled after the 13-beam receiver (Staveley-Smith et al. 1996) used for the successful Parkes Multibeam Pulsar Survey2 (Manchester et al. 2001), which detected ∼700 pulsars, including many MSPs and binary pulsars. ALFA was designed to be sensitive to short-period binary pulsars and MSPs out to large distances, and primarily searched at low galactic latitudes with |b| < 5◦ and longitudes within Arecibo’s accessible ranges, 32◦ ≤ l ≤ 77◦ and 168◦ ≤ l ≤ 214◦ . The first several years of observations for the survey were collected using the WAPP autocorrelation spectrometers (Dowd et al. 2000) which used 256 channels across 100 MHz bandwidth for each of the seven beams; however, the much more sensitive Mock spectrometers3 , with 300-MHz bandwidth, were installed at Arecibo in 2007, and have been used for the PALFA survey data collection since early 2009. The same same sky is being covered again using the new hardware, as the upgrade is expected to lead to many more pulsar discoveries due to the improved sensitivity as well as the ability to better mitigate radiofrequency interference (RFI) during the search procedure. The PALFA survey has thus (as of March 2012) far discovered over 90 pulsars, including several MSPs, young isolated pulsars (e.g., Hessels et al. 2008), rotating radio transients (RRATs) (e.g., Deneva et al. 2009), and pulsars in binary systems including the young, relativistic binary J1906+0746 (Lorimer et al. 2006) discussed in Chapter 4 of this thesis, J1903+0327, a massive 1 http://arecibo.tc.cornell.edu/palfa/ 2 http://www.atnf.csiro.au/research/pulsar/pmsurv/ 3 http://www.naic.edu/∼astro/mock.shtml  32  millisecond binary pulsar in an eccentric orbit (Champion et al. 2008; Freire et al. 2011), and two intermediate-mass binary pulsars (IMBPs). In addition, the Einstein@Home volunteer distributed computing project has been undertaking a full-resolution search of PALFA data since 2009 (Knispel et al. 2010, 2011), and the second pulsar discovered by Einstein@Home is one of the two new PALFA IMBPs . There were two stages of data processing in this survey: a quicklook pipeline and the full pipeline (see Cordes et al. 2006; Hessels 2007; Deneva 2010 for more details). The quicklook processing is done in quasi-realtime: offline, but within hours of obtaining the data. The data are first decimated in the time domain, and then are dedispersed at a reduced number of trial DMs, and the resulting time series are Fourier-transformed and searched using two different methods for both periodic signals (using the standard search procedure described by Lorimer and Kramer (2005)), and isolated, dispersed pulses (using a single-pulse search; Cordes and McLaughlin 2003, see Deneva et al. 2009). The quicklook processing uses the pulsar search software package SIGPROC4 . The long processing has several search pipelines in use at different institutions. Most processing sites, including UBC, McGill University, National Radio Astronomy Observatory (NRAO) in Charlottesville, and West Virginia University, employ a long processing pipeline that uses the search software PRESTO (Ransom 2001). Cornell University processes full-resolution PALFA search data using a completely independent pipeline and full-resolution single-pulse search. The Swinburne University of Technology implements the PRESTO pipeline to search for periodic signals, and the Cornell pipeline to search for single pulses. Additionally, the Albert-Einstein-Institut Hannover uses its own pipeline for its volunteer distributed computing project, Einstein@Home. The PRESTO pipeline uses a search method similar to that in the quicklook stage, except 4 http://sigproc.sourceforge.net/  33  that 1) the data are kept in full resolution, 2) an additional stage is introduced to remove RFI from the DM zero time series, and 3) an additional search parameter is included to account for the the possibility of orbital modulation of the pulse TOAs due to acceleration by a binary companion (acceleration searching; Johnston and Kulkarni 1991; Ransom 2001). Naturally, the long processing is much more involved than the quicklook processing, and therefore requires much more computing power and time. The pulsar candidates are then viewed by eye using a candidate viewer originally written by P. Lazarus of McGill and based on the REAPER software designed for the Parkes Multibeam Pulsar Survey (PMPS; Faulkner et al. 2004) and ranked. Promising candidates are then confirmed by follow-up observation. Recently, candidate viewing and ranking logistics have been consolidated on the cyberska.org collaboration website.  2.2  The author’s contributions to the PALFA survey  Some of the author’s contributions to the PALFA survey are outlined below: Observing and Quicklook Processing Performing observations using the Arecibo telescope to search for new pulsars, both on-site and remotely, running the quicklook pipeline on the data that resulted and looking at pulsar candidates (one resulting in the discovery of J1906+0746, the young, relativistic binary pulsar discussed in Chapter 4). Data Processing and Ranking Candidates Ran ∼10% of the long processing pipeline on the computer cluster at UBC, and ranked resulting candidates using the candidate viewer. RFI Excision One of the challenges in identifying good candidates for follow-up in any pulsar survey is the existence of RFI, which can not only manifest as false pulsar candidates, but which can also decrease the potential for discovering faint new pulsars that have spin frequencies (or harmonics) near the frequency of the RFI. There are two stages during the 34  search procedure where RFI excision is possible: before the data are recorded (for example, using filters on the receivers), or before the time series are created at the trial DMs. As a final measure, having a list of known RFI frequencies can be useful in minimizing the amount of human time needed in candidate selection. Although the ALFA receiver does use filters, many sources of RFI remain problematic, such as a radar at the Arecibo airport which has a 12-second period. It is therefore necessary to focus on offline RFI excision using software. In the long processing of the PALFA data, an RFI excision stage searches individual beams and pointings for signals that appear at a dispersion measure of zero (pulsed signals that are of extraterrestrial origin must travel through the ISM and are thus dispersed, whereas terrestrial signals generally are not dispersed). However, some RFI is quite faint, which is problematic because they are not always identified and/or flagged as RFI. The Parkes Multibeam Pulsar Survey (PMPS) (which used a 13-beam receiver) successfully employed a cross-correlation algorithm that took advantage of the fact that its multiple beams points towards several different locations on the sky at once (and thus any signal that appeared in multiple beams at the same time - or in any given beam for multiple pointings - was likely to be RFI). The author adapted this algorithm for the PALFA survey data, and tested its effectiveness in helping to detect a known bright, slow pulsar in a set of ALFA pointings. While the algorithm did succeed in characterizing some RFI, it did not make a significant improvement in aiding the detection of the pulsar. Additionally, the algorithm posed a logistical problem: it required all beams and adjacent pointnigs to be processed together, while at the time of this investigation each beam was processed individually. For the preceding reasons, the algorithm was not implemented at the time.  35  Chapter 3  The intermediate-mass binary pulsar J0621+1002 The formation mechanism of most binary pulsars with low-mass white dwarf (WD) companions is well-understood. The majority of pulsars with WD companions have short (1.39 to 15 ms) spin periods, extremely low eccentricities, and low (∼0.15 M to ∼0.4 M ) companion masses, making up a class of low-mass binary pulsars (LMBPs; Camilo et al. 2001). Their properties are consistent with having been spun up by a low-mass companion over a long, stable period of mass transfer through Roche lobe overflow with an accretion disk (Alpar et al. 1982). The stable transfer of angular momentum afforded by a low-mass companion allows the pulsar to spin up to very low spin periods over time, while the magnetic field of the pulsar undergoes a process of being buried (which is not yet understood: e.g. Cumming et al. 2001), resulting in a magnetic field strength several orders of magnitude lower than those observed in non-recycled pulsars. The X-rays produced from the accretion disk during the spin-up process have been predicted to account for the observed class of low-mass X-ray binaries (LMXBs), a connection that has since been supported in several ways: by estimates of similar birthrates for both classes of objects (Lorimer 2001), comparison of observed masses with the theoretical orbital-period-core-mass relation (Rappaport et al. 1995), the verification of the theoretical orbital-period-eccentricity relation (Phinney 1992) and by observation (e.g. Archibald et al. 2009).  36  Similarly, the observed double-neutron-star systems (DNSs) containing a pulsar in orbit around another neutron star can generally be explained by an unstable period of hypercritical mass transfer followed by a common envelope phase and expulsion of the envelope due to the loss of orbital energy (e.g., Smarr and Blandford 1976). In this scenario, the period of mass transfer from the companion to the pulsar is brief, as the companion undergoes a supernova explosion soon after the CE phase. This leaves a mildly spun-up pulsar with a neutron star companion (Dewi and van den Heuvel 2004), or a young pulsar with a mildly spun-up companion, depending on which neutron star is seen as the pulsar. The class of binary pulsars known as intermediate-mass binary pulsars (IMBPs) consists of pulsars with relatively high-mass (  0.5M ) WD companions, higher eccentricities than the  LMBPs, and generally shorter orbital periods (e.g. Camilo et al. 2001). These properties of IMBPs are not consistent with the standard LMBP formation mechanism: the high-mass WD companions require higher-mass companion progenitors, and the long pulsar spin periods suggest a shorter period of mass and angular momentum transfer, which is consistent with a more massive companion when we assume a correlation between mass transfer and pulsar spin period. Although several scenarios have been suggested to explain the IMBP systems, two are highlighted here. The first scenario (van den Heuvel 1994) involves a neutron star in a tight orbit around a massive companion progenitor which undergoes common envelope (CE) evolution until the envelope is quickly expelled and a white dwarf companion remains with a mildly-spun-up neutron star with a period of a few tens of milliseconds. This is more likely for IMPBs in relatively tight orbits with WD companions whose progenitors were significantly more massive than the neutron star. The second scenario involves disk accretion with periods of hypercritical mass transfer, followed by the contraction of the progenitor envelope (Tauris et al. 2000; Taam et al. 2000). This produces a mildly spun-up neutron star with an orbital period between ∼ 3 and ∼ 70 days, longer than in the first scenario. 37  Recent precise measurements (e.g. J1614-2230, whose mass of 1.97 ± 0.04M is the highest precisely measured NS mass to date (Demorest et al. 2010) and the eccentric binary millisecond pulsar with a mass of 1.667 ± 0.021M (Freire et al. 2011)) have established that the distribution of pulsar masses is actually more broad than the tight Gaussian distribution (1.35 ± 0.04M , Thorsett and Chakrabarty 1999) that had previously been thought to exist. This may reflect the broad range of formation mechanisms required to explain the all of the observed binary pulsar systems. The IMBPs are just one example of a class of pulsar that cannot be explained by the standard LMBP formation mechanism, and which must be investigated further and probed through precise measurements. There are comparatively fewer IMBPs known than LMBPs, and accordingly fewer precise mass measurements of these pulsars. As a result, there are fewer constraints on possible mass transfer histories. Of the sixteen known IMPBs, only two (J0621+1002, Splaver et al. 2002 and J1802-2124, Ferdman et al. 2010) currently have precise mass measurements. The observed IMBPs can be split into two major categories (e.g. Ferdman et al. 2010): those that have orbital periods Pb less than ∼ 3 days, and those that have Pb greater than ∼ 3 days. This distinction by orbital period is of particular importance, as Pb largely determines which of the two above evolutionary histories is able to explain the systems. The CE scenario is only possible for systems with tight orbits, whereas the disk scenario requires a wider orbit. Due to the small number of IMBPs known, and the even smaller number of IMBPs with precise measurements, it has been difficult to place constraints on potential mass transfer histories. However, the two known pulsars with precise mass measurements fall into different IMBP sub-classes: J0621+1002 has a long orbital period, whereas J1802-2124 has a tight orbit. J0621+1002 was discovered by Camilo et al. (1996) to contain a 28.9 ms pulsar in a 8.3 day orbit about a white dwarf companion. It has a relatively high eccentricity of 0.0025. Using data that spanned five years, Splaver et al. (2002) were able to produce the first precise mass 38  measurement of an IMBP. The total system mass was found to be 2.8(3)M , and the pulsar and +0.27 WD masses were estimated with 68% confidence limits to be 1.70+0.32 −0.29 M and 0.97−0.15 M ,  ˙ respectively. The masses were determined through a measurement of the periastron advance, ω, which is made possible due to the system’s relatively high eccentricity (see Figure 3.1 for an illustration) and statistical arguments about the system’s orbital inclination. The other IMBP with a precise mass measurement, J1802-2124, contains a 12.6ms pulsar in a 16.8-hour binary orbit to have a pulsar mass of 1.24 ± 0.11M and a white dwarf mass of 0.78 ± 0.04M (Ferdman et al. 2010; measured through the system’s Shapiro delay). The properties of J1802-2124 were found to be consistent with having undergone CE evolution, but this is not a plausible scenario for J0621+1002 due to its longer orbital period. Understanding its mass could lead to constraints on the process operating in the disk/hypercritical accretion scenario. We observed J0621+1002 in the fall of 2006, over nine consecutive days. Adding our new ˙ The error on the data to the Splaver et al. data set, we expect a significantly better estimate of ω. measurement of ω˙ decreases with the amount of time according to:  δ ω˙ ∝ T −3/2 Pb  (3.1)  where T is the time baseline and Pb is the binary period (Damour and Taylor 1992). Our new observations provide a baseline T of 4220 days (∼ MJD 49794 to 54014) as compared with 2298 days in Splaver et al. 2002 (∼ MJD 49794 to 52092), and Pb is not observed to have changed on this timescale. We thus expect the new observations to provide a measurement of ω˙ with an error that is reduced to  Tall Tsplaver  ∼  4220 −3/2 2998  ∼ 0.4 of the previous value.  39  ω= ω2  Δω /Τ  ω2  Τ  / Δω = ω  ω1 ω1  ˙ The pulsar in a Figure 3.1: Illustration of how a more eccentric orbit facilitates a better detection of ω. more eccentric orbit (left) about its centre of mass causes ω to be more easily measured at any point in the orbit, thus allowing a better detection of ω˙ over a given time span. Additionally, a more eccentric binary system, all else being equal, will have a higher ω˙ (as ω˙ ∝ (1 − e2 )−1 ), so that for a given time T the more eccentric system will have a greater change in ω and thus will afford a better measurement of ω˙ (though this depends on other factors such as the pulsar’s flux density, spin period, etc.). In each diagram, the black dot represents the pulsar, and the + symbol represents the centre of mass of the binary system.  40  3.1  Data and analysis  In September and October 2006, we acquired Arecibo data to better constrain the periastron advance of J0621+1002 and, in turn, the pulsar and companion masses. We took data using the Arecibo telescope at two frequencies (430 MHz and 1400 MHz) over 9 consecutive days. As J0621+1002’s orbital period is 8.3 days, this provided coverage of one full orbit. The data were taken separately at each frequency - half the observing time on each day was spent using each receiver. Arecibo Signal Processor (ASP) 430 MHz The 430-MHz data were taken in four 4-MHz channels using the Arecibo Signal Processor (ASP) backend (Demorest 2007, Ferdman 2008) using two polarizations and 8-bit sampling. The data were coherently dedispersed (§1.3.1; Hankins and Rickett 1975) using a local value of the pulsar’s DM, and were folded online using the pulsar’s ephemeris. 1400 MHz The ASP data were centered at 1410 MHz and collected using two polarizations and 8-bit sampling over a total of 64 MHz split into 16 subbands, and were coherently dedispersed and folded online. ASP Data reduction The ASP data were flux calibrated in each polarization using a reference source with a noise diode source injected at the receiver. The data were then summed over both polarizations in time and in frequency to obtain 30-minute total-power integrations using the software package ASPFitsReader (Ferdman 2008). We note that the 430 MHz ASP profiles look slightly different from the profiles taken with the older coherent dedispersion machine Mark 4 (Stairs 1998), which is unexpected since both machines employ the coherent dedispersion technique and 41  should produce comparable profiles. We do not understand why this is the case, as similar effects have not been reported for other pulsars, and as we do not expect this pulsar to exhibit geodetic precession, profile changes due to changing geometry of the pulsar emission beam with respect to our line of sight are not expected. It may be caused by systematic or instrumental effects such as the use of 4-bit versus 8-bit sampling, or different fast Fourier transform (FFT) lengths in the dedispersion process. Ultimately, we fit an offset between the Mark4 and ASP data sets so that this discrepancy in profile shape does not affect the orbital parameters (though it could affect the measurement of the DM). Wideband Arecibo Pulsar Processor (WAPP) Three of the four available Wideband Arecibo Pulsar Processors (WAPPs, Dowd et al. 2000) were used to record data near 1400 MHz, which were taken simultaneously with the ASP processor (the fourth IF was sent to ASP). 1400 MHz The three WAPPs each used a 50 MHz bandpass, centered at 1145, 1195, and 1500 MHz, with 192 autocorrelation lags using 3-level sampling at an interval of 32 µs. The WAPP data were folded in real time using pre-computed values of the pulse period based on the pulsar’s ephemeris. The lags were then converted to spectra, calibrated using a reference noise diode and dedispersed offline by collaborator David Nice, who also formed the WAPP times of arrival (TOAs) for this work.  3.1.1  Times of arrival  Times of arrival (TOAs) were computed using the method described in § A separate standard profile was computed and used for the new data at each frequency and for each processor, and an offset was fit between the WAPP data at each frequency, and the ASP data. The offsets between the individual WAPPs were required to allow for profile evolution with frequency and/or 42  timing offsets. Since we are reasonably confident that the ASP data at both 430 and 1400 MHz have the same systematic timing delay, we aligned the fiducial points of the standard profiles at both frequencies to the same phase so that we were able to fit a single offset for both frequencies when timing the data (and hence derive a reliable DM). To create standard profiles for the ASP data, we first created cumulative folded profiles for each day’s data at both frequencies. For each frequency, we then chose as a standard profile the cumulative profile from the day which provided the highest signal-to-noise ratio. We aligned the ASP profiles for the two frequencies such that the bin with the highest signal falls into the same profile bin. While creating the TOAs, we did not rotate the ASP standard profiles to a phase of zero (as is the common practice). We did this so that we could be sure that the profiles at 430 MHz and 1400 MHz were properly aligned so that it was not necessary to fit an offset between the ASP data at the two frequencies. In addition to requiring one fewer offset in the timing of this pulsar, aligning the ASP standard profiles allowed for a better measurement of the dispersion measure (DM) at the 2006 epochs, which is determined from the relative delay between a given pulse at two different frequencies. Figure 3.2 shows the standard profiles for the ASP data at 430 and 1400 MHz.  3.2  Timing  The data collected in 2006 were combined with the data described in Splaver et al. (2002) to obtain an overall timing solution with better constraints on the orbital parameters. The Splaver et al. data set contains TOAs from the Arecibo, Green Bank 140-foot, and Jodrell Bank telescopes from March 1995 to July 2001 (MJD 49794 to 52092), at frequencies ranging between 370 and 1400 MHz. For more information about the earlier data, see Table 1 of Splaver et al. 2002. The uncertainties on the earlier TOAs had been adjusted in Splaver et al. (using the form 43  Figure 3.2: Standard profiles used for J0621+1002 at 1400 MHz and 430 MHz for the ASP coherent dedispersion machine on the Arecibo telescope (note that this figure is a repeat of Figure 1.5). Shown are the cumulative profiles for each frequency (from the day having the best signal to noise ratio for that receiver). The templates were shifted so that the profile bin with the highest signal is in the same bin for both frequencies. Axes are flux density versus pulse phase (where one neutron star rotation is 28.3ms for 0621+1002, Splaver et al. 2002).  44  √ σ = a σ 2 + b2 , where σ is the error on one TOA, and a and b are constants for a given machine and frequency) so that the reduced χ 2 for the TOAs from each machine at each observatory was equal to 1, i.e. so that: 1 (tT OA − tmodel )2 = 1. ∑ ν i a2 (σi2 + b2 )  (3.2)  for each set of TOAs (where ν is the number of degrees of freedom, and tT OA and tmodel are the observed and predicted times of arrival, respectively). The adjustments used in Splaver et al. were kept fixed in our analysis. When we included the new WAPP and ASP TOAs, we performed a similar adjustment to the new TOA uncertainties by weighting them so that χ 2 for each set of data was ∼ 1. This treatment of the uncertainties on TOAs is standard practice for pulsar timing. Table 3.1 of this thesis contains our measured and calculated parameters that resulted from our timing analysis. We note that although most parameters are consistent within error with the values listed in Splaver et al. (2002), a few have changed slightly. We have improved the precision of the proper motion of the system, an expected effect of the increased time span of the observations, and the values of µα and µδ are consistent with the previous values. We also have a better measurement of the orbital period, owing to the fact that more complete orbits have happened between the first and last data set; however, we note that our current value of Pb differs from the previous estimate by roughly 2σ . The epoch is kept the same as in Splaver et al. 2002 because it is also the reference point for the DM polynomial, and also because there is much more data in the earlier epoch than in the 2006 epoch.  3.2.1  Dispersion measure changes  A challenging feature of the timing of J0621+1002 is that its DM varies on a short timescale. The Splaver et al. data required a 17th-order polynomial to describe the DM over the course  45  Parameters Right ascension, α (J2000.0) . . . . . . . . . . . . . . Declination, δ (J2000.0) . . . . . . . . . . . . . . . . . . Proper Motion, µα = α˙ cos δ (mas/year) . . . Proper Motion, µδ = δ˙ (mas/year) . . . . . . . . Spin Period, P (ms) . . . . . . . . . . . . . . . . . . . . . . Spin Period Derivative, P˙ (10−20 ) . . . . . . . . . . Epoch (MJD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ephemeris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orbital Period, Pb (days) . . . . . . . . . . . . . . . . . . Projected Semimajor Axis, x (lt s) . . . . . . . . . Orbital Eccentricity, e . . . . . . . . . . . . . . . . . . . . Epoch of Periastrona , T0 (MJD) . . . . . . . . . . . Longitude of Periastrona , ω (degrees) . . . . . . Rate of Periastron Advanceb , ω˙ . . . . . . . . . . . Dispersion Measurec , DM0 (cm−3 pc) . . . . . . Calculated Parameters Mass Function, fmass . . . . . . . . . . . . . . . . . . . . . Total Mass, M (M ) . . . . . . . . . . . . . . . . . . . . . . Pulsar Massd , M1 (M ) . . . . . . . . . . . . . . . . . . . Companion Massd , M2 (M ) . . . . . . . . . . . . . . Inclination Angled , i (degrees) . . . . . . . . . . . . .  Our Values 06:21:22.11107(1) 10:02:38.7414(9) 3.5(1) -0.2(5) 28.853860730495(1) 4.733(2) 50944 DE405 TT(BIPM) 8.3186805(1) 12.0320747(3) 0.00245744(4) 50944.75686(3) 188.817(1) 0.0102(2) 36.6010(6) Value 0.027026849(2) 2.32(8) 1.53+0.10 −0.20 0.76+0.28 −0.07 24+19 −0  Splaver et al. Values 06:21:22.11108(3) +10:02:38.741(2) 3.5(3) -0.3(9) 28.852860730049(1) 4.732(2) 50,944.0 DE200 TT(BIPM01) 8.3186813(4) 12.0320744(4) 0.00245744(5) 50,944.75683(4) 188.816(2) 0.0116(8) 36.6010(6) 0.027026841(4) 2.81±0.30 1.70+0.32 −0.29 0.97+0.27 −0.15  Table 3.1: Timing parameters for J0621+1002 including the data from Splaver et al. 2002 and the 9-day observing campaign taken for this thesis in 2006. a The parameters ω and T are highly covariant; observers should use the more precise values ω = 0 188◦.815781 and T0 = 50, 944.756830176. b The value of ω ˙ listed here is different from those in Tables 3.2 and 3.3. The difference arises from the use of the complete 2006 data set in this table (amounting to nine days), as opposed to the results in Tables 3.2 and 3.3, which use the subset of the 2006 data that have good TOAs at both 430 and 1400 MHz (amounting to seven of the nine days). c The DM value listed here is the constant term in a 17th-order polynomial that describes DM of the data from Splaver et al. (2002). The DM of the 2006 data was modelled using an offset with a gradient. All DM parameters were fit simultaneously with the other fit parameters. See §3.2.1 for further discussion of the DM variations of J0621+1002 throughout the course of these observations. d The masses and inclination angle are the most likely values derived from the corresponding probability density functions in 3.3.  46  of that data span. Due to the large gap in coverage between the old data and the 2006 data, we kept the DM model for the Splaver et al. data as a seventeenth-order polynomial (allowing the coefficients to vary in the fit), but fit a separate DM model for the new data (which represents a comparatively short amount of time after the five-year gap in coverage) while simultaneously fitting for the orbital, spin, and astrometric parameters. In light of the short-timescale DM variations present in the earlier data, we investigated the behaviour of the DM over the course of the new observations. We fit a separate DM offset for each day of the 2006 observing campaign where we had good data at both 430 MHz and 1400 MHz (which amounted to 7 of the 9 days). A cursory glance at the resulting DM offsets for each day (points with error bars, shown in Figure 3.3), suggests a significant variation in DM over the new data which can be described relatively well by a simple model. We have tested a total of four models of the DM for the new data: the model using seven individual DM offsets discussed above, and three simpler models, to obtain a sufficiently low χ 2 using the fewest parameters possible. For clarity, we labelled the models as follows: (a) a single DM offset with no gradient; (b) a single DM offset with a gradient; and (c) one DM offset with gradient for the first four days, and one DM offset with no gradient for the last three days. The model using 7 individual DM offsets is labelled as model (d). Models (b) and (c) are plotted in Figure 3.3 for comparison with model (d), and we find that models (b) and (c) appear to be equally consistent with the individual DM offsets produced by model (d). Figure 3.4 shows residuals resulting from the four options for describing the DM of J0621+1002. The results are tabulated in Table 3.2. Since model (b) has fewer free parameters than either models (c) or (d) ˙ we ultimately adopted it for our timing model. but produces the same low χ 2 and a consistent ω, While we ultimately allowed the coefficients in the DM polynomial to vary while fitting for the remaining timing parameters to obtain our final timing solution, the values of the reduced χ 2 and ω˙ shown in Table 3.2 and in Figures 3.3 and 3.4 were computed while fixing the DM 47  polynomial for the earlier (pre-2006) data determined in the Splaver et al. paper. We obtained the DM polynomial coefficients from Splaver et al. by running TEMPO on the pre-2006 set of TOAs using the parameter file that was used to obtain the published values; the polynomial coefficients that resulted from this were those that were fixed in this part of the analysis. Our reason for fixing the DM polynomial coefficients for this test is that the DM offsets for the new epochs are largely covariant with the constant term in the DM polynomial, making it difficult to understand and illustrate the behaviour of the DM at the new epochs. We found that the reduced χ 2 values in Table 3.2 are a good representation of the validity of the DM models in question. To test this, we compared the following three different treatments of the DM: 1) fixing the DM polynomial and fitting all DM offsets in the 2006 epochs; 2) fitting the DM polynomial but fixing the first DM offset in the 2006 epoch; and 3) fitting the DM polynomial and all DM offsets in the 2006 epoch. The reduced χ 2 values and binary parameters resulting from the three different DM treatments are listed in Table 3.3, which shows that the values of the binary parameters resulting from a given DM model do not depend significantly on our treatment of the DM polynomial.  48  Figure 3.3: Offsets from the DM value of DM0 = 36.6010(6) pc cm−3 . The points with error bars are the values obtained while fitting for seven different DM offsets at the seven different dual-frequency days that were observed in 2006. The points are the same on each of the two plots. The lines in the top plot represent models b (single offset with a gradient) and c (two-bin model).  49  Figure 3.4: J0621+1002 residuals from the 2006 Arecibo campaign using four different models for the DM for the 7 of those 9 days where we had TOAs at both 430 MHz and 1400 MHz (while fixing the earlier DM at the polynomial determined in Splaver et al.). Red points are 430 MHz ASP data; blue points are 1400 MHz ASP data; and green points are 1400 MHz WAPP data. The plots are as follows: (a) The top plot shows residuals from fitting the DM with a single value; (b) using a single value plus a gradient; (c) using a two-bin model: an offset + gradient over the first four days and an offset without gradient over the last three days; and (d) the bottom plot shows residuals resulting from using seven individual values for DM, one for each day in the campaign where we had data at two frequencies. Compare with the χ 2 values and corresponding ω˙ values in Table 3.2 (also written on the plots above). Note that these values use only the 2006 epochs that have dual-frequency TOAs. Two days (MJDs 54005 and 54008) did not have data at 430 MHz, and thus were removed from this DM assessment. Also, there were no 1400 MHz ASP data available for MJD 54013, which is why there are no blue points on that day (yet we still were able to include this day in this analysis since we had 1400 MHz WAPP and 430 MHz ASP TOAs). The value of ω˙ changes slightly when the single-frequency days are included in the fit.  50  Reduced ω˙ 2 χ (a) Single offset 1.291 0.0107(2) (b) Single offset with gradient 1.008 0.0099(2) (c) Two−bin model 1.006 0.0100(3) (d) 7 offsets 1.003 0.0102(3) Previous result for comparison Splaver et al. value 0.0116(8) Description  M 2.48(8) 2.21(8) 2.26(9) 2.32(12) 2.8(3)  Table 3.2: J0621+1002: Models for Dispersion Measure (DM) and corresponding ω˙ and M values. See Figure 3.3 for a comparison of the DM offset values. See Figure 3.4 for a comparison of the post-fit residuals for each model. The values in this table result from fixing the DM polynomial, but allowing all DM offsets for the 2006 data to vary (corresponding to fitting scheme #1 in Table 3.3) Note that the value of ω˙ for model (b) listed in this table differs from the value reported in Table 3.1. This is because the values in this table were derived using only the 2006 epochs that have dual-frequency TOAs. Two days (MJDs 54005 and 54008) did not have data at 430 MHz, and thus were removed from this DM assessment. The value of ω˙ changes slightly when the single-frequency days are included in the fit.  51  Fit Scheme  2 χReduced  (a) single offset  1 2 3  (b) single offset with gradient  Description  ω˙  M (M )  ω (◦ )  e  (◦ /yr)  a1 (lt s)  T0 (MJD)  1.291 1.283 1.284  0.0107(2) 0.0106(2) 0.0106(2)  2.48(8) 2.45(8) 2.45(8)  188.816(1) 188.816(1) 188.816(1)  0.00245730(3) 0.00245731(4) 0.00245731(4)  12.0320727(2) 12.0320727(3) 12.0320727(3)  50944.75684(3) 50944.75683(3) 50944.75683(3)  1 2 3  1.008 1.026 1.028  0.0099(2) 0.0099(2) 0.0099(2)  2.21(8) 2.21(8) 2.21(8)  188.817(1) 188.817(1) 188.817(1)  0.00245746(4) 0.00245745(4) 0.00245745(4)  12.0320746(3) 12.0320745(3) 12.0320745(3)  50944.75686(3) 50944.75686(3) 50944.75686(3)  (c) two−bin model  1 2 3  1.006 1.022 1.025  0.0100(3) 0.0100(3) 0.0100(3)  2.26(9) 2.25(9) 2.26(9)  188.817(1) 188.817(1) 188.817(1)  0.00245741(4) 0.00245740(4) 0.00245740(4)  12.0320746(3) 12.0320745(3) 12.0320745(3)  50944.75686(3) 50944.75686(3) 50944.75686(3)  (d) 7 offsets  1 2 3  1.003 1.021 1.022  0.0102(3) 0.0102(3) 0.0102(3)  2.32(12) 2.31(12) 2.31(12)  188.817(1) 188.817(2) 188.817(2)  0.00245745(5) 0.00245744(5) 0.00245743(5)  12.0320745(3) 12.0320744(3) 12.0320744(3)  50944.75686(3) 50944.75686(3) 50944.75686(3)  Table 3.3: J0621+1002: Models for Dispersion Measure (DM) and corresponding ω˙ and M values. See Figure 3.3 for a comparison of the DM offset values. See Figure 3.4 for a comparison of the post-fit residuals for each model. Note that these values use only the 2006 epochs that have dual-frequency TOAs. Two days (MJDs 54005 and 54008) did not have data at 430 MHz, and thus were removed from this DM assessment. The value of ω˙ changes slightly when the single-frequency days are included in the fit.  52  Fit scheme 1: fitting first offset but fixing polynomial Fit scheme 2: fixing first offset and fitting polynomial Fit scheme 3: fitting first offset and fitting polynomial  3.2.2  Measuring the periastron advance, ω˙  The goal of the 2006 observing campaign was to update our timing model to better constrain the orbital parameters of the system, including a more precise measurement of the periastron advance ˙ and potentially a detection of Shapiro delay in the system (s and r). Having decided on the (ω) single-bin-with-gradient model for the DM of the 2006 data, we fit the combined set of TOAs using the TEMPO software package, fitting for spin and astrometric parameters and also for binary orbital parameters using the Damour and Deruelle (1986) theory-independent model for orbital motion. We obtained the set of parameters shown in Table 3.1, including five Keplerian ˙ which has an updated value of 0.0102(2)degrees per parameters and the advance of periastron, ω, year. Note that the error bars in Table 3.1 are not doubled from the values output by the TEMPO package (as is typically done when significant reweighting of the data is required, and as is done in this thesis in the chapter on J1906+0746). The reason for this is to maintain consistency with the results from Splaver et al. (in which the TEMPO error bars were not doubled), and also because the instrumental errors for the ASP data in this analysis are mostly reliable due to the 8-bit sampling afforded by ASP (see Ferdman et al. 2010). We note that the error on ω˙ has been reduced from 0.0008◦ year−1 (in Splaver et al. 2002) to 0.0002◦ year−1 with the addition of data from the 2006 Arecibo campaign. This amounts to decreasing the error on ω˙ to a factor of 0.25 of the previous error, which is lower than the factor of 0.4 predicted by Equation 3.1. We attribute the additional decrease in uncertainty to the use of ASP, which dedisperses coherently, has 8-bit sampling and increased sensitivity over the machines used to collect the earlier data.  53  3.2.3  Calculating the total mass  The value of ω˙ has lowered slightly from the value listed in Splaver et al. If we assume general relativity is the correct theory of gravity, and that the observed apsidal motion is completely attributable to general relativistic effects (as opposed to distortions of the secondary star; e.g. Smarr and Blandford 1976, which was considered and dismissed in Splaver et al. 2002), the total mass is related to ω˙ through equation 1.16 (Damour and Deruelle 1985), which can be rearranged to find that: M=  1 T  ω˙ 3  3/2  Pb 2π  5/2  1 − e2  3/2  (3.3)  Our reduced value of ω˙ thus translates into a lowering of the total system mass, as M ∝ ω˙ 3/2 . Accordingly, we calculate an updated total system mass of 2.32(8)M (as compared with 2.8(3)M from Splaver et al.). In addition to the theory-independent (Damour and Deruelle 1986; DD) model, we also fit a separate model assuming general relativity to be correct (Taylor 1987b; Taylor and Weisberg 1989, DDGR), where the total mass (M=m1 +m2 ) and companion mass (m2 ) are free parameters. The general relativity model finds the best fit value of M to be 2.33 ± 0.08 M (while fixing m2 at 0.76M , the most likely value as determined in §3.3). While using the maximum likelihood value of m2 from the theory-independent model to calculate the value of M determined by GR is somewhat circular, it cannot be avoided because the two masses are not separately well-measured and is still useful as a consistency check on our models and calculations. We find that the two values are indeed consistent.  54  3.3  Pulsar and companion masses  The masses of the pulsar and companion can be constrained using the Keplerian mass function f , which relates the total system mass to the inclination angle of the system:  f=  (m2 sin i)3 (m1 + m2 )2  =  4π 2 (a1 sin i)3 = 0.027026849(2)M G Pb2  (3.4)  Since we observe the projected semimajor axis a1 sin i and the binary orbital period Pb , we can calculate the value of f from those fitted parameters, and we are left with a relation between the masses and the inclination angle (Equation 3.4). Thus, an understanding of the probability density functions (PDFs) of m2 and cos i will provide an understanding of the PDFs of m1 and m2 . Following the method outlined in the appendix of Splaver et al. (2002), we performed a grid over values of the cosine of the inclination angle and the companion mass m2 in order to find the pair of those parameters that best describes the data. We used uniform priors in cos i because, a priori, our only constraint on the inclination angle for this system is that it cannot be close to edge-on (as we do not see a significant Shapiro delay in the timing residuals). We therefore assume that all projections of the orbit onto the plane of the sky (i.e. cos i; see Figure 1.6) are equally likely. We also assume a uniform prior for the companion mass; since we assume the companion is a WD, its maximum possible mass is set by the Chandrasekhar limit of 1.4M , and we have 0 < m2 < 1.4M . We performed a regular 200 by 200 grid in cos i and m2 , allowing 0 < cos i < 1 and 0 < m2 < 2M (with m2 extending past the Chandrasekhar limit so as to note the behaviour of the contours and PDFs in this region). For any given point in the grid, we used the inclination angle and companion mass to derive the corresponding ω˙ and Shapiro delay (r and s) values. We then fixed r, s, and ω˙ in the timing model but allowed all other parameters to vary, and computed the χ 2 value that resulted. 55  Figure 3.5: J0621+1002 companion mass versus pulsar mass. The χ 2 contours were obtained by running ˙ r, and s at each point while fitting the rest TEMPO on a regularly spaced grid of m2 and cos i. We fixed ω, of the parameters, and calculated the χ 2 resulting from running TEMPO at each point. The above contours were then calculated by transposing the m2 and cos i grid to a grid in m1 and m2 (as described in §3.3). ˙ The solid curved lines are the cutoff values for The dashed lines are the 1- and 2- σ values limits for ω. different inclination angles (with the shaded region below indicating i of 90◦ ). The upper shaded region is defined by the cutoff of m2 equal to 1.4M , as the companion is a white dwarf and has an upper mass limit dictated by the Chandrasekhar Limit, though we note that this limit depends slightly on the composition of the compact object.  56  Figure 3.6: Probability density functions (PDFs) for parameters m1 (pulsar mass, top), m2 (companion mass, middle), and cos i (cosine of the inclination angle, bottom) for J0621+1002. These were produced using the procedure explained in the Appendix of Splaver et al. 2002. For each PDF, the most likely value and the values containing 68% of the probability are indicated by vertical lines. The shaded region contains 68% of the probability around the most likely value. The values are tabulated in Table 3.4.  57  Once we had this grid of χ 2 values over cos i and m2 , we found the minimum χ 2 value, χ02 . We then calculated the likelihood at each point in the grid, again following Splaver et al. (2002): p ({t j }|m2 , cos i) =  1 exp −∆χ 2 2  (3.5)  where ∆χ 2 = χ 2 (m2 , cos i) − χ02 and {t j } are the data. This yielded the contour plot shown in Figure 3.5 (top panel), where we show contours enclosing 68% and 95% of the probability in the region 0 < m2 < 1.4M . We used the cos i - m2 grid to produce a second grid in the pulsar mass m1 and the companion mass m2 . To do this, we calculated the value of m1 at each point in the cos i-m2 grid, using Equation 3.3 (and the fact that m1 = M − m2 ). We binned the data along m1 and m2 to obtain a regular 60 by 60 grid in m1 and m2 (with the requirement of a non-zero likelihood at each point), and normalized each bin by the number of points in that bin, effectively averaging the likelihood over all (m2 ,cos i) points contained within a particular bin. We then plotted contours containing 68% and 95% of the probability, shown in Figure 3.5 (bottom panel). In both grids, the grey regions are those that we have excluded as possible solutions: the top region in both plots is excluded by the assumption that the companion is a white dwarf (and thus has m2 < 1.4M ), and the bottom region in the m1 - m2 grid is excluded from the requirement that sin i ≤ 1 (and as a 3/2  result, m1 ≤ m2 f −1/2 − m2 , from Equation 3.4). We have plotted lines of constant inclination in the m1 - m2 plot, which were obtained by fixing the inclination angle and solving Equation 3.4 for m1 in terms of m2 . The total mass was then calculated from the value of ω˙ and errors on ω˙ obtained from our ultimate timing solution using Equation 3.3, and plotted as the dashed, straight lines in the figure. We calculated probability density functions (PDFs) of cos i, m1 , and m2 to find the most likely values and the corresponding 68% confidence levels. To calculate the probability density 58  Estimated Parameter Pulsar Mass, M1 (M ) . . . . . . . . . . . . . . . . . . . . Companion Mass, M2 (M ) . . . . . . . . . . . . . . . Inclination Angle, i (degrees) . . . . . . . . . . . . . .  Value from PDF 1.53+0.10 −0.20 0.76+0.28 −0.07 24+19 −0  Splaver et al. value 1.70+0.32 −0.29 0.97+0.27 −0.15  Table 3.4: 68% confidence estimates of the pulsar and companion masses and inclination angle for J0621+1002. Our updated values, in the first column, include the data from Splaver et al. 2002 and the 9-day observing campaign taken for this thesis in 2006. The second column lists the 68% limits reported in Splaver et al. 2002  functions (PDFs) of cos i and m2 , we used the cos i - m2 grid to marginalize p (m2 , cos i|{t j }) (the joint posterior probability density function of m2 and cos i). We then used the m1 − m2 grid described in the previous paragraph to similarly produce the PDF of m1 (Figure 3.6, top panel). The corresponding estimates of the pulsar and companion masses and the inclination angle are listed in Table 3.4.  3.4  Results and implications  We have determined 1σ values of the pulsar and companion masses to be 1.53+0.10 −0.20 M and 0.76+0.28 −0.07 M , respectively, which are both lower than previously reported in Splaver et al. 2002  (though within 1σ of the previous values; see Table 3.4 for a comparison). The slight lowering of ˙ is a result of these values, reflecting the smaller measured value of the periastron advance, ω, having data that spans a longer baseline (ten years as opposed to five years in 2002), ultimately providing a more robust and believable result, with a decreased error that is somewhat better than our prediction from Equation 3.1. The 68% contours in Figure 3.5 show no detection of the Shapiro delay, but we have obtained a 95% upper limit of 43◦ on the inclination angle of the system. Our updated measurements of m1 and m2 allow us to better discuss the potential formation 59  mechanisms of the binary system. We find the pulsar and companion masses to be less massive than suggested by the Splaver et al. (2002) result. If we assume that this long-period system has undergone a disk accretion evolutionary scenario with short-lived periods of hyper-accretion as in Tauris et al. (2000), we can infer from the modest pulsar mass that only a moderate amount of mass has been transferred in this process. This is qualitatively consistent with the pulsar being only mildly recycled, given the standard assumption that there is a correlation between the amount of mass transferred by the companion during the accretion process and the final spin period of the pulsar (though population studies suggest that a more complex model is required to explain the full distribution of MSPs; e.g. Kiziltan and Thorsett 2009, Kiziltan et al. 2010). It is clear that further study of IMBPs is required in order to confidently know how they fit into our current understanding of MSP evolution. While the above evolutionary path does explain the measured properties of J0621+1002, the discovery of new long-period IMBPs capable of precise mass measurements is necessary in order to develop a complete understanding of this rare type of system.  60  Chapter 4  The young, relativistic binary pulsar J1906+0746 4.1  Introduction  As rare windows into stellar systems that have undergone at least one supernova, the pulsars in binary systems can be observed with high precision, yielding a wealth of information about the endpoint of stellar evolution. We can fit timing models to the pulsar’s times of arrival (TOAs) to accurately describe the orbital motion of the pulsar around its companion, which can lead to constraints on the masses of the pulsar and its binary companion. In combination with other information about the system, such as the spin period and period derivative of the pulsar, the orbital parameters, and the nature of the companion, these mass estimates provide rare evidence of the mass transfer history of the binary pair, and can act as a tool in understanding the evolutionary processes that have produced the system. In the vast majority of observed binary pulsar systems, we see the first-born compact object as a pulsar. The pulsars usually have short spin periods and low spin-down rates, meaning that they are extremely stable rotators with characteristic ages of ∼ 10Gyr. Because recycled pulsars are so stable and therefore can be seen as radio pulsars for comparatively long periods of time, we see many more of them than young pulsars in binary systems. The millisecond pulsars (MSPs), which  61  have spin periods of about 1-10 ms, are usually found in low-mass binary pulsar (LMBP) systems around low-mass white dwarfs (WDs), whereas pulsars with more massive WD companions, neutron star (NS) companions, generally have longer spin periods (10-200 ms) and have lower characteristic ages (e.g. Lorimer 2008). This is consistent with a spin-up picture where the amount of mass transferred from the companion to the pulsar depends largely on the length of the mass-transfer stage, and hence, on the mass of the companion (Alpar et al. 1982). The common element in all these systems is that the observed pulsars show evidence of having been spun up by their companion (i.e. they have higher characteristic ages and lower magnetic fields than the general pulsar population). J1906+0746 is one of only a handful of known doubly-degenerate relativistic binaries where the pulsar is believed to be the younger of the two compact objects. The other known systems include the WDs binaries J1141-6545 and B2303+46, and the second pulsar in the double pulsar system J0737-3039B (see Table 4.1 for a list of known binary pulsars in relativistic orbits). The 144-ms pulsar J1906+0746 was first discovered in the quicklook results from precursor PALFA observations (see Chapter 2) in 2004 (Lorimer et al. 2006). When 1906+0746 was retrospectively detected in a 35-minute observation from the Parkes Multibeam Survey collected in 1998, it became apparent from the high degree of acceleration that the pulsar was in a shortperiod binary orbit around a companion. Follow-up observations with the 76 m telescope at Jodrell Bank found it to be in a 3.98-hour binary orbit with an eccentricity of 0.085, making J1906+0746 the relativistic binary pulsar with the second-shortest known orbital period (after the double pulsar J0737-3039A/B whose orbit is 2.4 hours). It also was clear from the Parkes data that the geometry of the system changes on a short timescale, as the pulse profile in 2004 contained an interpulse component that had not been visible at the earlier epoch. These profile changes are likely due to geodetic precession, the general relativistic effect that causes spinning objects to precess about the total angular momentum vector of the system (Damour and Ruffini 62  1974, Barker and O’Connell 1975), an effect seen in other binary pulsars (J0737−3039 B (Breton et al. 2008), J1141−6545 (Hotan et al. 2005, Manchester et al. 2010), B1534+12 (Stairs et al. 2004), and B1913+16 (Weisberg et al. 1989)). J1906+0746 is a young pulsar, with its high spin-down rate (P˙ ∼ 2 × 10−14 s/s) and a characteristic age τc of roughly 112 kyr. As the lifetimes of young pulsars are much shorter than those of recycled or normal pulsars, it is relatively rare to see young pulsars in binary systems. If the companion is another compact object, the pulsar would have evolved more recently than its companion, and would be the newer of the two objects, as opposed to the old, recycled pulsars seen in the majority of pulsar binaries. Seeing a young pulsar in a binary system allows us to observe binary systems from a perspective different from the typical recycled scenario, which opens the possibility of learning about the binary evolution of such systems from a rare perspective. Since the discovery of J1906+0746, it has been monitored with the Arecibo, Green Bank, Nanc¸ay, Jodrell Bank (Lovell) and Westerbork Telescopes over a time span of five years since its initial detection in the PALFA survey. We here present here the follow-up timing analysis using the data from the Arecibo, Green Bank, and Nanc¸ay telescopes. This analysis allows us to measure our currently-known ephemeris to a higher precision, and also to measure two more post-Keplerian orbital parameters, giving us over-constrained values for the pulsar and companion masses if we assume general relativity.  4.2  Observations and data  For the timing follow-up of this pulsar, we have obtained data using the Arecibo 305-metre telescope in Puerto Rico and the Green Bank Telescope (GBT) in West Virginia, and we also 63  Pulsar  Period (ms)  Pb (days)  Eccentricity  Pulsar Mass (M )  Companion Mass (M )  Companion Type  1.3381+0.0007 −0.0007  NS  Young Pulsars in Relativistic Binaries J0737-3039B1  2773.5  0.102  0.08778  J1141-65452  393.9  0.198  0.17188  J1906+07463  144.1  0.166  0.08530  B2303+464  1066.4  12.340  0.65837  1.2489+0.0007 −0.0007 1.27+0.01 −0.01 1.323+0.011 −0.011 +0.10 1.34−0.10  1.02+0.01 0.01 1.290+0.011 −0.011 +0.10 1.3−0.10  WD WD or NS WD  Recycled Pulsars in Relativistic Double Neutron Star Binaries J0737-3039A1  22.7  0.102  0.08778  B1534+125  37.9  0.421  0.27368  J1756-22516  28.5  0.320  0.18057  B1913+167  59.0  0.323  0.61713  B2127+11C8  30.5  0.335  0.68139  1.3381+0.0007 −0.0007 1.3332+0.0010 −0.0010 +0.017 1.312−0.017 1.439+0.0002 −0.0002 1.358+0.010 −0.010  1.2489+0.0007 −0.0007  1.3452+0.0010 −0.0010 +0.018 1.258−0.017 1.3886+0.0002 −0.0002 1.3540.010 0.010  NS NS NS NS NS  Recycled Pulsars in Long-Period (Pb >1 day) Double Neutron Star Binaries J1518+49049  40.9  8.634  0.24948  0.72+0.51 −0.58  2.00+0.58 −0.51  NS  Total Mass (M ) J1753-224010  95.1  13.638  0.30358  Not measured  NS  J1811-173611  104.2  18.779  0.82801  2.56+0.09 −0.09  NS  J1829+245612  41.0  1.176  0.13914  2.5+0.2 −0.2  NS  Table 4.1: Known pulsars in relativistic and/or double neutron star binary systems 1 Kramer et al. 2006; 2 Bhat et al. 2008; 3 this thesis; note that J1906+0746 may have a neutron star or a white dwarf companion; 4 Thorsett et al. 1993, Kulkarni and van Kerkwijk 1998; 5 Stairs et al. 2002; 6 Ferdman 2008; 7 Weisberg et al. 2010; 8 Jacoby et al. 2006; 9 Janssen et al. 2008; 10 Keith et al. 2009; 11 Corongiu et al. 2004; 12 Champion et al. 2005  64  include data from the Nancay telescope. The author was responsible for the Arecibo and GBT observations between 2005 and 2009, having submitted many of the telescope proposals and having done most of the observing for those projects. Arecibo Observations Data from the Arecibo telescope were taken using the L-Wide (L-band) receiver, which has a frequency range of 1.15 - 1.73 GHz and a sensitivity of 9-11 K/Jy, and system temperature of 25-40 K1 . It has a dual linear native polarization and a beam size of 3.1x3.5 arcminutes at 1.42 GHz. We used two backends simultaneously: the Wideband Arecibo Pulsar Processors (WAPPs) filterbank machine (Dowd et al. 2000), and the Arecibo Signal Processor (ASP) coherent dedispersion machine (Demorest 2007; Ferdman 2008; see §1.3.1 for more details on the coherent dedispersion process). Wideband Arecibo Pulsar Processor (WAPP) The WAPPs are four individual machines, each able to record 100 MHz of bandwidth for each of two polarizations. In our observations, we used only three of the four WAPPs to collect data, allowing the fourth IF to be instead passed to ASP for collection there. The three WAPPs, centred at 1170 MHz, 1370 MHz, and 1570 MHz with a bandwidth of 100 MHz each, accumulated 512 lags at a rate of 120µs. The two polarization channels were autocorrelated online, and the lags were saved to disk. They were subsequently converted to spectra before being summed and folded at a local value of the pulsar’s period. Arecibo Signal Processor (ASP) Data were taken using the ASP coherent dedispersion machine with a 16-MHz bandwidth, using four 4-MHz channels, centred on 1400 MHz. The data were folded using the best local value for the pulse period, and were collected using either 60- or 30-second integration times (the earlier epochs had longer integration times than the later epochs). 1 http://www.naic.edu/∼astro/RXstatus/Lwide/Lwide.shtml  65  Green Bank Observations Data from the GBT were taken using the L-band receiver, which has a frequency range of 1.15-1.73 GHz. The receiver has a gain of 2.0K/Jy and a system temperature of 20K above the background temperature, and a beam size of 9 2 . Pulsar Spigot The GBT data were collected with the Pulsar Spigot card (Kaplan et al. 2005) using the wideband spectrometer (Escoffier and Webber 1998). These data were collected in 1024 channels over 800 MHz, of which ∼600 were used (as the size of the bandpass from the receiver is smaller than the total bandwidth of the spectrometer). Green Bank Astronomical Signal Processor (GASP) The GASP coherent dedispersion machine, which is a clone of ASP at the GBT, collected 64 MHz of bandwidth split over sixteen channels centred at 1400 MHz. The data were dedispersed and folded in each channel using the best available value for the pulse period, and were collected using 60-second integrations. Nanc¸ay Observations J1906+0746 was monitored on a weekly basis with the Nanc¸ay telescope near Orl´eans, France, between 2005 and 2009. The pulsar was observed at L-band, centred at 1398 MHz, and was collected using two polarizations. Berkeley-Orl´eans-Nanc¸ay (BON) The Berkeley-Orl´eans-Nanc¸ay (BON) coherent dedispersion machine was used to collect data in four sub-bands over 64 MHz, producing dedispersed and folded profiles, integrated every 2 minutes. The Nanc¸ay data were collected by collaborators Isma¨el Cognard and Gregory Desvignes at the Universit´e d’Orl´eans, (see Desvignes 2009 for more details about the observations). 2 https://safe.nrao.edu/wiki/bin/view/GB/Operate/FrontEnds and http://www.gb.nrao.edu/electronics/GBTelectronics/Receivers/greg.html  66  4.3  Data reduction  The WAPP, ASP and GASP data were flux-calibrated using a noise diode signal injected into the receiver, in each polarization individually. Where good calibration observations were not available, we normalized the flux density in each profile by the root-mean-square (RMS) across the profile for the coherently dedispersed profiles, and we weighted all channels equally for the WAPP filterbank data. A continuum source was used to calibrate the ASP and GASP data for a significant portion of the epochs, and when such data were not available, recorded values of the noise diode temperatures were used. The WAPP data were calibrated using pre-recorded values of the calibrator temperatures in each polarization3 . We note that we originally reduced the WAPP data using a version of the SIGPROC code that we now know swapped the signals from the two polarizations. We have re-reduced the WAPP data, applying the appropriate calibrator temperatures to each IF before summing them. The polarizations were summed, and for the timing and profile studies in this thesis, the total signal, summed across all frequency channels, was used. Five-minute time integrations were used for all Arecibo and GBT data to create time-averaged pulse profiles. The ASP and GASP data were reduced using the data reduction package ASPFitsReader (Ferdman 2008). The WAPP data used the SIGPROC4 and SIGFOLDMSP (written by I. Stairs) data reduction packages. Since J1906+0746 is in a relativistic binary orbit that changes on a short timescale and has a high degree of timing noise, it is imperative that the signal is always folded with an up-to-date ephemeris. This, however, can only happen once we have an adequate timing solution for the epoch in question. For this reason, once we obtained sufficient Arecibo and GBT data to compute a new ephemeris that extended to the the data included in this thesis, we went back and re-folded the data using that updated ephemeris, so as to ensure that the data had the highest signal-to-noise 3 http://www.naic.edu/  phil/cals/cal.datR5  4 http://sigproc.sourceforge.net/  67  possible. This was fully possible for the WAPP data, which were recorded and stored as a time series and folded offline; however, the coherently dedispersed ASP and GASP data were recorded as a series of 30- or 60- second integrated pulse profiles (which were subsequently summed to create 5-minute integrated profiles). Although we were able to re-align the ASP and GASP profiles using the updated ephemeris, we are not able to correct for the intra-integration smearing that is present within each 30- or 60-second profile that was recorded to disk. We note that there is some overlap between the ASP and WAPP data for timing; we used the WAPPs centred at 1170MHz, 1370MHz, and 1570MHz along with the ASP data centred at 1400MHz. While there is some redundancy, the overlap is not too bad as the WAPP centred at 1370MHz has a significantly wider bandwidth than ASP. Also, we did not use the Spigot data in our timing analysis for this pulsar; the only GBT data set that we used in the timing solution was the set of coherently-dedispersed GASP data. The Nanc¸ay profiles were reduced by collaborators at the Universit´e d’Orl´eans using the PSRCHIVE software package5 (Hotan et al. 2004). These data were not flux-calibrated; they were normalized by the RMS of the noise.  4.4  Profile evolution  The profile of 1906+0746 changes drastically over time. Since its discovery in 2005, there has been a prominent, yet ∼ 80% weaker, interpulse at roughly 180 degrees from the 2004 main pulse. It should be noted, however, that the retroactive discovery of 1906+0746 in data from 1998 from the Parkes Multibeam Survey showed no such interpulse, indicating that the geometry of the system has changed significantly over the course of the past ten years. We attribute this profile evolution to geodetic precession, a general relativistic effect which 5 http://psrchive.sourceforge.net/  68  changes the system geometry, and hence, our viewing angle. Geodetic precession is the precession of the pulsar’s spin angular momentum vector about its total orbital angular momentum vector, and is measurable in binary pulsar systems involving relativistic speeds. We can write the following expression for the time-averaged precession rate of the pulsar system (Barker and O’Connell 1975):  Ωgeod = T  2/3  2π Pb  5/3  1 m2 (4m1 + 3m2 ) 1 − e2 2 (m1 + m2 )4/3  (4.1)  where T = GM /c3 = 4.925490947µs, m1 and m2 are the pulsar and companion masses, respectively (in solar masses), Pb is the orbital period, and e is the eccentricity. For J1906+0746, the geodetic precession period is ∼ 169 years, or a rate of 2.1 degrees per year. As our baseline for observing this system spans more than five years, we expect that the geometry has shifted by roughly ten degrees since its discovery in 2004. The geometry has changed even more significantly - by roughly 20◦ , since the archival data in the Parkes Multibeam Survey in 1998, consistent with the vastly different shape of the pulse profile at that epoch. Although it is interesting that we can see the secular profile changes in J1906+0746, the changing profile shape poses a problem in the creation of times-of-arrival (TOAs) for the system. The time-varying shape allows for ambiguity in the fiducial point of the profile, which translates into additional timing noise for the system. The fiducial point of a pulse profile, usually defined by the peak of the fundamental frequency, determines the given time of arrival (TOA), and so if the fiducial point of a pulse profile changes with time, we need to account for this in order for the recorded value of the TOA to correspond to the actual time of the pulse arrival time. In order to ensure that the fiducial point of each profile is consistent, and to reduce the resulting timing noise, we have decided to 1) use a series of gaussian standard profiles developed from the well-modelled epochs of ASP, GASP and WAPP data, and 2) align the gaussian templates as  69  described in section §4.5.  4.5  Gaussian fitting and template evolution  To understand the profile evolution and to create TOAs that are consistently aligned from epoch to epoch, we modelled the standard profile for each individual observation using gaussian components. We summed up the data for each epoch, and fitted sets of 1, 2, or 3 (as necessary) gaussians to each of the pulse and each interpulse (separately), using the gaussian fitting package BFIT (Kramer et al. 1994; see Figure 4.1 for an example of the gaussian decomposition for one of the epochs of GBT observations with GASP). We experimented with several different methods of aligning the gaussian templates, with the goal of identifying one component that would allow for a consistent alignment from epoch to epoch. We identified the most stable gaussian as the tallest component for most epochs (Component A), and we found that smoothest alignment was achieved by keeping the phase of that component constant for most of the epochs (as in Figure 4.2, which shows this behaviour for a subset of the ASP and GASP summed profiles). For the modified Julian day (MJD) range from 54700 onwards, we could not reliably identify Component A in the profiles, and so instead aligned the tallest component for those epochs (Component B) and introduced a phase shift to align Component B in those epochs with Component B from the last epoch with a well-defined Component A. The full collection of gaussian-modelled profiles is shown in Figure 4.3. This method of aligning the profiles seems to produce a fairly monotonic behaviour in the phase of the interpulse (iillustrated by the sloped line in following the interpulse in Figure 4.3). The modelled profiles for ASP and GASP are shown in Figure 4.4; the modelled profiles for the WAPPs are shown in Figure 4.5. These were used as standard profiles for timing.  70  Figure 4.1: Example of a summed profile using the GASP coherently-dedispersed data from the Green Bank Telescope (GBT) at 1400 MHz on MJD 54390. The main pulse (left) and interpulse (right) were each modelled separately using three gaussian components, shown above. The data are plotted in black, the individual components are plotted in blue, and the sum of the components is plotted in red.  71  Figure 4.2: Illustration of how the gaussian profiles were aligned. The thick black vertical line at phase 0.25 marks the location of the fiducial point. The vertical black line at a phase of 0.75 is used to trace the location of the interpulse over time. The red lines represent the main pulse’s component − usually the tallest − that was chosen to define the fiducial point for that profile. These components were aligned to the fiducial point at phase 0.25, except for those epochs at MJD 54700 or later − where the corresponding component seemed to have disappeared − which were aligned with respect to a different component and shifted accordingly. The alignment of the profiles for the post-MJD 54700 is marked by the vertical line extending from MJD 54700 to 55300 (note that this vertical line marks is not centred on the red peak, as it is on a bin boundary and is on one side of an even peak). The blue lines are the other gaussian components in the profiles; the number of components required for each of the main pulse and interpulse varied from epoch to epoch, which explains why some of the epochs in this plot have two main pulse components while others have three (and, similarly, why the interpulse has either one or two components, depending on the epoch). Here, multi-gaussian fits are shown for a subset of the summed profiles for coherently dedispersed profiles at 1400 MHz taken using the Green Bank Telescope (GASP) and the Arecibo telescope (ASP). The GASP profile evolution is shown for a subset of data ranging from MJD 53748 (July 2005) to 54836 (January 2009), and the ASP profile evolution is shown for a subset of data from MJD 53872 (May 2006) to 55046 (August 2009).  72  Figure 4.3: The fits of the pulse and interpulse of J1906+0746, based on WAPP (Arecibo; spectrometer, at 1200 MHz (red), 1400 MHz (green) and 1500 MHz (blue)), ASP (Arecibo; coherent dedispersion; magenta, 1400 MHz), and GASP (Green Bank Telescope; coherent dedispersion; cyan, 1400 MHz) observations, from July 2005 to August 2009, each modelled with several gaussian components. The pulses are spaced vertically based on observation date, and the interpulse is magnified by a factor of ten relative to the main pulse. The vertical line for the main pulse (left) illustrates the chosen alignment, whereas the vertical line for the interpulse demonstrates the marked phase shift of the interpulse relative to the main pulse. The gap in data between MJD 54166 and MJD 54390 (for GBT) and between MJD 54178 and MJD 54545 (for Arecibo) is due to maintenance (painting at Arecibo and track repair at the Green Bank Telescope).  73  Figure 4.4: Evolution of the Gaussian construction of coherently dedispersed profiles at 1400 MHz taken using the Green Bank Telescope (GASP; red; 1400 MHz) and the Arecibo telescope (ASP; blue; 1400 MHz). The GASP profile evolution is shown for data ranging from MJD 53748 (July 2005) to 54836 (January 2009), and the ASP profile evolution is from MJD 53872 (May 2006) to 55046 (August 2009). These profiles were created using multiple-Gaussian fits to the data at 1400 MHz. The gap in data between MJD 54166 and MJD 54390 (for GBT) and between MJD 54178 and MJD 54545 (for Arecibo) is due to maintenance (painting at Arecibo and track repair at the Green Bank Telescope).  74  Figure 4.5: The fits of the pulse and interpulse of J1906+0746, based on WAPP (Arecibo; spectrometer) observations at each of three frequency bands (1200 MHz (red), 1400 MHz (green) and 1500 MHz (blue)) from July 2005 to August 2009, each modelled with several gaussian components. The pulses are spaced vertically based on observation date, and the interpulse is magnified by a factor of ten relative to the main pulse. The vertical line for the main pulse (left) illustrates the chosen alignment, whereas the vertical line for the interpulse demonstrates the marked phase shift of the interpulse relative to the main pulse. The gap in data between MJD 54178 and MJD 54545 is due to maintenance (painting).  75  Figure 4.6: Flux density of the main peak of the J1906+0746 pulse profile versus MJD for GASP (black X’s) and ASP (red filled triangles) data. We assumed a 20% error bar on each value.  4.6  2-dimensional beam model  It is possible to use a collection of the gaussian components at different epochs to produce a model of the pulsar’s emission beam (which has been done for other pulsars, e.g. J1141-6545 (Hotan et al. 2005), J0737-3039B (Perera et al. 2010), and B1913+16 (Weisberg et al. 1989)). For this analysis we require reliably flux-calibrated data, and so we have used only the ASP and GASP epochs for which we have good calibration data. We note that the flux density of J1906+0746 has been varying over time, and the flux densities of the main peak are shown for the ASP and GASP epochs that have reliable calibration data. This is shown in Figure 4.6, and we see that the ASP and GASP data produces flux density estimates for the pulsar beam that are consistent with one another. We used the gaussian templates of the available flux-calibrated ASP and GASP data to create a two-dimensional map of the pulsar beam. We first assumed a geometry of the system as  76  determined by the polarimetry of Desvignes (2009), which assumes an inclination angle i of 43 degrees as determined by the timing solution presented in Kasian et al. (2008). Adopting code written by Michael Kramer, we entered the values of the relevant geometrical angles determined by Desvignes (2009) and mapped our observed flux-calibrated profiles onto the corresponding locations on the surface of the pulsar. The result is a two-dimensional map of the emission region corresponding to the main pulse of the pulsar, as shown in Figure 4.7. This may be compared to similar beam maps that have been produced for the two other known young pulsars in compact, relativistic binary systems: J1141−6545 (Manchester et al. 2010) and J0737−3039B (Perera et al. 2010). The two-dimensional beam map for the main pulse of J1906+0746 is somewhat more compact than that of J1141−6545, which extends over a broader range of angles; also, the evolution of the J1141−6545 beam is more regular than that of J1906+0746, which seems to have a patchier structure. By contrast, the beam map for J0737−3039B appears to have a horseshoe shape, different from either of the others. We do acknowledge, however, that as these beam maps are a function of our observed lines of sight through the emission beam, we do not have a complete beam map of either pulsar. In particular, the J1906+0746 beam appears to stop abruptly at the June 2006 line of sight in Figure 4.7. This effect arises from the lack of flux-calibrated, coherently-dedispersed data prior to this time.  4.7 4.7.1  Timing Times of arrival  Times of arrival (TOAs) were created for the profiles resulting from the iterative data reduction process (§4.3), using the gaussian templates created as in §4.5. For the WAPP Arecibo data, we created separate profiles for each epoch and each frequency. The gaussian-derived templates arising from the three WAPPs centred at 1170, 1370, and 1570 MHz, are shown in Figure 4.5. We 77  Line of sight June 2006  Line of sight June 2009  Figure 4.7: Greyscale 2D map of the emission beam of J1906+0746 based on the available flux-calibrated ASP and GASP pulse profiles. Plot was generated using code written by Michael Kramer and adapted to the geometry of J1906+0746 as determined by Desvignes (2009). The dashed lines mark the line of sight through the emission beam at the first and last MJD in the set of profiles used to produce the beam map. The dotted circular lines are centred about the pulsar’s magnetic axis.  78  note that the 1370 MHz WAPP data is somewhat redundant with the ASP data, but as the WAPPs have a larger bandwidth and thus contain more data than just that covered by ASP, we kept it in the analysis. The standard practice in creating TOAs is to rotate the peaks of the standard profiles to a phase of zero (which is normally what defines the fiducial point); here, we did not do this as we wanted to preserve the alignment of the gaussian-derived templates as in Figures 4.4 and 4.5.  4.7.2  TEMPO pulsar timing software package  We began using the package TEMPO2 to fit the TOAs from J1906+0746. This pulsar has a large amount of timing noise that is difficult to decouple from the orbital parameters, which we attempted to model as a polynomial and with FITWAVES (Hobbs et al. 2004), but which we ultimately removed by fitting a large number of offsets between epochs. We eventually switched fitting packages, choosing instead the original TEMPO, when it became clear that we required a better understanding of the error bars on our data than was possible with the newer TEMPO2. Using TEMPO, we re-weighted our data so that the reduced χ 2 of the fit was equal to 1 for each data set (and overall). The overall timing solution is presented in Table 4.2, and the resulting residuals are shown in Figure 4.8. We note that the uncertainties listed for all measured and derived parameters have been doubled from the nominal values given by TEMPO after the data were re-weighted.  4.7.3  Measurement of post-Keplerian parameters  In order to get a handle on the post-Keplerian parameters, we began by using only Arecibo WAPP data. This is because it is the highest signal-to-noise data that we were able to retroactively go back and re-fold with updated ephemeredes so as to eliminate the possibility of introducing 79  Figure 4.8: Residuals are plotted versus MJD for the entire data set. Note the very large timing noise in the pre-fit residuals. Green, blue, and cyan residuals represent WAPP Arecibo data centred at 1170 MHz, 1370 MHz, and 1510 MHz, respectively. Magenta represents the ASP Arecibo data (centred at 1400 MHz), yellow represents the GASP Green Bank data (centred at 1400 MHz) and red represents the Nanc¸ay data, centred at 1336 MHz. Although the 1370 MHz WAPP data is somewhat redundant with the ASP data, the WAPPs have a larger bandwidth and thus contain more data than just that covered by ASP, and we thus we kept it in the analysis.  80  Measured Parameter Right ascensiona , α (J2000.0) . . . . . . . . . . . . . . . . . . . . . . . . Declinationa , δ (J2000.0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spin Period, P (ms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spin Period Derivative, P˙ (×10−18 ) . . . . . . . . . . . . . . . . . . . Epoch (MJD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dispersion Measure, DM (cm−3 pc) . . . . . . . . . . . . . . . . . . . Ephemeris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orbital Period, Pb (days) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Projected Semimajor Axis, x (lt s) . . . . . . . . . . . . . . . . . . . . . Orbital Eccentricity, e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Epoch of Periastron, T0 (MJD) . . . . . . . . . . . . . . . . . . . . . . . . Longitude of Periastron, ω (degrees) . . . . . . . . . . . . . . . . . . Rate of Periastron Advance, ω˙ . . . . . . . . . . . . . . . . . . . . . . . . Time Dilation and Gravitational Redshift Parameter, γ . . Orbital Period Derivative, P˙b (10−12 s/s) . . . . . . . . . . . . . . . Excess Orbital Period Derivative, P˙b (10−12 s/s) . . . . . . . . Total Mass, Mtotal (M ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Companion Mass, m2 (M ) . . . . . . . . . . . . . . . . . . . . . . . . . . . Derived Parameter Total Mass, Mtotal (M ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulsar Mass, m1 (M ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Companion Mass, m2 (M ) . . . . . . . . . . . . . . . . . . . . . . . . . . . Rate of Periastron Advance, ω˙ . . . . . . . . . . . . . . . . . . . . . . . . Time Dilation and Gravitational Redshift Parameter, γ . . Orbital Period Derivative, P˙b (10−12 s/s) . . . . . . . . . . . . . . . Galactic Latitude, l (degrees) . . . . . . . . . . . . . . . . . . . . . . . . . Galactic Longitude, b (degrees) . . . . . . . . . . . . . . . . . . . . . . . Mass Function, fmass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristic Ageb τc = P/2P˙ (kyr) . . . . . . . . . . . . . . . . . . ˙ 1/2 (1012 G) Surface Magnetic Fieldb , BS = 3.2 × 1019 (PP) c Distance to Pulsar , d (kpc) . . . . . . . . . . . . . . . . . . . . . . . . . .  DD Value 19:06:48.97(3) 07:46:28.4(7) 0.144072470100(18) 2.02784(10) 53898 217.780(2) DE405 TT(BIPM) 0.16599304687(10) 1.4199661(17) 0.0853012(5) 53897.85026236(18) 68.2115(4) 7.5841(5) 0.000456(5) -0.52(2)  DD Value  DDGR Value 19:06:48.97(3) 07:46:28.4(7) 0.14407247017(2) 2.02777(10) 53898 217.780(2) DE405 TT(BIPM) 0.16599304689(10) 1.4199556(17) 0.0852989(5) 53897.85026222(18) 68.2111(4)  0.03(2) 2.6133(2) 1.290(11) DDGR Value 1.323(11) 7.5841 0.000455 -0.565  41.5982 0.1470 0.1115673(2) 110 1.7 5.40+0.56 −0.60  0.1115678(3) 110 1.7 5.40+0.56 −0.60  Table 4.2: Timing parameters for J1906+0746 using the data from Lorimer et al. 2006 and additional data with Arecibo, the GBT, and Nancay telescopes used in this thesis. The first column contains the parameters measured and derived using the DD (Damour and Deruelle 1986) model-independent timing model, and the second column contains parameters measured and derived using the DDGR (Taylor 1987a) timing ˙ γ, model, which assumes general relativity to be the correct theory of gravity. The DD model measures ω, and P˙b , which can each be used to put constraints on the masses of the pulsar and companion. The DDGR model measures the total mass M and the companion mass m2 directly, and the post-Keplerian parameters can be derived from the values of the masses. All error values are twice the error bars output by TEMPO. a The position was fit along with the other parameters in TEMPO. b Calculations of B and τ of the pulsar should normally use a value of P˙ that includes corrections from c S the Shklovskii effect and the effect of the differential Galactic acceleration; however, the corrections are unnecessary for the level of precision reported for BS and τc in this Table. c The distance to the pulsar was calculated using the NE2001 model (Cordes and Lazio 2002), which estimates pulsar distances based on the Galactic distribution of free electrons.  81  badly-folded data into the fit (as discussed in §4.3). We removed all long-term timing noise contributions by inserting (and fitting for) timing offsets around each epoch. This allowed us to focus on minimizing the residuals based only on intra-epoch (and hence, orbital-scale) variations. Since there was some ambiguity as to the phase connection when the phase offsets were included, we began by using only the WAPP TOAs, and iterated each TEMPO fit by hand, as opposed to using the option to do this automatically within the software package. This allowed us to ensure that the fits were consistently phase connected from one iteration to the next. Once we were satisfied that we had a phase-connected solution that fit the WAPP data well, we included the ASP, GASP and Nanc¸ay data into the fit. This ensured that the initial values of the model parameters for the fit were reasonable and that when we included all three machines, we were able to obtain a reproducible solution.  Estimating the measurability of γ, the time dilation/gravitational redshift parameter  Our timing solution presented in Table 4.2 includes a measurement of the gravitational redshift/ time dilation parameter γ = 0.000456(5), which is notably lower than the value presented in Kasian et al. (2008), which stated a measurement of γ = 0.0004930(84). This discrepancy led us to investigate the measurability of γ for this pulsar, given the geometry of the J1906+0746 system and our data coverage and quality, with the goal of assessing whether this variation in γ might be expected in any similarly observed data set, or whether it is unexpected (which would suggest that there is a problem with our analysis). As an initial test, we ran TEMPO over different subsets of our data, recording the value of γ for each subset. We noticed that the value of γ changed within our estimated errors over different MJD spans, as is shown in Figure 4.9. To determine whether this is consistent with what we would expect for the geometry of the 82  system and the quality of our data, we simulated a set of data with a similar temporal distribution and integration times for the Arecibo (WAPP) and Green Bank (GASP) data only. We simulated data using our best ephemeris, but added gaussian noise (at the level of the error on the real data sets) to each time of arrival. We did this for four different seed values (for the random number generator used to add the noise), and the resulting γ measurements for those four simulated data sets are shown in Figure 4.10. While most of the γ values do overlap with one another for a given seed, it is possible to have values for different data spans that vary by more than one standard deviation (e.g., looking at Figure 4.10(a)). This suggests that the variation we see in our real data might be reasonably expected for a similarly observed set of TOAs. As a final test to assess our γ measurement’s dependence on the system’s position in its periastron precession cycle (which affects how we view the geometry of the system on the sky), we simulated data over various points spanning one whole cycle. This was previously done for other systems (1913+16 and 1534+12, as well as other generic binary pulsar systems), as in Figure 5 in Damour and Taylor (1992). We used simulated data to create a version of this plot based on the geometry of J1906+0746 (Figure 4.11). From this plot, we see that our set of TOAs (which were collected when ω was ∼ 68◦ to78◦ ) correspond to relatively low theoretical fractional uncertainties, and we are moving towards even better measurability over the next few years. Furthermore, we have simulated TOAs (as described earlier in this section) for J1906+0746 using different values for ω, so as to better understand the variation in the γ values at different points in its precessional period. Figure 4.12 shows the measured values of γ for two simulated sets of TOAs using two different seed values. From Figure 4.12, we find that for each simulated orientation of the pulsar’s orbit, the fractional uncertainty of γ varies in a way consistent with Figure 4.11, and that the measured values based on different subsets of the TOAs are not necessarily consistent with each other within the (doubled) TEMPO error bars. The result of this exercise suggests that the measured value of γ varies over different data 83  lengths, and that there is an intrinsic limit to how well we can hope to measure γ for small data ranges. As it also appears that more data provides a more robust measurement of γ (and the most accurate estimation of the appropriate uncertainty), we conclude that most reliable γ measurement is generally likely to be that computed from the longest data span available. We also note that, based on Figures 4.11 and 4.12, our sensitivity to γ changes over the course of one precession period, and as we are moving from ω ∼ 68◦ (at epoch) to ω ∼ 78◦ (at the end of our data set) and higher with time, we are moving towards better sensitivity to γ in the coming years. We conclude that the value of γ arising from the timing solution in this thesis is likely to be more robust than our previously reported value in Kasian et al. (2008) , and that its inconsistency with the previous value is not altogether unexpected, in light of the simulations presented in this section.  Measuring P˙b , the orbital period derivative  The observed P˙b requires two corrections to arrive at a value which can be compared to the general relativity (GR) prediction. These are the differential Galactic acceleration and the Shklovskii effect. Differential Galactic acceleration causes the relative acceleration of the pulsar system - its location in the Galaxy being different than that of the earth - due to the gravitational potential of the Galaxy to appear as a contribution to P˙b . The Shklovskii effect is the incorporation of the Doppler effect due to the proper motion of the pulsar on the sky into the measured value of P˙b . Although we do not have enough information about the proper motion of the pulsar to measure the magnitude of the Shklovskii effect (Shklovskii 1970), we can estimate the Galactic contribution and thus set a limit on the Shklovskii contribution and therefore a limit on the proper motion of the system. From Nice and Taylor (1995) we can write the orbital period decay as follows:  84  Figure 4.9: TEMPO fit values of γ over various ranges of MJD. For each of these fits, six iterations were performed, fitting for the period, period derivative, basic Keplerian orbital parameters, the rate of precession ω˙ and the time dilation/gravitational redshift parameter γ of the system were fitted. The orbital period derivative P˙b was fit only in the case of the whole data set (the green bar in the centre of the plot); for the rest of the MJD ranges the value for P˙b was fixed at the value obtained from fitting the whole data set. Note that the black rectangle represents the value of γ reported in Kasian et al. (2008).  85  53500  54000  54500  55000  53500  54000  MJD  (a) seed1  53500  54000  (c) seed3  55000  54500  55000  (b) seed2  54500 MJD  54500 MJD  55000  53500  54000 MJD  (d) seed4  Figure 4.10: TEMPO fit values of γ over various ranges of MJD for simulated data with similar spacing to our own. The data were generated using our best ephemeris based on Arecibo and Green Bank data only, but with gaussian noise added on the order of the errors on our real data. The three black horizontal lines represent the real value of γ (centre line) and its error values. The size of the error bars on the real value of γ comes from the timing fits and is not relevant to the simulations.  86  Figure 4.11: Confirmation of Figure 5 from Damour and Taylor [1992]; fractional uncertainties of the post-Keplerian parameter γ, for our best ephemeris for J1906+0746. This was produced by simulating data sets centered at each of 21 orbital phase bins, and measuring γ for each set. Each data set consisted of 21 consecutive TOAs averaged over 5-minute integrations, once every 50 days for 5 years.  P˙bobs = P˙bint + P˙bGal + P˙bShk  (4.2)  where P˙ Gal is the Galactic contribution and P˙bShk is the Skhlovskii contribution to P˙b . The Galactic contribution can be written as: P˙b Pb  Gal  =  a · nˆ c  (4.3)  where a is the differential acceleration in the field of the galaxy, nˆ is the unit vector along our line of sight to the pulsar, and c is the speed of light in a vacuum. The Shklovskii effect (Shklovskii 1970), which produces an always-positive increase in the period derivative of a pulsar due to its observed proper motion across the sky, has a magnitude of:  87  50000  50500  51000  MJD  Figure 4.12: Comparing fitted values of γ for simulated data, at various points in the system’s precession period. In each case, the centre value of the phase is noted, where each data set is 4 years long, each containing 30 fake observations of 1.75-hour and 6-hour (for Arecibo and Green Bank, respectively) using 5-minute integrations. The three black horizontal lines in each plot represents the real value of γ (centre line) and its error values. The size of the error bars on the real value of γ comes from the timing fits and is not relevant to the simulations.  88  P˙b Pb  Shk  = µ2  d c  (4.4)  where µ is the total proper motion of the binary system, and d is the distance to the pulsar. Since we can estimate the Galactic contribution to our measured P˙b and we can assume that P˙bint is equal to the value determined by GR (P˙bGR ), we can write the Shklovskii contribution as follows: P˙b Pb  Shk  =  P˙b Pb  obs  −  P˙b Pb  GR  −  P˙b Pb  Gal  (4.5)  Our best fit value of the orbital decay P˙bobs is -0.52(2)×10−12 seconds per second, which is consistent with the value predicted by GR, P˙bGR = -0.565×10−12 (computed from fitting the DDGR model to our set of TOAs; Damour and Deruelle 1986, Taylor and Weisberg 1989). Following Nice and Taylor (1995), we can write the components of the dot product a · nˆ as (a · n) ˆ planar = − cos b  Θ2o Ro  (a · n) ˆ vertical = 3.24 × 10−11 m s−2  cos l +  β sin l + β 2 2  1.25 z + 0.58 z (z2 + 0.0324)1/2  (4.6)  (4.7)  (Kuijken and Gilmore 1989) where Θ0 = 220km/s and R0 = 7.7kpc are the Galactic rotation speed and Galactic radius (Eisenhauer et al. 2005), respectively, l and b are the Galactic latitude and longitude of the pulsar (measured values from Lorimer et al. 2006 for J1906+0746 and listed in Table 4.2), d is the distance to the pulsar (Lorimer et al. 2006 and listed in Table 4.2), β=  d R0  cos b − cos l, and z = d sin b is the distance from the plane of the galaxy to the pulsar.  For J1906+0746, the planar and perpendicular components are −3.9 × 10−19 and −2.9 × 10−23 , respectively. The resulting expression for the Shklovskii contribution to our measured P˙b can be  89  written as: P˙b Pb  Shk  = µ2  d = c  P˙bobs − P˙bGR Pb  −  1 c  (a · n) ˆ planar  2  + (a · n) ˆ vertical  2  1/2  (4.8)  Using the above values and solving for µ, we can infer a maximum proper motion of 5.5 mas/year or transverse velocity of v = µd ∼ 141 km/s. This is a reasonable limit based on published values of velocities of other relativistic pulsars (e.g. Hobbs et al. 2005), particularly the relativistic binary pulsars with measured proper motions B1913+16 (with a proper motion of 1.6 mas/year or transverse velocity ∼ 75 km/s; Weisberg et al. 2010), B1534+12 (with a proper motion of 25.15 mas/year or transverse velocity ∼ 122 km/s; Stairs et al. 2002), and J0737-3039 (with a transverse velocity of 9 km/s; Deller et al. 2009). Our results imply that the orbital period decay P˙b for J1906+0746 is consistent with the value predicted by general relativity when we assume a proper motion of 5.5 mas/year for the system.  4.7.4  Mass measurements  ˙ the gravitational redHaving obtained reasonable estimates of the advance of periastron ω, shift/time dilation parameter γ, and the orbital decay P˙b for J1906+0746, we can use these three parameters to place constraints on the masses of the pulsar (m1 ) and companion (m2 ). If we use the relationships between the masses and the post-Keplerian parameters that arise when we assume that general relativity is the correct theory of gravity (Equations 1.16, 1.17, and 1.18), each parameter provides an allowed set of (m1 ,m2 ) pairs. These regions can be plotted as regions in m1 - m2 parameter space. The intersection of the allowed regions represents the most likely values of the pulsar and companion masses. The mass-mass diagram for our timing solution of J1906+0746 is shown in Figure 4.13. From the mass-mass diagram, we find that the three measured post-Keplerian parameters provide 90  Figure 4.13: Mass-mass diagram for our best ephemeris for 1906+0746 using Arecibo WAPP and ASP data from MJD 53534 to 55046, Green Bank GASP data from MJD 53552 to 54987, and Nanc¸ay data between MJD 53527 and 54870. The lines represent the values of m1 and m2 allowed by the three measured post-Keplerian parameters: ω˙ (the solid line), γ (the dotted lines) and P˙b (the dashed lines). The value of P˙b used here includes the Galactic correction calculated in §  91  consistent values of the pulsar and companion masses. These regions are also consistent with the masses predicted by general relativity. When we fit our TOAs to the DDGR (Damour and Deruelle 1986, Taylor and Weisberg 1989) GR binary model, we obtain estimates of m1 = 1.323(11)M and m2 = 1.290(11)M (shown as a dot in Figure 4.13), which falls within the overlapping regions from the post-Keplerian parameters’ constraints.  4.8  Dispersion measure variations  We used the WAPP data to investigate the DM variation over time because it contains more spectral information (512 lags, which can produce up to 512 frequency channels) than do the ASP and GASP data (which have a maximum of 64 channels) and can thus provide a better estimate of the DM using data from a short time interval.  4.8.1  Secular DM variation  For each epoch where we had WAPP data for J1906+0746, we used TEMPO to fit for the DM using only TOAs from that day. We used our best global timing solution and allowed only the DM to vary for any given epoch. Figure 4.14 shows the resulting DM values at each epoch. The error bars are too small to be seen, but they are not representative of the true uncertainty on the DM values, as we have fixed all other fit parameters in order to observe the behaviour of the DM. We also note that while there are overall variations in the DM over time, there does not appear to be an overall long-term behaviour that lends itself to being included in our timing analysis in a meaningful way. Also, it is possible that the effects we do see in DM variation may be explained in part by a profile evolution that varies with frequency.  92  Figure 4.14: DM vs MJD for all epochs where WAPP data was available for J1906+0746. We find that the secular variation in DM does not warrant including the variations into our timing model. We note that the particularly low DMs measured for MJD 53810 may be explained in part by profile evolution that varies with frequency.  93  4.8.2  Orbital DM variation  The measured DM of a pulsar in a binary system may vary with orbital phase if there is an asymmetric distribution of plasma in within the binary orbit or if the companion has a substantial atmosphere through which the pulsar emission beam must travel. Variations in DM over orbital phase have been seen in several binary pulsars (e.g., B1957+20 (Fruchter et al. 1995), and J20510827 (Stappers et al. 2001)). For this reason and in an attempt to distinguish between a neutron star and a less compact companion, we investigate the behaviour of the DM of J1906+0746 over orbital phase. For each epoch where we had WAPP data, we split the TOAs into 16 bins across the observation, and calculated the DM for each of the 16 bins individually, while fixing the other timing parameters at the best-fit values determined in §4.7. We then plotted the value of the DM versus orbital phase for each epoch, as in Figure 4.15. We find that while the variations at most epochs are somewhat significant within the stated error bars (which we have doubled from the values reported with TEMPO, as is the standard practice in pulsar timing), we found that there were no compelling overall trends in DM over the course of an orbit. We found that the epochs at MJD 54020 and 54178 showed the possibility of significant DM trends over the course of an orbit; however, when we split those epochs into 32 and 64 phase bins (Figure 4.16), only MJD 54020 showed mild evidence of a real trend over the course of the observation. We conclude that overall, the data show no significant evidence of orbital DM variations; this does not rule in or out any type of companion.  4.9  Orbital aberration  While we attribute the profile changes that we see in §4.4 to geodetic precession, which is an effect seen only in strong gravitational fields, it is also possible that the special relativistic effect 94  Figure 4.15: DM versus orbital phase for all epochs where WAPP data was available for J1906+0746. The bottom plot shows the DM over orbital phase for all of the epochs together. The outliers in this plot correspond to the outliers in Figure 4.14, and may be explained in part by profile evolution that varies with frequency.  95  Figure 4.16: DM versus orbital phase for two epochs (MJDs 54020 and 54178) showing the largest DM variation. The WAPP data were used to calculate the DM at each phase bin.  96  of aberration may contribute to the observed profile changes of a pulsar in a binary orbit (Damour and Taylor 1992, Rafikov and Lai 2006). Aberration on an orbital timescale, which has been measured in the double neutron star B1534+12 (Stairs et al. 2004), arises from the relativistic velocities with which the pulsar and companion travel in their orbit. Using Equation 1.11 we find that the velocity of the pulsar at periastron is similar for J1906+0746 and B1534+12, at v p ∼ 0.001c. Thus, given the detection of orbital aberration in B1534+12, we might reasonably expect a similar detection in this pulsar. The observed result has two components: a longitudinal delay that shifts the pulse profile in phase while keeping the shape of the pulse intact, and a latitudinal delay that shifts the observed emission angle with respect to the pulsar’s spin axis (Rafikov and Lai 2006). Since the pulsar profile shape is thought to be related to the emission geometry, the latter may result in measurable profile changes over the course of a binary orbit. We do not expect to detect the longitudinal component of the delay, as its effect on the profile over the course of an orbit is a uniform shift in phase which is independent of the emission pattern (and hence independent of the profile shape) and would simply be absorbed into the overall timing results; however, the latitudinal component of the delay manifests as a change in profile shape that varies over the course of an orbit, and thus may be detectable on an orbital timescale. If detected, we can combine the profile changes due to orbital aberration with the secular changes due to geodetic precession to put limits on the geometry of the system (Stairs et al. 2004). The polarimetry data for J1906+0746 have been fit to the classical rotating vector model (RVM) by Desvignes (2009), which resulted in the following measured angles (assuming an inclination angle of i = 43◦ , from timing results presented in Kasian et al. (2008)): the current angle between ◦+51 0 the spin and magnetic axes, α = 80◦+4 −6 ; the geodetic precession phase ΦSO = 109−79 ; and the  precession cone opening angle (or misalignment angle) δ = 110◦+21 −55 . A detection of orbital aberration could constrain further angles and would allow for a measurement of the geodetic 97  precession period independent of the profile beam model, which would provide a consistency check.  4.9.1  Observations  To search for profile changes on an orbital timescale, we require several days’ worth of complete orbital coverage collected over a short time period, so that the contribution of the profile evolution from geodetic precession is negligible. Since the orbital period of the pulsar is ∼ 4 hours, and the full precession period is ∼ 47 years, we can be confident that any observed changes at different orbital phases in such observations can be attributed solely to to the change in the observed emission cone direction as the pulsar moves at a relativistic orbital velocity. We thus collected GBT GASP data during two separate campaigns - over four days between October 4 and 12, 2006, and over 14 days between March 9 and 23, 2008 - that have allowed us to search for profile changes on an orbital timescale (see §4.2 for details of the observations). We chose to use the less sensitive GBT over the Arecibo Telescope for these campaigns because it is fully steerable (whereas the Arecibo telescope is not), allowing us to track the pulsar over the course of at least one full orbit during each day of both campaigns. We chose to use the GASP data instead of the SPIGOT data because the GASP data are coherently-dedispersed and have had dispersive effects entirely removed from the pulse profile. Using SPIGOT would leave some intra-channel DM smearing in the profiles, which is not ideal for studies of the pulse shape. We do note, however, that a disadvantage of using GASP is that the data were folded online using the best ephemeris at the time of the observation and recorded as profiles, as opposed to having recorded the entire raw time series in each channel. It is therefore not possible to return to the raw time series to re-compute better-aligned integrated profiles later, once we have determined an updated ephemeris using more data. Since the relativistic J1906+0746 changes on such a short timescale, this can be a disadvantage as the inclusion of more data often leads to an updated 98  ephemeris which produces better folded profiles. Ultimately, however, we consider that the coherently-dedispersed GASP data are still better for this analysis than the SPIGOT data.  4.9.2  Method  To measure any changes in the pulse profile over the course of an orbit, we used the following prescription (which is adapted from the technique used by Ferdman et al. 2007), treating each campaign independently. We produced time-averaged profiles, realigned at a local value of the period, at a rate of one per five minutes, and created a total profile by summing all of the profiles within the campaign. For each five-minute integrated profile, we then calculated the mean anomaly M corresponding to that profile’s reference time, using the TEMPO package. From M, we calculated the eccentric anomaly E using Kepler’s Equation (Equation 4.9, where e is the pulsar’s eccentricity), which we solved using the Newton-Raphson method. The true anomaly ν, which is the observed orbital phase, is then calculated from equation 4.10:  M = E − e · sin E  tan  ν = 2  1+e E tan 1−e 2  (4.9)  (4.10)  For all 5-minute integrated profiles within a given campaign, we binned the profiles into 8 orbital phase bins (using the calculated value of ν as the phase). For each bin, we rotated each profile within the bin to be aligned with the total (orbit-averaged) profile, and scaled each profile (as well as the total profile) to a uniform height, to account for possible flux density variations due to scintillation. We then summed the aligned, scaled profiles in each bin. To determine whether there was any difference between the overall profile and each of the binned ones, we subtracted the total profile from each of the binned profiles. The binned profiles and binned difference 99  profiles for each of the campaigns are in figures 4.17 and 4.18.  4.9.3  Results  The difference profiles in Figures 4.17 and 4.18 show mostly flat profiles, except at ν = 0.31 for the October 2006 campaign, in which there is a hint of a residual in the interpulse difference profile (and potentially in the main pulse). However, there is no real evidence of a significant difference in profile shape over the course of an orbit. The nondetection of a significant orbital profile variation implies that J1906+0746 has a small aberration amplitude. Aberration causes the observed angle between the line of sight and the spin axis of the pulsar, ζ , to be shifted by an amount  δA ζ =  β1 [− cos ηS(ψ) + cos i sin ηC(ψ)] , sin i  (4.11)  (Stairs et al. 2004), where the following quantities are defined by timing: the characteristic velocity β1 ≡ nx/ (1 − e2 ); the orbital frequency n = 2π/Pb ; the projected semimajor axis x = a1 sin i/c of the binary orbit; and C(u) and S(u) are functions of the (time-dependent) longitude of periastron ω and the true anomaly ψ, defined as C(u) ≡ cos [ω + ψ] + e cos ω and S(u) ≡ sin [ω + ψ] + e sin ω. The angle η is the angle of the projection of the pulsar’s spin axis at a given epoch onto the plane of the sky, as measured counterclockwise from the ascending node. Our results showing no profile variation with orbital phase suggests that the amplitude of δA ζ is too small to be detectable. We therefore cannot place a useful constraint on the angle η.  4.10  Nature of the companion  Our timing results produce a companion mass of 1.290(11)M and a pulsar mass of 1.323(11)M . It is not clear from the companion mass alone whether it is a WD or a NS, leaving its nature a 100  Figure 4.17: J1906+0746 pulse and interpulse for 8 orbital phase bins for four days of data in October 2006 are shown. Note that the interpulse has been magnified by a factor of 8 relative to the main pulse. The uppermost plots show the main pulse (left) and interpulse (right), summed over the four days of data. The set of 8 lower plots show the pulse (left) and interpulse (right) at each of 8 orbital phase bins, with the corresponding difference profile (i.e. the difference between the profile at a given orbital phase bin and the summed profile) shown immediately below each one. The difference profiles show no evidence of profile changes on an orbital timescale within the noise.  101  Figure 4.18: J1906+0746 pulse and interpulse for 8 orbital phase bins for three days of data in March 2008 are shown. Note that the interpulse has been magnified by a factor of 8 relative to the main pulse. The uppermost plots show the main pulse (left) and interpulse (right), summed over the three days of data. The set of 8 lower plots show the pulse (left) and interpulse (right) at each of 8 orbital phase bins, with the corresponding difference profile (i.e. the difference between the profile at a given orbital phase bin and the summed profile) shown immediately below each one. The difference profiles show no evidence of profile changes on an orbital timescale within the noise.  102  puzzle. For some binary pulsars it is possible to observe the WD companion optically; however, as discussed in Lorimer et al. (2006), this is not a viable option for J1906+0746. We would expect a WD companion to have an age of at least ∼1 Myr (see the following section for details), which, at the distance and position in the galaxy, would have a magnitude of at least 29, too faint to see from the Earth with current telescopes. Thus, if the companion is a WD, it would not be possible to confirm this with direct measurements of the object itself. In the case of a double neutron star binary, it may be possible for the companion to be seen as a second pulsar (as in the double pulsar system, J0737-3039A/B, Lyne et al. 2004). We have therefore performed searches for pulsed emission from the companion using the software package SIGPROC (Lorimer 2001) using the WAPP Arecibo data and Spigot Green Bank data. For several of the observations, we created a time series dedispersed at the dispersion measure of the known pulsar, and transformed it into the rest frame of the companion for a range of possible projected semimajor axes. We then searched for periodicities in the data and folded the transformed time series for further inspection. Our search of observations for a second pulsar signal has not produced any convincing candidates. We conclude that if the companion is indeed a neutron star, it must be either a pulsar that is beamed away from our line of sight, or a pulsar with a low luminosity. Using the radiometer equation we can estimate the maximum luminosity the companion can have if it is indeed a pulsar that is beamed towards us. We first determine Smin , the minimum flux density detectable with the system as: Smin = β  σmin Tsys + Tsky (l, b) G n ptobs ∆ν  We P −We  (4.12)  (Dicke 1946; Dewey et al. 1985) where σmin is the threshold detection signal-to-noise ratio (SNR) (which we take to be 8), n p is the number of summed polarizations (2 in this case), ∆ν is the bandwidth (600 MHz with the Spigot; 100 MHz for each of the 3 WAPPs used during a typical 103  Arecibo observation), β is the quantization factor (we take β ∼1.2 for 3-level quantization, following Hessels et al. 2007), G is the antenna gain (∼2.0 for the L-band receiver at the GBT6 and ∼10 for the L-wide receiver at Arecibo7 ), Tsys is the system temperature in Kelvins (20K and 25K for the L-band receivers at the GBT and Arecibo, respectively), Tsky (l, b) is the temperature of the sky at the location of the source (Haslam et al. 1982, scaled to the appropriate frequency using a spectral index of -2.6), We is the effective pulse width of the pulsar, and P is the pulse period. For an integration time of tobs ∼8 hours (representing the longest observation searched at Green Bank) and ∼2 hours (for Arecibo) and assuming an effective width of 10% (a realistic estimate, as for a 15 ms pulsar, the effective width would be 1.5 ms, longer than both the DM smearing across a frequency channel and the sampling time), we find a flux density limit Smin ∼19.7 µJy for Green Bank and Smin ∼19.3 µJy for Arecibo. For a pulsar at a distance of 5.4 kpc, this implies that if the companion of J1906+0746 is a pulsar, it is either beamed away from us, or has a maximum luminosity of 7.2 mJy kpc2 (or 7.1 mJy kpc2 using the Arecibo observations). Comparing this with the L-band luminosities of the recycled pulsars in known DNSs (J0737-3039A with a luminosity of 6.5 mJy kpc2 (Burgay et al. 2006; Taylor and Cordes 1993); B1534+12 with a luminosity of 3.5 mJy kpc2 (Kramer et al. 1998; Taylor and Cordes 1993) and B1913+16 with a luminosity of 574 mJy kpc2 (Kramer et al. 1998; Taylor and Cordes 1993)), we conclude that our search had the sensitivity to have detected a recycled pulsar with a luminosity similar to that of the known DNS pulsars. Given that we do not have a direct detection of the companion and that the companion mass is ambiguous as to the nature of the companion in and of itself, we turn to the collection of known double neutron star (DNS) and relativistic WD binaries with precise mass estimates to assess how the masses of the pulsar and companion in the J1906+0746 system compares to the 6 http://www.gb.nrao.edu/∼fghigo/gbtdoc/sens.html 7 http://www.naic.edu/∼astro/RXstatus/Lwide/Lwide.shtml  104  measured masses of the other binaries (Table 4.1). Our previously-reported estimates of the pulsar and companion masses (Kasian et al. 2008), at 1.248(18)M and 1.365(18)M respectively, fit significantly better into our observed collection of DNSs than do our updated values. This, along with the fact that a more massive recycled companion is easy to explain by the standard model for DNS evolution, is why we had originally suggested that the companion was a second NS. However, the updated mass estimates presented in this thesis favour a more massive pulsar and a less massive companion, no longer fitting nicely into the known set of DNSs. The recycled pulsars in the known DNS systems are generally more massive than - or at least comparable to - the masses of their companions, which can be explained by the fact that they accreted mass during the mass-transfer phase of their evolution. This is not the case with J1906+0746: if the companion is a NS, it would be the recycled object, and thus would have accreted at least some mass from its companion. The fact that the companion here is 1.290(11)M - lower than all but one of the recycled pulsars in known DNS systems listed in Table 4.1 (with the exception being J1518+4904, whose pulsar and companion mass measurements have much larger uncertainties than the others and are thus less reliable measurements, but whose massive (∼2 M ) companion has been suggested to have been formed through an electron-capture supernova (Janssen et al. 2008). However, when we look at the masses of the young pulsars in known relativistic binaries around massive WD companions, our measured values are more similar to those in Table 4.1.  4.11  Implications  We have obtained an updated timing solution for J1906+0746 that allows for the measurement ˙ γ and P˙b . We measured pulsar and companion masses of three post-Keplerian parameters, ω, of 1.323(11)M and 1.290(11)M , respectively, which imply a lower companion mass than our 105  previously-reported result (Kasian et al. 2008), and is suggestive of a white dwarf companion, which would imply that the NS was created after the WD, a scenario that is not only rare observationally (with an order of magnitude fewer known recycled pulsar-WD systems) but which also requires a different mass transfer history than the basic model that explains the majority of the observed binary pulsars. The existence of young pulsars in binaries around WDs was predicted by Dewey et al. (1985) and Tutukov and Yungelson (1993), and was subsequently confirmed by the detections of the the 12-day binary B2303+46 (Thorsett et al. 1993; later identified as a NS-WD system by observation of the WD companion; Kulkarni and van Kerkwijk 1998) and the relativistic J1141-6545 (Kaspi et al. 2000; Bhat et al. 2008). They do not fit the traditional spin-up scenario, and an evolutionary channel that explains this class of system is outlined in Tauris and Sennels (2000). In this model, the binary progenitor involves a primary star with mass between 5 and 11M and a secondary with initial mass between 3 and 11M . The primary evolves and overflows its Roche lobe, and the secondary accretes a substantial amount of mass during this phase, which lasts ∼1 Myr. At some point after the primary forms a WD, the now-massive secondary evolves and a CE is formed for a second, short, mass-transfer phase. The envelope is ejected, and a supernova later occurs, forming the observed young pulsar. While we expect that the above is the most likely scenario for J1906+0746, the possibility remains that the companion is a second NS. If this is the case, the system may have formed through the standard DNS evolution; however, recent population synthesis calculations based on the known set of pulsars (Belczynski et al. 2010) suggest that a common formation mechanism for DNS involves the first NS forming through an electron capture supernova and the second forming via core-collapse supernova (EC+CC formation channel). Schwab et al. (2010) reported that, of a set of binary pulsars with well-known masses, no DNSs were found to be consistent with having had an EC as the first supernova; however, their study had used outdated mass values 106  for J1906+0746 (Kasian et al. 2008). Our most recent mass values, presented in this thesis, suggest that the system may indeed have been created through the EC+CC channel, or through two EC supernovae. The system’s low eccentricity implies that the double EC model may be slightly more likely; however, the pulsar’s comparatively high mass may argue against this. If the first NS was indeed formed by an EC, as supported by Belczynski et al. 2010, this would argue somewhat against a ”double-core” evolution of the system (e.g., Bethe and Brown 1998; Schwab et al. 2010).  107  Chapter 5  Conclusions and future directions High-precision timing of binary pulsars has produced unprecedented tests of evolutionary scenarios in addition to acting as probes of physics in extreme conditions. Of the observed collection of binary pulsars, only a fraction offer the opportunities for precise mass measurements that are essential to constraining details of the mass transfer histories that formed the systems. Through updated measurements of masses and orbital parameters, the two binary systems studied in this thesis confirm the validity of GR and have provide improved constraints on the mass transfer histories of each class of object. We have updated the precise mass and orbital parameter measurements for PSR J0621+1002, a result important for our unfolding knowledge of the relatively rare class of IMBPs. While there is one other known pulsar in this class with a precise mass estimate, it requires a different formation mechanism than does J0621+1002, leaving only one mass measurement to constrain each of the evolutionary channels. While the models explaining both channels (van den Heuvel 1994; Tauris et al. 2000; Taam et al. 2000) do appear to work for the observed IMBPs, the small number of observational results available to test their validity leaves room for much more progress in this area. J0621+1002 itself still has the potential for new results and better measurements. It has been five years since the last set of observations in 2006 discussed in this thesis. New observations will lower the uncertainty on the periastron advance and the masses (as given in Equation 3.1) by  108  a significant amount from the values presented in Chapter 3. Furthermore, recent and upcoming advances in the hardware at the Arecibo Observatory - a coherent dedispersion backend that covers the full 600 MHz of the L-band receiver (a clone of the GUPPI machine at the Green Bank Telescope; Demorest et al. 2010)- will dramatically improve the uncertainty on the TOAs and will provide yet more precise measurements for J0621+1002. The uncertainty on ω˙ and the masses are not the only potential scientific gain from a longer time span and smaller TOA errors: we currently do not see evidence of a Shapiro delay in the system, but with narrower limits on the masses, we may be better able to constrain both the Shapiro delay and the inclination of the system, which would lead to a better understanding of the system as a whole. In light of other precisely-measured masses of neutron stars and white dwarfs in relativistic binaries (listed in Table 4.1), our measured pulsar and companion masses in J1906+0746 suggest that it is more similar to the observed young pulsars in WD systems than to the observed DNSs (although an optical confirmation is unlikely due to high extinction in the direction of the pulsar). If the companion is indeed a WD, this implies that the NS was created after the WD, a scenario that is not only rare observationally (with an order of magnitude known than recycled pulsar-WD systems) but which also requires a different mass transfer history than most observed pulsars in binary systems. We suggest that it likely formed through an evolutionary channel outlined by Tauris and Sennels (2000) if the companion is a WD. However, the possibility remains that the companion is a second NS, in which case the system would likely have undergone an electron capture supernova, followed by a core-collapse supernova (Belczynski et al. 2010; Schwab et al. 2010), though there is also the less plausible scenario of an evolution similar to that for B1913+16. There is still much more to be studied with J1906+0746. Further timing of J1906+0746 will produce a better measurement of the orbital decay, producing a more stringent test of GR. Also, regular timing of the pulsar using the 76.2-metre Lowell Telescope at the Jodrell 109  Bank Observatory has revealed that the pulsar’s flux has been decreasing drastically since the observations in this thesis were recorded - so much so that it its signal is nearly undetectable at Jodrell Bank (Andrew Lyne, private communication). This is likely because the pulsar is precessing away from our line-of-sight, an effect that has long been been predicted for B1913+16 (Istomin 1991; Kramer 1998) and has been seen in J0737-3039B (Perera et al. 2010). The fact that we are entering into a phase where the pulsar signal will likely not be visible to us emphasizes the importance of continuing to monitor J1906+0746 with the far more sensitive Arecibo Observatory, which has ten or more times the gain and which should be able to observe the pulsar for the next few years before it fades away entirely. As the precession period for J1906+0746 is 169 years, the geometry of the system is changing on a relatively short timescale. Once its signal is no longer measurable even at Arecibo, it should still be monitored periodically for when it (or the companion, should it be a NS) precesses back into our line of sight. The contributions described in this thesis add improved constraints on evolutionary models afforded by the growing collection of interesting binary pulsars. While a vast array of binary pulsars are known today, it is imperative not only that the known systems are continually studied with long-term timing, but also that large-scale surveys continue to search for new and existing types of binary pulsars, so that we may further develop our understanding of the full variety of formation mechanisms for binary pulsars and, ultimately, compact objects in general. There are several large-scale surveys that are either currently being undertaken or on the horizon. The PALFA survey, while it began as a five-year survey, is ongoing using the 300-MHz Mock spectrometers1 installed at Arecibo in 2009. This promises to yield an increased number of pulsars via the full pipeline as compared with the older data taken with the WAPPs that account for most of the data that have been fully processed to date. Another imminent prospect is a 1 http://www.naic.edu/∼astro/mock.shtml  110  pulsar survey to be undertaken with the Low Frequency Array (LOFAR)2 in Holland, expected to discover ∼1000 new pulsars at low radio frequencies (see Stappers et al. 2011 for an overview of current pulsar studies with LOFAR). The next-generation radio telescope the Square Kilometre Array (SKA)3 has pulsar studies as a primary science goal and will carry out large-scale pulsar surveys with unprecedented sensitivity when it is fully built and operating (e.g., Taylor and Braun 1999). It currently has two precursor telescopes under construction: the Australian Square Kilometre Array Pathfinder (ASKAP)4 (Johnston et al. 2007; Stairs et al. 2010) and the Karoo Array Telescope (MeerKAT)5 (de Blok et al. 2010), both of which will conduct precursor pulsar surveys over the next several years. There are many exciting new prospects in the field of pulsar astronomy that promise to both increase the size of our known sample of binary pulsars and advance our knowledge of these unique probes of stellar evolution and of fundamental physics. 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The calibration code ASPCal has the option of using a continuum calibrator, or of simply using known calibration temperatures where no continuum calibration files are available. Where no good calibration data was taken for a pulsar on a particular epoch, the data may be normalized by the RMS of the noise. The raw data are then converted to profiles with a user-defined number of bins, with the option of summing a user-specified number of profiles together. The profiles can then be converted to ascii format through the AFR function ASPStokes. These ascii profiles can be converted to TOAs by using the code PSPMTOA (below, which was used to create the TOAs in this thesis) or using the newer code ASPToa which implements the same algorithm.  128  BFIT BFIT is an interactive program written by Michael Kramer (Kramer et al. 1994) that implements Simplex and Levenberg-Marquardt fitting algorithms to fit a user-specified number of gaussian components to a pulse profile. The user inputs the initial gaussian parameters, uses the Simplex algorithm to improve the parameters, and then uses the Levenberg-Marquardt algorithm to find a set of parameters that produces the smallest χ 2 . BFIT was used in §4.5 to create noise-free models of the standard profiles of J1906+0746. There, we fit the main pulse and interpulse of the profile separately. PRESTO PRESTO6 is a software package developed by Scott Ransom (Ransom 2001) that is used primarily to prepare pulsar data, search for new pulsars, and fold pulsar data. PRESTO is particularly good at finding pulsars in binary systems and those in globular clusters, through the Fourier-domain acceleration search and phase modulation search techniques described in Ransom et al. (2002) and Ransom et al. (2003) respectively. For the material in this thesis, PRESTO was used for searching in the long processing for the PALFA survey (see Chapter 2), but was not used for the analyses of either J0621+1002 (Chapter 3) or J1906+0746 (Chapter 4). PSPMTOA PSPMTOA is code that employs a matching algorithm, FFTFIT (Taylor 1992), to calculate the time of arrival of one pulse profile (or data profile) with respect to a (usually higher signal-to-noise) reference profile. The matching algorithm first Fourier Transforms each profile and finds the phase of the fundamental frequency for each. It then calculates the phase difference between the phases of the fundamental frequency of the data profile and 6 http://www.cv.nrao.edu/  sransom/presto/  129  the reference profile. Finally, it computes a time of arrival for the data profile by shifting the phase of the reference profile to zero and adding the calculated phase difference. While rotating the reference profile so that its fundamental frequency is at a phase of zero is the standard practice for creating TOAs, we did not do this for J1906+0746. For this pulsar we did not shift the reference profile to a phase of zero because we specifically aligned the reference profiles at different epochs so as to have a consistent profile evolution with time. PSRCHIVE PSRCHIVE7 (Hotan et al. 2004) is a pulsar data analysis package that can generally manipulate and view data, and is capable of both polarimetry and timing analysis. It was used to produce profiles for the J1906+0746 Nanc¸ay data (which were later used to create TOAs using PSPMTOA). SIGFOLDMSP SIGFOLDMSP is a set of tools created by Ingrid Stairs specifically to fold pulsar data for the purpose of high-precision timing. It was used to calibrate, dedisperse and fold the J1906+0746 WAPP data (see §4.3). It uses SIGPROC filterbank data files as input, but employs a slightly different dedispersion and folding procedure. SIGPROC SIGPROC8 is a pulsar software package that prepares, searches, and folds pulsar data. Developed by Duncan Lorimer, it converts raw telescope data into a standardized filterbank format, which can then be dedispersed and converted into a time series and either searched for periodicities or folded at a known pulsar’s period. SIGPROC was used in the PALFA survey for the quicklook pipeline (see Chapter 2) and in converting the raw J1906+0746 7 http://psrchive.sourceforge.net/ 8 http://sigproc.sourceforge.net/  130  WAPP data to filterbank format before being folded using SIGFOLDMSP (see §4.3). TEMPO TEMPO is a pulsar timing software package, written in FORTRAN by Joseph Taylor and collaborators. It takes as input two files: one containing a list of the TOAs for the pulsar (which includes information about which observatory recorded each TOA) and one containing a list of model parameters for the pulsar, including its spin, astrometric, and binary (if applicable) parameters (see §1.4.2 for more details about pulsar models). The TOAs are first transformed into the reference frame of the Solar System Barycentre, and are then enumerated before a least-squares fitting algorithm is used to compute the model parameters that produce the lowest χ 2 . TEMPO2 TEMPO29 is a pulsar timing package developed mainly by George Hobbs and Russell Edwards at the Australia Telescope National Facility (ATNF) (Hobbs et al. 2006). It is based on the original TEMPO code but is written in C and expands upon the original TEMPO. It was developed in part to be able to process data from multiple pulsars simultaneously (particularly for the purpose of detecting the gravitational wave background). In this thesis, TEMPO2 was used briefly to take advantage of its FITWAVES function to model the long-term timing noise in the J1906+0746 residuals. Ultimately, however, TEMPO2 was not used for the timing of either J0621+1002 or J1906+0746, as we chose to use the original TEMPO to time both pulsars.  9 http://www.atnf.csiro.au/research/pulsar/tempo2/  131  


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