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Searching for planets Walker, Andrew R. 1993

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We accept this thesis as conformingto the required standardSEARCHING FOR PLANETSByAndrew R. WalkerB. Sc. (Astronomy) University of British Columbia, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESGEOPHYSICS AND ASTRONOMYTHE UNIVERSITY OF BRITISH COLUMBIA1993© Andrew R. Walker, 1993In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.Geophysics and AstronomyThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1Z1Date:AbstractAs part of a larger program precise radial velocities (PRVs) have been obtained by useof a hydrogen fluoride (HF) cell over the period 1980 to 1992, for twenty-one dwarf andsubgiant stars (luminosity classes IV and V) together with eleven giants and supergiants(luminosity classes I, II, and III). A typical PRV measurement has an accuracy of15ms -1 .As part of this thesis a full analysis method has been developed, and applied to, theHF dwarf and subgiant program data, in an effort to find evidence for extra-solar planets.Although no such evidence was found we do find that about one half of the HF programstars show significant secular trends in their radial velocities, which may indicate signalsat periods longer than we are currently sensitive to. Detection limits are set in the formof minimum detectable planetary masses for each of the stars.Periodicities in the differential equivalent width of the Call infrared triplet line(AEWc„H) data are found for o2 Eri, a Dra, 61 Cyg A, and HR8832 which may resultfrom a stellar cycle, analogous to the Solar cycle. Correlations between the radial velocityand AEWcan data are found for 36 UMa and # Cora.llTable of ContentsAbstract^ iiList of Tables viList of Figures^ ixAcknowledgement xi1 INTRODUCTION 11.1 Astrometry ^ 21.1.1^Ronchi Grating ^ 31.2 Pulsars 41.3 T Tauri stars ^ 51.4 Direct Imaging 51.5 Precise Radial Velocities ^ 61.5.1^Fabry-Perot et alon 81.5.2^Iodine absorption cell ^ 81.5.3^HF absorption cell 102 HF absorption cell 112.1 The choice of gas ^ 112.2 Data reduction 132.2.1^Errors ^ 152.2.2^Further improvements ^ 17ill3 Intrinsic Variations 203.1 Intrinsic Variations ^ 203.1.1^Granular convection ^ 213.1.2^Active Regions 214 Data Analysis Methods 244.1 Least-Squares-Fitting with MINUIT^ 244.1.1^Additions to MINUIT 254.2 Cross-Correlation ^ 285 Applications of Data Analysis Methods 305.1 Generalized periodogram ^ 305.2 Trends ^ 335.3 Cross-Correlation ^ 335.4 Minimum mass    346 Proof of the Concept 376.1 Error Analysis ^ 376.2 Periodogram 406.3 Cross Correlation ^ 417 Results 437.1 Periodicities ^ 437.2 Correlations 467.3 Secular trends ^ 498 Binary Stars 52iv9 Current Detection Limits^ 569.1 Astrometric detection limits  5610 Conclusions^ 59Appendices 60A HF P1W Program Stars^ 60B Spectroscopic Binary 99C Secular Acceleration^ 101Bibliography^ 104List of Tables5.1 Minimum detectable masses for 0.25, 0.5, 1.0, and 10.0 year periods. . . . 366.2 Error analysis comparison for y Per ^  407.3 Periodicities in the AEWcai data  447.4 Correlations between the PRV and AEWcaz data^ 487.5 Trends in the PRV data ^  507.6 Trends in the AEIVcal data  517.7 Trends in the ATeff data^  518.8 Known binary systems and references for best orbits^ 528.9 x2/v values for fits to PRV data ^  54A.10 HF PRV program stars ^  61A.11 r Cet PRV data  62A.12 r Cet PRV data ...continued ^  63A.13 t Per PRV data ^  64A.14 c Per PRV data ...continued ^  65A.15 Cet PRV data ^  66A.16 e Eri PRV data  67A.17 e Eri PRV data ...continued ^  68A.18 o2 Eri PRV data ^  69A.19 o2 Eri PRV data ...continued ^  70A.20 x1 Ori PRV data ^  71viA.21 a CMi PRV data ^  72A.22 a CMi PRV data ...continued ^  73A.23 a CMi PRV data ...continued  74A.24 0 UMa PRV data ^  75A.25 0 UMa PRV data ...continued ^  76A.26 36 UMa PRV data ^  77A.27.36 UMa PRV data ...continued ^  78A.28 Q Vir PRV data ^  79A.29 Vir PRV data ...continued ^  80A.30 /3 Corn PRV data ^  81A.31 /3 Com PRV data ...continued  ^82A.32 61 Vir PRV data ^  83A.33 61 Vir PRV data ...continued ^  84A.34 Boo A PRV data ^  85A.35 Boo A PRV data ...continued ^  86A.36 36 Oph A PRV data ^  87A.37 36 Oph B PRV data  88A.38 Q Dra PRV data ^  89A.39 o Dra PRV data ...continued ^  90A.40 Q Aql PRV data ^  91A.41 p Aql PRV data ...continued ^  92A.42 i Cep PRV data ^  93A.43 7/ Cep PRV data ...continued ^  94A.44 61 Cyg A PRV data ^  95A.45 61 Cyg A PRV data ...continued ^  96A.46 61 Cyg B PRV data ^  97viiA.47 HR 8832 PRV data ^  98C.48 Secular accelerations, dv,/dt, for PRV program stars ^ 103viiiList of Figures2.1 Spectrum of HF 3-0 vibration rotation band ^  122.2 PRV data for 36 Oph A, 36 Oph B, and 36 Oph B - A ^ 193.3 Ann versus LN.,(R — I) for e Eri ^  236.4 Fit to the radial velocity data for 7 Per, where the solid line gives thefit, the empty circles radial velocity measurements of the secondary fromthe literature, the full cirdes radial velocity measurements of the primaryfrom the literature, and the triangles the PRV measurements of the primary. 386.5 Fit to the visual binary data for 7 Per, where the solid line gives the fitand the cirdes the visual binary data from the literature^ 396.6 Periodogram of 7 Cep PRV residual data. The solid line gives the powerand the dashed lines indicate the 50, 90, and 99 percent significance levels. 416.7 Cross-correlation function for the y Cep PRV residual and AEWcaH data The solid line gives the correlation coefficient, r, and the dotted line thesignificance   427.8 Generalized periodogra.m for r Cet PRV data. In the upper plot the dottedline gives the minimum detectable mass, the dashed line x 2 /v. In the lowerplot the solid line gives the power and the dotted lines the significance atthe 50, 90, and 99 percent significance levels  44ix7.9 Generalized periodogram for o2 Eri AEWcau data. In the upper plotthe dotted line gives the minimum detectable mass, the dashed line x2/v.In the lower plot the solid line gives the power and the dotted lines thesignificance at the 50, 90, and 99 percent significance levels. ^ 457.10 Phased o 2 Eri AEWcar data^  467.11 Generalized periodogram for r Cet ATeff data. In the upper plot, the solidline gives the amplitude, the dotted line gives the minimum detectableamplitude, and the dashed line gives the x 2/v value for the fit. In thelower plot the solid line gives the power associated with the period, andthe dotted lines give the 0.5, 0.9, and 0.99 significance levels for the power. 477.12 Cross-correlation function for 36 UMa PRV and AEWcari data. The solidline gives the correlation coefficient, r, and the dotted line the significance. 487.13 Correlation between AEWoazi and PRV data for 36 UMa ^ 498.14 Predicted radial velocities compared to PRV measurements ^ 538.15 Predicted difference velocities for 61 Cyg compared to PRV measurements 559.16 Current Detection Limits for sini=1, D=2pc. ^  57B.17 Binary orbit parameters ^  100C.18 Secular acceleration due to high proper motion^  101C.19 Geometry of secular acceleration due to high proper motion ^ 102AcknowledgementI would like to thank my supervisor, Dr. Gordon Walker, for providing me with theopportunity to join this research project, his guidance and involvement throughout, andfor teaching me all I ever wanted to know about sarcasm. Thanks also to:• Greg Fahlman for acting as the second reader of this thesis and providing manyuseful suggestions• Dave Bohlender and Ana Larson, fellow members of the HF group, who gave memany useful suggestions throughout the course of this thesis• Stephenson Yang for his example and dedication throughout the time that I haveknown him He is worthy of emulation both as an astronomer and an individual• Alan Irwin for continuing to challenge me at all times• my fellow astronomy graduate students at UBC, who have all helped at one timeor another• CB900 for the fun she afforded me throughout the summer months• my parents for the continued support and many letters... "I know not what this place is, or who I am.I only know that I am here until I am somewhere else."—Tsao Hseuh-Chin, "Dream of the Red Chamber"Chapter 1INTRODUCTIONGiven the ever increasing precision with which astronomical measurements can bemade it has, within the last decade, become possible for astronomers to begin the searchfor planetary systems around stars other than our Sun.Planets, brown dwarfs, and stars are classified according to their mass. Stars andbrown dwarfs are believed to form from the fragmentation and gravitational collapse ofinterstellar gas clouds. The least massive object which it is thought to be possible toform from such a process has a mass of 0.02M® . However, hydrogen core burning willnot occur for bodies with a mass of less than 0.08M0 . Thus, it is generally agreed thatmasses ranging from 0.02 — 0.08M0 will be classified as brown dwarfs, while objects ofmass greater than 0.08Me will be referred to as stars.Objects of mass less than 0.02M0 are thought to necessarily form from particleaccretion in the circumstellar disks of protostars, with the resulting bodies being referredto as planets. However, there is no reason why objects more massive than 0.02M 0 shouldnot form from such a process, and so there is a degree of uncertainty in the classificationof a body with a mass of 0.02 — 0.08M0 . The nature and frequency of planetary systemsare of astrophysical interest for a number of reasons:• the increase in knowledge of planetary formation and constraints for the theory• the instrumental improvements made by those searching for planets will be applicablein many other fields of endeavor• the formation of a list of candidate stars for the NASA Search for Extraterrestrial1Chapter 1. INTRODUCTION^ 2Intelligence (SETI) programThere are several methods being used in an attempt to detect extra-solar planetarysystems, and we briefly discuss some of these in the rest of this chapter.1.1 AstrometryThe astrometric method, which measures a star's position relative to some referenceframe over a period of time, relies upon the reflexive motion of the star due to an orbitingplanet. At a distance of 10pc from our solar system the Sun would be seen to exhibita periodic motion in space with an amplitude of N 0 5 mill' i-arcsec (mas), due to thepresence of Jupiter. In general we would have that:aMpd = (1.1)where a' is the semi-major axis, in mas, of the projected orbit as seen at a distance ofd parsecs, a is the semi-major axis of the orbit in astronomical units, Mp is the mass ofthe planet, and Ms is the mass of the star.Clearly, a cc el and so the method is inherently restricted to nearby stars, given afinite measurement accuracy. The technique will be most sensitive to massive planets inorbits with large semi-major axes or, equivalently, long periods. A positive attribute ofthe astrometric method is that measurements will reveal a signal with any orientationof the plane of the system with respect to the observer. Thus, orientation alone will notgive rise to a negative result, making such a result inherently more useful.Chapter 1. INTRODUCTION^ 31.1.1 Ronchi GratingAt the present time there is only one search being conducted for planetary systemsbased on the astrometric methods. The program is led by George Gatewood [17] and uti-lizes the 0.76m "Thaw" refractor and its Multichannel Astrometric Photometer (MAP).The MAP uses a dozen photometers, located just behind the focal plane, each of whichis aligned with one of the stars in the field, either the object star or one of the back-ground stars. Situated in the focal plane is a Ronchi grating - a glass plate with a ruleof opaque lines imposed on it. The lines, in this case, are roughly the same width as thespacing between the lines, this width being equivalent to the diameter of a stellar imagein the focal plane containing about 80% of the light from the star, or, equivalently, about0.2mm.The ruling is pulled through the focal plane causing the output of each photometer,sampled at intervals of about 0.lsec, to vary nearly sinusoidally as the star which itis observing is blocked to a lesser or greater degree by the opaque lines of the rulingThe phase difference between the object star and each of the reference background stars,together with the number of lines between each, gives an accurate indicator of the relativepositions of the stars in the field in the direction in which the ruling was pulled throughthe field. Rotating the ruling through 90° and repeating the procedure will fix the relativepositions for both axes.Assuming the reference stars to be fixed, on average, in the field, measurements overtime will give the relative positions of the object star over the period of observations.The program, in its fifth year, is as of this year observing 15 stars with 16 observationsper year. At a distance of 1pc this method claims to be able to be theoretically capable ofdetecting the reflex motion of the Sun due to Jupiter in about five years of observations.Chapter 1. INTRODUCTION^ 41.2 PulsarsThe first claim of discovery of a planet in orbit around a pulsar was made by Baileset al. [1],[29] in July of '91. Unfortunately, the result was subsequently found to be dueto an error in the reduction process. However, in January of '92 Wolszczan and Frail [48]claimed to have found two planets in orbit around the pulsar PSR1257+12. This resulthas better stood the test of time, and represents the first strong evidence for planetsoutside of our of Solar System.The method relies upon the extremely accurate period determination (in this caseAPIP = 1.6 x 10 -12 ) of the pulsar. The pulse arrival times are measured over a periodof time and, after correcting for the effect of the motion of the Earth, timing residualsare calculated by subtracting the expected arrival time from the observed arrival timefor each pulse. It was found that the observed residuals could be explained by assumingthat the pulsar was being orbited by two "planets". The "planets" will cause a reflexivemotion in the pulsar, leading to the observed timing residuals. The mass of the "planets"were found to be 3.4Me/ sin i and 2.8Me/ sin i where i is the inclination angle of theplane of the orbits with respect to the observer's line of sight and Me is the mass of theEarth.This method is extremely sensitive, and in theory would be able to detect bodies withmasses lower than that of the Moon. The precise detection limit is set by the accuracywith which the pulse arrival times can be measured. The obvious, and severe, limitationis that it can only be used to detect planets around pulsars. As a result it is of clearlylimited use, and we must rely upon other methods to detect planets around less exoticstars.Chapter 1. INTRODUCTION1.3 T Tauri starsThis method probably provides the least direct method for providing evidence of otherplanetary systems.One possible site of planet formation is in the circumstellar disks of T Tauri stars,young objects that are thought to represent the last stages in protostellar evolution.They are believed to still be enshrouded by dust clouds, and are strong infrared sources.Their spectral energy distribution gives evidence for a radial temperature dependence ofthe form T(r) a r -", where pAny planets which form within these disks would "sweep out" gaps in the material dueto tidal perturbation, accretion, and possibly resonance effects. As there is a monotonicdecrease of temperature with radius a gap in the disk would give rise to a gap in thespectral energy distribution, corresponding to the peak in the Planck function of the"absent" temperatures.Marsh and Mahoney [31] present evidence for such gaps in the spectral energy dis-tributions in the case of four T Tauri stars. Clearly such evidence is circumstantial atbest and given that this is a relatively new area of research the results are still highlytentative.1.4 Direct ImagingDirect imaging, as the name suggests, involves taking an image of a planet itself. Thiswas attempted by Gordon Walker and collaborators in September '92 during a two nightobserving run at the Canada-France-Hawaii (CFH) telescope, using HR Cam [45].The largest problem to be overcome is that of the image of the planet becoming lostin the noise of the stellar light. In an effort to avoid this a small mirror with a 5" centralhole was used. During observations the star image was centered on the hole, so nearlyChapter 1. INTRODUCTION^ 6all its light would pass through the hole, while the area around the stellar image wouldbe reflected to the CCD detector. In an attempt to remove the scattered stellar lighteven further images were taken in groups of ten, with the detector being rotated, aboutthe center of the hole, by 90° between groups. Assuming the scattered stellar light tobe circularly symmetric one can then take the difference between images which wereobtained with 180° difference in rotation angle to remove all the remaining stellar light,while any planets or background stars would give rise to two images, a positive one anda corresponding negative one separated by 180°.Clearly, the analysis of this data, which constitutes some thousand images for fivecandidate stars, must be done with extreme care in order to disentangle any planetaryimages. This is now being attempted and the early results appear promising. Thismethod is best suited to discovering large planets of high albedo, with relatively largeseparations from the star, as if they are closer than 2.5" they will be lost within thecentral hole.It is claimed that, in theory, detection of a Jupiter-sized planet beyond about 3" fromthe primary would be possible [45].1.5 Precise Radial VelocitiesThe precise radial velocity (PRV) method measures the relative radial velocity of astar over a period of time, in an attempt to detect the reflexive motion of the star dueto an orbiting planet. An observer in the plane of Jupiter's orbit would observe the Sunto undergo a variation in radial velocity with an amplitude of ti llms -1 , due to thepresence of the planet. In general the amplitude, K, of such a signal is given by:K= —2.7r a sin i  1 ^(1.2)Chapter 1. INTRODUCTION^ 7where P is the period of the orbit, a the semi-major axis, e the eccentricity, and i theangle of inclination of the plane of the orbit to the star-observer line.Clearly, K oc t, and so this technique will be most sensitive to planets in short-periodorbits. One disadvantage with this method is that if i = 90° (i.e. the plane of the orbit isperpendicular to the observer's line of sight) then no signal will be detected (i.e. K = 0).Thus, a negative result must always be qualified by the possibility that sin i is near zero.Another inherent disadvantage of this method is that any intrinsic variation of the starmay either obscure or mimic the signature expected from the presence of a planetarysystem. Thus, great care must be taken to allow for this when drawing conclusions fromthe results.One feature that all the PRV techniques discussed below share is that of discardingthe standard procedure for determining the dispersion relation of an object spectrum.Traditionally, this has been done by taking a reference spectrum immediately before orafter the object spectrum. The reference spectrum, which typically uses an iron-argon(Fe-Ar) or cadmium-neon (Cd-Ne) discharge tube as the light source, utilizes emissionlines of known wavelength to determine a dispersion relation which is then applied to theobject spectrum. One problem with this is that, unless the system is perfectly stable,the dispersion relation will change with time due to flexure and we are not determiningthe dispersion relation for the time at which the object spectrum was taken. Anotherproblem is that the reference spectrum is obtained by introducing the arc light at somepoint along the optical path, usually by means of a flappable mirror. Thus, the opticalpaths followed by the arc light and star light will be different, leading to a further sourceof error.Another feature common to all PRV methods is the necessity of making correctionsfor the changes in velocity of the observing site with respect to the barycenter of oursolar system, the so-called barycentric correction.Chapter 1. INTRODUCTION^ 81.5.1 Fabry-Perot etalonThis effort is being led by R.S. McMillan [32],[33],[34] using a 0.9m telescope atKitt Peak. The stellar image is fed into a fiber-optic cable which acts to scramble thelight and to give a uniformly illuminated output, the brightness distribution of which islargely insensitive to changes in seeing, guiding, brightness, focus, and shape. The outputend of the fiber is fed to a tilt-tunable Fabry-Perot etalon, which has, in the measuredwavelength range of 4250-4600A, interference orders of width 50mA separated by640mA. The transmitted interference orders are separated spatially by means of anechelle grating.The wavelength of each sampling point, corresponding to each interference order,is determined uniquely by the etalon, the spacing and zero-tilt position of which aremeasured about 100 times per night. Prior to an observation the etalon must be tilt-tuned to sample points at dose to the same positions in the stellar spectrum where theywere previously sampled. Any stellar Doppler shift will change the relative intensity ofeach sampling point, in proportion to the slope of the spectrum at each point. About12% of the sampled points, which comprise some 6% of the total spectrum, lie on steepslopes of the spectral profile and are useful for determining a stellar Doppler shift. Theremaining sampling points are used to normalize the intensity levels between successiveobservations.An accuracy of ±10ms -1 is claimed for this method, although this high level ofaccuracy relies in part on numerous observations.1.5.2 Iodine absorption cellEfforts to measure PRVs for nearby stars by means of an iodine absorption cell arecurrently being made by two separate groups, Marcy and Butler [30] and Cochran andChapter 1. INTRODUCTION^ 9Hatzes [12]. We will discuss only the Marcy and Butler system as they are presentlyfurther ahead in terms of achieving the desired goal.Thermal fluctuations and mechanical instabilities within a spectrograph may causeboth shifts in the spectrum and changes in the point-spread function (PSF), both of whichwill give rise to spurious stellar Doppler shifts. In an effort to account for these effectsand also to impose a precise wavelength calibration on the stellar spectrum Marcy andButler decided use an iodine (/2 ) absorption cell to impose the /2 absorption spectrumon the stellar spectrum.The cell is a sealed unit, containing / 2 vapor at 0.01atm and maintained at atemperature of 50±0.1C, with a length of 10cm and diameter of 5cm. During observationsthe cell is placed in the stellar beam, the light passing through the flat Pyrex windowsat both ends of the cylindrical cell. The observed spectrum, 46,(A), may be representedby:/c,b,(A) = k(/,(A AMT/,(A + AA/2 )) 0 PSF (1.3)where TI, is the intrinsic transmission function for the / 2 cell, determined from a high-resolution spectrum, AA/A 400000, with a signal-to-noise ratio of S/N Ce 1000. I, isthe intrinsic stellar spectrum, which is found by observing the star without the cell inplace and then deconvolving the PSF from the spectrum to yield the intrinsic spectrum.A least-squares method is used to determine the values of AA., AA13 , and the PSF.The corrected stellar Doppler shift is given by AA, — AA/ 2 . Any spurious shifts due toinstabilities in the instrumentation will be accounted for either by AA/2 or PSF terms,and the corrected stellar Doppler shift is precisely determined as the intrinsic / 2 spectrumacts as an excellent wavelength calibrator.Chapter 1. INTRODUCTION^ 10The spectrograph used provides wavelength coverage over 3800-9500A with a reso-lution of 40000, which is insufficient to resolve the / 2 lines but the analysis we havedescribed does not require it to. Given a signal-to-noise ratio of S/N = 200 an accuracyof 25ms -1 is claimed for an individual measurement.1.5.3 HF absorption cellThe use of a hydrogen fluoride (HF) absorption cell forms the basis of this thesis, andit is discussed at length in the following chapter.Chapter 2HF absorption cellThe data analyzed for this thesis has been obtained over the past twelve years at thecoude spectrograph at CFH, using an HF absorption cell and a Reticon detector. TheHF cell is used to impose absorption lines of a very well determined wavelength on thestellar spectrum, to provide a very precise wavelength calibration simultaneous with thestellar observation.2.1 The choice of gasThe initial choice of gas to be used in the absorption cell was made based on fivecriteria presented by Campbell and Walker [8]. Essentially these conditions sought a gasthat would provide a set of strong absorption lines with an absorption path of less thana few meters. Further, there should be regions between the strong lines where unblendedstellar lines would be visible. Finally, the spectrum should be in a region not overlappingwith any telluric lines. Although Marcy and Butler [30] have since shown that the onlyessential criteria are the relatively short absorption path and avoidance of telluric linesthis was not appreciated at the time.The gas selected by Campbell and Walker, based on their criteria, was HF, using theR branch of the 3-0 vibration rotation band in the region 8670 — 8770A. A spectrum ofthe gas over this region is seen in figure 2.1.HF meets all the criteria imposed, although has the inherent disadvantage of beingextremely toxic. The gas will cause extreme discomfort at concentrations above 5ppm,1 1nigur"'W-Th0.80.2Chapter 2. HF absorption cell^ 128669.352 8685.942^8716.8888675.854^8699.616^8737.7723, I pixel numberFigure 2.1: Spectrum of HF 3-0 vibration rotation bandprimarily to the eyes and respiratory tract. Greater concentrations may cause death onvery short exposures. As a result of these properties caution must be used when dealingwith it, and the cell and other handling equipment must be constructed of non-reactivematerials. The cell itself is made of a lm length of monel (an alloy of nickel, copper,iron, and manganese) tube with sapphire windows.Although the boiling point of HF is 19.7°C it is still highly polymerized at tempera-tures below 70°C. To avoid complication of the spectrum due to polymerisation the cellis heated to about 100°C, with the pressure of the gas being stabilized by maintaininga reservoir of liquid HF, connected to the cell, at 0°C. The vapor pressure of HF at0°C is 356torr (c..d 0.5atm), which provides absorption lines of sufficient strength and hasthe added advantage that any leak in the cell will tend to result in air being pulled in,8762.2852 _I150000 500^1000Chapter 2. HF absorption cell^ 13rather than HF being forced out. The temperature and pressure are monitored duringobservations, and periodically, about 2 times per year, the HF would be flushed andreplenished. More recently it was decided that this procedure was unnecessary and nowmore HF is simply added to the system when it is thought to be needed.A typical set of observation would consist of several stellar spectra taken with theHF cell in place (star+HF) and also numerous HF reference spectra (ref HF) which areflat-fields taken with the HF cell in place, flat-fields with the HF cell removed, and darks.Also, for each star a reference spectrum is obtained in the absence of HF (ref star) onone occasion. During exposures a mid-exposure time is calculated which is essential indetermining the barycentric correction to be applied. A signal-to-noise ratio of f.•2 1000 isthe goal for all star+HF spectra, with the ref star, ref HF, and flat-fields ideally havinga signal-to-noise ratio somewhat higher than this.2.2 Data reductionThe reduction method is now a fully automated procedure, requiring the user onlyto provide a list of frames to be used in the process. All of the CFH data acquired todate can be reduced in about 3 days on a network of SUN workstations. This rapidityof reduction is essential as it means that any change in the reduction procedure canbe quickly and simply tested. Too long a reduction process would prohibit numerouschanges to the code.As it stands now there are 3 distinct stages to the reduction process:(1) each spectrum is pre-processed by subtracting a dark frame, dividing by a flat-field, and fitting to the continuum.(2) the ref HF and ref star are used to separate the star+HF into a stellar, sep star,and HF, sep HF, component. The reference frames are suitably shifted and stretched soChapter 2. HF absorption cell^ 14as to align them with the corresponding features in the star+HF frame, by which thestar+HF is then divided, to give the sep star and sep HF framesstar + HFsep star =  ^ (2.4)aligned ref HFstar + HFsep HF = (2.5)aligned ref starThe instrumental profile, or PSF, is critical in determining the stellar radial velocityas a change in the PSF can mimic a change in the radial velocity. To account for thisthe PSF is determined for the sep HF frame by assuming that the sep HF lines haveno intrinsic asymmetry and that the intrinsic widths of the lines are known. The lineprofiles are modeled by a pseudo-Lorentzian, with an exponent of 2.08 rather than 2, anda different half-width for each side of the line to model the asymmetry.Thus, one obtains a relationship between the instrumental width, the difference be-tween the modeled and intrinsic width of the sep HF lines, and the asymmetry, thedifference between the fitted widths for the two halves of a sep HF line, versus wave-length. This information is then used to "deconvolve" the instrumental profile from thesep star spectrum, by subtracting the instrumental profile from the observed sep starprofile for each stellar line, to yield an "intrinsic" stellar spectrum, such as we wouldhope to see in the absence of instrumental effects.At the same time measurements are made of such quantities as AEWcan., the changein equivalent width of the Call line relative to the ref star, ATeff, the change in theeffective temperature of the star, and A(R — /), the change in R — I of the star on theJohnson photometry system. For the latter two quantities the line-depth ratio of linessensitive to changes in ATeff and A(R — I) is used to calibrate the effect [5].Allowance is also made for changes in the wavelength of the HF lines due to changesin the temperature and pressure of the cell, which is monitored and recorded throughoutChapter 2. HF absorption cell^ 15an observing period.(3) in the final stage of the reduction a Doppler shift is determined for the HF linesin the sep HF frame relative to the HF lines in the ref HF frame. Similarly, a Dopplershift is determined for the stellar lines in the star frame relative to the stellar linesin the ref star frame. The difference in these two Doppler shifts is used to determinea radial velocity for the star relative to the radial velocity of the ref star frame, TheDoppler shift of the HF lines is used to account for any spurious Doppler shifts resultingfrom instrumental changes. A barycentric correction, determined from "The JPL ExportPlanetary Ephemeris" [41], is made to obtain the final relative radial velocity.As the final step in the reduction procedure run corrections are applied [27]. The runcorrections, which are thought to be necessary due to an observed secular trend in theaccumulated data sets, are determined by fitting low-order polynomial trends to eachof the data sets for each star. The weighted mean of the resulting residuals for eachobserving run is used as the run-correction. Run corrections are applied to the PRV,AEWcar, balm and /(R — I) data sets for each star.2.2.1 ErrorsThe errors in the HF PRV measurements can be attributed to two sources: the randomerrors due to photon noise, detector read-out noise, guiding, temperature and pressurefluctuations in the cell and the systematic errors which will result from the alignment ofthe cell, diffraction grating, detector, and other components of the instrumentation. Itis essentially the random errors resulting from the photon noise which will impose theultimate limit on the potential accuracy of the data. A useful equation is presented byWalker [42]:Chapter 2. HF absorption cell^ 16u.,(2 — d)n = 4^d2 6A2 (2.6)where d is the line depth as a fraction of the continuum, Id is the line width, and n is thenumber of detected photons per A in the continuum necessary to make a la detectionof a wavelength displacement EA. Using this equation and assuming d = 0.2, w = 0.2 A,that there are twenty stellar lines in the spectrum, and a signal-to-noise ratio of 1000,then we find that the limiting accuracy is of the order of 5ms-1 . In addition to thissystematic errors may result in a further source of noise. The largest systematic errorwill probably arise from the alignment of the cell, mosaic grating, and detector prior toeach run. Any change in these settings, during a run, due to thermal flexure or any otherreason will result in further random noise within the data accumulated for that run.In an effort to estimate the importance of the systematic errors we look at the PRVdata for the two components of each of the binary systems we are monitoring, namely 61Cyg and 36 Oph, the latter of which is in fact a triple system [11]. We consider the binarysystems simply because both components would generally be observed in the same run.If systematic errors play an important role then looking at the difference between theradial velocities of the A and B components should remove the systematic errors betweenruns. Thus, the difference in the velocities should show less scatter than the individualvelocities. The difference velocities, shown in figure 2.2 for 36 Oph, are calculated bytaking the difference between velocities which were obtained during the same run. Thoseruns in which only one component was measured are ignored for the purpose of this test.The scatter in the residuals from straight line fits to the A, B, and B-A data sets aregiven by 15.86, 18.93, and 20.39 ms -1 respectively. A similar analysis for the 61 Cygdata sets yields 16.03, 15.85, and 15.40 ms -1 respectively. Assuming random Gaussiannoise then we would expect the scatter simply to add in quadrature. However, in bothChapter 2. HF absorption cell^ 17cases the scatter for the B-A data set is lower than the expected value, by 4.3 ms -1 for36 Oph and 7.1 ma -1 for 61 Cyg. This implies, although at what significance level isuncertain, that there is a correlated component to the error of the order 5 ma -1 .2.2.2 Further improvementsAt the present time it is felt that there are a number of improvements that couldbe made to both the observing instrumentation and the reduction method to reduce theerrors in the radial velocity measurements below their current value of N 15ma -1 . Anyphysical modifications would first be made at the Dominion Astrophysical Observatory(DAO) 1.2m telescope, whose coude spectrograph is the original of which the CFH spec-trograph is a copy, and where there is a second HF system being used for about fivenights per month to monitor the intrinsic variations in the radial velocities of giant stars.Amongst the changes currently being considered are:• use of a charge-coupled device (CCD) detector. This would allow many shortexposures to be obtained, something not viable with the Reticon detector due to its highreadout noise, and so giving better barycentric corrections. Typically the barycentriccorrection will change by N 10ms-1 over an exposure (assuming an exposure time ofthirty minutes and a slope to the barycentric correction of 20ms - ihr -1 ).• use of fiber optic for carrying light from the Cassegrain focus of the telescope tothe entrance aperture of the HF cell. This would provide consistent illumination of thespectrograph slit irrespective of such factors as focus, seeing, and guiding. The flat-fieldlamp could also be fed through the same fiber to provide similar illumination of the slitfor the stellar and flat-field light, allowing for better flat-fielding of the data. The extentto which this may improve the accuracy of the PRV measurements is unclear, but at thepresent time the fiber feed has the highest priority of all the proposed modifications.• elimination of the 4 grating mosaic. The mosaic grating essentially gives 4 overlaidChapter 2. HF absorption cell^ 18spectra, all of which may be displaced slightly with respect to each other and havediffering dispersion relations, leading to large errors in the reduction procedure. Onepossibility would be to use a single grating, with the penalty paid in correspondingloss of light, the other to offset each spectrum on a CCD detector and reduce of eachof the 4 spectra separately, combining the derived radial velocities for each at the endof the reduction process. As of yet no effort has been made to determine the degree ofmisalignment within the mosaic so it is impossible to estimate the degree of improvementthis change might bring about. A 4 grating mosaic approach is also causing problemswith the CFH Conde F/4 Spectrograph Project, where one of the gratings gives FWHMssignificantly larger than the other three [19].• lowering the HF pressure in the cell. It is hoped that if the HF pressure withinthe cell can be controlled to match the width of the HF lines with those of the star thenany changes in the instrumental profile will have the same effect on both sets of lines,reducing or removing the need to model the PSF. This would provide greater consistencyin determining the centers of the stellar and HF lines from run to run, so improvingthe PRV accuracy. An inconsistency of 1% of the FWHM value for the line centerdetermination between the two sets of lines will give rise to an error of •-•-• 10ms -1 .• better determination of the instrumental profile. In the present reduction methodthe PSF is handled in an overly simplistic manner. Efforts to better model the PSF mayyield higher accuracy in the radial velocities, although the investment in man-hours forthe necessary programming would be considerable. This change would, in theory, havethe same effect as the preceding one, allowing for better determination of the line centersand so improving the PRV accuracy by the same degree. However, the best approachmight be to attempt both modifications simultaneously, as it may prove impractical tochange the HF pressure within the cell for each new star that is observed during a run.0000<Sz000cP8^o00 001111111Chapter 2. .11F absorption cell36 Oph A KOV^36 Oph B K1V^36 Oph 13 — A000100191500 00050000 000 8ig 0o000 0 00 o °00015010050U)0 0—500111111 1 1111 1 111 0—9000106000^9000 6000^9000HJD (-2440000)6000—50—1000Figure 2.2: PRV data for 36 Oph A, 36 Oph B, and 36 Oph B - AChapter 3Intrinsic VariationsThe purpose of this thesis is to address the question as to whether or not there areany planetary systems around any of the nearby stars currently being monitored withthe HF system. The data obtained with this technique is summarized in appendix A.Due to the large intrinsic variations of the giant stars which will obscure any evidence ofa planetary system, we will consider only the dwarfs and subgiants.There are four parameters which are measured by the reduction procedure and will beof use in the analysis: PRV, AEWcari, ATeff, and A(R — I). The latter two quantitiesare determined from a calibration of temperature and color sensitive lines respectively[5]. Although different lines were used to calibrate for each we see in figure 3.3 the twoquantities are strongly correlated and so we will consider only ATeff .3.1 Intrinsic VariationsOnce an observational system capable of measuring differential radial velocities on theorder of a few ma' has been attained there are still problems to be faced before one canunambiguously claim a planetary detection given the expected signal. The greatest ofthese results from the intrinsic variation of the differential radial velocity, which is causedby such factors as granular convection, active regions, stellar pulsations, and others.20Chapter 3. Intrinsic Variations^ 213.1.1 Granular convectionThe convective blueshift of the Sun, typically 300ms -1 , is caused by the hotter,and hence brighter, rising portions of the solar surface. These regions will give rise to ablue-shifted component to the solar absorption lines, while the sinking material will giverise to a red-shifted component, with the blue-shifted contribution dominating, due to itsgreater brightness. The pattern of the solar granulation is believed to vary with the solarcycle, possibly giving rise to a signal which would mimic that of a planet of the sameorbital period as the period of the solar cycle. Unfortunately, the HF group has obtainedonly minimal data on the radial velocity of the Sun with time. However, Dravins [14]claims that changes in the convection pattern could give rise to spurious radial velocityvariations of N 30ms'. This claim was supported by Deming [13] who found a changeof this magnitude in the apparent radial velocity of the integrated solar disk over theperiod 1983-85. However, more recently Wallace et al. [46] found that the change in theapparent radial velocity of the Sun due to the granular convection is at most 5ms- 1 overthe period 1976-86. This view is supported by McMillan et al. [35] who find an upperlimit to this variation of 4ms -1 over the period 1987-92.3.1.2 Active RegionsActive regions (e.g. flares, spots, plages, etc.) on the Sun are associated with increasedchromospheric activity and intense localized magnetic fields. The granulation in theseareas tends to be more fragmented with smaller granules, leading to a much reducedconvective blue-shift. Thus, active regions ,which may cover 10-20% of the solar surface atmaximum, are thought to give rise to changes in the apparent radial velocity, modulatedby the solar rotation period as features are carried across the solar disk. The changes inapparent radial velocity are believed to arise from changes in the stellar line asymmetriesChapter 3. Intrinsic Variations^ 22as surface features are carried across the disk of the star.Many stars are thought to exhibit activity cycles similar to that of the Sun, and so thecomments we have made concerning the Sun are, to a greater or lesser extent, applicableto the nearby stars being monitored by the HF group.In an effort to disentangle the changes in radial velocity resulting from intrinsic ac-tivity from those resulting from the presence of a planet, the chromospheric activityindicator AEWcaz, the change in equivalent width of the Call infra-red triplet line atA8662 (the so-called Z line), is used, which has been shown to be a useful indicatorof chromospheric activity [38]439]. We also consider ATE f1, the change in the effectivetemperature. Any correlation between these quantities and the measured relative radialvelocities would be strong evidence for an intrinsic variation.10—10000oSs° 00o 0°o°0 o^oo.0<90 °000000I° o^ —00oChapter 3. Intrinsic Variations^ 23c Eni K2V—40^—20^0^20^40ATeff (K)Figure 3.3: ATeff versus A(R — I) for c EriChapter 4Data Analysis MethodsThe two methods used to perform the required analysis of the data are:• least-squares-fitting of a given function to a time series• cross-correlation between quantities4.1 Least-Squares-Fitting with MINUITIn order to fit a given a function to a time series by use of the least-squares-fittingmethod it was decided that the best approach would be to use MINUIT, a functionminimization and error analysis package developed at CERN [25], [2]. MINUIT providesthe user with many commands to determine the parameter values of a given functionhaving the best fit to a time series, The user must supply MINUIT with a subroutinewhich will calculate the x 2 value, defined by:1x2 = Ec-o.,2 (N- y(xi))2)^ (4.7)where yi is the ith data point obtained at time x i , y(xi) is the value of the function tobe fitted at x i , and of is the error associated with the value of yi.MINUIT, via the commands of the user, alters the parameters of the given functionin order to minimize x 2. To this end MINUIT has several minimization techniques atits disposal, but the ones used most heavily in this research were the Nelder and Meadmethod [36] and the Davidon-Fletcher-Powell algorithm [15], [16]. Further information isgiven in the cited references. The user must also provide MINUIT with initial parameter24Chapter 4. Data Analysis Methods^ 25values. These values can often be critical, as one of the faults common to all least-squaresmethods is their inability to determine the global, as opposed to a local, minimum.Frequently least-squares algorithms will find only a local minimum, although MINUITprovides several other algorithms which attempt to ensure that a global minimum hasbeen found. However, these methods are far from foolproof and so it is advisable for theuser to select the initial parameter values based on any prior knowledge, and, if necessary,to run MINUIT several times with varying initial parameter values.Finally, it is best to provide functions for the first derivatives of x2 with respect toeach parameter. This allows MINUIT to operate much more efficiently, saving up toa factor of ten in computing time, as it no longer has to determine the first derivativesnumerically, and also more precisely as numerical calculations of the first derivatives tendto be less precise.4.1.1 Additions to MINUITAlthough MINUIT provides many useful commands and output options it does notinclude several desirable features which were added as subroutines.Significant PlacesThe fitting of a function to a time series is often plagued by two or more parametersthat are highly correlated. A high correlation between two parameters indicates that ifone is to follow a path of of minimum x2 then changing one of the correlated parameterswill necessitate a change in the other. A contour map of x2 plotted as a function of thecorrelated parameters will show a ravine like structure. It is notoriously difficult to findthe global minimum for a minimum which has large correlations between its parameters.Although MINUIT will display a correlation matrix, a matrix of the correlation ofeach parameter with every other parameter, upon request it is also useful to determineChapter 4. Data Analysis Methods^ 26the number of significant figures to which each parameter must be quoted to avoid sig-nificantly increasing the value of x 2 . For a parameter uncorrelated with any other itserror will give the necessary number of significant figures. However, for parameters whichare highly correlated with other parameters the associated parameter error typically un-derestimates the required number of significant figures. Thus, the required number ofsignificant figures is independently determined, and is taken as the number of significantfigures required before x 2 increases by less than 1 part in 106 .Error AnalysisAnother fault of MINUIT is its tendency to underestimate the errors associated witheach parameter. Thus, it was decided to calculate the errors in a separate subroutine.The curvature matrix, a, is defined by:1 aY(zi) OY(xi)^82y(xi)^1  82x2 akajk E( -oa(^Y(x.)).9a.oad— 2 &oaa; Oakwhere ai is the ith parameter. To first order the curvature matrix is given by:aik = x--.1 1 ay(x i) ay(xi) )Z-d‘cri ‘ 4%1 Oakand the error matrix, f, is simply defined as the inverse of the curvature of the errormatrix,e = a-1 , and the error associated with the ith parameter, ca , is then given by:Crai =eii^ (4.10)(4.8)(4.9)Statistical QuantitiesFinally, subroutines are added to give several statistical quantities which will be ofuse in analyzing the results:Chapter 4. Data Analysis Methods^ 27• x2/v, where v is the number of degrees of freedom for the fit, which is equal to thenumber of data points to be fitted minus the number of free parameters used. x2/v isexpected to have a value near unity for a good fit. A value much less than unity indicatesthat the errors associated with the measurements have been overestimated, while a valuemuch greater than unity suggests either a poor fit or underestimated errors.• Ft,„,„, which is defined by:= (X! X2)1' (4.11)X Avwhere X2 is the chi-squared value resulting from the fit to a given model, v is the numberof degrees of freedom for this fit, x: is the chi-squared value resulting from the fit toa zeroth order polynomial, vc is the number of degrees freedom for the offset fit, andAv = vc — v. The larger the value of F the more one is justified in going to the morecomplex model compared to the simple offset.• Q(FIvi , v2 ) which is defined by:v2 vi)Q(Flvi, v2) =^2 ' 2where Iz (a,b) is the incomplete beta function, which is in turn defined by:(4.12)fx ta-1 (1 — t)6-idtIz (a, b) =  ^(a, b > 0)^(4.13)fo e- 1 (1 — t)b-1 dtQ gives a measure of the significance level at which the hypothesis "model 1 has asmaller variance than model 2" can be rejected. A small numerical value implies asignificant rejection, which implies a high confidence in the hypothesis "model 1 has avariance greater than or equal to model 2". Thus, a smaller value of Q indicates greaterjustification of the more complex model - given that model 1 is the offset and model 2 isthe more complex function.Chapter 4. Data Analysis Methods^ 284.2 Cross-CorrelationTo determine the cross-correlation function (CCF) for time series of unevenly sampleddata is far from trivial. The approach we use was proposed by Scargle [37] in 1989. TheCCF, p, is defined by:PxY(t) = .7.-1(PxY(uP)) (4.14)where .F-1 denotes the inverse Fourier transform and pxy = FTx(co) FT;,(ca) , whereFT denotes the discrete Fourier transform, and the * superscript indicates the complexconjugate. The code presented by Scargle was slightly adapted to allow weighting of thedata. It should be noted that the CCF, although definable for any lag, is meaningfulonly when there is a significant overlap between the two data sets. One problem withthe use of this CCF is the existence of a zero-lag spike resulting from correlated errorsin the data sets. This may be difficult to distinguish from a "real" effect.A second cross-correlation technique was used as a check on the Scargle algorithm,and also to resolve the difficulty associated with the zero-lag spike. This time the Pearsoncorrelation coefficient, r, defined by:E(zi - 7)(v+ -VE(xi — ) 2 1/E(yi — 0 2is determined as a function of the time lag between the two data sets. A linear interpo-lation was used between data points in one of the data sets, primarily because it givesrise to the simplest calculations and there is little, if anything, to be gained by using amore complex interpolation function.The combination of cross-correlation functions we are using should be able to detectany significant correlation with a zero time lag, but for a non-zero lag will be sensitive tor = (4.15)Chapter 4. Data Analysis Methods^ 29any correlation only if the variability has a time scale on the order of several months, thetypical sampling interval, or more. Any variability more rapid than this with a non-zerolag between the data sets will simply not be detected due to undersampling of the data.Chapter 5Applications of Data Analysis MethodsIn using the PRV data to search for evidence of a planetary companion around each ofthe candidate stars we are essentially looking for a signal which has the characteristics ofa spectroscopic binary orbit, while at the same time attempting to detect spurious signalswhich may be caused by intrinsic variations. To this end various analysis packages werewritten, and are briefly described below:5.1 Generalized periodogramTraditionally the Fourier power spectrum has been used to estimate the power con-tributed by a range of frequencies to the total variance of a set of data. However, Lomb[28] claimed that for the case of unequally sampled data a better approach is that ofthe least-squares spectrum, which reduces to the Fourier power spectrum in the case ofequally sampled data. Lomb uses the model:= a cos 27rfti b sin 2irfti (5.16)given a set of observations y i (i = 1, 2, 3...) (where each measurement is determinedby the signal value, y i , and the error of the measurement, ei) with zero mean obtainedat times ti. Where necessary a constant value is subtracted from the measurements toensure a zero mean. Lomb then further defines:30Chapter 5. Applications of Data Analysis Methods^ 31^CC = >2 coo 2.7r fti^ (5.17)i=1SS = >2^2214 (5.18)i=1^CS = E cos 22-fti sin 271-fti^(5.19)i=1^YC = E yi cos 27rfti (5.20)i=i^YS = E yi sin 27( fti^ (5.21)1=1We can then define the normalized periodogram by:yc2 ys2"2 (5 .22)P(f) = n( CC + —SSwhere x2 is the chi-squared value for the data for a constant zero value model. Thisequation is equivalent to:P(f) = n (x2x:) x2(5.23)where x: is the chi-squared value for the residuals from the sinusoid for a constant zerovalue model.For the generalized periodogram we simultaneously fit a "parent function" and thesinusoid. The parent function is used to allow for a non-zero mean, secular trends, or aperiodic signal in the data other than that which we are looking for. The choice of theparent function will depend upon the nature of the data being fitted. The normalizedperiodogram is now defined by:2P(i) = (n — m) (43 — X p+8 )4 (5.24)Chapter 5. Applications of Data Analysis Methods^ 32where Xp is the chi-squared value of the residuals from the parent function, 4 +8 is thechi-squared value of residuals from the parent function plus sinusoid, and m is the numberof free parameters in the parent function. The parent function and sinusoid are fittedsimultaneously to avoid problems with the correlation between parameters of the twofunctions. A better fit is obtained with simultaneous determination of the parameters.For our purposes the parent function is a second order polynomial, and we determine theperiodograms for the PRV, AEIVc„H, and ATefi data for each of our candidate stars.In order to determine the significance associated with the generalized least-squaresperiodogram we determine the periodogram for each of 100 data sets with the datashuffled randomly in time. These randomized data sets have the same observation timesand associated errors as before. The significance of the peak at any given frequency isdefined as the fraction of times that the power in the original data set exceeds that ineach of the randomized data sets. A low significance indicates a high certainty in therebeing no signal at that frequency. However, a high significance merely indicates a lowcertainty in there being no signal at that frequency. A periodogram is useful to excludefrequency ranges from further consideration. The reader should be extremely cautiousof concluding the existence of a periodic signal from a peak in a periodogram, regardlessof how significant it may be.We also determine the window function of the data set using the classical periodogram.The window function, G(w), is defined by:NO^ No1G(CL) = iv-; ((E cos wt; )2 + (E sin (4.02 )^(5.25).1=1^1=1where No is the number of data points, w the angular frequency, and t, the time ofobservation of the jth data point. Peaks in the periodogram which have correspondingpeaks in the window function are most likely to be due to the sampling of the data, andChapter 5. Applications of Data Analysis Methods^ 33not to any variation of the data with the frequency associated with the peak.5.2 TrendsAs the PRV data covers only an 12 year time span, a periodogram is of no usewhen looking for a period which is significantly longer than this. However, we can lookfor secular trends in the data which may be indicative of a long period. In order to dothis we fit the data with a zeroth, first, and second order polynomial and calculate the Fstatistic for the two higher order polynomials with respect to the zeroth order polynomial,a simple offset fit. When the F statistic indicates that the data is better fit by one ofthe higher order polynomials we run a Monte-Carlo simulation, in which we repeatedlyrandomize the data in time and refit it. This allows us to calculate the significance of thehigher order polynomial fit, and so whether or not the data shows a significant seculartrend.5.3 Cross-CorrelationA procedure for determining whether or not there is any correlation between the PRVand AEWcan. data, and the PRV and ATeff data is useful for a variety of reasons.A periodic signal in the PRV data, which may be taken as evidence of a planet,may also be caused by the chromospheric activity of the star. This would, hopefully, beindicated by a correlation between the PRV and AEWcan data. Alternatively, given thatthere is a correlation between the PRV and AEIVcciii data the chromospheric activitymay be obscuring the signal due to the presence of a planet. If we can remove theeffects of the correlation then the planetary signal may become evident. Thus, the datais searched for correlations from a time lag of —1000 to 1000 days. It was felt that thisrange covered all reasonable time lags while allowing for adequate time resolution.Chapter 5. Applications of Data Analysis Methods^ 345.4 Minimum massThe minimum mass of the planet detectable is estimated as a function of the period foreach of the candidate stars. This is done by creating a sinusoidal signal, which implicitlyassumes a circular orbit, sampled at the same times as the original data, and thenadding noise, based on the errors of the original data. The noise value is calculated froma Gaussian distribution with a standard deviation of 1.5 times the error value associatedwith that point. The factor of 1.5 is used as the PRV errors seem to be consistentlyunderestimated at this level.The amplitude of the sinusoid is increased until the signal is detected at the 99%significance level. This is determined by demanding that the sinusoid is a better modelof the data than a simple offset at the 99% level, based on the F statistic. We thenfurther demand that the chi-squared value for the originally generated artificial data isless than that of at least 99% of the randomized data sets.Assuming a primary mass of 1M0 we then calculate the value of (Ms sin i)min , theminimum detectable secondary mass, given a signal of the determined amplitude. Re-peating this procedure for a range of periods we are able to determine the minimumsecondary mass versus period. This relationship is useful as a secondary check of theperiodogram of the PRV data. The periodogram analysis also provides the "secondarymass" as part of the output , again assuming a primary mass of 1M 0 , and a signal of thesame amplitude as the fitted sinusoid. If the inferred secondary mass for a given periodis less than the corresponding minimum detectable mass then we can be sure that thereis no detectable signal at that period.The minimum mass analysis also allows us to determine a lower limit to the value ofMs sin i, versus period. In the event that the primary mass is significantly different from1M0 then we can use the relationship:Chapter 5. Applications of Data Analysis Methods^ 35(Ms Sill i)mi oc 3 (5.26)It is worth noting that the minimum mass so derived represents a strict lower limitIn reality the lower limit on the detectable mass is probably significantly higher thanthis due to the complication of the signal by intrinsic variations, effects of more thanone planet, soft binary companions, secular changes, and possibly other factors not evenconsidered. However, the range of values does indicate the sort of planetary mass thatthis system is sensitive to, given the length of the data string. The minimum detectablemasses for the periods 0.25, 0.5, 1.0, and 10.0 years are given for each of stars in 5.1.Chapter 5. Applications of Data Analysis Methods^ 36HR HD name Sp. type (minimumP=0.25 yrdetectableP=0.5 yrmass) x sinP=1.0 yri (MJupiter)P=10.0 yr.509 10700 r Cet G8V 0.32 0.41 0.54 1.00937 19373 t Per GOV 0.44 0.57 0.84 1.49996 20630 rs1 Cet G5Vvar 0.53 0.65 1.00 1.791084 22049 e Eri K2V 0.39 0.48 0.69 1.261325 26965 o2 Eri K1V 0.47 0.61 0.88 1.472047 39587 x1 Ori GOV 0.72 0.89 1.31 2.142943 61421 a CMi A F5IV 0.36 0.46 0.59 1.143775 82328 9 UMa F6IV 0.67 0.87 1.02 2.704112 90839 36 UMa F8V 0.46 0.60 0.70 1.544540 102870 # Vir F9V 0.33 0.44 0.52 1.004983 114710 )3 Com F9.5V 0.42 0.53 0.68 1.355019 115617 61 Vir G5V 0.42 0.53 0.67 1.355544 131156 4 Boo A G8V 0.39 0.52 0.69 1.426401 155886 36 Oph A KOV 0.68 0.84 1.25 2.666402 155885 36 Oph B K1V 0.63 0.71 1.02 2.107462 185144 o Dra KOV 0.38 0.43 0.63 1.237602 188512 /3 Aql G8IV 0.34 0.39 0.54 1.077957 198149 i Cep KOIV 0.34 0.39 0.53 1.038085 201091 61 Cyg A K5V 0.40 0.51 0.69 1.308085 201092 61 Cyg B K7V 0.48 0.58 0.98 1.898832 219134 K3V 0.52 0.67 1.00 2.08Table 5.1: Minimum detectable masses for 0.25, 0.5, 1.0, and 10.0 year periods.Chapter 6Proof of the ConceptPrior to investigating the PRV data using all of the techniques already discussed wepresent test cases to demonstrate that the analysis yields the expected results.6.1 Error AnalysisAs confirmation of our error analysis method we use a simultaneous least-squares-fitto the radial velocity measurements from the literature of both components of 7 Per(rvi , rv2 ), the PRV measurements of the primary component (prv i ) together with visualbinary data (p, 0). The models are given below:^9(t) =^tan-1(tan(f(t) + w) cos i)^(6.27)a(1 — e2) cos( f + w) ^p(t) (6.28)1 e cos AO cos(O — n)rvi (t) = K(0 1+7^(6.29)rv2 (t) = —K(0 1 r+ r^(6.30)prvi(t) = rvi(t) 71,pry (6.31)where K is defined by:2r sin i 3.0856 x 1016 tan aK (t) =  ^(cos(f(t) + w) + e cos w)^(6.32)e2^P(sec)^w37Chapter 6. Proof of the Concept^ 38and f, the true anomaly, is defined in Appendix B. The remaining parameters are de-scribed in table 6.2. The fit to the radial velocity data is seen in figure 6.4, where thesolid line gives the fit, the empty circles radial velocity measurements of the secondaryfrom the literature, the full circles radial velocity measurements of the primary from theliterature, and the triangles the PRV measurements of the primary. The fit to the visualbinary data is seen in figure 6.5, where the solid line gives the fit and the circles thevisual binary data from the literature.Figure 6.4: Fit to the radial velocity data for -y Per, where the solid line gives the fit, theempty circles radial velocity measurements of the secondary from the literature, the fullcircles radial velocity measurements of the primary from the literature, and the trianglesthe PRV measurements of the primary.We choose this particular model as it is the most complex, and so provides the mostChapter 6. Proof of the Concept^ 39Figure 6.5: Fit to the visual binary data for y Per, where the solid line gives the fit andthe circles the visual binary data from the literature.stringent test for our error analysis. The derived parameters and associated errors werethen compared to the errors calculated from a Monte-Carlo method, where Gaussiannoise is added to the data set and the parameters recomputed a total of one thousandtimes for good statistical validity. In table 6.2 we present the parameter values and errorsderived from the simultaneous least squares fit, together with the errors found from theMonte-Carlo simulation.As can be seen from table 6.2 our error values are in good agreement with each other.Parameters 1 and 5 (period and r) have low error values in the Monte-Carlo methodcompared to the error analysis in the simultaneous least squares fit. This results fromthe high correlation, with a correlation coefficient of 0.94, between these two parameters,Chapter 6. Proof of the Concept^ 40No. symbolparameterunits^descriptionsimultaneous 1.s.f.value^errorMonte-Carloerror1 P days period 5328.81 0.74 0.362 e eccentricity 0.7774 0.0011 0.00113 w radians periastron —0.1840 0.0012 0.00124 fl radians ascending node 4.2544 0.0043 0.00445 r days epoch 2948.02 0.77 0.426 i radians inclination 1.5957 0.0061 0.00617 a arcsecs semimajor axis 0.1450 0.0013 0.00138 w arcsecs parallax 0.01358 0.00017 0.000139 -ti ms-1 offset —1440 200 21010 r mass ratio 1.433 0.022 0.02211 72 ms-1 offset 1740 230 24012 71,pry ms-1 offset 380 200 210Table 6.2: Error analysis comparison for 7 Perwhich has resulted in an underestimation in the error for the Monte-Carlo method.6.2 PeriodogramAs an independent check of the periodogram algorithm we analyze the -y Cep PRVresidual data, obtained after the removal of a stellar binary orbit, with K = 1645ms -1 ,from the original data, together with the AEWcall data.These data sets are selected as they have known periodicities [44] of relatively lowamplitude. From our periodogram analysis we derive a period of 940 days for the PRVresidual data and 930 for the AEWc,,n- data. These compare with the previously citedvalues of 922.56 f 20 and 906 ± 29 respectively.Thus, our periodogram analysis retrieves the known periods at a very high significancelevel, as can be seen from the periodogram of the PRV residual data in diagram 6.6, wherethe solid line gives the power as a function of frequency, and the dashed lines show the50, 90, and 99 percent significance levels. The peak at a frequency of lyear -1 is due toC)0206040I^I\428X26 r;C.)oCO.9^IC0.5...OOCChapter 6. Proof of the Concept^ 41the sampling of the data with an annual period, and the peak at very short frequenciesis due to a trend in the data which can be fitted by a period of 18 years.7 Cep K0111 [residuals]frequency (years - ')1^2^3I^1^ 1- 1012OOfrequency (days -1 )Figure 6.6: Periodogram of -y Cep PRV residual data. The solid line gives the power andthe dashed lines indicate the 50, 90, and 99 percent significance levels.6.3 Cross CorrelationThe cross-correlation function between data sets is the least certain of all the analysistechniques for a number of reasons, such as the poor and uneven time sampling of thedata and relatively low signal-to-noise ratio. This results in a very noisy correlationfunction which may be difficult to interpret, which proved to be the case more with theScargle algorithm than with the simple linear interpolation method.Again, to confirm our analysis methods, we use the 7 Cep PRV residual and AEWcai/1000-—1000^—500 At (Says)^500Chapter 6. Proof of the Concept^ 42data. These data sets are used as they are known to exhibit a significant correlation, inthat they both show sinusoidal variations of similar period. The epoch difference of zerophase between the two signals is given as 84.3 ± 32.2 days ([44] ). The correlation functionfrom the linear interpolation method is seen in figure 6.7, with the solid line giving thecorrelation value as a function of time lag and the dotted line showing the significance.y Cep K0111 [residuals]Figure 6.7: Cross-correlation function for the 7 Cep PRV residual and L1EWcaH data.The solid line gives the correlation coefficient, r, and the dotted line the significanceAs we would expect the cross-correlation function shows a peak at a time lag of 0days, with r = 0.31 and a significance of 0.85. Although we would normally considersuch a peak not to be sufficiently significant it is still useful to know that a peak is found,even if at a relatively low level.Chapter 7Results7.1 PeriodicitiesAfter analysis of the PRV, AEWcaz, and ATeff data of the twenty-one dwarfand subgiant stars of the HF program using the generalized least-squares periodogrammethod, we reached the following conclusions:• PRVIn the case of the PRV data no significant periodicities were found between 100 daysand •-• 15 years. A typical result is shown in figure 7.8, where, in the upper plot, thesolid line gives the secondary mass, in Jupiter masses, assuming that the amplitude ofthe fitted sinusoid at the given period is due to a companion, with a primary mass ofMe . The dotted line gives the minimum detectable mass, and the dashed line gives thex2 /v value for the fit. For the lower plot the solid line gives the power associated withthe period, and the dotted lines give the significance levels (at 0.5, 0.9, and 0.99) for thepower.In the case of a true periodicity we would expect the secondary mass to exceed theminimum mass, and the power to exceed the 0.99 significance level. At the same timewe would expect the x2/v value to drop to around unity.• AEWcanIn the case of the AEWcan, we find significant periodicities for four stars, which arelisted in table 7.3 with the more important parameters of the fit.43Chapter 7. Results^ 44Figure 7.8: Generalized periodogram for r Cet PRV data. In the upper plot the dottedline gives the minimum detectable mass, the dashed line x 2/v. In the lower plot the solidline gives the power and the dotted lines the significance at the 50, 90, and 99 percentsignificance levels.HR HD name Sp. type P (years) K (mA)1325 26965 o2 Eri K1V 9.24 ± 0.07 7.68 ± 0.147462 185144 a Dra KOV 7.21 ± 0.06 5.63 ± 0.118085 201091 61 Cyg A K5V 6.86 ± 0.03 12.99 ± 0.138832 219134 K3V 10.34 ± 0.22 7.22 ± 0.22Table 7.3: Periodicities in the AEWcar dataThe generalized periodogram for the o2 Eri AEWain is given in figure 7.9, where000 01^bl^1^1001 11.I I^/1./^I^J .^\r I k 801./ I 160 X240frequency (years - ')1 2 32 13020.9920c.cc^1 09eco--rnChapter 7. Results^ 45in the upper plot, the solid line gives the amplitude, the dotted line gives the minimumdetectable amplitude, and the dashed line gives the x 2/v value for the fit. For the lowerplot the solid line gives the power associated with the period, and the dotted lines givethe significance levels (at 0.5, 0.9, and 0.99) for the power. The peak in the periodogramat a frequency of 0.0005 years' is readily apparent, and the data is phased to thisperiod in figure 7.10.o2 Eri K1VINDfrequency (days - I)Figure 7.9: Generalized periodogram for o 2 Eri ZIEWcair data. In the upper plot thedotted line gives the minimum detectable mass, the dashed line x 2/v. In the lower plotthe solid line gives the power and the dotted lines the significance at the 50, 90, and 99percent significance levels.A T, f fAs with the PRV data we find no significant periodicities in the ATeff data betweenI^ I60§I^ IChapter 7. Results^ 46o2 E6 K1V0^ 0.5 1phaseFigure 7.10: Phased o2 Eri AEWcai data..100 days and ti 15 years. Again a typical negative result is shown in figure 7.11, where,in the upper plot, the solid line gives the amplitude, the dotted line gives the minimumdetectable amplitude, and the dashed line gives the x 2/v value for the fit. For the lowerplot the solid line gives the power associated with the period, and the dotted lines givethe significance levels (at 0.5, 0.9, and 0.99) for the power. The peak at a frequency of", 1.6 yrs-1 , although exceeding the 0.99 significance level, is not associated with a trueperiodicity as the detected amplitude does not exceed the minimum detectable amplitudeat this frequency. Further, and perhaps more convincingly, when the data is phased tothis frequency there is no discernable signal.201 0E0—10—20Ia0a0.9c3frequency (years - ')1^2oco0000 0rnT Ccl CIIV243Xz/v••-■0.5403020103020i.aa. 10I I^I^IChapter 7. Results^ 47frequency (days -1 )Figure 7.11: Generalized periodogram for r Cet AT.11 data. In the upper plot, the solidline gives the amplitude, the dotted line gives the minimum detectable amplitude, andthe dashed line gives the x 2/v value for the fit. In the lower plot the solid line givesthe power associated with the period, and the dotted lines give the 0.5, 0.9, and 0.99significance levels for the power.7.2 Correlations• AEWcairSignificant correlation between the PRV data, after removal of the secular accelerationdue to proper motion and binary orbits, and AEWcal was found for two of the twenty-one program stars. These are listed in table 7.4, where we give the value of r (Pearson'scorrelation coefficient), the significance as a fraction of unity determined from Monte-Carlo simulations, and the time lag for the correlation. The last column gives the slopeChapter 7. Results^ 48of the linear best fit to the data, together with the associated error.HR HD name Sp. type r significance St A EWcan ZAP RV(m /ms -1 )4112 90839 36 UMa F8V 0.668 0.961 0.0 0.21 ± 0.044983 114710 13 Com F9.5V 0.617 0.930 0.0 0.43 ± 0.08Table 7.4: Correlations between the PRV and AEWcaz dataWe note from table 7.4 that there are no significant correlations between the data foran obvious non-zero time lag. A plot of the correlation coefficient, shown as the solidline, and the significance, shown as a dotted line, as a function of the time-lag is givenin figure 7.12 for 36 UMa. A plot of the AEWc an data as a function of the PRY datafor 36 UMa is given in figure 7.13.• To. fThere were no significant correlations found between the PRV data, after removal ofthe secular acceleration due to proper motion and binary orbits, and the AT eff data.7.3 Secular trendsAnalysis of the data for secular trends revealed several data sets which show suchtrends. These are listed below in tables 7.5, 7.6, and 7.7. The tables give the order, eitherone or two, of the polynomial which best fits the data, together with the significance ofthe fit determined from a Monte-Carlo simulation with one thousand randomized datasets. Only those fits for which the significance exceeds 0.95 (z_a 2o) are listed.• PRVThe PRV data is analyzed for secular trends after removal of accelerations, if neces-sary, due to the star being in a binary system (see Chapter 8) and the proper motion (seeChapter 7. Results^ 4936 UMa F8VU)C0U)0Figure 7.12: Cross-correlation function for 36 UMa PRV and LIEWcair data. The solidline gives the correlation coefficient, r, and the dotted line the significance.Appendix C). As table 7.5 indicates approximately one half of the PRV program starsshow significant secular trends in the PRV data. This is in good agreement with theresults from Campbell et al. [10] who find that seven out of sixteen stars show significantsecular trends, compared to ten out of twenty-one in our case.• DEWcairAs table 7.6 indicates approximately one half of the PRV program stars also showsignificant secular trends in the LIEWcati data.• OTelfAs table 7.7 indicates only three of the PRV program stars show significant seculartrends in the ATell data.I^I'^I^1^IT^1^11050—5—10—100^—50I^,^I 0 50 100PRV (ms-0Chapter 7. Results^ 5036 UMa FM/Figure 7.13: Correlation between ZIEWcam and PRV data for 36 UMaHR HD name Sp. type order ofpolynomialsignificance1325 26965 o2 Eri K1V 1 0.9962943 61421 a CMi A F5IV 1 0.9983775 82328 0 UMa F6IV 1 0.9674112 90839 36 UMa F8V 2 1.0004540 102870 /3 Vir F9V 2 0.9974983 114710 )3 Com F9.5V 1 0.9985544 131156 Boo A G8V 1 1.0006402 155885 36 Oph B K1V 2 0.9977462 185144 a Dra KOV 1 0.9667957 198149 q Cep KOW 1 0.992Table 7.5: Trends in the PRV dataChapter 7. Results^ 51HR HD name Sp. type order ofpolynomialsignificance937 19373 t Per GOV 2 0.9991084 22049 c Eri K2V 1 1.0001325 26965 o2 Eri K1V 2 0.9974112 90839 36 UMa F8V 2 0.9984983 114710 f3 Com F9.5V 1 1.0005019 115617 61 Vir G5V 1 0.9915544 131156 Boo A G8V 2 0.9746401 155886 36 Oph A KOV 2 0.9836402 155885 36 Oph B K1V 2 1.0007462 185144 a Dra KOV 2 0.9898832 219134 K3V 2 0.999Table 7.6: Trends in the LIEWcan dataHR HD name Sp. type order ofpolynomialsignificance509 10700 r Cet G8V 2 0.9682047 39587 xl. Ori GOV 2 0.9776402 155885 36 Oph B K1V 2 0.992Table 7.7: Trends in the ATefi dataChapter 8Binary StarsAlthough double line spectroscopic binaries were deliberately excluded from the ob-serving list several are known to be components of binary systems. We list them in table8.8.HR HD name Sp. type reference1325 26965 o2 Eri K1V [49],[21],[47]2047 39587 X2 Ori GOV [23]2943 61421 a CMi A F5IV [24]5544 131156 Boo A G8V [49],[22],[47]6401 155886 36 Oph A KOV [49],[6]6402 155885 36 Oph B K1V [49],[6]8085 201091 61 Cyg A K5V [49], [26]8085 201092 61 Cyg B K7V [49],[26]Table 8.8: Known binary systems and references for best orbitsThe orbital parameters of x 2 Ori [23] and a CMi A [24] based on PRV, conventionalradial velocities, astrometric, and visual binary data, have been discussed at length inthe papers indicated, and we will not address them further here. The remaining membersof binary systems all have well determined parameters which can be found in the literat-ure. Using these parameters we can compare the PRV measurements with the predictedradial velocities as a function of time. The only free parameter is a simple offset, which52Chapter 8. Binary Stars^ 53essentially converts the predicted absolute barycentric radial velocities to the same zeropoint as the PRV measurements. The results are shown in figures 8.14, 8.15, 8.16, and8.17 for each of the six members of binary systems which we are considering, where thesolid line gives the predicted values from the orbital parameters, and the points are thePRV measurements.02 Eri K1VwFigure 8.14: Predicted radial velocities compared to PRV measurements for o 2 Eri. Thesolid line gives the predicted values from the orbital parameters, and the points are thePRV measurements.The goodness of fit to each of the data sets is reflected in the x 2/v values for each,which are given in table 8.9.Clearly the worst fit is that of Boo A where the predicted velocity gradient is steeperthan that which appears to be observed. The cause of this is unclear, but is most likelyChapter 8. Binary Stars^ 54( Boo A G8V2001000—100—2001980^1985 year^1990Figure 8.15: Predicted radial velocities compared to PRV measurements for Boo A.The solid line gives the predicted values from the orbital parameters, and the points arethe PRV measurements.due to poorly determined orbital parameters. It is worth noting that two other researchgroups (Marcy and Butler using an iodine cell and McMillan using a Fabry-Perot) haveverbally reported a similar trend to the PRV group in their data.In the case of 61 Cyg the consistency of the orbital parameters with the velocitygradient seen from PRV measurements is best checked by considering the difference inthe radial velocities of the two components. The differences in the PRV measurements,given the non-simultaneous observing times, are taken as the differences between themean PRV values for each star on a single run. In the cases where either star wasnot measured at least once each on a given run then no difference is taken. The resultChapter 8. Binary Stars^ 5536 Oph A KOV^36 Oph B K1VU)2001000-100-2001980^1985^1990 1980^1985^1990year yearFigure 8.16: Predicted radial velocities compared to PRV measurements for 36 Oph A,B.The solid line gives the predicted values from the orbital parameters, and the points arethe PRV measurements.of this analysis is seen in figure 8.18, with the solid line giving the velocities from thedetermined orbital parameters and the points giving the difference velocities betweenPRV measurements for the two components.Unfortunately the relatively short baseline of the PRV observations in relation to thebinary periods of the systems, together with the shallow velocity gradients, means thatthe PRV measurements provide very little additional constraint on the determination ofthe orbital parameters.100507r24a.-5061 Cyg A K5V^ 61 Cyg B K7V100- -50Chapter 8. Binary Stars^ 56' '19185'^'1919 0-1 (1%Eid^'19196 1980year^yearFigure 8.17: Predicted radial velocities compared to PRV measurements for 61 Cyg A,B.The solid line gives the predicted values from the orbital parameters, and the points arethe PRV measurements.HR HD name Sp. type X2iv1325 26965 o2 Eri K1V 3.45544 131156 E Boo A G8V 4.06401 155886 36 Oph A KOV 1.66402 155885 36 Oph B K1V 2.58085 201091 61 Cyg A K5V 3.18085 201092 61 Cyg B K7V 2.2Table 8.9: x2/v values for fits to PRV data10050-50-1 00^6000^7000^8000^9000J.D. (-2440000)Chapter 8. Binary Stars^ 57Figure 8.18: Predicted difference velocities for 61 Cyg compared to PRV measurements.The solid line gives the predicted values from the orbital parameters, and the points arederived from the PRV measurements.Chapter 9Current Detection LimitsThe current detection limit set on the masses of planetary bodies orbiting nearby starsis imposed by the PRV measurements of the HF group and the astrometric measurementsmade by Gatewood. While we have a good understanding of the limits set by the PRVdata this is not as true for the astrometric data, although we know that Gatewood hasmade no claims for a planetary detection as of yet.9.1 Astrometric detection limitsAssuming the simplest case of a single planet in a circular orbit with the plane of theorbit perpendicular to the observer's line of sight then the angular perturbation, O p, ofthe star is given by:M,Op = 0.952( —m ) 13 D (9.33)Pwhere 01, is the angular perturbation measured in mas, P the orbital period in years,MP the mass of the star in solar masses, M, the mass of the planet in Jupiter masses,and D the observer-star distance in pc.We further assume that D = 2pc and M9 = 1Me , and estimate the minimum de-tectable mass of the planet versus period in a similar manner to the determination ofthe minimum mass for the PRV data. Gatewood [18] claims an accuracy of ti lmaa forhis observations, with 15 observations per year per star, over the last 5 years. Usingthis information we are able to estimate the current detection limits that Gatewood has582 I^I^1^I^I^I^I^'I^I^I^I f^I^IPRVastrometryChapter 9. Current Detection Limits^ 59reached. Figure 9.19 shows the current detection limits from both PRV and astrometricdata.—3^—2^—1^0^1^21og 10[period (years)]Figure 9.19: Current Detection Limits for sini=1, D=2pc.When using the above figure as an indication of the current detection limits it shouldbe remembered that the limits are determined by making various assumptions, all ofwhich give rise to the most optimistic case. For the PRV case some of the factorseffecting this limit include the level of intrinsic variation, number of planets in the system,orientation of the plane of the orbit with respect to the observer, and the mass of thestar, Mp The astrometric case will also be effected by other planets in the system, andthe distance of star from the observer. Considering only the more important factors ineach case we have that:Chapter 9. Current Detection Limits^ 60PRViimit oc"^13111astrometriciimit cc DM?(9.34)(9.35)Clearly, the primary consideration in the current detection limit is how the observa-tions are taken as a function of time, and the error associated with each data point. Theastrometric limit will be reduced with further time as Gatewood is still making observa-tions. However, the PRV limit will remain where it is until either the HF group resumesobserving at CFH, or one of the other PRV groups reaches and exceeds the limit set bythem.Chapter 10ConclusionsAnalysis of the PRV data yields no evidence for periodicities, and hence no evidencefor extra-solar planets, although the secular trends found in the data may be indicativeof periods significantly longer than 15 years. If the search for extra-solar planets isto continue in a meaningful way it is probably time for some changes to the currentapproach. Higher accuracy is imperative and there seems to be no reason why errors oflms -1 or less could not be achieved if sufficient effort were made. At the same timegreater collaboration with other groups, using whatever methods, would greatly facilitatefurther research.Although it is much too early to conclude anything about the frequency of planetarysystems the fact that no group has yet made a definite claim for an extra-solar planetdetection, or at least one which was not subsequently retracted, suggests that such sys-tems may not be as ubiquitous as was once thought. However, at the present time allof the detection methods are only just theoretically capable of detecting a Jupiter massplanet around a nearby star. There is obviously a lot of room for improvement, and everincreasing baselines provide ever increasing constraints on what may be present.This field of research is exciting, relevant, and presently at the forefront of precisionin astronomical measurements. Regardless of the final conclusions the astronomical com-munity in general can not help but benefit from the knowledge gained by the attemptsto find planets outside of the Solar System.61Appendix AHF PRV Program Stars62Appendix A. HF PRV Program Stars^ 63HR HD name Sp. type I obs.509 10700 r Cet G8V 2.41 68937 19373 c Per GOV 3.25 46996 20630 ic1 Cet GSVvar 3.95 341084 22049 6 Eri K2V 2.54 651325 26965 o2 Efi K1V 3.29 422047 39587 x1 Ori GOV 3.61 382943 61421 a CMi A F5IV -0.27 983775 82328 0 UMa F6IV 2.47 434112 90839 36 UMa F8V 4.08 564540 102870 (3 Vir F9V 2.86 744983 114710 13 Com F9.5V 3.46 575019 115617 61 Vir G5V 3.82 535544 131156 Boo A G8V 3.75 586401 155886 36 Oph A KOV 3.99 266402 155885 36 Oph B K1V 4.02 357462 185144 u Dra KOV 3.66 567602 188512 13 Aql 081V 2.59 597957 198149 n Cep KOIV 2.27 588085 201091 61 Cyg A K5V 3.54 508085 201092 61 Cyg B K7V 3.54 348832 219134 K3V 4.23 32617 12929 a Afi K2III 0.54 45915 18925 -y Per G8111+ 2.20 171457 29139 a Tau K5III -1.31 612990 62509 )3 Gem KOIIIb -0.11 393748 81797 a Hya K3III 0.16 505340 124897 a Boo K211p -1.67 1296859 168454 8 Sgr K3IIIa 1.02 227948 197964 72 Del KOIII 2.84 578974 222404 7 Cep KOIII 1.93 732061 39801 a Ori M1.5Iab -2.50 1768308 206778 6 Peg K21b 0.58 46Table A.10: HF PRV program starsAppendix A. HF PRV Program Stars^ 64J.D.(-2440000)PRV(ms 1 ) aAEWcau(mA)^aAT(K)^aA(R - I)(mmag) a4532.039 -49.6 41.2 2.61 1.33 -13.3 22.5 -3.3 5.14534.014 -26.7 21.6 1.32 1.01 -15.6 19.5 -1.8 4.34621.743 21.8 22.1 2.63 1.15 -12.2 13.2 0.7 3.24653.739 -1.0 13.2 -0.59 0.75 -26.0 15.1 4.3 3.44654.723 -7.0 15.0 -0.71 0.66 -29.7 16.1 5.5 3.64771.134 -4.0 11.94913.980 -13.9 16.0 0.48 0.60 -32.8 13.5 4.8 3.14926.856 3.6 13.4 -0.60 0.60 -4.0 8.0 -0.2 1.94957.900 -6.0 16.1 0.10 0.56 -29.6 20.4 4.1 4.75148.111 -13.5 11.4 -0.28 0.61 -3.9 15.5 9.6 6.65166.084 5.6 10.3 -0.18 0.64 3.9 5.4 -1.8 1.45213.044 -1.9 8.9 2.00 0.65 -19.2 10.7 2.1 2.85276.906 -24.6 12.7 1.79 0.70 -35.5 23.2 7.9 5.25711.722 11.2 15.1 -1.08 0.60 -24.3 20.0 5.6 4.55712.800 22.4 12.6 -1.39 0.86 -23.5 14.8 4.6 3.35712.824 -13.9 10.3 -1.18 0.60 4.6 6.0 -2.3 1.55902.075 -15.8 12.1 0.68 0.55 7.3 5.0 -1.8 1.26283.071 -11.6 12.9 2.17 0.49 -7.0 12.2 2.5 3.06283.083 12.9 12.1 3.92 0.66 16.1 7.8 -3.3 2.16047.810 -3.9 10.0 0.16 0.51 -1.2 5.9 -0.2 1.56047.822 -3.3 9.8 -0.69 0.51 10.7 6.1 -3.0 1.56048.780 12.8 9.8 0.05 0.66 4.8 14.0 5.8 5.66393.856 -7.2 20.3 -1.87 0.65 -37.5 40.6 10.3 9.06393.864 -19.6 14.5 -0.94 0.65 -28.0 30.6 7.6 6.86394.877 -12.4 13.9 -0.52 0.60 -53.0 41.4 14.0 9.16604.128 -2.2 9.66605.120 -1.1 8.3 1.30 0.47 -13.7 10.7 3.1 2.56725.850 -2.9 8.7 1.86 0.64 8.2 5.5 -2.3 1.36725.859 -2.4 7.1 2.45 0.69 15.7 8.5 -4.1 2.06726.877 -1.5 8.4 1.50 0.58 0.8 6.6 4.5 3.66784.845 3.1 11.0 1.49 0.51 16.2 9.1 -4.4 2.16785.866 -8.7 7.1 -1.34 0.60 13.5 7.9 1.7 3.66834.777 -3.2 8.9 1.70 0.62 -11.1 10.0 2.1 2.36864.733 7.0 10.7 -0.89 0.64 -2.9 6.1 1.0 1.46865.731 2.8 9.3 -0.29 0.57 -5.5 6.6 5.6 2.86962.126 30.0 13.97020.090 10.1 12.4 1.63 0.61 27.7 12.0 1.8 6.77021.078 8.3 8.8 0.85 0.51 -7.2 24.3 1.2 5.87101.971 -7.3 7.7 -0.44 0.57 2.3 19.8 0.0 4.77102.977 9.8 8.4 2.21 0.66 -25.9 29.0 6.9 6.5Table A.11: r Cet PRV dataAppendix A. .11F PRV Program Stars^ 65J.D.(-2440000)PRV(m3 -1 ) aAEWcarr(mA)^aAT(K) aA(R - I)(mmag) a7159.823 -16.5 13.8 -1.56 0.59 0.1 24.7 -0.5 5.97160.840 6.8 10.4 0.17 0.66 19.4 6.3 -4.5 1.57307.132 3.3 9.77308.127 -0.3 10.57339.074 23.2 12.0 -2.95 0.59 17.1 16.1 -3.4 4.07340.047 21.8 13.0 -0.82 0.62 -7.2 18.3 2.5 4.37340.055 16.3 11.9 -1.52 0.63 -8.6 14.8 2.7 3.57371.003 10.3 8.8 -1.55 0.60 -1.4 15.5 0.4 3.77371.013 14.8 5.1 -0.76 0.54 -16.3 18.5 4.4 4.27372.024 0.4 14.1 -2.39 0.68 -49.8 33.6 12.8 7.57454.849 -11.1 9.4 0.17 0.73 5.7 7.8 -1.3 1.87519.852 -2.1 10.9 -1.68 0.57 -24.6 11.6 4.8 2.77545.734 -1.3 14.0 1.11 0.58 -21.3 12.0 5.3 2.67699.130 11.7 19.57788.046 -18.9 14.5 -1.56 0.53 -14.2 6.4 3.4 1.47788.948 -9.1 7.6 -0.81 0.56 -7.8 6.5 1.9 1.67788.953 -5.2 7.4 -2.38 0.54 -3.7 10.7 8.4 5.37894.840 4.6 14.5 -1.28 0.70 -6.8 8.6 1.0 2.08113.013 13.6 10.4 0.38 0.56 8.5 5.4 -2.7 1.38114.010 10.3 12.7 0.79 0.49 -30.5 32.0 8.4 7.28114.016 8.1 11.6 0.62 0.52 7.7 17.4 -1.7 4.18290.802 5.6 10.4 4.39 0.95 -20.5 12.2 3.9 2.78471.049 -14.8 12.3 -1.25 0.52 -38.5 24.9 8.5 5.58472.000 -9.9 17.6 1.66 0.67 -72.4 32.3 16.7 7.08577.875 -53.3 12.3 0.27 0.62 2.5 6.5 -0.7 1.68578.843 -13.4 8.3 -0.10 0.59 -3.9 6.0 0.8 1.48818.100 6.5 10.4 -0.90 0.51 -3.2 21.0 0.5 4.98818.115 10.6 12.9 -0.48 0.52 4.2 18.4 -1.4 4.5Table A.12: r Cet PRV data ...continuedAppendix A. HF PRV Program Stars^ 66J.D.(-2440000)PRV(ma -1 ) aAEWcal(mA)^aAT(K)^aA(R - I)(mmag) a4621.774 31.1 24.0 0.42 0.76 -9.1 10.8 0.4 2.84654.778 15.4 17.9 1.35 0.67 -7.2 10.7 0.5 2.54655.740 25.9 18.2 1.88 0.62 -56.2 19.3 10.6 4.44914.002 -5.6 21.0 2.05 0.58 -4.0 16.3 -1.4 3.94926.884 -5.3 13.3 0.32 0.58 -11.6 19.2 2.0 4.44957.928 -9.1 17.6 1.62 0.62 38.3 50.0 -9.6 11.35149.116 -43.4 27.7 2.83 1.44 13.7 28.3 -3.2 6.45276.938 18.9 14.6 -0.15 0.62 -6.3 11.2 1.3 2.65711.761 39.9 16.8 0.54 0.60 -17.5 12.7 3.1 3.05712.844 15.7 10.8 -0.52 0.52 18.2 11.0 -4.5 2.46047.886 -13.0 9.4 0.27 0.44 -8.1 12.8 1.5 3.06048.936 1.9 8.1 0.62 0.42 -18.1 11.0 3.8 2.66284.041 23.6 23.7 0.56 0.73 -12.0 23.9 3.5 5.46284.059 18.6 30.3 2.39 0.71 77.7 65.9 -17.6 14.56393.889 12.1 17.3 -1.01 0.35 42.9 16.9 -9.3 3.76394.901 18.2 19.7 0.08 0.52 33.6 17.3 -7.4 3.86725.928 -8.5 13.0 -1.29 0.40 20.7 8.9 -3.8 2.06726.902 -2.8 11.6 0.72 0.38 14.4 11.1 -2.5 2.46784.872 -0.6 13.5 0.48 0.71 3.0 14.5 0.0 3.36785.955 -11.1 10.3 -2.82 0.55 -3.4 22.7 1.2 5.16834.894 4.2 14.4 -0.80 0.62 -23.4 13.4 4.6 3.06864.831 8.3 13.8 0.68 0.41 -44.4 23.9 9.5 5.66866.734 12.0 10.8 -2.40 0.41 0.3 12.4 1.0 2.77020.101 -14.6 6.9 -1.25 0.50 15.1 12.0 -3.0 2.77021.089 -7.8 8.6 -0.25 0.47 19.2 11.8 -3.9 2.67101.993 14.1 9.9 -1.17 0.64 2.8 21.4 -0.5 4.87102.997 18.0 13.2 -1.26 0.64 9.2 19.3 -1.8 4.47159.848 9.8 9.7 -0.46 0.42 -49.3 27.8 10.4 6.87160.871 -10.8 10.8 -0.48 0.65 -1.4 22.2 0.2 5.07229.835 -14.7 32.8 -3.24 1.94 -60.7 43.7 12.0 9.87339.097 0.8 16.6 -2.80 0.77 -12.7 21.4 3.4 4.97340.080 -9.9 11.4 -0.14 0.60 7.9 11.0 -0.5 2.57371.061 8.2 15.4 0.64 0.54 97.3 27.2 -20.0 6.57372.039 -12.1 11.3 0.06 0.60 10.4 8.3 -1.3 1.97454.876 -11.0 9.5 -1.71 0.76 -10.2 20.9 2.9 4.77519.884 8.0 7.3 0.09 0.58 -26.0 9.6 5.3 2.47545.759 -7.3 13.6 -0.10 0.97 11.2 10.5 -1.7 2.47788.068 13.6 11.5 0.62 0.40 -47.9 20.7 11.1 5.27788.986 -9.2 12.8 -0.84 0.47 9.0 9.6 -0.9 2.17788.995 -7.3 14.2 -0.11 0.46 22.3 9.7 -3.7 2.2Table A.13: t Per PRV dataAppendix A. HF PRV Program Stars^ 67J.D.(-2440000)PRV(ma') oA EWcari(mA)^aAT(K) aA(R - /)(mmag) a7894.890 12.3 10.6 2.71 0.68 -18.4 7.5 4.8 1.88113.042 -3.0 9.8 -0.38 0.44 17.8 23.0 -3.9 5.18114.053 4.1 12.0 0.44 0.38 41.6 38.7 -9.6 8.68471.082 -22.2 6.8 1.34 0.52 -28.8 23.9 5.0 5.68577.911 28.5 19.3 1.64 0.55 -31.4 20.7 7.0 4.98578.890 25.7 12.3 1.13 0.49 -15.2 19.0 3.5 4.4Table A.14: c Per PRV data ...continuedAppendix A. HT PRV Program Stars^ 68J.D.(-2440000)PRY(ma') aAEWcaz(mÄ)^aAT(K) aA(R - I)(mmag) a4926.912 -9.9 16.9 -2.92 0.62 52.0 25.3 -12.9 6.44957.956 -49.5 17.4 -17.91 0.90 18.6 57.8 -7.5 13.65276.997 11.5 12.5 -4.34 0.78 9.7 16.8 -2.8 4.15711.777 4.9 12.3 11.64 0.55 -9.7 7.1 1.1 1.75712.867 9.0 10.5 2.02 0.57 7.9 11.0 -3.0 2.66048.818 -9.2 10.3 8.80 0.66 -10.2 7.9 1.5 1.96393.924 0.1 14.5 -4.51 0.72 49.3 21.6 -11.1 5.66394.922 -9.7 14.6 -2.21 0.79 52.2 23.6 -11.8 6.06725.958 -14.4 10.0 -6.06 0.71 16.8 8.4 -3.4 2.26726.923 -24.9 9.1 -10.39 0.84 9.2 12.7 -1.6 3.06785.894 -1.0 10.5 3.35 0.64 32.7 14.9 -7.6 3.86834.808 -10.1 9.0 -9.13 0.70 43.1 12.9 -10.6 3.16864.769 9.3 10.5 -1.10 0.48 -6.6 10.7 1.3 2.46865.777 -18.6 15.9 -6.32 0.52 -19.8 14.5 4.2 3.27021.111 15.0 11.2 -7.42 0.54 6.1 14.3 -1.5 3.47102.025 -23.5 10.9 -10.47 0.76 19.2 11.4 -4.2 2.97103.029 -33.0 12.9 -15.14 0.73 8.0 15.6 -2.0 3.67159.878 -22.7 11.2 -3.26 0.62 -4.9 8.1 1.2 1.97160.896 -34.8 13.9 -11.40 0.65 8.5 13.7 -2.1 3.17339.122 59.9 14.1 7.48 0.72 -14.2 13.2 4.1 3.07340.105 37.9 14.9 18.49 0.61 -25.2 11.7 6.5 2.77371.087 52.8 14.0 14.10 0.71 -20.6 8.9 5.3 2.17372.058 21.1 14.6 12.14 0.68 -13.2 7.2 3.2 1.77454.899 -3.0 14.4 5.96 0.79 -21.0 15.2 5.7 3.47545.777 23.2 11.4 5.94 0.59 13.4 10.1 -3.0 2.67788.096 -1.6 6.8 0.31 0.52 -4.8 5.4 0.9 1.27789.016 9.8 6.2 4.66 0.40 8.3 10.3 -1.2 2.57789.032 9.6 8.2 4.76 0.42 10.8 14.3 -1.9 3.37894.918 23.8 12.1 5.00 0.68 -1.3 9.9 0.1 2.58113.070 2.3 9.9 -3.08 0.50 6.2 11.0 -1.5 2.68114.074 -16.5 13.6 -0.71 0.55 0.0 9.6 -0.1 2.38472.067 41.5 29.6 -5.50 0.96 -6.2 7.7 0.0 1.98577.960 -41.2 17.4 -11.93 0.86 103.2 46.9 -24.8 11.18578.921 -3.7 11.7 -9.06 0.70 8.5 15.5 -1.6 3.6Table A.15: is 1 Cet PRV dataAppendix A. HP PRV Program Stars^ 69J.D.(-2440000)PRV(ms-1 ) aAEWcar(mA)^aAT(K)^aA(R - I)(mmag) a.4534.088 -13.0 22.9 22.26 1.12 -15.9 18.8 -1.2 4.24558.978 11.4 30.0 22.46 0.96 -1.8 21.7 -0.8 5.14558.992 12.2 30.9 19.23 1.04 -4.5 19.4 -0.3 4.64621.814 -14.9 16.8 9.43 0.79 -59.2 43.3 12.6 10.04653.844 -40.2 19.8 6.65 0.83 -4.3 19.5 0.3 4.84655.769 -16.6 20.8 8.16 0.69 -21.3 16.7 4.2 4.14686.746 7.5 17.8 11.90 0.87 -39.7 22.5 9.0 5.24914.024 2.0 11.5 13.58 0.70 -36.8 29.5 6.4 6.84926.932 -5.2 11.7 7.66 0.64 -29.0 30.4 6.1 7.04957.980 4.5 14.4 12.86 0.69 -61.3 40.7 13.2 9.85166.120 -4.3 11.9 3.41 0.65 -15.3 14.9 3.3 3.55277.025 7.1 13.6 0.41 0.64 8.5 23.5 -3.0 5.55357.715 11.5 17.8 -5.33 1.48 -33.1 19.9 7.4 4.55390.756 -8.8 16.1 5.21 0.96 5.2 25.3 0.6 5.95711.836 2.2 14.7 13.40 0.56 -63.5 29.9 5.2 4.85712.889 15.0 14.8 12.76 0.52 -9.5 16.7 1.3 3.96047.919 16.0 8.2 6.14 0.53 2.7 13.5 -1.0 3.26047.935 18.0 10.6 6.89 0.48 -3.9 17.1 1.1 3.96048.964 15.9 11.2 4.52 0.56 5.2 15.6 -1.7 3.76284.127 19.4 19.8 -4.05 0.68 -35.9 25.2 9.8 6.26284.140 34.8 22.16393.944 38.5 13.3 3.52 0.42 5.8 18.3 -1.6 4.36394.941 21.3 11.8 0.03 0.47 26.6 10.7 -6.6 2.66725.985 19.6 10.2 1.52 0.49 -1.6 19.4 1.2 4.56726.940 25.7 11.1 1.56 0.51 9.7 17.8 -2.1 4.26784.896 28.8 15.6 3.23 0.99 -18.8 43.7 5.3 10.36785.916 10.9 9.7 0.79 0.48 16.6 12.1 -4.1 2.96834.836 -9.7 15.7 2.48 0.60 -58.0 34.2 13.6 7.86834.846 -13.1 18.3 2.50 0.64 -16.5 21.4 3.2 4.96864.804 -8.2 15.5 -10.90 0.41 -45.6 21.5 6.0 4.46865.808 -12.7 14.4 -12.19 0.46 -54.6 23.5 8.1 5.26866.756 -1.6 9.9 -7.48 0.44 -13.7 19.5 3.6 4.66866.763 -11.2 12.9 -6.93 0.49 -33.3 19.7 3.1 4.37020.121 -27.0 10.3 -7.49 0.49 36.4 7.7 -8.8 1.97021.130 -7.0 10.7 -10.11 0.45 24.0 17.9 -5.8 4.27102.051 2.3 12.2 1.99 0.47 13.4 15.0 -3.4 3.77102.058 -11.3 13.0 0.77 0.52 14.6 12.7 -3.8 3.27103.051 -16.5 14.1 6.67 0.69 16.6 26.5 -3.3 6.37103.059 -3.7 14.9 6.52 0.67 7.0 25.0 -0.7 5.87159.912 0.7 12.2 9.81 0.47 -39.4 23.6 10.0 5.3Table A.16: c Eri PRV dataAppendix A. HP PRV Program Stars^ 70J.D.(-2440000)PRV(ma') aAEWcan(Ira)^aAT(K)^aA(R - I)(mmag) a7160.915 -22.2 9.3 6.62 0.59 -17.2 17.8 6.3 4.87160.923 -25.1 12.5 5.41 0.61 -16.8 21.3 3.3 5.97228.768 -29.2 13.0 6.80 0.80 5.9 23.3 5.1 5.67228.776 -10.9 18.7 4.73 1.03 4.8 21.7 2.2 6.17340.125 2.2 9.9 8.78 0.72 -18.8 22.6 5.8 5.17371.120 14.0 14.1 -3.33 0.52 -8.7 17.2 2.7 3.97372.080 24.1 8.8 4.11 0.54 -3.6 13.9 1.0 3.37372.087 2.9 10.8 5.82 0.60 -1.6 17.3 0.6 4.17454.915 8.9 11.8 -7.59 0.66 -24.7 21.4 7.2 4.97519.922 -10.9 12.9 -1.86 0.66 -18.4 19.0 4.0 4.37545.794 3.1 13.7 -5.17 0.57 18.2 13.7 -4.0 3.37545.802 -3.1 18.7 -3.98 0.53 4.3 15.8 -0.9 3.87788.115 8.6 10.0 -7.10 0.41 -12.7 15.7 3.9 3.57789.060 -15.9 10.5 -12.83 0.44 12.9 15.7 -2.5 3.77789.067 -7.2 9.4 -12.02 0.43 -1.5 21.2 1.2 4.87894.966 -31.2 9.1 -10.24 0.61 5.8 11.6 -1.4 3.38113.089 -12.7 10.1 -5.53 0.42 17.9 14.1 -4.3 3.38113.096 -14.9 12.3 -8.11 0.49 22.5 14.2 -5.4 3.38114.093 -0.9 10.2 -7.13 0.45 4.2 15.4 -1.1 3.68471.105 -4.7 8.5 3.69 0.55 -25.8 18.1 5.3 4.18471.118 2.8 10.3 4.42 0.49 -26.3 18.2 5.4 4.18472.126 63.1 26.0 9.11 0.86 -35.1 27.5 7.6 6.48577.985 3.8 13.3 2.14 0.50 5.9 18.0 -1.0 4.28577.998 3.0 15.3 1.67 0.44 -12.4 20.0 3.4 4.68578.986 0.1 12.0 -1.78 0.46 -11.7 19.9 3.6 4.5Table A.17: e Eri PRV data ...continuedAppendix A. HF PRV Program Stars^ 71J.D.(-2440000)PRV(ms- 1 ) QAEWcall(mA)^aAT(K)^aA(R - I)(mmag) a4559.033 -15.4 24.5 1.68 0.98 -18.7 8.0 3.3 1.94653.887 11.4 18.5 -4.36 0.90 -3.3 10.7 -2.4 2.34655.819 4.2 15.2 -4.71 0.65 -11.7 5.2 1.4 1.54686.771 60.2 42.0 -2.60 1.16 25.1 37.5 -0.4 9.24914.041 13.8 14.8 -5.91 0.75 -12.1 13.6 0.1 3.34926.970 7.1 15.8 -3.68 0.61 -14.5 13.6 2.8 3.24958.001 12.9 12.5 -4.11 0.64 -5.7 11.5 -0.6 3.15277.048 30.3 15.8 -6.61 0.55 7.9 8.3 -2.6 2.05357.750 -12.4 16.1 -3.87 1.16 -15.3 42.2 7.5 10.65711.869 -2.7 10.5 -8.20 0.55 -43.1 44.1 13.3 11.25712.906 -0.4 12.5 -7.86 0.58 -26.9 42.2 8.1 10.96048.011 -29.1 8.4 -5.06 0.40 12.4 5.7 -3.2 1.46048.860 -5.6 6.7 -7.05 0.51 -18.6 16.2 2.2 3.56393.960 -3.4 14.3 -3.40 0.48 2.7 9.5 5.1 4.06394.976 22.3 12.3 -2.22 0.55 -43.9 67.6 14.1 15.36726.007 3.0 11.0 0.65 0.45 20.4 7.6 -4.8 1.96726.955 -1.1 11.0 2.53 0.46 -14.6 49.9 5.7 11.66784.923 12.6 10.4 3.72 0.98 -16.9 11.9 5.3 2.96785.934 -19.8 7.2 3.79 0.58 -15.9 40.6 6.7 10.56834.867 -0.9 13.7 6.87 0.68 -6.8 12.4 0.6 2.96865.841 8.9 13.0 4.17 0.51 -10.0 7.0 2.9 1.76866.794 19.0 10.9 4.55 0.45 0.8 6.4 1.0 1.67020.139 3.5 7.77021.144 23.9 11.27102.080 -5.2 8.9 12.35 0.53 -55.9 46.7 15.6 10.47103.075 22.6 9.2 10.58 0.52 -0.1 8.9 5.4 3.87159.934 -4.2 8.0 9.09 0.69 -26.0 13.7 5.6 3.27160.940 0.3 13.2 7.36 0.77 -16.5 13.5 2.5 3.07371.135 26.9 15.97372.109 23.4 10.6 7.13 0.66 -31.6 47.3 10.0 10.97455.036 13.3 16.3 7.30 0.82 0.0 5.1 0.7 1.37519.960 -15.0 9.5 7.81 0.66 1.7 7.4 1.6 2.97545.819 10.8 11.2 2.03 0.50 6.7 9.9 -4.1 1.57636.732 -60.4 16.5 -2.32 0.92 13.7 11.4 -5.1 2.57788.128 -0.7 11.2 0.14 0.41 13.8 9.0 -2.8 2.17789.082 0.3 12.3 0.63 0.39 -35.3 48.2 11.1 11.07894.998 -11.0 6.4 1.37 0.70 -36.9 41.8 13.1 10.58113.110 -14.6 13.5 -0.13 0.62 17.7 5.3 -4.1 1.48114.105 1.2 13.6 -1.21 0.54 -20.6 46.4 7.0 10.78472.101 14.5 13.5 -4.70 0.96 -5.6 15.1 0.6 3.6Table A.18: o2 Eri PRV dataAppendix A. HF PRV Program Stars^ 72J.D.(-2440000)PRV(m8-2 )^aAEWccar(mA)^aAT(K)^aA(R — I)(mmag) a8578.025 —7.1 9.6 —7.47 0.54 —11.8 8.1 2.9 2.08578.965 8.0 11.0 —6.42 0.59 5.3 9.6 2.5 1.3Table A.19: o2 Eri PRV data ...continuedAppendix A. HF PRV Program Stars^ 73J.D.(-2440000)PRV(ms -1 )^aLIEWcar(mA)^oAT(K)^oA(R - I)(mmag) a4958.035 8.5 25.9 9.55 0.68 -31.4 22.8 5.0 5.85277.090 8.0 15.4 -6.97 0.72 7.0 7.7 -2.0 1.75357.798 53.9 39.3 -0.76 1.23 31.4 23.3 -9.3 5.45389.901 -28.0 32.0 4.99 0.76 40.7 19.5 -3.5 4.15711.905 28.7 16.2 -4.72 0.60 6.5 4.6 -2.2 1.15712.935 -8.6 12.0 -6.01 0.76 -4.7 13.3 0.2 3.35809.732 -18.5 12.4 -8.88 0.76 10.9 6.7 -3.0 1.55810.739 40.5 16.7 -9.25 0.56 10.0 6.1 -2.9 1.46048.901 24.1 10.9 1.14 0.56 -34.8 20.7 9.1 5.06393.983 42.1 38.8 -1.79 0.48 8.5 14.6 -1.1 3.16394.996 12.5 19.9 7.07 0.64 -2.1 14.1 1.3 3.06538.815 11.2 20.5 -2.47 0.54 0.8 10.0 1.9 2.26726.033 -16.7 13.5 -1.30 0.58 4.3 8.3 -0.3 1.86727.009 1.2 12.1 0.55 0.64 -39.3 30.7 9.5 6.46727.025 -6.2 14.6 0.51 0.69 -39.0 33.6 9.7 7.06784.953 40.5 17.8 3.27 0.68 -7.2 17.5 0.6 4.56785.980 -25.3 19.3 -2.18 0.63 -8.5 12.8 0.7 3.06834.933 -32.8 28.8 0.90 0.68 -17.5 12.3 2.4 2.66864.871 -0.8 15.3 1.45 0.54 -1.6 7.2 -0.2 1.66865.876 3.1 21.4 8.12 0.65 -20.3 9.5 4.2 2.47102.106 16.6 18.8 7.36 0.64 -2.5 11.5 1.3 2.57159.958 -20.7 19.2 5.51 0.75 -35.2 16.3 7.5 3.87160.961 -14.5 16.8 1.28 0.64 -19.4 15.8 3.4 3.87228.801 -6.1 30.8 7.25 1.96 11.7 9.1 -0.7 2.47229.804 -35.1 18.1 0.31 0.85 -9.0 6.1 2.5 1.37372.126 25.5 11.37455.064 -6.7 17.2 -5.20 0.85 -14.9 20.1 4.4 4.37519.995 -18.1 12.8 1.53 0.59 -0.1 7.9 1.1 1.67545.846 5.6 27.8 -0.29 0.60 -4.4 14.8 2.4 3.77545.858 6.0 31.9 -0.46 0.64 -10.8 14.7 3.7 3.77636.718 -20.5 29.07788.141 -8.8 14.3 -1.69 0.56 -7.0 7.3 2.4 1.67789.102 -16.1 14.7 -0.49 0.59 -35.2 26.9 8.4 5.78113.130 -1.4 12.4 -0.67 0.54 7.4 5.9 -1.5 1.38114.129 5.3 12.1 -1.19 0.48 -1.3 7.4 0.4 1.68290.855 -30.5 19.3 -9.16 2.25 8.9 20.2 0.1 4.68578.072 -9.3 16.3 -0.94 0.51 -7.0 6.1 -5.2 4.68579.040 -0.1 10.4 3.22 0.50 3.9 7.0 -0.6 1.6Table A.20: x 1 Ori PRV dataAppendix A. HF PRV Program Stars^ 74J.D.(-2440000)PRY(ms -1 ) aAEWca.r(mA )^aAT(K) aA(R - I)(mmag) a4534.134 57.5 19.6 -2.75 1.12 -68.5 57.0 11.8 12.54559.079 14.5 31.1 1.01 0.81 -3.1 18.8 0.1 4.14559.081 48.5 33.3 0.78 0.80 -9.7 18.9 1.4 4.24560.072 -3.4 28.6 -0.91 0.82 -9.4 18.1 1.3 4.14560.085 20.4 29.8 2.86 0.93 -15.1 14.8 2.9 3.34560.100 13.8 30.1 -0.01 0.95 -1.2 24.9 -0.2 5.44560.112 13.6 26.9 -1.01 0.67 -5.0 14.8 1.0 3.34560.126 24.7 28.4 1.53 1.06 -15.4 16.8 2.6 3.84560.140 8.0 28.5 -2.13 0.76 -11.1 17.7 1.8 3.94621.935 -5.6 15.5 1.33 0.89 12.1 18.1 -4.1 4.24627.917 5.4 19.2 -0.90 0.63 20.2 12.4 -5.6 2.64627.945 14.8 17.8 -1.30 0.70 -2.4 11.0 -0.1 2.54627.966 17.7 20.8 -1.44 0.70 4.5 12.2 -1.6 2.74628.005 6.6 21.4 0.30 0.76 2.7 12.7 -1.4 2.84628.024 2.8 22.1 0.15 0.75 7.4 15.8 -2.5 3.54628.048 26.2 21.3 0.65 0.83 4.0 15.5 -1.3 3.44629.952 6.3 19.6 1.30 0.68 -17.3 11.4 2.9 2.54629.964 4.5 26.5 3.00 0.72 -18.3 14.5 2.8 3.24629.976 13.9 24.7 1.41 0.65 -16.8 11.9 2.7 2.64629.991 28.8 22.4 0.70 0.62 -12.0 9.8 2.1 2.24630.006 8.1 27.1 0.65 0.65 -11.6 11.2 1.7 2.54630.048 36.2 23.3 -0.96 0.77 6.7 22.7 -2.1 5.04654.878 -4.6 15.1 1.31 0.72 2.5 14.8 -1.1 3.24655.855 -15.0 17.2 0.06 0.67 -0.7 10.8 -0.5 2.44686.811 89.1 27.1 -3.59 1.06 -29.6 27.8 4.1 6.24686.812 39.3 40.8 -1.03 0.94 -26.3 25.8 3.9 6.04753.744 11.6 20.6 1.46 0.62 31.0 19.5 -6.3 4.24914.068 15.3 26.6 -0.60 0.82 -43.3 35.8 6.2 7.84926.992 -11.7 26.1 -0.24 0.84 -37.9 32.2 0.3 3.24958.048 38.0 28.4 -0.94 0.86 -6.0 14.1 0.1 3.25277.109 40.7 10.9 0.17 0.66 -5.1 14.6 0.9 3.35356.888 -4.7 26.9 -4.67 1.34 33.8 37.9 -5.7 7.35390.894 19.6 15.3 0.70 0.78 6.2 18.6 0.0 4.25390.898 14.6 14.5 0.08 0.73 1.9 19.7 1.0 4.55390.902 16.5 16.0 -0.59 0.77 13.0 26.6 -2.3 6.15390.906 32.2 11.4 0.48 0.66 3.6 24.6 -0.4 5.75458.749 6.1 23.55711.957 17.0 11.0 -0.59 0.56 -2.4 12.5 0.1 2.85712.952 -0.6 13.9 1.52 0.71 10.2 14.8 -2.5 3.25809.748 -6.4 19.7 -1.70 0.65 7.5 19.4 -1.6 4.2Table A.21: a CMi PRV dataAppendix A. RE PRV Program Stars^ 75J.D.(-2440000)PRV(ms 1 ) aAEWcal(mit. )^aAT(K) aA(R - I)(mmag) a5809.750 0.6 11.6 -0.35 0.63 -12.7 17.6 2.3 3.95810.775 -5.0 13.1 -0.96 0.53 -0.7 16.4 0.6 3.65810.776 -25.6 9.5 1.47 0.55 9.7 22.4 -3.2 4.95810.780 -23.4 10.1 1.36 0.61 8.0 22.1 -2.9 4.95810.781 -4.3 10.2 0.49 0.61 10.0 18.2 -1.3 4.06048.050 -10.4 9.6 -1.36 0.62 11.9 11.9 -2.0 2.76048.052 -6.7 11.5 0.33 0.62 13.7 13.0 -2.3 2.96393.902 -25.1 17.5 2.03 0.55 5.2 13.2 -0.7 2.96393.905 -19.3 20.2 0.66 0.66 3.5 17.5 -1.3 3.86393.997 16.0 19.7 -0.96 0.55 -7.6 19.5 1.3 4.36394.112 3.3 12.9 -0.79 0.58 16.6 21.9 -2.6 4.96394.116 37.0 28.6 -0.11 0.61 29.0 29.9 -4.4 6.96394.885 23.4 17.2 0.82 0.64 4.5 15.6 -0.5 3.26394.888 11.2 21.2 -0.81 0.59 1.4 16.6 -0.5 3.46395.014 13.2 9.5 -0.08 0.56 5.7 14.0 -1.6 3.06395.117 15.9 23.0 -1.12 0.62 28.4 20.4 -5.3 4.66395.122 45.1 24.0 -1.00 0.56 15.0 14.9 -2.2 3.46538.841 -28.3 13.7 -0.63 0.47 18.3 14.9 -4.5 3.26538.843 -28.9 11.7 -0.35 0.52 13.4 14.5 -2.7 3.16726.046 -4.9 10.5 0.24 0.60 -2.3 10.0 1.1 2.36726.048 3.7 9.2 0.14 0.57 -3.5 10.5 1.3 2.46727.043 43.2 10.0 -0.15 0.55 -8.1 14.7 2.7 3.36727.044 26.6 9.7 -0.37 0.59 4.9 10.0 -0.5 2.26784.972 59.2 17.3 0.92 0.73 -22.0 11.6 4.6 2.66784.973 43.5 24.9 -0.91 0.89 -33.1 20.3 6.5 4.66784.975 53.5 21.1 -0.59 0.92 -27.5 10.3 6.3 2.36784.976 17.9 13.2 0.07 0.68 -9.6 15.8 2.0 3.46866.822 -30.6 13.7 -0.78 0.61 9.9 15.6 -1.0 3.36866.82 -34.1 14.6 0.96 0.65 21.8 15.7 -3.2 3.46866.823 -15.8 16.6 1.39 0.74 19.1 12.4 -2.6 2.76866.824 3.2 18.5 1.17 0.82 26.1 . 18.9 -3.9 4.26866.825 -17.0 13.6 -0.61 0.65 21.6 19.6 -3.1 4.26866.827 -17.6 14.7 1.25 0.79 24.2 17.6 -3.7 3.87159.971 -16.5 14.5 2.01 0.60 0.8 9.5 0.8 2.07160.978 -32.4 16.8 -1.88 0.57 14.0 13.2 -2.2 2.87160.979 -27.0 13.4 0.59 0.63 -25.7 10.8 6.2 2.57306.732 -21.8 18.8 0.55 0.59 -18.1 21.5 3.5 4.97306.735 3.8 8.9 -0.96 0.57 37.0 21.2 -8.9 4.77307.720 -14.2 9.77455.076 -2.0 13.5 0.84 0.89 -5.6 12.7 2.4 2.9Table A.22: a CMi PRV data ...continuedAppendix A. .11T PRV Program Stars^ 76J.D.(-2440000)PRV(ma') aAEWcar(mA)^aAT(K) aA(R - I)(mmag) a7545.871 -33.7 13.7 0.15 0.64 3.3 16.1 -0.4 3.67545.873 -32.8 14.8 0.43 0.69 10.6 10.4 -1.3 2.37635.841 11.4 18.2 -0.06 0.53 4.3 37.6 -1.2 8.57635.843 12.3 30.2 0.87 0.61 4.5 38.1 -1.0 8.77788.149 7.7 12.6 0.44 0.56 -54.0 60.9 14.4 13.47788.150 11.6 13.07789.109 -12.8 7.2 -0.43 0.54 0.7 11.7 1.0 2.67789.111 -6.9 4.8 -0.49 0.53 -0.3 12.7 0.8 2.87993.745 -20.1 12.3 0.53 0.80 -35.0 26.9 7.6 6.58406.722 -32.4 21.48406.723 -39.8 15.78406.724 -21.9 20.18406.725 -24.3 16.48578.089 12.5 15.4 -1.33 0.75 -1.5 16.4 0.3 3.58578.090 25.7 17.5 -1.06 0.96 2.3 20.8 -1.1 4.48578.091 5.3 8.8 0.28 0.81 14.4 18.3 -3.3 3.98578.092 5.5 7.6 -0.75 0.75 15.9 20.8 -3.9 4.48578.093 -33.2 14.2 -0.49 0.81 26.0 20.2 -5.7 4.3Table A.23: a CMi PRV data ...continuedAppendix A. HF PRV Program Stars^ 77J.D.(-2440000)PRV(ms - 1 ) aAEWcan(mik)^aAT(K) aA(R - I)(mmag) a6394.025 34.8 24.5 -1.14 0.44 -8.9 7.4 2.4 1.96395.033 22.8 21.7 0.39 0.42 -5.6 8.6 1.6 2.26537.933 -10.1 17.8 0.09 0.43 7.1 8.3 -2.1 2.26538.889 -24.1 24.2 -2.18 0.58 8.3 9.0 -1.9 2.46603.758 22.3 16.2 -0.25 0.43 6.1 8.3 -1.1 2.36604.735 8.5 10.36726.061 -4.4 14.6 -0.15 0.42 -4.9 6.3 0.5 1.36727.073 47.7 17.1 0.42 0.54 0.7 8.8 0.3 2.36727.079 30.2 19.1 0.59 0.68 6.9 10.7 -1.3 2.86784.996 15.1 16.7 2.01 0.57 15.2 27.2 -3.8 6.86834.956 -5.7 40.2 -0.69 0.68 16.3 12.7 -4.1 3.66864.916 -15.4 11.7 -0.52 0.48 0.3 7.1 -0.3 1.56865.910 -37.3 12.2 -0.67 0.42 2.2 7.2 0.0 1.86960.736 4.7 22.06961.739 -24.7 36.2 1.73 0.71 -36.4 15.4 6.0 3.67102.123 39.5 14.7 2.57 0.50 -6.0 9.9 1.9 2.67103.091 32.8 12.1 0.35 0.41 10.8 10.7 -2.6 2.76786.004 -6.3 14.9 -2.46 0.51 10.0 13.6 -1.3 3.57159.979 1.4 12.8 0.79 0.39 15.4 13.9 -2.3 3.87160.986 2.8 17.4 -1.56 0.46 -10.6 16.6 5.5 4.07229.048 -15.9 29.7 -0.09 0.62 9.3 15.9 -2.1 4.07229.863 0.7 16.7 -1.36 0.59 -15.1 6.5 0.1 3.57306.748 -8.1 27.9 -2.96 0.70 4.2 6.3 -1.2 1.77307.742 -9.4 17.7 -0.19 0.48 -23.4 11.3 3.5 2.17338.741 -15.4 20.5 2.56 0.43 22.8 9.9 -5.1 2.77339.747 -22.7 23.2 0.18 0.52 26.9 17.1 -6.5 5.07455.099 -1.2 7.8 -0.58 0.68 -18.5 9.5 3.3 1.67520.025 5.6 13.9 0.46 0.53 -7.1 10.2 2.5 2.57545.908 -14.2 22.6 -0.38 0.50 -5.5 8.3 0.7 1.97545.914 -20.3 28.6 -2.46 0.66 -8.6 12.8 0.9 2.97635.740 19.8 22.1 0.90 0.41 10.6 12.5 -2.7 3.47636.750 45.9 38.8 -0.03 0.62 13.1 20.2 -3.0 5.47698.767 26.2 25.6 -0.41 0.71 33.0 18.1 -6.2 5.17699.747 -18.6 16.7 -0.42 0.61 29.0 21.1 -5.2 5.97699.754 -27.7 31.4 0.77 0.61 28.4 20.8 -5.4 5.87789.130 -12.1 13.7 -0.44 0.37 -1.1 7.7 -0.1 1.77993.770 -40.3 20.9 -0.05 0.61 11.0 14.8 -2.1 3.98291.913 -28.7 17.3 0.54 1.06 1.9 14.4 0.8 3.88405.744 -27.2 69.6 0.08 0.91 -22.3 14.8 4.8 4.08405.750 -24.5 58.4 -0.74 0.83 -26.8 14.7 6.8 4.0Table A.24: 9 UMa PRV dataAppendix A. HF PRV Program Stars^ 78J.D. PRV AEWcarz AT A(R — I)(-2440000) (ms -1 )^o (mii)^a (K)^a (mmag) a8406.785 —7.1^49.8 0.53^0.67 —11.8^9.0 2.2^2.38579.001 —11.9^14.0 1.28^0.55 5.1^6.4 —1.5^1.48579.012 —6.0^22.6 1.06^0.64 26.2^11.5 —6.9^2.8Table A.25: 8 UMa PRV data ...continuedAppendix A. HF PRV Program Stars^ 79J.D.(-2440000)PRV(ms-1 ) aLIEWca,H(mA)^aAT(K) aA(R - I)(mmag) cr4686.881 -17.3 69.6 2.94 0.82 67.5 47.8 -16.2 11.34745.811 24.8 24.5 -0.70 1.20 11.7 20.2 -5.4 4.84914.122 47.0 22.1 3.29 0.80 -10.7 11.6 -0.5 2.74927.105 10.1 14.3 1.30 0.66 12.9 23.5 -2.8 5.14958.082 52.0 21.7 2.59 0.74 -43.8 23.3 6.1 5.05390.063 -14.1 19.2 -0.48 1.00 17.9 20.7 -3.3 4.65458.795 27.1 22.15712.000 -16.5 13.1 -1.52 0.60 4.1 12.8 -1.8 2.85712.989 2.8 14.1 -1.49 0.64 -5.0 8.5 0.4 1.85809.808 23.2 12.7 1.53 0.58 -1.6 7.3 0.5 1.75809.824 17.9 10.2 -1.41 0.47 4.5 10.2 -0.8 2.45810.838 1.6 13.7 -0.87 0.52 21.1 15.8 -4.2 3.95863.816 -26.8 22.6 -0.40 0.66 -61.5 19.6 10.5 4.96048.113 -2.5 11.6 0.15 0.71 -2.8 13.0 0.4 2.96048.996 -33.3 20.9 -0.78 0.75 -10.4 12.1 1.8 2.66215.826 31.4 17.3 1.94 0.73 -19.1 27.2 4.5 6.26394.066 -11.0 10.3 -2.86 0.49 -13.2 11.9 2.7 2.66395.071 -25.5 11.9 -2.12 0.48 -0.1 12.0 0.3 2.76537.900 -6.5 9.5 -0.13 0.53 1.5 9.5 -0.3 2.26538.926 -5.6 8.7 -0.57 0.55 10.6 9.2 -2.3 2.26603.798 24.4 11.3 -2.07 0.73 22.3 20.0 -4.8 4.86604.765 -2.9 9.0 0.26 0.51 11.3 13.6 -2.3 3.36726.107 -13.3 9.4 -0.44 0.55 -12.6 9.3 2.8 2.06727.099 22.8 11.4 2.17 0.68 -3.5 13.6 0.8 3.06727.123 2.1 10.7 2.77 0.60 -12.1 13.0 2.8 2.86785.034 -2.3 9.9 -0.29 0.54 -10.0 13.2 1.5 2.96786.031 -18.4 11.1 -4.14 0.58 0.5 11.1 0.1 2.46834.984 -5.1 15.0 -2.79 0.72 -6.8 17.0 1.4 3.76864.945 -2.8 12.2 0.21 0.40 -1.7 12.1 1.0 2.76865.933 -2.2 13.3 -0.61 0.40 17.2 6.1 -3.4 1.56960.763 -22.5 14.6 -1.03 0.58 -27.1 15.0 5.3 3.56961.772 -35.0 19.2 -1.56 0.60 -22.5 14.1 4.2 3.37102.150 8.5 10.67103.121 -14.3 12.0 -1.30 0.55 9.1 12.3 -1.4 2.77160.008 -11.7 8.6 -0.58 0.55 -2.8 16.8 1.5 3.67161.007 -23.9 11.7 -1.05 0.68  16.7 16.8 -3.0 3.77229.897 9.5 10.3 3.88 0.75 35.8 19.9 -6.7 4.77306.768 14.2 13.5 -0.54 0.84 -7.1 19.0 0.8 4.47307.765 8.1 14.2 0.92 0.80 14.0 16.8 -3.6 4.07338.762 3.7 11.1 3.55 0.58 -11.5 10.0 2.9 2.3Table A.26: 36 UMa PRV dataAppendix A. HF PRV Program Stars^ 80J.D.(-2440000)PRV(ma') aAEWoail(mÄ)^aAT(K) uA(R - I)(mmag) a7339.764 9.0 14.7 0.02 0.83 -21.8 21.3 5.0 4.97371.735 -32.5 14.97455.116 -2.1 15.6 -1.31 0.86 -5.0 16.3 2.2 3.67520.060 -4.7 11.5 -0.76 0.70 -7.2 8.2 0.7 1.87545.966 -16.1 18.9 1.42 0.71 -9.6 18.0 2.3 3.97545.987 -34.2 16.4 0.18 0.73 -6.1 14.1 1.9 3.17635.759 -8.4 20.4 -2.86 0.82 43.2 22.6 -9.8 5.47636.772 -1.8 17.5 0.32 0.68 11.6 18.3 -3.1 4.27698.802 31.0 16.2 -0.09 0.86 28.1 14.0 -4.9 3.47699.778 -16.8 24.1 -3.28 0.86 30.1 17.7 -5.4 4.27789.143 -2.3 11.47993.820 23.1 13.8 -0.88 0.78 36.3 20.8 -7.5 5.08291.940 27.5 13.9 6.88 1.07 -11.6 20.7 1.9 4.58405.778 10.6 23.4 4.39 0.53 6.6 10.0 -1.6 2.38406.818 25.7 20.7 4.91 0.64 -37.9 15.8 8.0 3.98579.100 36.7 13.7 1.26 0.53 -1.5 9.6 0.3 2.1Table A.27: 36 UMa PRV data ...continuedAppendix A. HF PRV Program Stars^ 81J.D.(-2440000)PRV(ms-1 )^aAEWcar(nt)^aAT(K)^aA(R - I)(mmag) a4559.136 -65.2 36.0 3.14 2.07 11.2 42.4 -4.6 8.74654.023 15.8 24.4 -2.63 0.58 9.5 23.3 -3.6 4.84686.929 58.2 22.4 -0.02 0.72 -5.3 14.9 0.6 3.24687.940 13.1 15.8 1.26 0.69 3.1 7.3 -1.0 1.74745.871 -6.5 20.9 3.04 1.08 -38.5 17.5 6.2 4.24753.802 -10.5 18.6 -0.28 0.61 -24.5 27.5 5.2 6.24769.796 68.6 23.2 1.27 0.74 -41.1 21.2 8.6 4.94927.169 27.0 11.64958.105 1.2 14.4 -1.64 0.68 -3.1 27.2 -1.6 5.65147.771 30.8 17.3 -1.29 1.01 -33.8 27.2 6.9 6.35277.142 6.2 12.2 1.03 0.58 12.8 20.0 -3.0 4.15391.003 31.0 17.4 2.12 0.97 48.4 40.0 -7.9 8.55458.836 32.1 18.85713.062 -28.6 10.0 0.70 0.64 23.9 19.7 -5.4 4.05809.857 -2.0 9.8 -0.33 0.52 8.8 14.5 -0.3 3.35809.863 12.0 9.7 -1.89 0.56 21.5 16.0 -3.2 3.75810.879 1.1 6.5 -1.76 0.50 3.9 13.1 0.1 3.05864.777 7.5 12.2 -0.30 0.51 -20.2 11.4 2.2 2.95864.788 15.0 13.6 -1.11 0.51 -15.9 8.8 1.7 2.25901.737 21.9 9.96048.142 -26.0 10.9 0.65 0.57 15.1 9.0 -2.8 1.86049.147 -69.8 9.5 2.08 0.61 -0.3 15.3 0.1 3.26049.122 80.4 11.2 0.70 0.62 9.2 14.9 -2.0 3.06136.991 -58.3 30.0 -0.83 1.83 6.1 29.4 -1.0 6.26216.763 7.2 8.5 -0.59 0.55 22.0 11.6 -3.4 2.86216.778 1.4 8.6 -0.54 0.52 2.9 9.3 0.2 2.16394.096 14.4 12.1 0.45 0.52 5.9 14.0 -0.8 2.96395.100 -18.4 8.3 -0.84 0.44 20.2 10.8 -3.8 2.16537.853 6.6 11.9 0.80 0.64 8.3 8.7 -0.9 2.06603.841 7.5 9.1 0.88 0.51 -12.0 11.3 3.1 2.66604.798 6.3 10.9 0.29 0.51 -17.8 11.8 4.2 2.86633.736 3.5 8.76726.142 -25.0 8.5 1.55 0.43 8.6 20.7 -1.7 4.26727.144 -12.9 9.0 1.51 0.49 11.6 19.1 -2.3 3.86785.065 -9.2 10.0 1.12 0.79 -12.2 11.2 3.4 2.56786.072 -22.6 8.0 1.36 0.52 15.0 14.2 -2.9 2.86835.019 -17.3 16.8 0.01 0.66 -10.2 17.3 3.4 3.76864.976 -15.9 24.2 -0.01 0.47 4.5 21.2 1.9 4.36865.987 10.5 13.4 0.54 0.51 11.8 12.7 -1.5 2.56960.790 2.0 15.5 -1.10 0.58 -51.5 18.7 10.8 4.6Table A.28: Q Vir PRV dataAppendix A. HF PRV Program Stars^ 82J.D.(-2440000)PRY(ms-1 ) aAEWcau(mÄ)^aAT(K)^aA(R - I)(mmag) a6961.798 5.3 12.1 -0.76 0.60 6.7 16.4 -0.7 3.77019.726 -9.8 9.47020.725 -15.8 11.07103.151 -11.5 10.77160.041 -10.1 9.8 -0.45 0.47 19.4 30.9 -3.7 6.47161.027 -13.0 9.2 -0.09 0.52 19.1 21.1 -3.5 4.37161.038 -7.1 10.7 -0.39 0.51 30.6 20.7 -5.9 4.17229.025 -3.2 10.6 -1.27 0.78 25.6 20.8 -4.0 4.37229.941 -7.4 12.0 -1.15 0.71 23.4 31.3 -4.2 6.47306.793 4.9 19.3 0.55 0.81 -22.4 26.4 5.8 5.97307.794 14.9 10.8 -0.38 0.67 6.4 23.4 -1.1 5.27338.783 -11.3 17.2 -1.51 0.66 -12.8 16.3 3.6 3.87339.786 -10.6 13.1 -2.62 0.69 -1.8 12.7 1.7 2.97370.774 0.0 11.0 0.41 0.77 -9.4 9.8 2.8 2.37371.754 -18.3 11.9 -0.49 0.78 -11.6 14.9 2.7 3.57455.137 -8.4 12.4 -0.41 0.69 8.8 14.4 -0.6 3.07520.092 -19.7 7.5 -1.91 0.62 10.7 13.4 -2.8 2.77546.008 -33.2 12.8 -1.42 0.66 9.5 18.4 -1.5 3.87546.015 -24.7 11.3 -1.56 0.70 9.5 18.4 -1.7 3.87635.780 17.4 11.3 2.79 0.56 -3.3 16.4 1.3 3.57636.810 -1.2 11.3 0.73 0.67 -19.3 18.1 4.6 4.27698.841 50.8 15.1 -0.28 1.06 -12.1 22.7 4.1 5.17699.824 61.0 15.8 0.25 1.03 -3.1 13.3 2.9 3.07895.020 -2.9 11.2 -1.94 0.76 19.5 19.8 -3.7 4.17993.859 3.7 9.9 -0.09 0.69 -9.5 16.0 2.5 3.48112.738 26.3 10.5 2.01 0.71 -30.1 16.5 6.3 4.08113.732 32.8 10.6 2.65 0.64 -39.9 21.8 8.1 5.38291.966 -10.2 15.0 -1.20 0.91 7.0 13.7 -1.6 2.88291.977 -8.5 11.6 -1.09 0.77 9.4 18.9 -2.0 3.98405.818 11.5 16.2 -2.73 0.56 -33.2 25.9 6.6 6.28470.738 -6.4 11.1 -1.61 0.47 -19.1 11.7 3.2 2.98579.136 60.6 13.8 2.22 0.45 27.5 25.3 -5.2 5.28579.149 75.1 14.9 2.72 0.42 23.5 23.7 -4.4 4.98817.754 39.2 16.6 -2.10 0.74 21.5 22.4 -3.9 5.2Table A.29: 9 Vir PRV data ...continuedAppendix A. HF PRV Program Stars^ 83J.D.(-2440000)PRV(ma') oAEWcair(mA)^aAT(K) aA(R - I)(mmag) a4654.054 17.6 20.9 5.17 0.75 -9.6 15.4 0.3 3.34655.979 30.3 15.4 2.82 0.64 7.7 10.2 -3.3 2.24686.976 -10.8 28.8 7.49 0.68 -8.4 8.2 1.0 2.04745.749 20.0 27.4 5.55 1.18 -9.9 28.4 0.2 6.44753.823 15.6 25.7 2.63 0.69 16.5 22.6 -4.1 5.24769.828 18.0 19.5 7.36 0.60 26.3 15.8 -5.7 3.74958.123 12.4 12.1 -2.76 0.74 -20.8 12.9 1.9 3.05147.816 -14.5 17.8 -5.62 0.69 4.5 6.5 -1.1 1.65165.811 -7.3 19.8 6.42 1.17 5.1 13.5 -1.0 3.25391.131 55.3 30.3 5.43 0.83 -2.9 24.5 3.5 5.55458.867 -2.3 17.95713.088 27.2 13.4 8.96 0.52 -1.7 6.9 0.0 1.65809.887 14.5 15.1 8.16 0.37 24.0 38.7 -4.5 8.95810.892 20.2 7.8 8.07 0.40 -8.0 4.5 2.2 1.05864.810 17.0 13.1 4.53 0.50 -24.8 8.5 3.2 2.25901.760 29.1 11.3 3.88 0.56 -7.2 5.3 2.1 1.36216.823 11.4 12.4 3.00 0.60 -2.2 8.0 0.9 1.96394.130 4.2 13.5 -0.17 0.46 -2.7 7.4 0.2 1.66394.155 -12.2 17.7 0.25 0.43 13.4 6.3 -2.9 1.46537.967 11.4 11.7 -0.09 0.53 3.4 9.0 -0.7 2.06603.921 2.4 7.6 1.41 0.51 3.9 6.1 -0.5 1.56604.889 -0.7 7.0 1.23 0.43 -22.4 10.5 5.2 2.66633.820 4.0 11.7 -2.62 0.81 -20.0 11.8 4.7 2.96785.093 16.4 11.4 -0.06 0.45 10.1 4.7 -2.1 1.06835.039 11.6 14.8 -5.80 0.66 7.2 13.1 -1.0 2.96864.999 6.4 20.4 -6.61 0.80 14.8 15.6 -1.4 3.46866.940 -7.9 10.5 -7.41 0.81 -8.8 8.1 2.6 1.76960.807 -37.4 18.1 -6.63 0.60 -32.8 17.9 7.4 4.26961.847 -47.8 19.5 -7.80 .0.65 -60.6 33.2 13.5 8.07019.795 -24.1 10.9 -0.33 0.60 -53.9 24.6 11.5 6.17020.749 -21.0 8.5 0.26 0.57 -24.0 14.3 5.2 3.47160.062 -5.5 11.4 -2.60 0.60 2.3 10.1 0.3 2.27161.065 16.4 11.1 -4.15 0.58 -4.6 8.6 -0.5 0.67229.076 -2.2 12.6 -1.61 0.54 2.5 6.0 0.8 1.37230.001 -11.7 9.7 -2.25 0.60 -3.0 13.0 1.4 2.87306.809 -3.3 18.5 -1.78 0.48 52.5 28.8 -11.9 7.07307.813 -18.6 16.2 -1.88 0.52 -18.0 10.1 3.9 2.47338.796 -33.9 10.0 -5.91 0.68 12.5 7.6 -2.0 1.87339.799 -9.0 20.9 -6.09 0.60 28.5 6.4 -5.7 1.67370.794 -3.4 18.0 0.92 0.57 4.9 7.3 -0.8 1.7Table A.30: /3 Com PRV dataAppendix A. HF PRY Program Stars^ 84J.D.(-2440000)PRV(ms -1 ) aAEWcar(mA)^o.AT(K) aA(R - I)(mmag) a7371.767 -19.0 12.9 1.74 0.67 - 11.1 12.0 2.6 2.97546.029 8.0 12.5 -2.90 0.64 0.9 9.3 -0.6 2.07546.040 6.2 18.1 -3.26 0.65 1.5 6.8 -0.3 1.57635.832 -11.9 14.2 -5.62 0.56 4.6 5.9 -0.5 1.47636.828 -3.9 11.7 -4.70 0.62 3.1 6.3 -0.1 1.57698.860 32.9 19.2 -3.52 0.93 -15.1 10.7 4.9 2.67787.712 13.4 6.2 -2.70 0.52 56.7 26.6 -11.8 6.57788.705 2.1 8.3 -2.21 0.55 -0.8 9.2 1.3 2.27895.037 10.1 12.5 -3.67 0.78 2.9 6.1 -0.6 1.47993.875 -26.9 9.0 -3.80 0.71 6.8 7.2 -1.1 1.58112.757 -12.9 20.5 -2.02 0.61 25.4 12.9 -5.9 3.08113.750 -26.3 9.2 -4.95 0.68 -6.5 7.4 1.3 1.88292.006 3.7 12.7 -6.74 1.25 -4.4 8.9 0.4 1.98405.841 8.1 18.4 -0.38 0.61 -13.1 14.4 3.0 3.48406.859 8.2 22.7 1.21 0.83 -16.5 16.4 3.6 3.98470.770 -8.3 14.3 1.28 0.89 -24.1 16.2 4.1 3.98817.784 -18.6 23.8 -6.83 0.90 -46.7 21.1 9.7 5.2Table A.31: )3 Com PRV data ...continuedAppendix A. HF PRV Program Stars^ 85J.D.(-2440000)PRV(ms 1 ) aAEWcal(mA )^aAT(K)^aA(R - I)(mmag) a4655.010 25.8 17.0 -0.10 0.59 15.0 9.5 -4.1 2.54687.011 117.0 29.0 -1.68 0.71 10.7 12.3 -1.5 3.14687.977 21.7 17.3 0.58 0.70 12.3 9.7 -1.3 2.44745.923 -14.5 29.0 3.85 1.20 7.7 15.7 -0.8 3.74753.860 30.9 20.9 1.78 0.73 2.9 12.2 2.2 2.64770.755 59.4 34.2 1.51 0.73 -14.2 9.9 1.6 2.94958.154 30.2 13.5 -0.10 0.69 18.7 18.7 -2.1 4.05148.801 -15.8 12.0 0.07 0.72 13.4 15.1 -4.1 4.45458.915 -9.4 18.75713.118 -26.9 13.4 2.52 0.63 -15.7 8.9 4.2 2.05809.918 9.8 12.8 0.59 0.67 -13.3 13.3 1.9 3.55810.916 3.0 9.6 1.46 0.57 -12.4 6.4 2.0 1.65864.877 -23.9 12.5 2.75 0.78 24.8 11.7 -7.9 3.66216.859 -17.3 9.3 -0.98 0.51 6.8 9.2 -1.6 2.66216.898 -26.0 11.2 0.06 0.51 9.7 9.3 -0.4 2.46395.144 3.4 13.5 0.88 0.69 12.7 7.6 -2.7 2.26538.004 10.6 13.5 1.02 0.68 -4.2 7.2 0.3 1.96603.881 4.2 9.7 0.40 0.59 2.1 8.4 -5.0 3.76604.834 7.6 8.4 0.35 0.62 -4.9 12.1 -1.8 2.86633.770 -0.3 8.1 -1.40 0.79 7.5 7.7 -0.8 2.16785.134 7.2 8.2 0.42 0.53 -1.2 15.2 3.3 3.46786.107 0.3 9.4 -0.78 0.52 0.1 5.9 -0.6 1.56835.070 26.4 14.2 -0.69 0.76 42.6 34.0 -4.9 7.86865.031 17.9 13.0 0.66 0.47 -12.0 5.4 1.4 1.26866.021 17.0 9.9 -0.39 0.54 2.6 4.7 0.2 1.26866.973 6.2 11.3 0.18 0.60 2.4 5.7 -0.3 1.56960.835 -30.9 11.8 -3.67 0.83 -4.1 9.5 0.5 2.86961.820 -11.1 13.3 -2.37 0.75 -6.5 9.4 -0.3 2.77019.759 -17.4 8.9 0.17 0.57 9.8 9.5 -0.2 2.07160.097 22.9 7.2 -0.67 0.69 -25.3 19.0 -0.6 3.37161.094 23.4 8.9 0.07 0.56 7.0 10.7 1.3 1.37161.118 28.8 10.2 0.77 0.65 -14.4 7.3 0.8 1.17229.110 5.8 16.7 2.23 0.73 4.0 15.3 -4.2 3.27229.969 6.9 12.8 0.43 0.78 -20.0 14.8 1.1 2.77306.839 -12.5 12.3 -1.65 0.66 -30.5 14.5 2.8 3.67307.837 5.2 14.8 -0.61 0.66 2.5 8.9 0.8 2.17338.817 -9.7 7.5 0.06 0.60 -17.6 10.7 2.9 2.77339.819 -11.6 9.8 -1.49 0.68 -19.3 11.1 -4.2 5.07370.818 -29.4 8.6 -0.73 0.59 -9.9 9.5 -3.0 4.87371.787 -30.1 9.1 -1.19 0.60 4.5 14.0 -2.2 4.0Table A.32: 61 Vir PRV dataAppendix A. HF PRV Program Stars^ 86J.D.(-2440000)PRV(ms -1 ) oAEWcail(mA)^oAT(K) aA(R - I)(mmag) o7520.124 14.3 8.2 0.42 0.71 -1.2 5.8 -0.4 1.57546.060 3.4 11.4 0.76 0.65 0.2 7.3 0.1 1.97546.078 3.3 15.0 1.47 0.65 -2.4 7.5 0.0 2.07635.806 -8.2 11.3 0.41 0.73 1.8 8.0 1.1 1.97636.865 2.9 12.5 -1.59 0.70 31.4 14.5 -3.8 3.57698.891 2.6 14.3 2.15 0.77 12.5 7.7 0.3 1.87993.898 11.3 12.6 0.65 0.74 -5.5 8.7 0.8 1.58112.782 -11.0 10.7 0.07 0.47 -1.0 11.1 2.2 3.08113.777 -28.3 10.8 -1.64 0.51 17.4 7.8 -3.3 2.18405.870 8.2 13.2 0.14 0.56 21.8 8.2 -5.5 2.18471.766 -16.5 12.1 -1.29 0.55 -12.4 19.6 -3.1 3.68818.739 35.2 33.9 1.17 1.69 -12.0 11.6 2.0 3.68818.760 2.1 14.1 -1.92 0.62 -26.7 15.3 9.1 4.2Table A.33: 61 Vir PRV data ...continuedAppendix A. BF PRV Program Stars^ 87J.D.(-2440000)PRV(m.5 -1 ) aAE Wain(mA)^aAT(K) aA(R - I)(mmag) a4654.097 -41.9 21.7 12.63 0.76 -2.9 20.8 -1.1 4.74656.090 -44.1 19.0 8.04 0.84 -4.1 18.9 -1.0 4.24687.061 -26.8 26.9 11.76 0.61 6.8 9.7 -2.5 2.34688.043 -53.2 26.2 12.64 0.86 -31.6 16.7 5.5 4.14746.014 -106.6 30.3 1.38 1.18 20.8 18.1 -6.7 4.14753.915 -30.2 22.2 0.28 0.70 -24.0 25.2 4.6 5.84769.884 -42.5 17.9 4.84 0.66 -1.2 13.0 0.1 3.25147.847 -58.5 25.5 7.92 0.76 -6.3 12.2 1.7 2.95713.157 -94.5 15.2 -8.64 0.60 13.2 11.2 -3.7 2.65390.123 -13.7 15.8 -9.81 0.88 35.0 22.5 -7.1 5.05458.971 -41.4 20.25809.948 -13.1 8.5 8.55 0.70 -27.4 9.2 6.8 2.15810.942 -20.8 7.6 5.49 0.65 -16.8 7.9 4.4 1.85863.966 -2.6 14.8 6.82 0.59 -16.9 14.0 1.6 3.45901.818 -11.7 8.7 4.42 0.58 -5.7 8.6 1.9 2.16216.939 -9.4 11.8 6.96 0.60 41.7 20.6 -8.4 4.96216.968 3.2 11.1 7.93 0.51 16.3 11.1 -3.5 2.56283.777 -23.5 17.7 -2.62 0.58 4.0 9.8 0.5 2.36538.050 53.0 12.7 9.06 0.68 -9.5 10.0 2.5 2.46538.980 12.4 11.2 1.95 0.62 -17.6 8.9 4.6 2.06603.956 -28.0 9.3 -0.85 0.58 0.4 10.4 0.3 2.56633.857 -14.8 7.6 0.98 0.67 3.2 11.7 0.1 2.76786.142 -28.5 12.7 -9.71 0.63 5.0 26.6 0.3 5.96835.103 -22.9 11.2 -2.65 0.60 27.4 30.6 -7.4 6.76865.069 -19.7 13.6 -6.96 0.52 12.3 11.6 -2.4 2.66866.076 -6.0 14.8 -5.55 0.57 42.4 25.6 -9.8 5.56960.867 -22.5 13.6 -9.97 0.54 5.3 19.2 -0.4 4.56961.879 -61.6 16.2 -8.12 0.56 -14.5 20.1 3.1 4.67019.835 -9.1 7.6 -4.67 0.60 12.7 12.3 -2.6 2.97020.775 -22.3 8.0 -14.24 0.48 12.5 14.5 -3.3 3.37160.136 8.4 5.8 -0.97 0.55 17.3 11.9 -3.6 2.67160.163 -10.7 12.8 1.47 0.59 14.0 10.7 -2.6 2.47161.151 -9.9 9.0 -5.97 0.49 22.7 13.3 -5.1 2.97229.143 18.5 15.3 8.48 0.81 16.4 23.7 -3.3 5.37230.026 33.8 12.2 5.17 0.70 15.5 37.4 -3.8 8.37306.886 -23.0 14.9 7.33 0.66 -19.1 17.2 3.3 4.07307.863 13.7 18.3 10.95 0.83 0.9 21.6 -1.1 4.87338.844 -11.9 14.5 11.06 0.74 -17.5 18.2 4.6 4.37339.837 -6.8 22.0 8.74 0.93 -22.8 27.2 5.3 6.37370.874 1.5 11.3 12.10 0.93 -0.7 14.6 1.1 3.4Table A.34: Boo A PRV dataAppendix A. HF PRV Program Stars^ 88J.D.(-2440000)PRV(m3 -1 ) aA EWcair(mA)^aAT(K) aL(R - I)(mmag) a7371.866 -7.6 14.6 8.11 0.70 -8.9 24.6 2.1 5.67546.113 24.0 12.8 6.96 0.70 -3.3 12.7 0.5 2.97635.892 18.2 10.0 -0.98 0.70 28.6 25.8 -6.9 5.77636.896 11.7 12.6 -3.17 0.56 37.7 20.9 -8.8 4.67698.934 30.3 17.4 -1.14 0.72 9.4 18.4 -0.9 4.37787.748 35.1 10.7 -14.11 0.46 15.3 15.7 -3.1 3.67788.724 33.3 11.4 -16.75 0.68 48.0 27.6 -9.9 6.57895.073 41.5 13.0 2.87 0.79 2.5 7.8 -0.4 1.97993.922 63.9 8.8 5.50 0.75 1.8 10.5 0.1 2.38112.811 50.6 12.3 1.65 0.55 -12.8 14.9 2.8 3.68113.813 16.8 14.2 2.92 0.45 -2.9 11.6 0.5 2.78406.888 82.8 24.4 -3.08 0.55 26.0 15.1 -6.1 3.48406.908 68.3 20.7 -3.13 0.53 29.2 20.4 -7.2 4.68470.799 46.7 21.7 -3.58 0.58 -7.4 15.4 0.4 3.68817.819 66.6 18.5 3.67 0.76 -52.7 21.4 12.1 5.28818.783 55.7 43.7 5.86 2.44 -21.6 22.0 4.4 5.38818.796 58.8 19.6 2.40 0.95 -65.7 24.1 14.7 6.18904.719 81.6 32.2 16.32 1.44 4.7 25.1 -4.2 6.5Table A.35: Boo A PRV data ...continuedAppendix A. HF PRV Program Stars^ 89J.D.(-2440000)PRV(m3 -1 ) aAEWcaz(mA)^oAT(K) aA(R - I)(mmag) a.5148.890 -27.3 16.4 -0.11 0.63 12.4 10.9 -1.4 2.76538.081 -21.8 16.3 -10.12 0.93 -12.4 14.5 -7.2 6.96604.977 -6.3 16.3 -8.08 0.81 8.7 24.1 0.1 5.76835.124 12.3 17.2 2.34 0.79 -29.9 16.1 8.8 4.66865.099 -12.5 15.2 14.47 0.61 -0.9 25.2 0.9 7.16867.085 -37.6 9.8 11.36 0.65 25.2 8.9 0.0 4.06960.935 -27.6 12.8 -0.39 0.72 -29.0 17.0 8.4 4.16961.940 -15.9 11.9 1.30 0.84 -38.3 21.4 -6.9 10.57020.842 -17.3 11.2 3.45 0.53 -24.4 20.9 5.2 5.37230.060 -9.0 13.8 -4.77 0.75 -1.3 15.3 5.8 3.97307.897 38.6 15.5 3.49 0.79 -4.5 17.2 1.2 4.27338.880 -1.4 16.0 1.61 0.71 21.3 8.2 -4.1 1.47339.876 -9.2 10.8 1.25 0.81 -16.5 14.1 6.7 3.37371.816 -21.2 11.5 -2.52 0.62 -9.8 10.8 4.2 2.87546.171 10.0 10.57635.934 11.2 11.4 10.84 0.64 -6.8 27.7 2.2 7.77636.959 -8.0 18.3 6.37 1.12 -15.1 25.4 3.7 7.07698.970 24.1 15.5 4.54 0.83 -14.9 28.8 5.7 7.07699.919 2.7 14.0 3.06 0.74 -31.6 20.5 4.1 2.77787.782 26.0 9.6 -5.10 0.68 9.1 16.6 -5.9 2.07788.747 0.2 10.1 -3.28 0.59 -19.8 17.1 7.3 4.18112.844 15.5 9.8 -3.58 0.55 -19.9 16.2 6.5 4.18113.866 -9.8 13.8 -5.03 0.54 -48.4 23.2 13.6 6.58405.928 36.8 11.7 -20.07 0.96 37.5 40.1 -9.5 9.68470.864 16.5 12.1 -17.65 1.17 -7.1 21.6 3.2 5.38817.863 21.1 13.2 -9.53 0.86 41.5 15.7 -9.1 3.7Table A.36: 36 Oph A PRV dataAppendix A. HF PRV Program Stars^ 90J.D.(-2440000)PRV(ms -1 ) aAE Wcan(mÄ)^aAT(K) aA(R - I)(mmag) a4654.150 84.0 26.8 19.20 1.19 -12.0 23.6 1.1 5.74656.138 120.8 17.4 17.69 0.85 -6.3 21.9 -0.2 5.34688.092 74.3 19.8 21.76 0.83 -4.0 24.4 -0.1 6.04753.962 70.3 23.2 21.49 1.12 -54.5 15.7 12.4 3.74770.890 141.7 36.7 26.07 0.76 -39.5 16.5 8.8 4.05147.893 88.7 15.0 14.54 0.76 13.8 25.2 5.2 3.95809.994 4.0 15.2 -5.57 0.61 16.9 23.6 -3.9 5.95864.023 -1.4 13.1 -3.50 0.56 -3.1 21.4 -2.3 5.36215.966 18.9 11.0 1.42 0.75 4.2 18.8 -1.2 4.66539.079 47.2 14.1 1.39 0.63 -12.1 21.5 2.6 5.26604.940 23.5 17.2 1.53 0.64 28.8 19.5 -7.3 4.96726.699 8.4 11.0 3.22 0.64 8.9 11.8 -3.6 2.86865.137 14.8 14.9 3.14 0.60 1.4 17.3 -0.6 4.36867.116 -19.1 15.8 0.88 0.93 -39.8 22.9 9.5 5.56960.902 22.4 12.0 1.29 0.72 18.2 22.1 1.6 3.46961.914 -2.0 13.6 3.62 0.93 16.9 31.6 4.8 4.67020.813 2.2 11.0 6.52 0.68 -7.0 11.6 0.6 2.97102.696 -22.5 9.0 4.65 0.73 8.5 8.6 -2.5 2.17230.096 -4.6 17.6 -6.64 0.95 14.6 12.6 -3.2 2.97306.923 -7.2 13.4 -0.63 1.00 30.0 18.6 -8.1 4.87307.937 -5.1 16.0 -4.41 0.93 -6.9 8.0 -0.1 2.07338.864 -7.8 16.3 -7.94 0.83 12.8 20.3 3.9 2.97339.862 -2.5 16.0 -8.14 0.76 -24.4 13.4 6.1 3.17370.852 -21.4 13.2 -12.24 0.76 22.8 14.4 -6.1 3.87371.836 -43.0 14.6 -12.15 0.70 15.6 13.9 -4.5 3.77635.966 -30.4 12.4 -18.37 0.90 7.5 15.5 -2.2 3.77699.880 16.9 13.3 -19.20 0.86 -1.9 18.2 1.7 4.47787.808 -17.2 10.6 -21.15 0.81 20.7 18.8 -5.6 4.97788.766 1.8 13.1 -20.37 0.90 14.0 12.4 -4.5 3.08113.845 -36.2 10.2 -6.33 0.51 -21.6 16.4 4.7 4.08405.959 -9.8 12.8 -0.18 0.83 22.1 12.5 -6.4 3.18406.949 -31.6 13.3 -4.27 0.65 -22.0 16.2 5.0 3.78470.836 -58.2 14.1 5.19 0.55 0.0 12.9 -2.3 3.28818.820 -29.5 64.9 15.90 3.08 -64.2 24.5 15.3 6.18818.839 -23.1 11.1 19.70 1.03 -2.3 14.1 -0.4 3.4Table A.37: 36 Oph B PRV dataAppendix A. HF PRV Program Stars^ 91J.D.(-2440000)PRV(ms-1 )^aAEWcau(mÄ)^aAT(K)^aA(R - I)(mmag) a4687.137 -67.1 20.5 4.78 1.03 13.1 12.4 -4.2 3.24688.138 -31.6 31.5 0.32 0.64 38.5 28.7 -9.6 7.04746.073 0.7 19.0 -2.02 0.96 -11.0 14.6 0.0 3.64754.012 -5.2 19.1 1.77 0.81 -1.9 16.8 0.1 4.04769.949 65.9 26.1 -0.96 0.76 15.2 12.1 -4.0 3.15147.972 -11.0 13.6 -0.94 0.76 2.4 11.4 -0.1 2.95276.772 1.1 12.3 7.61 0.60 -3.5 10.5 0.3 2.65459.029 -5.8 13.65810.080 -7.6 11.7 6.92 0.46 -2.5 9.2 1.5 2.65811.020 -0.4 9.9 5.42 0.48 -18.5 10.5 3.3 2.95864.108 8.7 10.5 5.78 0.64 -6.1 8.2 -0.6 2.05901.874 -6.0 12.2 11.40 0.77 -10.6 10.6 3.4 2.66216.055 -19.0 12.5 3.35 0.54 -3.6 7.8 1.1 1.96217.031 8.9 11.5 3.21 0.47 12.0 9.1 -2.5 2.26393.707 -13.0 13.2 -1.49 0.51 0.5 12.4 -0.1 3.06394.711 -4.7 11.8 -2.46 0.54 4.9 12.3 -1.0 3.06539.027 -24.2 12.1 -1.50 0.46 4.1 10.2 0.2 2.86603.983 1.5 9.4 -4.14 0.66 18.8 15.8 -3.3 3.96605.016 -4.7 8.8 -2.65 0.67 -10.7 10.1 2.9 2.66633.890 18.4 11.2 -3.31 0.76 4.6 9.7 -0.2 2.46725.703 -6.4 7.1 -1.59 0.60 -8.6 12.4 -0.6 2.86726.736 -11.2 8.5 -0.78 0.75 7.5 6.3 -2.1 1.76785.705 -10.3 11.6 -3.87 0.54 10.5 11.3 -2.3 2.76866.121 4.3 10.7 -5.79 0.44 -20.1 15.7 5.2 3.96960.965 5.1 8.0 -4.75 0.66 4.4 16.6 -1.4 4.06961.961 1.0 13.2 -4.80 0.86 2.2 14.9 -0.7 3.67019.878 -14.1 9.1 -3.35 0.55 4.8 11.0 -0.6 2.77020.870 -16.0 8.9 -6.16 0.46 5.5 11.7 -0.9 2.97101.723 -14.8 10.7 -4.50 0.51 -21.2 11.3 5.2 2.87102.734 -5.3 14.8 -5.54 0.45 -20.4 14.3 5.4 3.37160.693 21.8 13.27230.150 3.3 9.9 -5.83 0.75 16.6 11.4 -2.1 2.77307.004 -0.9 9.0 -6.57 0.64 20.1 11.8 -5.2 2.97307.968 -3.5 9.8 -5.61 0.57 -0.1 13.0 -0.1 3.17338.928 -9.2 9.0 -4.71 0.64 0.0 15.9 1.3 3.87339.889 -19.5 9.2 -3.94 0.68 8.2 10.3 -0.7 2.67370.892 -5.2 8.5 -4.63 0.66 7.0 11.4 -0.9 2.97371.887 -0.2 9.7 -4.28 0.70 6.7 16.0 -0.8 3.97454.721 22.4 11.6 -6.14 0.73 -36.1 21.4 2.3 2.57635.990 20.5 16.7 -2.04 0.61 -44.9 13.2 7.9 3.5Table A.38: a Dra PRV dataAppendix A. .11F PRV Program Stars^ 92J.D.(-2440000)PRV(ms -1 ) aAEWcar(mit )^aAT(K) aAP - I)(mmag) a7636.996 34.8 14.5 -1.99 0.60 -21.5 13.1 2.2 3.27699.001 12.8 11.8 -2.90 0.71 -8.5 11.5 3.7 3.07787.847 17.6 10.6 1.64 0.52 -0.8 9.2 0.7 2.27787.864 11.3 9.5 2.04 0.45 8.1 8.8 -1.3 2.17788.790 27.5 10.8 3.48 0.42 -10.8 9.3 3.0 2.37994.109 15.4 21.2 6.05 0.90 -16.1 17.8 -1.1 2.28112.865 6.2 8.2 10.28 0.46 7.9 10.0 -1.4 2.48113.886 2.2 8.9 8.36 0.51 9.8 12.2 -1.7 3.08405.986 18.1 14.2 4.79 0.56 -2.5 13.7 0.8 3.38406.971 -12.0 12.1 3.65 0.50 19.4 8.1 -4.5 2.08470.908 -7.5 8.1 0.69 0.60 -1.6 10.3 -0.9 2.48577.704 -20.2 13.2 -0.10 0.55 -7.9 11.5 2.3 2.88577.728 7.1 13.2 1.31 0.62 -9.6 9.4 3.0 2.28817.908 18.0 8.8 2.33 0.67 5.0 14.3 -1.3 3.58818.905 30.0 10.0 1.38 0.70 -48.5 32.8 10.6 8.08904.801 -22.3 29.6 -0.80 0.93 17.7 28.6 -3.2 8.5Table A.39: a Dra PRV data ...continuedAppendix A. HF PRV Program Stars^ 93J.D.(-2440000)PRV(ms 1 ) aAEWcar(mA)^aAT(K) aA(R - I)(mmag) a4754.053 -29.0 20.7 -0.41 0.66 3.4 32.8 -0.6 7.74769.993 -13.0 11.4 -1.66 0.72 -27.4 34.6 6.7 8.04926.737 -20.8 16.6 2.93 0.77 3.5 12.2 -2.3 2.94957.708 -17.7 9.4 0.15 0.65 0.9 24.1 -2.2 5.75147.948 8.9 18.9 0.32 0.66 -10.9 16.1 2.5 3.75165.887 9.4 15.2 -2.80 1.03 1.6 7.6 -1.2 1.95212.861 -0.6 11.3 -1.21 0.75 -12.8 35.4 1.4 8.25276.740 -8.8 9.6 1.75 0.69 6.2 20.2 -2.3 4.85459.083 -4.5 17.95810.098 2.5 8.1 0.18 0.48 -15.3 10.6 3.8 2.55811.064 -5.1 11.4 -1.27 0.51 3.9 4.9 -1.3 1.25864.142 -2.5 14.55901.934 15.6 9.5 0.70 0.59 -16.9 10.3 3.9 2.36047.733 -35.5 14.1 1.31 0.56 -6.3 11.8 0.5 2.76216.020 10.4 9.6 0.27 0.55 -7.1 8.8 1.3 2.06282.892 -11.3 10.5 1.87 0.50 9.9 11.2 -1.2 2.76282.902 -7.4 11.2 0.61 0.55 -6.8 12.0 6.4 3.96394.725 -11.0 11.7 0.46 0.47 -0.1 15.1 -0.1 3.56604.032 7.4 8.2 0.58 0.53 -3.1 11.3 0.7 2.76605.071 -5.3 8.6 -1.54 0.67 11.9 8.1 -3.0 2.06633.924 -1.5 12.2 2.43 0.77 4.6 7.9 -1.3 1.96725.735 11.3 6.6 -1.01 0.37 -7.4 7.2 1.3 1.66726.768 -0.1 5.7 -1.95 0.46 -6.4 9.3 1.0 2.16784.699 2.9 9.2 2.00 0.74 28.0 25.9 -7.0 6.16866.141 21.8 10.3 0.19 0.40 -30.1 38.2 9.1 9.06960.988 1.8 11.4 0.40 0.57 11.1 11.7 -3.3 2.86961.983 0.5 13.5 -0.32 0.64 17.1 22.3 -4.6 5.47019.908 11.2 8.9 1.48 0.47 -13.0 21.5 3.1 5.07020.898 -12.2 10.5 1.41 0.54 3.6 30.6 -0.4 7.17101.759 8.6 7.3 0.33 0.60 -21.7 26.6 5.5 6.07102.775 -1.1 9.6 2.12 0.64 -24.5 24.3 6.1 5.47230.121 2.1 10.2 -0.55 0.58 -25.5 24.5 7.2 5.67307.030 9.4 11.4 -0.96 0.57 -12.8 32.3 3.2 7.57307.988 -1.6 9.0 0.20 0.75 12.7 26.6 -3.7 6.47338.946 1.0 9.5 -2.04 0.49 -14.3 8.4 3.7 1.97339.907 12.5 8.0 -3.24 0.63 12.9 8.5 -2.7 2.17370.911 -1.2 9.1 -0.24 0.60 -1.7 8.0 0.4 1.97371.904 -0.2 8.6 0.92 0.56 7.1 6.1 -1.9 1.57453.848 2.7 11.7 -0.31 0.74 15.5 14.6 -3.6 3.37454.734 27.0 11.2 3.26 0.64 15.7 16.9 -3.4 4.0Table A.40: /3 Aql PRV dataAppendix A. HF PRV Program Stars^ 94J.D.(-2440000)PRV(ms -1 ) aAEWCall(mii )^aAT(K) QA(R - I)(mmag) a7636.020 -12.9 11.2 -0.81 0.51 15.9 9.0 -4.6 2.37637.032 -21.9 12.7 -1.51 0.54 5.7 9.1 -1.9 2.37699.025 -27.3 14.5 -2.85 0.78 9.6 10.1 -1.2 2.57700.012 -21.9 9.4 0.40 0.56 27.2 31.4 -5.4 7.47787.882 -5.6 8.4 0.01 0.52 9.9 26.4 -2.5 6.17787.888 -12.3 7.7 -0.67 0.53 -23.4 8.5 5.4 1.87788.806 -3.4 7.5 -0.10 0.47 -17.0 10.1 4.0 2.27994.133 -6.9 8.3 -1.15 0.70 -15.3 30.7 5.1 7.28112.885 7.3 10.0 1.55 0.50 0.6 15.4 -0.3 3.58113.905 -7.7 10.0 0.55 0.43 14.6 21.3 -3.1 5.08406.016 -15.1 10.0 -1.33 0.59 -12.5 11.2 2.8 2.58470.933 11.3 12.6 -1.68 0.71 14.3 33.1 -4.0 7.88470.941 12.5 12.2 -1.31 0.75 13.9 33.4 -4.1 7.88471.948 10.1 10.6 -2.52 0.62 3.1 30.4 -1.5 7.18577.757 6.4 9.2 -0.82 0.64 2.9 27.7 -0.3 6.38577.767 4.1 8.6 0.58 0.50 5.8 30.5 -0.8 7.08818.939 18.6 11.1 0.20 0.40 9.4 10.8 -3.2 2.68818.951 3.6 10.2 1.18 0.41 6.0 12.4 -1.9 2.98904.834 33.5 19.8 1.07 1.06 -24.7 30.9 2.4 7.7Table A.41: f3 Aql PRV data ...continuedAppendix A. HF PRV Program Stars^ 95J.D.(-2440000)PRV(ms -1 ) aAEWcall(mA)^oAT(K)^aA(R - I)(mmag) a4746.112 -34.8 22.5 -2.12 0.97 -8.5 16.1 2.9 6.34754.033 4.0 17.2 -1.00 0.63 40.4 21.9 -12.5 6.24770.019 -17.1 16.3 0.04 0.64 10.8 10.0 -2.8 2.94926.767 -19.2 13.0 0.27 0.51 11.2 19.6 -4.9 5.24957.736 -33.1 11.7 -2.48 0.67 -10.0 38.0 1.7 10.35148.000 6.7 13.1 -0.48 0.62 -0.9 10.4 0.2 2.95165.919 0.1 9.4 -0.04 0.66 4.9 6.9 -1.5 1.95276.800 -15.6 12.1 -0.55 0.54 0.7 12.6 -0.8 3.45459.061 -16.5 12.85811.082 -8.8 6.8 0.76 0.42 1.4 3.7 0.2 0.95865.035 -5.2 9.1 1.39 0.49 7.4 10.8 -5.1 2.95901.897 -71.0 11.7 0.78 0.59 4.7 4.9 -0.8 1.26048.747 -6.2 9.1 -0.76 0.51 0.0 12.5 3.0 2.26217.062 -27.7 8.1 -1.19 0.52 -2.0 8.2 0.8 2.26217.075 -15.4 8.2 -0.94 0.53 -0.2 9.2 -0.3 2.36283.950 -7.8 12.3 -0.45 0.61 -12.1 11.4 3.7 3.06283.956 -11.4 13.1 -0.94 0.50 -0.9 9.7 -0.3 2.16393.722 -19.6 12.7 1.75 0.56 -17.8 9.9 6.5 2.16394.755 18.9 13.1 0.65 0.46 -7.3 7.7 3.4 1.66604.013 -27.1 8.1 0.43 0.51 -10.3 9.9 1.6 2.86605.049 0.0 7.5 -0.14 0.48 -10.5 11.6 2.6 3.36633.908 -18.9 8.3 -0.06 0.71 -8.5 10.3 2.9 3.06725.723 -3.8 8.9 1.51 0.46 -5.7 8.0 1.9 2.16726.756 -23.4 7.0 0.66 0.48 -5.0 12.0 2.0 1.76784.750 -24.7 13.2 2.15 0.55 3.4 15.8 2.5 5.66866.154 23.9 10.6 -0.30 0.43 2.3 8.0 -1.0 1.86961.991 3.7 8.4 -4.36 1.37 -8.9 12.3 1.2 3.57019.945 24.7 4.5 -0.94 0.48 -20.1 11.6 5.3 3.47020.925 28.9 6.3 -2.15 0.45 -25.3 11.7 7.0 3.37101.746 -12.8 9.6 -0.52 0.46 2.2 12.7 -0.6 3.57102.759 -1.2 14.7 -1.22 0.56 -39.6 19.1 10.3 5.57159.699 15.6 9.6 2.54 0.47 -5.9 23.8 -8.5 6.37230.166 19.0 11.47307.051 12.6 16.5 -0.12 0.55 -8.1 16.7 0.8 4.77308.013 18.6 17.6 0.38 0.82 -25.0 20.4 6.1 6.07338.967 1.7 7.9 -4.68 1.62 -16.4 24.3 3.2 7.17339.926 0.9 10.2 -5.58 1.09 -5.3 13.4 0.1 3.47370.927 -2.7 8.2 -0.52 0.56 -10.3 9.8 0.8 2.37371.919 -17.3 7.7 0.15 0.63 -0.3 16.3 -0.9 4.57453.874 -16.0 9.0 2.19 0.64 11.0 24.4 -4.5 6.7Table A.42: n Cep PRV dataAppendix A. RE PRV Program Stars^ 96J.D.(-2440000)PRV(ms-1 ) aAEWcal(mA )^aAT(K) aA(R - I)(mmag) a7454.753 12.2 12.4 -1.59 0.69 -39.9 16.2 1.6 6.37519.763 -24.4 13.6 1.55 0.52 3.9 5.8 -1.7 1.97636.120 -0.7 14.3 -4.34 0.78 30.3 23.5 -7.8 6.87637.074 21.9 11.1 0.26 0.56 6.7 13.2 -2.6 3.67699.051 -33.4 14.4 -2.83 0.69 20.5 13.6 -3.9 3.97700.083 10.2 16.3 -4.09 0.71 24.3 10.9 -4.2 3.27787.918 3.8 7.8 0.99 0.40 13.3 7.1 -3.2 1.97787.923 11.3 7.6 1.91 0.35 12.1 9.3 -3.2 2.37788.831 24.7 6.4 1.04 0.38 21.2 12.4 -5.8 3.48112.908 22.5 14.2 -0.38 0.48 -2.0 9.0 0.1 2.48113.922 6.1 18.0 0.96 0.48 0.1 11.2 -0.1 3.18407.007 -8.9 10.4 -2.15 0.56 2.7 7.5 -1.2 1.88407.013 -26.2 9.7 -3.48 0.64 7.5 8.9 -1.9 2.48470.978 27.0 8.5 0.15 0.72 -10.1 7.1 1.2 2.08471.965 57.8 11.0 1.86 0.65 -2.6 6.8 -3.1 2.48578.724 11.1 16.5 -0.34 0.56 36.0 19.7 -9.1 5.18817.969 20.4 13.2 -0.96 0.60 0.9 17.9 -1.8 4.98819.008 -8.6 17.3 4.18 0.92 -0.2 23.6 0.7 6.7Table A.43: ri Cep PRV data ...continuedAppendix A. HF PRV Program Stars^ 97J.D.(-2440000)PRY(ma') aAEWcari(mil.)^aAT(K) a0 (R - I)(mmag) a4754.099 -7.3 20.0 5.62 0.93 20.2 20.1 -7.3 5.84770.090 38.9 30.3 12.98 0.90 -60.0 52.2 5.9 12.34926.816 34.6 14.1 11.43 0.75 32.4 13.2 -0.4 9.04957.780 23.6 14.2 5.62 0.80 -5.0 20.9 0.0 5.85148.046 44.8 20.3 -0.95 0.76 -8.8 19.7 4.3 4.95165.996 -11.2 14.9 3.44 0.68 -11.5 9.1 3.1 2.45276.828 3.4 10.2 0.48 0.59 -71.4 48.1 9.0 9.65810.133 -28.0 9.8 -12.32 0.52 1.2 8.0 -2.6 2.55865.087 -1.2 11.9 -12.45 0.50 -29.7 26.1 -0.1 4.65901.999 -9.2 10.2 -13.62 0.53 0.4 4.9 -1.3 1.36216.115 -1.7 9.4 -9.84 0.48 -12.2 14.4 4.9 3.76217.119 -9.1 11.56283.011 3.0 16.4 -15.53 0.48 1.6 9.8 1.8 2.16283.037 12.2 15.2 -13.87 0.55 6.8 7.2 -1.5 2.16393.748 -0.3 11.7 -5.79 0.43 -1.2 20.5 5.1 5.06394.770 30.7 20.9 -6.96 0.58 6.9 7.0 1.0 3.66539.123 -16.4 8.3 5.13 0.55 -6.1 6.8 5.2 4.66604.074 -20.3 8.4 -5.37 0.41 -43.7 20.7 9.8 5.66633.955 -1.6 11.9 -3.71 0.68 1.4 7.1 -0.9 1.56725.777 -2.9 8.1 7.71 0.59 -3.5 9.3 1.7 2.46726.804 -7.8 8.7 11.20 0.56 -3.0 13.1 1.2 3.86784.785 29.5 10.4 3.06 0.86 5.7 8.1 -1.4 2.16961.022 35.6 8.3 16.68 0.72 -14.3 14.7 6.5 3.46962.029 2.0 11.3 10.98 0.80 0.8 7.0 -1.8 1.87019.972 12.6 5.6 17.82 0.75 -82.3 51.1 15.4 12.77020.944 1.9 12.3 19.62 0.84 -81.1 49.9 16.5 12.97101.814 -28.0 9.5 21.73 0.84 -19.7 21.2 9.2 5.87102.819 -2.1 9.6 20.57 0.87 -26.0 20.6 10.1 5.77159.715 31.9 10.7 15.53 0.82 -7.1 13.6 2.9 3.87160.742 13.0 11.5 14.84 0.96 -22.3 21.9 6.7 6.77307.067 -14.8 12.4 20.14 0.94 0.7 7.7 6.7 8.27308.040 10.5 16.7 19.43 0.89 3.3 18.9 0.0 4.07338.985 10.1 8.6 13.79 0.81 -0.3 10.5 13.0 9.87339.952 13.4 11.1 14.93 0.86 -60.4 48.9 9.1 11.77370.961 3.9 11.6 9.70 0.62 -12.1 18.2 5.4 5.47371.933 5.3 10.1 10.57 0.68 -5.2 7.7 7.9 6.27453.891 7.0 10.4 6.82 0.96 -15.0 16.6 3.8 4.87454.767 -7.5 9.6 8.72 0.86 -12.5 11.8 12.8 7.27521.789 33.0 19.5 5.71 0.65 -2.5 7.3 -1.3 1.67636.069 -24.1 15.7 6.93 0.67 16.0 9.4 -5.6 3.0Table A.44: 61 Cyg A PRV dataAppendix A. HF PRV Program Stars^ 98J.D.(-2440000)PRV(ms- ') aAEWcair(mi.)^aAT(K) aLi(R - I)(mmag) a7699.073 -27.1 18.8 6.46 0.71 -7.4 8.5 1.8 2.77787.945 -19.1 8.6 -1.70 0.44 -13.4 24.2 -5.9 4.27788.868 -13.1 13.6 -1.25 0.36 -4.3 9.6 1.9 2.88112.922 -0.9 7.2 -1.59 0.44 -60.2 54.3 6.3 12.68113.938 -22.7 8.0 -5.64 0.52 9.7 4.1 1.5 3.58406.036 50.4 16.9 -12.65 0.69 -65.8 46.8 8.1 8.08407.038 12.3 20.6 -12.38 0.69 15.7 12.1 -5.8 3.78471.002 -24.3 9.0 -5.62 0.52 -3.7 7.9 -1.5 2.58577.796 -13.9 11.4 -7.21 0.49 0.3 4.1 -1.3 1.08818.004 23.6 15.3 -4.68 1.34 -10.2 28.4 -5.8 6.3Table A.45: 61 Cyg A PRV data ...continuedAppendix A. HF PRV Program Stars^ 99J.D.(-2440000)PRV(ms 1 ) aAEWcarr(mA)^oAT(K) aA(R - I)(mmag) a5148.970 -21.3 16.0 -3.13 0.67 -70.0 69.0 3.8 8.26393.771 -28.3 16.9 -1.49 0.68 9.7 15.7 -2.3 3.26394.793 18.5 17.2 -3.69 0.91 -7.1 15.4 0.9 3.26604.104 -26.6 9.1 -2.42 0.48 7.4 10.4 -0.9 2.26633.976 -25.1 12.5 4.76 0.78 -3.9 10.9 1.1 2.16725.805 -8.1 7.7 -2.15 0.45 5.0 24.3 -1.6 6.16726.829 -5.7 9.2 -2.62 0.50 35.9 28.5 -9.2 6.76785.756 -19.1 7.9 2.79 0.55 -1.1 12.7 -0.5 1.46961.054 18.4 12.0 6.68 0.70 9.2 13.8 -2.7 2.26962.050 -5.8 13.1 5.39 0.68 18.5 24.7 -5.8 5.67020.002 0.9 6.3 -3.19 0.48 -5.2 7.6 1.6 1.67020.967 4.1 7.2 -3.62 0.48 -10.0 6.9 3.3 1.67101.851 2.7 9.7 2.96 0.58 14.3 16.3 -3.1 3.87102.858 7.1 11.2 11.02 0.67 35.0 17.5 -7.6 4.07159.742 19.9 10.5 1.20 0.77 43.8 37.2 -12.0 8.67307.090 -28.8 8.4 -7.87 0.96 -5.0 19.4 1.1 4.77308.059 -8.4 11.2 -2.42 0.63 25.6 21.8 -4.3 5.97339.001 -2.8 14.1 2.85 0.89 -35.6 65.8 11.2 17.57339.969 -14.0 11.5 2.44 0.70 -3.3 19.6 0.5 3.87370.945 6.7 10.1 7.83 0.65 8.8 18.7 -1.1 4.27371.949 28.4 10.5 6.38 0.59 19.1 16.5 -4.9 2.47453.913 28.8 13.2 -2.73 0.99 5.9 21.9 -0.5 5.57454.782 5.4 13.7 -1.95 0.93 12.6 16.0 -2.2 3.77636.093 1.0 12.8 -5.54 0.62 14.8 27.2 -3.2 5.97699.095 -25.8 18.4 -10.47 0.73 -31.8 33.4 10.5 8.97787.966 2.3 11.2 6.79 0.60 -45.5 31.1 13.3 8.07788.850 5.1 10.4 8.04 0.52 -29.5 21.2 9.2 5.58112.938 14.7 7.3 5.82 0.56 -21.8 11.7 4.9 2.28113.953 11.3 7.8 1.06 0.58 -9.2 11.6 1.6 2.08406.062 -14.1 13.4 -3.73 0.63 45.5 28.0 -10.9 6.38471.828 40.0 12.2 -8.07 0.53 5.9 21.7 -4.3 4.08578.754 32.9 14.6 -7.04 0.62 8.0 17.5 -1.3 4.38818.038 6.2 13.5 -4.16 1.02 -17.1 51.4 -0.2 12.28819.034 -28.3 15.9 -4.72 1.06 27.9 36.0 -5.9 8.9Table A.46: 61 Cyg B PRV dataAppendix A. HF PRV Program Stars^ 100J.D.(-2440000)PRV(ms -1 ) aAEWcar(mA)^aAT(K)^aA(R - I)(mmag) a4957.844 1.5 15.7 -4.13 0.83 -10.1 49.7 -15.1 8.15149.032 2.3 14.5 -3.79 0.67 -44.1 25.7 9.8 5.16393.827 -15.2 11.8 6.24 0.59 -69.4 33.6 13.4 6.56394.829 -11.2 15.3 7.66 0.50 -44.8 27.7 9.1 5.56725.887 -32.0 11.2 8.11 0.54 -31.6 25.8 2.9 3.26785.811 2.6 8.9 2.07 0.55 -51.3 31.7 5.6 4.16834.729 30.8 13.9 9.81 0.67 -45.7 38.5 1.0 5.26961.099 -10.4 11.9 2.56 0.71 16.3 10.2 12.0 6.66962.084 28.1 12.9 3.08 0.60 1.0 10.0 2.4 2.57020.051 3.0 6.8 -2.28 0.60 -36.0 29.6 3.9 5.47021.036 11.1 10.7 -3.36 0.78 -58.3 27.5 14.3 6.27101.905 -2.8 8.8 -0.87 0.58 8.0 17.1 -3.3 3.37102.912 -2.6 9.8 0.23 0.63 2.7 14.2 0.9 3.27159.795 24.3 15.6 3.61 0.80 63.4 23.1 -7.2 4.57308.089 10.8 16.6 -3.06 0.66 0.2 20.2 10.6 5.17339.023 11.2 8.0 1.80 0.73 -44.6 34.0 7.0 7.37339.992 13.4 8.1 0.92 0.87 -36.0 35.7 -7.9 2.77340.014 4.8 9.2 0.97 0.89 -52.1 34.9 -1.8 2.47370.975 -14.5 10.6 1.23 0.84 -26.8 34.6 9.1 9.27371.984 -18.7 7.0 -0.03 0.71 -51.4 37.9 -4.0 2.37454.822 -16.0 11.0 -4.19 0.80 -56.4 39.2 -3.7 1.97521.828 10.5 11.2 -1.76 0.77 -35.6 50.3 13.6 8.97545.713 6.2 14.5 -4.16 0.84 22.3 14.3 -1.3 3.17788.010 -17.9 12.4 -7.49 0.69 19.2 6.5 -4.4 2.67788.901 -17.1 13.1 -6.36 0.68 11.8 17.5 2.1 4.68112.972 7.3 7.2 -6.81 0.72 -40.0 24.1 10.9 5.78113.983 -6.1 10.4 -6.42 0.83 -47.5 25.9 13.0 5.78290.742 5.1 17.3 -3.60 1.23 83.9 31.4 -18.3 6.58407.081 -11.4 12.7 -8.72 0.98 -57.8 27.2 11.0 4.48471.891 0.4 17.9 -8.72 0.86 1.6 19.2 2.2 4.78578.780 6.9 10.5 -7.37 1.37 -9.0 11.5 -16.1 8.88819.072 12.1 11.8 -2.77 1.03 -52.4 26.9 16.5 7.4Table A.47: HR 8832 PRV dataAppendix BSpectroscopic BinaryWe present the essential equations used to analyze spectroscopic binary orbits:^(cos(w f(t))+ e cos w)R = na sin (B.36)(1 — e2),where R is the heliocentric radial velocity, n = 2w/P, P is the orbital period, a is thesemi-major axis, e is the eccentricity, i is the angle of inclination of the plane of theorbit to the observer's line of sight, co is the argument of periastron, and f(t) is the trueanomaly. The true anomaly is defined in terms of the eccentric anomaly, E, by:f^Etan i = t 1 , e- )a tan—2 (B.37)where E is defined by figure B.20, which also shows the true anomaly, f, and the argumentof periastron,In turn the eccentric anomaly, E, is defined by:E—esinE=M^ (B.38)where M, the mean anomaly, is defined by:M = —2w (t — r)^ (B.39)where r is the time of passage of periastron. We are also able to define the amplitude,K, of the spectroscopic binary orbit, by:101Appendix B. Spectroscopic Binary^ 102Figure B.20: Binary orbit parametersK = —21. a sin i^ (B.40)P^1 e2and the mass function is defined by:M3 sin3 1^P^ = — e 2 )11C3^(B.41)(Mp M5 ) 2 271- Gwhere Mp is the mass of the primary component and Ms is the mass of the secondarycomponent.111 •observer17,(t =0)year, and 7r is the parallax.-— —v,(t--4T)ppt (t=--Appendix CSecular AccelerationThe secular acceleration of a star due to its proper motion may be calculated, to firstorder at least, by simply considering the geometry of the situation, which we representin figure C.21. The space motion, V, is assumed to be constant in time and we depictthe position and orthogonal velocity components of the star at times t = 0 and t = At.The proper motion of the star is given by p = 4, measured in arcseconds perFigure C.21: Secular acceleration due to high proper motionWe represent the geometry in a less physical but more easily interpreted manner infigure C.22. We recognize that B = FAT and from figure C.22:103Appendix C. Secular Acceleration^ 104Figure C.22: Geometry of secular acceleration due to high proper motion^—11 sin 0 = vr (t = 0) — vr (t = AT)^(C.42)7rA^ir sin FAT = vr (t = 0) — v„(t = AT)^(C.43)1^ /42206265 ir AT = vr (t = 0) — v,(t = AT)^(C.44)^v,.(t = 0) — vr (t = AT)^A'AT^= 0.0237^ms-lyear-1^(C.45)dv„^112^dt = 0.023 7^ms- lyear-1^(C.46)Using this result we determine the secular acceleration resulting from the propermotion of each of the PRV program stars. The results are given in table C.48.Appendix C. Secular Acceleration^ 105HR HD name Sp. type I dv,./dtms-lyr-1509 10700 r Cet G8V 2.41 +0.3937 19373 1. Per GOV 3.25 0.4996 20630 tc1 Cet G5Vvar 3.95 0.01084 22049 e Eri K2V 2.54 0.11325 26965 o2 Eri K1V 3.29 1.82047 39587 x1 Ori GOV 3.61 0.02943 61421 a CMi A F5IV -0.27 0.13775 82328 0 UMa F6IV 2.47 0.54112 90839 36 UMa F8V 4.08 0.04540 102870 /3 Vir F9V 2.86 0.14983 114710 /3 Corn F9.5V 3.46 0.35019 115617 61 Vir G5V 3.82 0.55544 131156 Boo A G8V 3.75 0.06401 155886 36 Oph A KOV 3.99 0.26402 155885 36 Oph B K1V 4.02 0.27462 185144 o Dra KOV 3.66 0.47602 188512 )3 Aql G8IV 2.59 0.17957 198149 n Cep KOIV 2.27 0.28085 201091 61 Cyg A K5V 3.54 2.28085 201092 61 Cyg B K7V 3.54 2.28832 219134 K3V 4.23 0.7Table C.48: Secular accelerations, dv,/dt, for PRV program starsBibliography[1] Bailes, M., Lyne, A.G., and Shemar, S.L. 1991 Nature 352, 311[2] Baden, R. 1989 "MINUIT at TRIUMF"[3] Bevington, P.R. 1969 "Data Reduction and Error Analysis for the Physical Sciences"[4] Black, D.C. and Scargle, J.D. 1982 Ap.J. 263, 854[5] Bohlender, D.A., Irwin, A.W, Yang, S.L.S., and Walker, G.A.H. 1992 Ap.J. 104,1152[6] Brosche, V.P. 1960 Astronomische Nachrichten 285, 261[7] Campbell, B. 1983, PASP, 95, 577[8] Campbell, B. and Walker, G.A.H. 1979, PASP 91, 540[9] Campbell, B. and Walker, G.A.H. 1985 "Proceedings of IAU Colloquium No. 88,Stellar Radial Velocities" eds. Philip, A.G.D. and Latham, D.W.[10] Campbell, B., Walker, G.A.H., and Yang, S. 1988, Ap.J. 331, 902[11] Cayrel de Strobel, G. Perrin, M.-N., Cayrel, R., and Lebreton, Y. 1989 Astron.Astrophys. 225, 369[12] Cochran, W.D., Hatzes, A.P., and Hancock, T.J. 1991 Ap.J. 380, L35[13] Deming, et al. 1987 Ap.J. 316, 771[14] Dravins, D. 1985 "Proccedings of IAU Colloquium No. 88, Stellar Radial Velocities"eds. Philip, A.G.D. and Latham, D.W.[15] Fletcher, R. 1970 Comput. J. 13, 317[16] Fletcher, R. and Powell, M.J.D. 1963 Comput. J. 6, 163[17] Gatewood, G.D. 1987, A.J. 84, 213[18] Gatewood, G.D. 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(1993) in press[28] Lomb, N.R. 1976 Astrophysics and Space Science 39, 447[29] Lyne, A.G. and Bailes, M. 1991 Nature 355, 213[30] Marcy, G.W. and Butler, R.P. 1992 PASP 104, 270[31] Marsh, K.A. and Mahoney, M.J. 1992 Ap.J. 395, L115[32] McMillan et al. 1985 "Proceedings of IAU Colloquium No. 88, Stellar Radial Veloc-ities" eds. Philip, A.G.D. and Latham, D.W.[33] McMillan, R.S., Smith, P.H., Recker, J.E., Merline, W.J., and Perry, M.L. 1986Instrumentation in Astronomy VI 627, 2[34] McMillan, R.S., Smith, P.H., Perry, M.L., Moore, T.L., and Merline, W.J. 1990Instrumentation in Astronomy VII 1235, 601[35] McMillan, R.S., Moore, T.L., Perry, M.L., and Smith, P.H. Ap.J. in press[36] Nelder, J.A. and Mead, R. 1965 Comput. J. 7, 308[37] Scargle, J.D. 1989, Ap.J. 343, 874[38] Shine, R.A. and Linsky, J.L. 1972 Solar Physics 25, 357[39] Shine, R.A. and Linsky, J.L. 1974 Solar Physics 39, 49[40] Solar System Exploration Division 1992 "TOPS: Towards Other Planetary Systems"[41] Standish Jr., E.M. 1990 Astron. and Astrophys. 233, 252[42] Walker, G.A.H. et a/. "GEMINI - Twin 8 Metre Telescopes"Bibliography^ 108[43] Walker, G.A.H., Yang, S., Campbell, B., and Irwin, A.W. 1989, Ap.J. 343, L21[44] Walker, .G.A.H., Bohlender, D.A., Walker, A.R., Irwin, A.W., Yang, S.L.S., andLarson, A. 1992, Ap.J. 398, L91[45] Walker, G.A.H., Walker, A.R., and Racine, R. 1993 in preparation[46] Wallace, L., Huang, Y.R., and Livingston, W. 1988 Ap.J. 327, 399[47] Widen, R. 1962, A.J. 67, 599[48] Wolszczan, A. and Frail, D.A. 1992 Nature 355, 145[49] Worley, C.E. and Heintz, W.D. 1983 "Fourth Catalog of Orbits of Visual BinaryStars"[50] Yang, S. 1980, Ph.D. thesis (Univ. of B.C.)

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