Applications of High-Resolution Astrometry to Galactic Studies

Transcription

1 Applications of High-Resolution Astrometry to Galactic Studies DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Samir Salim, M.S. ***** The Ohio State University 2002 Dissertation Committee: Approved by Professor Andrew Gould, Adviser Professor Marc Pinsonneault Professor David Weinberg Advisor Astronomy Graduate Program

2 ABSTRACT Astrometry is undergoing a revolution that started with Hipparcos satellite and is continuing with future missions like DIVA, FAME, GAIA or SIM; aswell as novel ground-based techniques. This dissertation investigates in detail several applications of high-resolution astrometry to studies of the Galaxy. For many of the studies presented here a catalog of high proper motion stars is required. The largest such catalog, Luyten s NLTT, constructed several decades ago, is of limited usefulness in its original form. We therefore construct its refined version, containing improved astrometry and photometry for the vast majority of the 59, 000 stars in NLTT. The bright end is constructed by matching NLTT to Hipparcos, Tycho-2, and Starnet; the faint end by matching to USNO-A and 2MASS. We improve Luyten s 6 positions to better than Proper-motion errors in NLTT ( 25 mas yr 1 ) are improved to 5.5masyr 1. Further, with our improved optical/infrared photometry we construct a reduced proper motion (RPM) diagram that, in contrast to the original NLTT RPM diagram, allows for the first time the classification of NLTT stars into main-sequence (MS) stars, subdwarfs (SDs), and ii

3 white dwarfs (WDs). We use this diagram to analyze the properties of our revised, and of the original NLTT. We also produce a list of new candidate nearby WDs. We use improved NLTT in selection of nearby microlensing candidates. SIM can measure a minute deflection in the source s apparent position, and so provide a precise (1%) mass determination of the nearby lens star (in many cases a SD). We search for lens-source encounters using Hipparcos, ACT and NLTT to select lenses, and USNO-A to select sources. Among 32 candidates from Hipparcos there are Proxima Centauri and Barnard s star. For NLTT lenses, the distance and the impact parameter are more poorly known, leading to large uncertainties in the amount of SIM observing time. However, using single-epoch CCD observations of the candidates, and the information from the revised NLTT, we have considerably reduced the uncertainties and produced a reliable list of targets. Three planned astrometry survey satellites, FAME, DIVA, andgaia, all aim at observing magnitude-limited samples. We argue that substantial additional scientific opportunities are within a reach if a limited number of fainter targets is included. Thus, we can increase the number of late-m dwarfs, L dwarfs, and WDs with good parallaxes by an order of magnitude, and enable good determinations of local mass functions (MF). In most cases, the candidate dim dwarfs are not yet known, and we present various methods to identify them. The presented analysis applies to DIVA as well. iii

4 By combining SIM observations with ground-based photometry, one can completely solve microlensing events seen toward the Galactic bulge, allowing one to measure the mass, distance, and transverse velocity of 100 lenses to 5% precision. This would allow the MF of the bulge objects, both luminous and non-luminous (remnants), to be measured. As an application of ground-based astrometry, we present a new geometrical method for measuring the distance to the Galactic center (R 0 ) by solving for the orbit of individual stars bound to the Sgr A*. We identify stars to which the method may be applied, and show that two of them could produce 1-5% accuracy of R 0 after 15 years of positional and radial velocity measurements. Further, we show that combining the measurements of the three stars, while the common center and mass are constrained, produces considerable improvements in the R 0 determination. By modeling the probability distribution over allowed orbital parameter space, we find that by 2010 the achievement of 3% precision is almost certain, while there is a 30% chance of obtaining 1% precision. These estimates would improve if the astrometry errors are reduced from the current 2 mas. For studying the stellar halo we propose observing proper motions of faint horizontal branch stars with FAME. Using them as standard candles, halo rotation can be precisely (2 km s 1 ) mapped out to 25 kpc, and the clumps in the kinematic space (halo substructure) detected. Finally, we propose using SIM astrometric iv

5 microlensing (in a fashion similar to that applied to get bulge MF) to shed light on the nature of MACHO objects and their relation to the dark halo. By simultaneous observations of microlensing events towards the LMC from SIM and the Earth, we expect to measure distances and masses of these objects. v

6 To my parents Mirjana and Yahya vi

7 ACKNOWLEDGMENTS I wish to express my gratitude to Andrew Gould for being a truly great adviser. I am also thankful to everyone at the Department of Astronomy for always being helpful, and for creating an excellent research environment. This work was supported by JPL contract , grant AST from the NSF, grant NAG from NASA, and Program for the Enhancement of Graduate Studies (PEGS) from The Ohio State University. I thank Staša for her love, which is the greatest support one can have. vii

8 VITA May 16, Born Belgrade, Yugoslavia B.S. Astrophysics, University of Belgrade M.S. Astronomy, The Ohio State University University Fellow, The Ohio State University Graduate Teaching and Research Associate, The Ohio State University PUBLICATIONS Research Publications 1. S. Salim and A. Gould, Sagittarius A* Visual Binaries : A Direct Measurement of the Galactocentric Distance. Astroph. J., 523, 633, (1999). 2. A. Gould and S. Salim, Photometric Microlens Parallaxes with the Space Interferometry Mission. Astroph. J., 524, 794, (1999). 3. S. Salim and A. Gould, Nearby Microlensing Events: Identification of the Candidates for the Space Interferometry Mission. Astroph. J., 539, 241, (2000). 4. I. Ferrin et al. Discovery of the Bright Trans-Neptunian Object 2000 EB 173. Astroph. J., 548, L243, (2001). viii

9 5. C. Flynn, J. Sommer-Larsen, B. Fuchs, D. S. Graff and S. Salim, A Search for Nearby Counterparts to the Moving Objects in the Hubble Deep Field. Monthly Notices of the Royal Astronomical Society, 322, 533, (2001). 6. Z. Zheng, C. Flynn, A. Gould, J. N. Bahcall and S. Salim, M Dwarfs from Hubble Space Telescope Counts. IV. Astroph. J., 555, 393, (2001). 7. A. Gould and S. Salim, Searching for Failed Supernovae With Astrometric Binaries. Astroph. J., 572, 944, (2002). 8. S. Salim, A. Gould and R. P. Olling, Astrometry Survey Missions Beyond the Magnitude Limit. Astroph. J., 573, 631, (2002). 9. S. Salim and A. Gould, Classifying Luyten Stars Using an Optical- Infrared Reduced Proper-Motion Diagram Astroph. J., 575, L86, (2002). FIELDS OF STUDY Major Field: Astronomy ix

10 Table of Contents Abstract... ii Dedication... vi Acknowledgments... vii Vita...viii ListofTables...xvi ListofFigures...xxi 1 Introduction AstrometryandAstronomy TheHipparcosRevolution FutureAstrometryMissions x

11 1.4 Future of Ground-based Astrometry? Refinement and Analysis of Luyten s Catalog of High Proper Motion Stars Introduction BrightStarsinNLTT Positional Errors of Bright NLTT Stars Strategy to Match Bright NLTT Stars Proper Motion Errors of Bright NLTT Stars FaintStarsinNLTT Strategy for Matching NLTT to USNO-A and 2MASS AdditionalMatches Positional Errors of Faint NLTT Stars Proper Motion Errors of NLTT Stars CommonProperMotionBinaries RevisedNLTTCatalog xi

12 2.4.1 FormatoftheRevisedNLTT Proper Motion Errors of the Revised NLTT ClassificationofNLTTStars Classification with the Original NLTT ClassificationwiththeRevisedNLTT CandidateNearbyWhiteDwarfs CompletenessofNLTT Completeness at Bright Magnitudes Bright-end Completeness as a Function of Galactic Coordinates CompletenessatFaintMagnitudes Completeness of Different Star Populations as a Function of GalacticLatitude DiscussionandConclusion Precise Masses of Nearby Stars 111 xii

13 3.1 Introduction Astrometric Microlensing with Space Interferometry Mission SelectionofMicrolensingCandidates PrinciplesofSelection CatalogsUsedinSelection EstimatesofErrors SearchingfortheCandidateEvents CandidateEvents ConfirmationofCandidateEvents RefiningEstimatesUsing2MASS ObservingCampaign DiscussionandConclusion Mass Function of Stellar-Mass Objects Mass Function in the Solar Neighborhood Late-MandLdwarfs xiii

14 4.1.2 WhiteDwarfs BulgeMassFunction Bulge Mass Function and the Microlensing DegeneracyofMicrolensingEvents Breaking the Degeneracy with Astrometric Microlensing Addition of Photometric Observations Simulations of SIM Observations Expected Precision of Mass Measurements Precise Distance to the Galactic Center Introduction Past Determinations of the Galactocentric Distance VisualBinaries AroundSgrA* PhysicalPrinciplesoftheMethod MethodofErrorDetermination xiv

15 5.4 Predictions of the Uncertainty of Galactocentric Distance Determination IndividualStars CombinedSolution Probability of Achieving a Given Precision DiscussionandConclusion Kinematics of Stellar and Nature of Dark Halo KinematicsoftheStellarHalo Introduction SelectingFaintA-typeStars HaloRotationMeasurement Substructure in the Galactic Halo NatureoftheDarkMatterHalo Introduction xv

16 6.2.2 MACHO Masses and Distances from Astrometric Microlensing Expected Precision of Distance and Mass Measurements Bibliography xvi

17 List of Tables 2.1 BrightNLTTstarspositionprecisions Bright NLTT stars proper motion precisions NumberofUSNO/2MASSmatches Newcandidatewhitedwarfscloserthan20pc Hipparcos and ACT events - lens star properties (astrometry and photometry) Hipparcos and ACT events - lens star properties (distance, kinematic andphysicalproperties) Hipparcos and ACT events - source star and event properties NLTTevents-lensstarproperties NLTT-sourcestarandeventproperties xvii

18 4.1 Uncertainties of microlensing parameters, Bulge (I = 15, ψ = 225, 5hours) RotationofthehalofromBHBstars Uncertainties of microlensing parameters, LMC (V = 20, arbitrary ψ, 20hours.) xviii

19 List of Figures 1.1 Astrometric accuracies of different missions Positional errors of bright stars in NLTT a close-up PositionalerrorsofbrightstarsinNLTT Differences between photographic photometry from NLTT and USNO PositionalerrorsoffaintstarsinNLTT Fraction of NLTT stars found in a rectangle as a function of V Fraction of NLTT stars found in a rectangle as a function of declination NLTTpropermotionerrors Difference between separation vectors of CPM binaries in NLTT and therevisedcatalog xix

20 2.9 Difference in relative proper motions for NLTT CPM binaries Differences between proper motions as given by Tycho-2 and our measurements based on identifying the stars in USNO and 2MASS Difference in the relative proper motion of the components of subdwarfbinaries Original reduced proper motion (RPM) diagram for NLTT stars Optical-infrared RPM diagram for NLTT stars Original NLTT RPM diagrams with stars classified using opticalinfraredrpmdiagram Completeness of the combined Hipparcos and Tycho-2 catalogs with respect to NLTT, as a function of R NLTT Completeness of bright-end NLTT with respect to Hipparcos/Tycho- 2,asafunctionofpropermotion Completeness of bright-end NLTT as a function of Galactic latitude Completeness of bright-end NLTT as a function of Galactic longitude Completeness of faint-end NLTT as a function of magnitude xx

21 2.20 Surface density of three different stellar populations as a function of Galacticlatitude Mass-luminosityrelation Reduced proper motion diagram for Hipparcos and NLTT stars Distance-modulus errors vs. distance modulus for Hipparcos stars Hipparcos color-magnitude diagram with candidate events CygA/Bmicrolensingevents Apparent magnitude proper motion diagram of candidate events Histogram of late-type dwarfs with precise parallax estimates using FAME Distribution over M V of white dwarfs with precise parallax estimates using FAME Evolution of R 0 fractional uncertainty from S0-1 orbits Evolution of σ R0 from S0-1 orbit with different values of σ vrad Contour plot of σ R0 from S0-1 orbit (t obs =15yr) xxi

22 5.4 Contour plot of σ R0 from S0-1 orbit (t obs =30yr) Contour plot of σ R0 from S0-2 orbit (t obs =15yr) Contour plot of σ R0 from S0-2 orbit (t obs =30yr) Evolution of σ R0 inacombinedsolution Probability of obtaining specific σ R PropermotiondistributionofA-typestars Estimate of the measurement error of halo rotation xxii

23 Chapter 1 Introduction 1.1. Astrometry and Astronomy The Merriam-Webster Dictionary defines astrometry as: a branch of astronomy that deals with measurements (as of positions and movements) of celestial bodies. It also lists that the term first appears around From this definition it is clear that astrometry is just one of the branches of astronomy, but its relation to astronomy and the role it plays in it, and also the way this relation and role have changed throughout the history requires further elaboration. We can say that to a great extent, from its earliest beginnings until the late 19th century astronomy was astrometry. The first time some ancient astronomer looked at the sky and recorded relative positions of stars in the form of a constellation, he or she was already making an astrometric measurement, albeit 1

24 a very crude one. And while there was not much to record in terms of stellar motions (except for the diurnal motion), following the apparently complex motions of planets prompted the first sound ideas about the physical underpinnings of the universe. Actually it was the lack of any observable relative motion of stars that imposed constraints on these early models of the universe namely the lack of parallax was one of the key arguments that the Earth was motionless, and as such occupying the central position in the universe. Despite the fact that the change of planetary positions was more interesting to observe, it was soon realized that in order to determine these changes accurately enough, there must also exist a good catalog of stellar positions. Most likely using some very simple apparatus for measuring relative stellar angles and the altitudes of stars passing the meridian, Hipparchus, in the 2nd century BC, was able to compile a catalog of stellar positions and apparent magnitudes of 850 naked-eye stars, with a typical accuracy of half a degree. The original catalog of Hipparchus was included in Ptolemey s Alamgest three centuries later, and possibly expanded with some of his own measurements. This catalog became a standard for centuries to come. The next major advancement in astronomy (or astrometry) that had profound consequences for the science as a whole (and actually for laying the foundations of modern science), came with Tycho Brahe in the 16th century, and his precise measurements of stellar and planetary positions. Using large instruments for 2

25 measuring angles, he was able to achieve arcminute precision the limit of naked-eye observations. His observations of some 800 stars were compiled by Kepler. The level of accuracy allowed Kepler to challenge the assumption of circular planetary orbits, and ultimately to formulate his laws of planetary motion, which paved the way for one of the greatest achievements in the history of science Newton s theory of universal gravity. With the introduction of telescopes, more and more of astronomical observations had aspects different from those of astrometry telescopes allowed for the exploration of physical features of the celestial bodies, thus setting the stage for what we today call astrophysics, which practically became synonymous with astronomy. The introduction of telescopes meant further advances in astrometry as well, since more precise astrometric measurements become possible. Armed with a telescope and the Newton s theory of gravity, a new field emerged celestial mechanics determining orbits of Solar System bodies and predicting their future positions. The successes of the celestial mechanics were demonstrated early on by the discovery of the periodicity of the Halley s comet and ultimately by the discovery of Neptune through gravitational perturbations on Uranus, by Le Verrier and Adams in mid 19th century. The aspects of astrometry related to stars also came to flourish. For the first time it was possible to measure a star s own (proper) motion in 1718 Halley found 3

26 that Arcturus, Procyon and Sirius could no longer be considered fixed stars. The Earth s motion was reflected in the abberation of light, discovered by Bradley, and more importantly, and what Bradley actually attempted to measure but it took a century before instruments became precise enough to do it, the parallax of another star was detected in 1838 by Bessell, thus obtaining the first distance to any star besides the Sun, and also ultimately proving that Earth orbits the Sun. This was also how astrometry touched upon the emerging field of astrophysics measuring stellar distances enabled their physical brightness to be known and compared to the Sun s, leading to the concept of HR diagram, the main sequence, and giving clues to stellar evolution. Proper motions coupled with distances produce two components of the physical velocity, enabling studies of the kinematics and dynamics of the Solar neighborhood, and later, of the Galaxy as a whole. Bessel is also credited with detecting wobbles in Sirius and Procyon, produced by companions, which at that time escaped optical detection. Besides this aspect of high-precision (sub-arcsecond) astrometry, the charting of the skies that included more and more stars continued. Flamsteed produced a catalog of 3000 stars in the early 18th century (including Halley s observations of stars in the southern hemisphere). This catalog reached a precision of 10. Around the mid-19th century, Argelander, after working for 25 years, produced a massive 4

27 catalog and charts containing 300,000 northern stars to 10th magnitude. This work was later expanded to the south. At approximately the same time the photographic plates came to be used in astronomy. Now positions of many stars could be measured on a single plate, and with yet greater precision. The realization of this capability of astrophotography led to the creation of a huge international program of producing a photographic atlas of the sky at a scale good enough for astrometric measurements, known as Carte du Ciel. Although the work was divided among many observatories (mostly in Europe and some in South Africa, South America and Australia), the project proved to be overwhelming, not only for its technical requirements where the quality and the number of plates was concerned (each was 2 square), but even more so when it came to measuring the positions of the stars from the plates to produce the accompanying catalog (Astrographic Catalog). The atlas aimed at reaching 14th magnitude, and the catalog which was never completed, was supposed to include stars to 12th magnitude. It is widely believed that the commitment of European astronomers to this burdensome project led to their falling behind their American colleagues, who at that time concentrated on the studies of extragalactic nebulae that resulted in one of the most profound discoveries, that of the expanding Universe and the Big Bang. It was a century after its conception that the project of Carte du Ciel reached its conclusion. 5

28 Later in the 20th century more efficient methods of photographing large swaths of the sky became possible with the introduction of Schmidt cameras and their large 6 field of view. The Palomar Observatory Sky Survey released in 1958 was a treasure trove for discoveries of every kind, from local asteroids to distant galaxy clusters. It was this kind of plates that William Luyten used in his half a century long effort to catalog all stars with high proper motion. He achieved this by blinking plates taken at different epochs, either manually or using simple plate measuring machines. This endeavor resulted in the catalog of nearly 60,000 stars moving faster than 0. 2yr 1, known as the New Luyten Two-Tenths (NLTT) catalog. In many aspects, such as depth, completeness and overall accuracy, this catalog is still unsurpassed. We found this catalog essential for many of the studies presented in this dissertation and that is why we pay special attention to it, and made considerable effort to bring this catalog up-to-date as to make it more useful for the variety of studies. Chapter 2 is thus completely devoted to this catalog. Besides inability to produce deeper and more precise all-sky catalogs of stellar positions (and proper motions), difficulties also plagued further improvements in narrow-angle astrometry, which is responsible for yielding stellar parallaxes. It is not only that the observations where technically difficult, but the blurring of images because of the Earth s atmosphere set the limit to the accuracy of individual astrometric measurement and also to the ultimate achievable accuracy, 6

29 thus limiting the volume of space that could be explored. As late as in the 1980s, the most sophisticated astrometric observations augmented by CCDs could at best reach a parallax precision of a few milli-arcseconds (mas), but even this for a very limited number of stars The Hipparcos Revolution Close to the end of the 20th century it appeared that astrometry, and its role in astronomy was all but dead. However, this condition was radically changed with the release of results from the Hipparcos astrometric satellite in Launched in 1989, the satellite was not able to reach the correct orbit and it appeared that the entire mission would fail. However, useful data where obtained in this faulty orbit as well. Without blurring from the Earth s atmosphere it was possible to achieve very high precision even with small aperture of Hipparcos telescopes by repeatedly making hundreds of positional measurements of the same star. The satellite carried two instruments. The main instrument performed observations of some 120,000 preselected stars, achieving the average positional, parallax and proper motion precision of 1 mas. This sample (approximately one half of the total number) was magnitude-complete to V 8. Of the fainter stars, to the limiting magnitude of the instrument of V 11.5, only some where observed mainly high proper motion stars drawn from NLTT, but also many astrometric standards for which 7

30 improved positions were desirable, and even stars that are being occulted by the Moon (presumably in order to use occultation timings to refine the lunar orbit.) This main catalog is known simply as the Hipparcos catalog (ESA 1997). The second instrument carried out measurements of all stars down to the magnitude limit, but with a 20 times lower precision. This is the Tycho catalog (ESA 1997), and it contains around 1 million stars. Precise parallaxes and proper motions of tens of thousands of stars in the Hipparcos catalog enabled many different studies. The HR diagram was calibrated with the unprecedented precision. The disputed distance to the Hyades was measured directly, leading to new estimates of the luminosity of stellar candles and redefining most of the cosmic distance ladder. Proper motions provided more secure estimates of Sun s motion with respect to the local standard of rest, identified clumps of stars in the velocity space, and produced estimates of the local mass density. Many more important results stemming from Hipparcos catalog could be mentioned. The larger, but less precise Tycho catalog also proved to be quite valuable. Namely, it was realized that the density of Tycho stars is high enough to enable precise astrometric calibration of wide field photographic plates, like that of POSS, which are otherwise difficult to calibrate because of severe distortions. However, for first generation POSS plates, taken in the 1950s, the 20 mas Tycho positions 8

31 obtained in 1991 would degrade to several arcsec because of imprecise proper motions. This is where the material taken for Carte du Ciel Astrographic Catalog came to the rescue. With modern computer technology it was relatively easy to reduce these old plates. With the mean epoch of 1907, the Astrographic Catalog (AC, Urban et al. 1998a) served as a perfect first epoch to compare with Tycho and derive proper motions with accuracy of 4 mas yr 1. This combination of AC and Tycho catalogs came to be known as the ACT catalog (Urban, Corbin, & Wycoff 1998b). Later, the data from the Tycho experiment were rereduced to reach 0.5 mag fainter limit, doubling the number of stars, and again these positions were combined with AC and approximately 150 other smaller catalogs, to produce Tycho-2 (Høg et al. 2000). With ACT stars serving as positional references, POSS-I and southern ESO/UKIRT plates were calibrated to produce the largest stellar catalog ever, USNO-A (Monet 1998), containing stars. ACT also served as a basis for astrometric calibration of the two catalogs derived from truly digital sky surveys: optical SDSS (York et al. 2000), and infrared 2MASS (Skrutskie et al. 1997). We used USNO-A and 2MASS extensively to refine astrometry and photometry of NLTT stars. 9

32 1.3. Future Astrometry Missions Building on the success of Hipparcos, new astrometric missions having greater accuracy and sensitivity were proposed. In the first group of these new missions we can include two missions aiming to achieve accuracies an order of magnitude better than that of Hipparcos Full-Sky Astrometric Explorer (FAME) and DIVA. Both should be complete to R 15, totaling some stars. The main expected scientific returns are that the primary distance calibrators such as Cepheids, RR Lyrae and low-metallicity MS stars will be calibrated directly, and with a great precision. Astrometric monitoring over several years of mission lifetime will also enable detection of wobbles induced by planetary and substellar companions on the primaries. Unlike the radial velocity method, astrometric method produces masses without uncertainties due to orbital inclination. A wealth of information on the distribution of visible and dark mass will come from precise proper-motion measurements of tracer populations. Neither FAME nor DIVA can transmit entire CCD frames they observe, therefore they require some pre-selection of stars that will be measured. FAME was supposed to have an input catalog with positions of stars brighter than R = 15, while DIVA has an on-board sensor that selects bright stars and transmits parts of the CCD array containing them. Our analysis has led us to conclude that 10

33 insisting on magnitude-limited samples, as it is planned, would lead to a loss of great scientific opportunities achievable by observing a limited number of fainter objects. These objects would have to be preselected based on scientific merit. In this dissertation ( 4.1), I emphasize improvements achievable using this approach in obtaining the local mass function and luminosity calibration of late-m and L dwarfs, and of white dwarfs. Also, by selecting faint horizontal branch stars and measuring their proper motions, valuable information on the motion, and kinematic substructure of the Galactic halo is achievable ( 6.1). Furthermore, observing proper motion of many faint quasars, whose motion is known a priori to be zero, enables multi-fold improvement in the definition of the reference frame. We have illustrated these principles using proposed characteristics of FAME. Recently, the funding for this satellite was terminated, however, the same principles can be applied to DIVA, scheduled for launch in A more ambitious project, but using the same techniques as Hipparcos and DIVA, is planned for early in the next decade. GAIA will have precision as high as 12 µas yr 1, and will measure 10 9 stars to V 20 (at which point precision falls to 160 µas yr 1 ). It will also measure radial velocities to V = 17. This will allow the full six-dimensional phase-space to be explored for a large part of the Galaxy. This will make feasible studies that give a full picture of the structure and evolution of the Galaxy. At this point it is too early to make any conclusions whether, as in the 11

34 case of FAME and DIVA, including still fainter samples of stars (beyond V = 20) is technically sound and scientifically justified. Still greater accuracies will be achievable with Space Interferometry Mission (SIM), scheduled for launch in It should be able to provide 4 µas yr 1 accuracy down to V = 20, regardless of magnitude. Unlike all the previous missions that are constantly scanning the sky and thus produce all-sky surveys, SIM will observe specific targets (some 40,000 during its 5 yr mission lifetime). Also, unlike the other missions, SIM uses optical interferometry to achieve this unprecedented accuracy. Scientific objectives, and therefore the targets to be observed will be defined by the winning proposals. Currently selected proposals (key projects) include a search for planets, obtaining direct distances to globular clusters, measuring proper motions of nearby galaxies, etc. One of the selected projects is astrometric measurement of microlensing events, headed by Andrew Gould. Classical photometric microlensing is in itself a very powerful technique, especially in the statistical sense, but becomes even more powerful when astrometric effects are observed as well so that distances and masses of lenses can be determined. In this respect, we investigate SIM s performance and principles required to obtain the bulge mass function of luminous and non-luminous objects ( 4.2), and the distances and masses of MACHOs ( 6.2). For rare cases of lensing by nearby 12

35 stars the only observable effect is astrometric and this allows their masses to be measured with high precision (Chapter 3). Figure 1.1 compares the astrometric accuracies of different missions as a function of magnitude Future of Ground-based Astrometry? It might seem that with the advent os space-based astrometry there is no place for astrometric studies made from the ground. However, this is not entirely true. The techniques such as speckle interferometry and adaptive optics in many cases efficiently counter the deleterious effects of the atmospheric seeing. Even better results in achieving high-resolution imaging, and therefore enabling astrometry of high precision, are expected from ground-based optical and infrared interferometers that include telescopes of large apertures. Unlike space missions, these facilities will operate for longer periods of time, thus enabling studies that take more time (for example, planets with longer periods). Also, they have greater collecting power than satellites and can operate in wavelengths not available to satellites. Observing in the infrared is necessary in studying the Galactic center, which suffers too much extinction in the optical band. Astrometry of stars lying as close as 1000 AU from the radio source Sgr A* already give strong indications that these 13

36 stars move in the gravitational potential of a supermassive black hole associated with Sgr A*. In Chapter 5 we propose a method that would combine these astrometric observations with radial velocity measurements to achieve an accurate distance to the Galactic center, a fundamental parameter in Galactic astronomy. In order for this method to be competitive, observations over a number of years are required, which is another reason why ground based observations are favored. After decades of neglect, it is clear that once again astrometry, now of very high resolution, plays a crucial role in modern astronomy, and that no field of astronomy or astrophysics can claim to be complete without results provided by and made possible by astrometry. 14

37 0.1 FK5 Mission Accuracy 10mas 1mas.1mas Hipparcos FAME 10uas GAIA SIM 1uas SIM (exceptional targets) 0.1uas V magnitude Fig Comparison of astrometric accuracies of different missions as a function of magnitude. 15

38 Chapter 2 Refinement and Analysis of Luyten s Catalog of High Proper Motion Stars 2.1. Introduction More than two decades after its final compilation, the New Luyten Two-Tenths Catalog (NLTT) of high proper-motion stars (µ >0. 18 yr) (Luyten 1979, 1980; Luyten & Hughes 1980) and its better known subset, the Luyten Half-Second Catalog (Luyten 1979, LHS) (µ >0. 5 yr), continue to be a vital source of astrometric data. They are still mined for nearby stars (Reid & Cruz 2002; Jahreiss, Scholz, Meusinger, & Lehmann 2001; Scholz, Meusinger, & Jahreiss 2001; Gizis & Reid 1997; Henry, Ianna, Kirkpatrick, & Jahreiss 1997), subdwarfs (Gizis & Reid 1997; Ryan 1992, 1989), and white dwarfs (Reid, Liebert, & Schmidt 2001; Schmidt et al. 1999; Liebert, Dahn, Gresham, & Strittmatter 1979; Jones 1972; Luyten 1970, 1977). NLTT is at the center of the controversy over whether 16

39 halo white dwarfs can contribute significantly to the dark matter (Reid, Sahu, & Hawley 2001; Oppenheimer et al. 2001; Flynn et al. 2001); and it is the primary source of candidates for astrometric microlensing events to be observed by the Space Interferometry Mission (SIM) (Chapter 3). Despite the advent of many new proper-motion surveys, including Hipparcos (ESA 1997), Tycho-2 (Høg et al. 2000), Starnet (Röser 1996), UCAC1 (Zacharias et al. 2000), as well as deeper but more localized surveys: SuperCOSMOS Sky Survey in the south (Hambly et al. 2001; Hambly, Davenhall, Irwin, & MacGillivray 2001), Digital Sky Survey (DSS)-based survey in the Galactic plane (Lépine, Shara, & Rich 2002), search for µ>0. 4yr stars in 1400 deg 2 (Monet et al. 2000), EROS 2 proper motion search in 400 deg 2 of high latitude fields (EROS Collaboration et al. 1999), and MACHO search in 50 deg 2 towards the bulge and the LMC (Alcock et al. 2001), NLTT remains unchallenged as a deep, all-sky, proper motion catalog. NLTT is an all-sky catalog with position and proper-motions (PPM) for stars above a proper-motion threshold of µ lim = 180 mas yr 1. It extends to V 19 over much of the sky, although it is less deep (V < 15) within about 10 of the Galactic plane and also in the celestial south (δ < 30 ). In addition to PPM, NLTT lists somewhat crude photographic photometry in two bands (B NLTT, R NLTT ), rough spectral types (usually based on photographic colors), as well as important notes on some individual stars, primarily common proper motion (CPM) binaries. 17

40 To be sure, the newer catalogs have superseded NLTT in certain domains. By observing a large fraction of the brighter (V < 11) NLTT stars, Hipparcos obtained vastly superior astrometry and photometry for about 13% of NLTT, although in its magnitude limited survey (V < ) it did not find any significant number of new high proper-motion stars not already catalogued by Luyten. Tycho-2, which combined re-reduced Tycho observations of 2.5 million stars with 144 ground-based catalogs (most notably the early 20-century Astrographic Catalog) to derive proper motions, includes PPM and photometry for several thousand additional NLTT stars, and also contains several hundred previously unknown bright (V < 11) high proper-motion stars. However, neither Hipparcos nor Tycho-2 probes anywhere near the faint (V 19) limit of NLTT. Moreover, their overlap with NLTT has never been systematically studied. UCAC (US Naval Observatory CCD Astrograph Catalog) is in the process of delivering a new all-sky PPM catalog down to R 16 based on CCD observations. The first release (UCAC1) covers 80% of the Southern hemisphere. While its photometry is only for a single band (close to R), UCAC1 can easily be matched to 2MASS (Skrutskie et al. 1997) with its JHK photometry, effectively creating a multi-wavelength PPM catalog. Unfortunately, the current release, UCAC1, excludes most of the NLTT high proper-motion stars, due to absence of these stars in Southern parts of USNO-A2 catalog (Monet 1998), which was used as a first epoch. (USNO-A2, and its earlier version USNO-A1, Monet 1996, were derived by measuring first generation Schmidt plates.) High 18

41 proper-motion stars pose an especially difficult problem for automated catalog construction: counterparts of slow-moving stars can be reliably identified at different epochs, but fast-moving ones are easily confused with pairs of unmatched, but unrelated stars, or even with spurious objects. These problems grow rapidly worse near the magnitude limit and towards the Galactic plane. Without either new and robust (but difficult to write) algorithms or a vast investment of manual labor, the only routes open in the face of these difficulties are to eliminate the potential high proper-motion stars from the new catalogs or to include them but to acknowledge that many may be spurious. These two approaches have been respectively adopted by UCAC1 and Starnet. (Starnet derives its proper motions for 4.3 million stars by combining the Nesterov, Kislyuk, & Potter 1990 reduction of Astrographic Catalog with GSC 1.0, Lasker et al ) There are two other PPM catalogs whose release is promised in the near future, USNO-B (Monet 2000) and GSC-II (Lasker et al. 1998, also known as GSC 2.3 ). Both are based on photographic astrometry and photometry down to or beyond the NLTT limit of V 19. They use a combination of first and second generation Schmidt plates to determine proper motions. Neither project has stated explicitly how they will handle high proper-motion stars. Ultimately, space missions such as FAME, DIVA, and/or GAIA will produce reliable catalogs of high proper-motion stars, since each star is observed hundreds 19

42 of times with great astrometric precision, thus eliminating the possibility of false matching. However, NLTT stars that are fainter than the FAME or DIVA survey limit of R 15 cannot be observed by them unless they are securely located prior to the mission. Hence, this is yet another reason for obtaining improved astrometry for these stars. While NLTT has proven incredibly valuable, it also has significant shortcomings. As mentioned above, its two-band photometry is relatively crude, so that classification of stars using the NLTT reduced proper motion (RPM) diagram (one of the main motivations for constructing the catalog) is rather uncertain: white dwarfs are easily confused for subdwarfs, as are subdwarfs for main-sequence stars. Very few of the NLTT stars have their optical magnitudes in standard bands available in the literature. This problem is not easily resolved by matching with other catalogs that have better photometry, such as USNO-A (photographic B USNO and R USNO : σ 0.3) or 2MASS (JHK: σ 0.03). This is because although a large fraction of NLTT stars have fairly precise ( 10 ) positions, a significant minority have much larger errors, making automated identification of counterparts in other catalogs quite difficult. Some applications require much higher precision proper motions than NLTT s characteristic mas yr 1. For example, even when faint NLTT stars can be identified in USNO-A (thus establishing their POSS I 1950s positions to 250 mas) 20

43 the NLTT proper-motion errors propagate to create 1. 5 position errors in 2010, too large to reliably predict viable astrometric microlensing events to be observed by SIM (Chapter 3), and so measure precisely the mass of the lens (high proper motion star). These errors can be reduced to 100 mas, which is quite adequate for our purposes, by matching NLTT stars first to USNO-A and then to 2MASS. In 2.2 we present the first step in the construction of a refined NLTT catalog: matching bright NLTT entries with those in more recent and higher-precision catalogs, primarily Hipparcos and Tycho-2, but also Starnet. By doing so, we characterize both NLTT s PPM errors and its completeness at the bright end for the first time. These results are of interest in their own right, but they also serve to guide our search procedure for USNO-A/2MASS counterparts at fainter magnitudes. That faint-end search is discussed in 2.3. The general approach is be to match (circa 1950) USNO-A stars with their (circa 2000) 2MASS counterparts using NLTT (1950 epoch) positions as a rough guide as to where to find USNO-A counterparts, and NLTT proper motions to predict the positions of their 2MASS counterparts. To correctly apply this approach and to understand its limitations, one must have a good grasp of the NLTT PPM error distributions, and for this it is best to compare NLTT with other PPM catalogs. 21

44 The bright-end and faint-end searches are complementary. On the one hand, Hipparcos/Tycho-2/Starnet become highly incomplete for V > 12, and so cannot probe faint magnitudes. On the other hand, the POSS plates that were scanned to produce USNO-A saturate for V < 11, leading to increasingly unreliable photometry, astrometry, and even identifications at bright magnitudes. Nevertheless, these searches do have some overlap at intermediate magnitudes, and we will exploit this overlap to check each method against the other. Hence, we push the bright-end search as faint as we can, incorporating Starnet (with its spurious high-proper motion stars). And we push the faint-end search as bright as we can, eliminating only the Hipparcos/NLTT matches before beginning the search. By combining the bright-end and faint-end searches we come to our revised catalog (Revised NLTT). The format and the properties of this catalog are described in 2.4. The Revised NLTT has a wide range of potential applications. Most notably, the resulting V J RPM diagram (where V is calibrated from B USNO and R USNO ) permits a much more reliable separation of different classes of stars than did the original B NLTT R NLTT RPM diagram. The construction and the analysis of RPM diagram is discussed in 2.5. Study of this diagram is useful in its own right, but can also guide the interpretation of RPM diagrams constructed of NLTT stars present in SDSS (York et al. 2000), making use of excellent SDSS photometry and 22

45 SDSS/USNO-A derived proper motions. A refined version of NLTT with improved astrometry and photometry could also be exploited to study binarity as a function of stellar population and to find new wide-binary companions of NLTT stars. Finally, in 2.6 we present a thorough study of NLTT s completeness. NLTT s completeness (or lack thereof) is central to the debate over the possibility that a significant fraction of the dark matter can be in halo white dwarfs. We first demonstrate that NLTT is in fact complete at the bright end, and explore this completeness as a function of the position in the Galactic coordinate system. Then we argue that if NLTT is complete at the bright end (V < 13), then one could use a bootstrap-type procedure to show that it is also close to complete at the faint end. Finally, we investigate the relative completeness of different types of stars in the Revised NLTT as a function of Galactic latitude Bright Stars in NLTT Positional Errors of Bright NLTT Stars To match NLTT stars with counterparts found in other catalogs, we have to start with NLTT s positions and proper motions. To devise a search strategy, it is therefore crucial that we first evaluate the error distributions of these quantities. 23

46 Positions in NLTT are nominally given to two different levels of precision, indicated by a flag: in right ascension (RA), either 1 second or 6 seconds of time and in declination (DEC), either 0. 1or1 of arc. The inferior precisions are the rule in the south (δ < 45 ), and the superior precisions are the rule in the north, although for δ>80, the RA is given at nominally inferior precision because 6 seconds of time still corresponds to a relatively small arc. What is the actual PPM error distribution for the 54, 000 NLTT entries with nominally good positional precision? To investigate this, we first select only Tycho-2 stars with proper motions µ>180 mas yr 1, i.e., the same limit as of NLTT. Using Tycho-2 proper motions (having typical errors of just 2 mas yr 1 ), we propagate their positions back to 1950, the epoch of NLTT. We then find all NLTT entries whose catalog coordinates lie within 3 of each Tycho-2 star many times larger than the nominal positional accuracy. To ensure a high level of confidence that the counterpart is real, we restrict consideration to stars for which there is one and only one Tycho-2/NLTT match, and for which the unique NLTT match does not have a flag indicating an inferior-precision measurement. Finally, we eliminate 84 matches for which the Tycho-2 proper motion disagrees with the NLTT proper motion by more than 75 mas yr 1. Figures 2.1 and 2.2 show the position differences (NLTT Tycho-2) of the resulting 6660 unique matches, on small and large scales respectively. The central portion of this distribution (Fig. 2.1) exhibits an 24

47 obvious rectangle with dimensions (1 s 6 ), i.e., exactly the precisions imposed by the rounding truncation of the catalog entries. Hence, one can deduce that for the majority of the entries within this rectangle, Luyten actually measured the positions to much better precision than they were recorded into NLTT. Also obvious in this figure is a halo of stars that have characteristic errors that are of order the discretization noise. We therefore model the distribution of Luyten s position measurements as being composed of two populations, with intrinsic Gaussian measurement errors (in arcsec) of σ 1 and σ 2. Given the discretization of the reported positions, the distribution of residuals in DEC ( δ) should therefore be, P ( δ) = 1 { [ q erf 2w [ +(1 q) erf ( ) ( )] c + w/2 δ c w/2 δ erf σ 1 σ 1 ( ) ( c + w/2 δ c w/2 δ erf σ 2 σ 2 )]}, (2.1) where c is the center and w is the width of the discretization box in DEC and q gives the relative normalizations of the two populations. We apply equation (2.1) to the N = 5495 stars lying in the strip 7. 1cosδ > α > 7. 9cosδ 0. 5, and fit only in the region shown in Figure 2.1, i.e., δ < 12. (The reason for offsetting the center of this box from 0 will be made clear in Table 2.1.) We find that when w is left as a free parameter, the best fit value is consistent with w =6, the value expected due to discretization. We then fix w and rederive the other 25

48 parameters. Next, we write a similar equation for the residuals in RA, P ( α) = sec δ { [ q erf 2w [ +(1 q) erf ( c + w/2 α σ 1 sec δ ( c + w/2 α σ 2 sec δ ) erf ) erf ( )] c w/2 α σ 1 sec δ ( c w/2 α σ 2 sec δ )]}. (2.2) We apply equation (2.2) to the N = 5022 stars in the strip 3. 3 > δ > 3. 7, and fit only in the region α < 12 sec δ. The width is again consistent with the expected value, w =15, so we again hold w fixed. Table 2.1 shows our results. Here N is the total number of stars in the subsample and N 1 = Nq is the number in the good-precision (σ 1 ) population. For both the α and δ directions, we find that σ , σ 2 6,andN That is, for more than half the full sample (4000/6660 = 60%), Luyten actually obtained the stellar positions to a precision of 1 even though he recorded his results much more coarsely. For most of the rest, his measurement errors were similar to the discretization noise. The offsets c may result from small systematic errors in Luyten s global astrometry, or from real offsets between his global frame and the ICRS that underlies Tycho-2 astrometry. In any case, these offsets are taken into account when we fix the intervals from which we draw stars to fit to equations (2.1) and (2.2). However, Figure 2.2 shows that there is an additional population, an outer halo beyond what would be predicted by extrapolating the behavior of the inner 26

49 two populations. The structure of the distribution shown in Figures 2.1 and 2.2 will lead us in to a layered approach to identifying NLTT stars. Because some stars have much lower position errors than others, we suspect that they may also have much lower proper-motion errors. To test this, we divide the above sample into two subsamples, those lying with a slightly broadened (16 8 ) rectangle and those lying outside it. For the stars in the rectangle, the RMS difference between the magnitudes of the proper motion as measured by NLTT and Tycho-2 is 18 mas yr 1, while for those outside the rectangle it is 24 mas yr 1. (Tycho-2 error are negligible in comparison.) Hence, the rectangle stars indeed have better proper motions. For the individual components of the proper motion vector, the corresponding RMS differences are 22 mas yr 1 and 27 mas yr 1 respectively. For random uncorrelated errors in RA and DEC, one would expect the magnitude RMS to equal the component RMS. The fact that the latter is larger is probably due to transcription errors in NLTT of the proper-motion direction (proper motion in NLTT is given as a magnitude and a position angle of direction). While the dispersions of this cleaned sample probably realistically characterize the intrinsic errors in the NLTT proper motions, they are lower limits on the RMS differences between NLTT and Tycho-2 for the catalog as a whole. This is mainly because binaries (which have been preferentially excluded from the 27

50 sample by demanding one-one matches) can cause proper-motions to differ when measured over different timescales. We use these estimates to guide our approach to matching, but will evaluate the dispersions on the matched sample again in after carrying out the match Strategy to Match Bright NLTT Stars We match NLTT sequentially to three proper motion catalogs of bright stars: Hipparcos, Tycho-2, and Starnet, each in succession containing more stars, but also generally poorer astrometry. That is, we first match to Hipparcos. We then remove from consideration all matched NLTT stars and match the remainder to Tycho-2 (or rather to the subset of Tycho-2 that is not associated with Hipparcos stars). We then repeat the procedure for Starnet. Since NLTT has about 59,000 entries, of which almost 13,000 have counterparts in these three catalogs, we are especially interested in developing procedures that can match automatically as many of these as possible, thereby reducing to a minimum the number that require human intervention. For each catalog, we therefore begin by matching stars inside a (16 8 ) rectangle. The chance that two unrelated high proper-motion stars will fall so close together is miniscule. We therefore place only very weak demands on matches: the magnitude of the vector proper-motion difference should be less than 100 mas yr 1,andthe V 28

51 magnitudes should agree within 1.5 mag. For Hipparcos, we use the Johnson V mag given in the catalog. For Tycho-2, we use the catalog s V T. For NLTT we use the red magnitude R NLTT (which is actually quite close on average to Johnson V, Flynn et al. 2001) except when it is not given, in which case we adopt (B NLTT 1) for the V mag. For Starnet, we use the red photographic magnitude which ultimately derives from the GSC 1.0. Of course, all these various magnitudes are not on exactly the same system, but because of the inaccuracy of photographic magnitudes, in particular those in NLTT, the systematic differences are not very important: we are interested only in a crude discrimination between stars of very different brightnesses. We conduct our search only for NLTT stars with R NLTT Singular matches from this rectangle search are accepted without further review. There are, however, many multiple matches in both directions. For example, if one component, say A, of a CPM binary matches to a star in a given catalog, the other component, B, will almost always match as well. If the CPM binary is sufficiently wide to have a separate entry in the catalog being searched (Hipparcos/Tycho-2/Starnet), it may yield 4 matches : A A, A B, B A, B B, of which the second and third are false. All such multiple matches are investigated, but in many cases they cannot be fully resolved because the true match to the companion is outside the rectangle or outside the catalog altogether. We return 29

52 to this problem below. The matches are then removed from both catalogs, and a second search on the remaining NLTT stars is then conducted inside a radius θ <120 but otherwise using the same criteria. These matches are also accepted without review: the main reason for separating the rectangle and circle searches at this stage is to reduce the number of multiple-matching candidates. After resolving double matches (where possible) we return to the rectangle, but loosen the criteria. We now demand only that the magnitudes of the proper motions be consistent within 80 mas yr 1 but place no constraint on the direction. This is to allow for transcription errors in the angle recorded in NLTT. We also loosen the tolerance on the agreement in V to 2.5 mag. The resulting new matches are then scanned manually. But again, since the chance that two unrelated high proper-motions stars will fall in the same rectangle is extremely small, virtually all of these matches are genuine. Next, we apply the same procedure to the 2 circle. All matches are again reviewed by hand, this time more critically. If, for example, the angle of the proper motion and the RA both disagree strongly, but the DEC agrees to within a few arcsec and the V mags also agree well, we assume that the match is real and that there are multiple transcription errors. Of course, we are more liberal for the regions where NLTT has worse-precision positions. Finally, we extend the search to θ <200 and with the weak constraints on proper-motion and magnitude agreement. We review the results with extreme caution. (We do not apply this last step to Starnet because it contains spurious high-proper motion stars). 30

53 After these automated, and semi-automated searches are completed on one catalog, we move on to the next. After they are all complete, we move on to one final manual search. In it, we plot the unmatched NLTT, Hipparcos, and Tycho-2 stars, each using a different color, on a map of the sky using vectors whose length, orientation, and thickness represent respectively the magnitude and direction of the proper motion, and the V mag of the star. This allows us to find counterparts of NLTT stars with major measurement and/or transcription errors. For example, we find three counterparts that disagree in DEC by exactly 1 but otherwise are in perfect agreement. We even find one that disagrees by exactly 11 in DEC and about 9 minutes of time in RA. That this entry is a transcription error is obvious from the name that Luyten assigned to the star 65 : 2751, which corresponds to its true declination, δ = 65. We then return to the problem of binaries. We examine every pair of matches separated by less than 2 in NLTT. In a large fraction of cases, these are each single matches of well separated stars, but we still check that we do not have the matches reversed, using the relative separation and orientation reported in the NLTT notes on CPM binaries. However, there remain many multiple NLTT matches to single stars in other catalogs, especially Hipparcos. We resolve these whenever possible using the Tycho-2 Double Star Catalog (TDSC, Fabricius et al. 2002) which contains PPM and photometry for multiple-component objects in Tycho and 31

54 Hipparcos, both actually associated multiples and spurious optical doubles. This catalog also contains many binaries that are treated by NLTT as single stars. For some of these, NLTT contains a note that the entry is actually a binary and gives its separation and (usually) the magnitudes of its components. For others, NLTT regards the object as a single star. We make a note of all these cases for our future work on binaries, but for the present treat all single-entry NLTT stars as single stars. Some TDSC entries do not list a proper motion. For a large fraction of the cases we checked, the positions for these entries are also significantly in error. We therefore do not make use of these entries unless there is corroborating information (from NLTT or 2MASS) that the positions are correct. For cases where TDSC does not resolve an NLTT binary or where the TDSC entry does not contain a proper motion, we check to see if the star lies in the 47% of the sky covered by the 2MASS release. If it does, usually 2MASS resolves the binary and we substitute 2MASS coordinates for those of the other (e.g., Hipparcos) catalog. We also note whether we believe that the catalog s photometry can really be applied to each component (or whether this magnitude actually refers to a blend or to the other component). In the latter case, we adopt V from NLTT rather than the catalog. For binaries not covered by TDSC or 2MASS, or for which these catalogs do not resolve the binary, we record the two NLTT stars as an unresolved binary. 32

55 Finally, in the spirit of pushing our bright catalog as faint as possible for later comparison with the faint catalog ( 2.3), we make a list of all NLTT CPM binaries for which one component is matched and whose fainter component has R NLTT 14.0, but is not matched. We search for these directly in 2MASS, using the coordinates of the first component and the separation vector given in the NLTT notes to predict the position of the second. We incorporate these by assuming that the proper motion of the first component is also valid for the second Proper Motion Errors of Bright NLTT Stars Altogether, we have matched 12,736 stars from NLTT to Hipparcos, Tycho-2, and Starnet (or in a few cases, to CPM companions of these stars that we found in 2MASS). We began this study by estimating the errors in positions and proper motions of the original NLTT catalog, but restricted to a relatively clean subset. Here we give the RMS differences between NLTT proper motions and those found in the three more modern catalogs. These differences can result from NLTT measurement errors or transcription errors, from real differences in the proper motion due to binarity, from misidentification of counterparts, or from proper-motion errors in the three modern catalogs. The last of these four causes can be quite significant for the relative handful of stars near the magnitude limits of these catalogs, particularly Hipparcos. Indeed, 33

56 we find that when Hipparcos reports errors larger than 10 mas yr 1, its true errors can be much larger than the tabulated errors. We also find that for the sample of stars common to NLTT, Hipparcos, and Tycho-2, the RMS tabulated Tycho-2 errors are substantially smaller than those of Hipparcos. Moreover, since these are established by a longer baseline of observation, they are more directly comparable to the NLTT proper motions in cases where the Hipparcos proper motion may be corrupted by a short-period (P < 5 yr) binary. We therefore, first substitute Tycho-2 for Hipparcos proper motions whenever the former are available. For purposes of comparing with NLTT we then eliminate all stars with tabulated proper-motion errors greater than 10 mas yr 1 in either direction. This removes 52 (0.6%) of Hipparcos stars, no Tycho-2 stars, and 23 (1.7%) of Starnet stars. After removal of these 75 stars, we expect that the proper-motion differences between NLTT and the three modern catalogs are dominated by the first three causes listed above. Table 2.2 lists these RMS values for various subsets of the catalog. Here Hipparcos refers to NLTT stars found in Hipparcos, Tycho-2 to stars found in Tycho-2 but not Hipparcos, and Starnet to stars found in Starnet, but not in either of the other two catalogs. Better precision stars are those with positions specified in NLTT to 1 second of time and 6 of arc (and generally lying in the range 45 <δ<80 ), and worse precision stars are the remainder. When two 34

57 NLTT stars, usually close components of a CPM binary, are matched to a single entry in the PPM catalogs, we compare the proper-motion measurements only once. Table 2.2 shows that among the stars with nominally better positions, those inside the rectangle have consistently lower proper motion errors than those outside the rectangle. For Hipparcos and Tycho-2, the stars with nominally worse positions are intermediate in their proper motion errors between these two categories, indicating that they are also probably a mixture of intrinsically better and worse precision measurements. However, for Starnet, the proper motion errors of the stars outside the rectangle as well as those with nominally worse position errors both have significantly worse proper motion errors. This may indicate that these stars suffer many more false matches. However these will be tracked down in our faint-end search ( 2.3). 35

58 2.3. Faint Stars in NLTT Strategy for Matching NLTT to USNO-A and 2MASS As mentioned in 2.2, we wish to push our faint search as bright as possible, thereby maximizing overlap with the bright search. While we expect that the overwhelming majority of the bright-search matches between NLTT and the three PPM catalogs (Hipparcos, Tycho-2, Starnet) are genuine, there is an important path to false matches. The true counterpart of the NLTT star may not be in any of the three PPM catalogs. Then, even though the real star may (most likely does) have a PPM that is very close to its NLTT values, our bright-star approach is to search farther and farther from the NLTT PPM in these catalogs. Eventually, we may find a barely acceptable match in these catalogs. Such cases will be easily uncovered by cross-checking the bright and faint searches. However, we cannot push our faint-star approach of matching counterparts from USNO-A and 2MASS too bright because bright stars are increasingly saturated in the POSS plates that were scanned to construct USNO-A, leading to increasingly unreliable PPMs and even identifications. 36

59 We therefore begin the faint search by removing from consideration all stars that were matched to Hipparcos in the first two ( rectangle and circle ) searches carried out in The Hipparcos completeness limit (V = 7.3) assures us that essentially all the very bright stars in NLTT are accounted for in this way. Moreover, the high-proper motion stars that entered the Hipparcos input catalog beyond its magnitude limit were drawn almost entirely from NLTT. (This is confirmed by the fact that in 2.2 essentially all Hipparcos high proper-motion stars were successfully matched to NLTT. By contrast, for Tycho-2, whose magnitude range strongly overlaps that of Hipparcos but was not constructed from an input catalog, there were several hundred non-matches.) Hence, the probability that the best match of a Hipparcos star to NLTT is a false match is very low. However, from the faint search we do not exclude Hipparcos stars that were matched using our more aggressive strategies, in order to have an additional check on the robustness of these identifications. Next, we restrict our search to portions of the sky covered by the (circa 1950) POSS I survey (δ > 33 ), since our entire approach fails farther south. USNO-A is a positional (and photometric) catalog, which is constructed by matching blue and red photographic plates. In order to minimize the number of artifacts masquerading as stars, USNO-A requires blue and red detections with position differences less than 2. Hence, in the non-poss I areas of the sky, where the blue 37

60 and red plates were taken many years apart, all stars with sufficiently high proper motion will necessarily be absent. For example, if the plates were taken 8 years apart, then the catalog will not contain any stars with µ>250 mas yr 1.Thisdoes not pose any problem for regions covered by POSS I because its blue and red plates were taken sequentially. Farther south, however, the plate epochs differ by of order a decade. There is a further wrinkle here. The first version of the USNO-A catalog, USNO-A1 (USNO-A1.0), is constructed by scanning POSS I plates all the way to their southern limit (δ 33 ) and supplements POSS I with additional southern surveys only south of this limit. However, USNO-A2 (USNO-A2.0), which has somewhat better precision, exploits southern catalogs in place of POSS I for the region δ < 20. Hence, we conduct our search using USNO-A2 wherever possible, but supplement this with USNO-A1 where necessary. We divide the search into two principle stages, which we dub the rectangle and the circle. In the rectangle stage, we first identify all USNO-A stars (NLTT candidates) that lie within a 16 8 rectangle 1 centered on the position predicted by using the reported NLTT proper motion to propagate the (epoch 1950) NLTT catalogued position to the epoch of the POSS plate underlying USNO-A. We then predict the position of the 2MASS counterpart of each such USNO-A star under the assumption that its proper motion is as given by NLTT. We use a map of 1 We consider genuine USNO stars throughout: entries added from Tycho are ignored. 38

61 2MASS coverage to determine if the star should lie within the 47% of the sky covered by the second 2MASS incremental release and, if it should, what the exact 2MASS epoch is at that position. We then query the 2MASS data base for all stars lying within 5 of this position. The size of this error circle is influenced primarily by the errors in NLTT proper motions, which are expected from to be about 25 mas yr 1 for stars in the rectangle. Since the difference in epochs is typically about 45 years, this translates to a 1. 1 error in predicted position in each dimension, far larger than the 130 mas and 250 mas position errors in 2MASS and USNO-A, respectively. A 5 circle will therefore capture all but the extreme outliers. Ideally, only the USNO-A candidate actually corresponding to the NLTT star will have a 2MASS counterpart because static stars will not match to anything in 2MASS. In general, this query can have 3 possible outcomes, and we can therefore define 3 classes of stars: non-matches, unique matches, and multiple matches. Unique matches are those NLTT stars for which our procedure generates one and only one 2MASS counterpart. Because the area covered by the rectangle is quite small, the overwhelming majority of unique matches should be genuine, even though we have not yet imposed any magnitude constraint on the selection procedure. We can therefore use the unique matches to study the color-color relations of counterparts in NLTT, USNO-A, and 2MASS. First, we find from the 39

62 overlap of USNO-A1 and USNO-A2 stars that the B USNO mags are not on the same system in the two versions of the catalog, which deviate by up to 1 mag. We obtain B A2 = B A B A B 2 A B 3 A B 4 A1, (B A1 > 13.07) (2.3) and B A2 = B A1 otherwise. Henceforth, when we write B USNO it refers to magnitudes converted to the USNO-A2 system. However, in the actual catalog we report the original USNO-A1 magnitudes for stars identified in that catalog. Next we compare USNO and NLTT photometry. Figure 2.3 shows this comparison (for our full catalog, not just the rectangle matches) as a function of R NLTT. Clearly, there are strong nonlinearities. We model these by, R USNO =0.9333R NLTT , (R NLTT > 10.39) (2.4) and R USNO = R NLTT for R NLTT < 10.39, and by (B R) NLTT (B R) USNO = R NLTT, (R NLTT < 16.5) (B R) NLTT (B R) USNO = R NLTT, (R NLTT 16.5).(2.5) Note that B NLTT is called photographic magnitude in NLTT. 40

63 Finally, we obtain very rough optical/ir color-color relations between USNO and 2MASS bands, R USNO J = (J K s ), B USNO J = (J K s ), (J K s > 0.6), R USNO J = (J K s ), B USNO J = (J K s ), (J K s < 0.6), (2.6) These last relations have a huge, 0.8 mag, scatter, and are not even continuous. They nonetheless are extremely useful in assessing the quality of candidate matches. Each multiple match is investigated and resolved by hand. The primary cause of multiple matches is common proper motion (CPM) binaries. Sometimes there are two USNO-A stars that each match to the same two 2MASS stars. In such cases, there is always a NLTT CPM binary. This is because USNO-A does not resolve binaries with separations < 5, whereas Luyten was able to resolve these easily by eye. Hence these cases are always resolved unambiguously by making use of the NLTT supplementary notes on CPM binaries. More frequently, there are two 2MASS stars matched to one USNO-A star, which is actually an unresolved binary. In the great majority of these cases, NLTT shows a CPM binary, so these are also easily resolved. In such cases, however, we cannot use the USNO-A position to obtain a reliable new proper motion since it is a blend of 41

64 two stars. For such stars, our catalog has an improved 2000-epoch position and new J and K s photometry, but not an improved proper motion nor better visual photometry (which is obtained from USNO). In some two dozen cases, we resolve the multiple match by finding a probable CPM binary that Luyten missed. Some of these binary candidates can be confirmed by investigating POSS I and POSS II images, but in most cases the companion is too faint in the optical band or is blended in the POSS images because the separation is of order 5 or less. We will present these new binary companions in future work on NLTT binaries. Finally, for each resolved multiple match, as well as for each unique match, we compare the B USNO and R USNO mags reported by USNO with the values that would be predicted on the basis of NLTT and of 2MASS photometry using the color-color relations established in using the unique matches. Even though these relations have large errors, they still help to identify wrong matches because random pairs of unrelated stars are likely to differ by many magnitudes, so by this standard even measurements with 0.8 mag errors can be very effective. The outliers are regarded as suspicious and put aside, while the remainder are accepted. Operationally, there are two classes of non-matches: 1) there are no USNO-A stars in the rectangle or 2) there are such stars but they all fail to match with 2MASS stars. Class (1) can occur because A) the NLTT position is in error by more than the size of the rectangle (which is the case for a sizeable minority of 42

65 NLTT stars), or B) USNO failed to detect the star. Class (2) can occur because A) the NLTT position is in error and there just happens to be an unrelated USNO star in the rectangle, B) the USNO star is the correct match but 2MASS has failed to detect the star, or C) the USNO star is correct but the NLTT proper motion is so far off that the 2MASS counterpart lies outside the 5 error circle. We ultimately attempt to distinguish among these five causes in but for the moment assume that that the correct USNO match lies outside the rectangle and continue our search for it in the circle. We now remove from consideration all NLTT stars that were successfully matched to USNO-A stars in the rectangle. The great majority of the remainder are unmatched. However, a small number were matched in the rectangle search, but are regarded as questionable matches because they are photometric outliers as determined using the relations We search for USNO-A/2MASS counterparts to both classes of stars by probing a circle of radius 2 in USNO-A centered on the NLTT position (updated using the NLTT proper motion to the epoch of the USNO-A POSS plate). Because the area being probed is now 350 times larger than in the rectangle search, the probability of false matches is proportionately larger. We therefore take several steps to reduce such false matches. 43

66 First, we demand that R USNO R NLTT < 2.2. These are approximately 5 σ limits. (Some NLTT stars do not contain an entry for R NLTT,inwhichcasewe us B mags.) Second, when we query the 2MASS data base at the 2MASS-epoch position, we ask whether the 2MASS star has any USNO-A stars within 3 and if so what the separation and mags of the closest one are. If the 2MASS star is associated with a USNO-A star at approximately the same position, we do not immediately eliminate the 2MASS star, but rather flag it. If the association is real, the 2MASS star could not be the genuine counterpart of the NLTT star because its proper motion would be < 70 mas yr 1, far below the NLTT threshold. However, the association might be due to chance proximity of a random field star. At high latitude, the probability of such a chance alignment is low, but in the difficult fields ofthegalacticplane,itisnot. Wealsodoareversecheck:weaskwhetherthere are 2MASS stars associated with USNO candidates (assuming no proper motion) within 2. The presence of a 2MASS star near the USNO 1950-epoch position will also indicate that the USNO candidate is not a NLTT star. For a large fraction of the difficult cases, we directly consult the digitized sky survey (DSS). This normally contains images from two well-separated epochs (POSS I and II), and thus usually allows one to spot the high proper-motion star. However, for the southern zones (approximately coincident with our USNO-A1 areas), the two DSS epochs are very close in time, making it extremely difficult to 44

67 spot moving stars. In some cases, we therefore consult the USNO web site, which contains digitized POSS I, but the cycle time for such searches is about 20 minutes, so this cannot be done in every case. This mostly affects regions very close to the Galactic center. The multiple matches are more complex than in the rectangle case. We again have large numbers of CPM binaries. These are usually easier to untangle than in the rectangle case because they are typically farther apart and so are resolved in USNO. It is then only necessary to check that the relative orientation of the 2MASS/USNO stars is the same as that given by the NLTT notes. However, there are now a large number of spurious matches. In a handful of cases, these turn out to be CPM companions of NLTT stars that were not found by Luyten. We will present these in the future. Unlike the CPM binaries found in the rectangle, these are mostly well enough separated that they are resolved in USNO. The great majority of the spurious matches are pairs of unrelated USNO-A/2MASS stars. We track these down using a variety of photometric and astrometric indicators and by consulting DSS, as discussed above. The nonmatches are of the same five classes that were described in the rectangle search. These are sorted out in

68 The entire procedure described above is carried out separately for USNO-A2 (δ > 37. 5) and for USNO-A1 ( <δ< 15 ). In each case, we demand that the entry originate from POSS I. The two catalogs are then combined, giving precedence to USNO-A2 when a match is found in both. In practice, we find a fairly sharp boundary at δ 20. Table 2.3 shows the number of matches in the four categories (rectangles,circles) (unique,resolved), for each of the two USNO catalogs, A1 and A2. Of the 23,681 USNO/2MASS matches, 18,442 (78%) lie inside the rectangle. The overwhelming majority of these are unique matches, and even the 3% that had multiple matches were relatively easy to resolve. Note that even for the majority of cases in which the star lay in the circle, there was only one USNO/2MASS pair whose separation was consistent with the NLTT proper motion. Thus, the high quality of the NLTT PPMs, combined with the paucity of stars over most of the sky, allowed us to match over 20,000 stars in two catalogs with very different passbands, at widely separated epochs, with only about a 1000 problem cases. However, these cases, which were mostly concentrated in Galactic plane, were often quite difficult to resolve. As is well-known, optical and infrared images of the plane are each extremely crowded, but often not with the same objects, and this fact generally gave rise to dozens, sometimes more than 100, false matches for a single NLTT entry. The correct match had to be laboriously identified from among 46

69 these. Thus, our method, which works amazingly well away from the plane, tends to become extremely bogged down within it. An alternative approach to finding proper motion stars in the plane, albeit one that would miss many red stars, would be to compare blue plates in which the majority of background stars would be removed. In we will see that that is exactly what Luyten did! Additional Matches Based on our analysis of the cases in which the PPM search found the NLTT star but the USNO/2MASS search did not, we conduct four additional types of searches, which we dub annulus, 2MASS-only, USNO-only, and CPM. The first is aimed at finding 2MASS counterparts to USNO stars in cases for which the NLTT proper motion is seriously in error, including the possibility that there is a transcription error in the direction of proper motion. Hence the search is conducted in an annulus around the position of the unmatched USNO star. In the bright-end search we found many examples of transcription errors of all types in NLTT, including in the position angle of the proper motion. We therefore search for 2MASS stars in an annulus around the position of all USNO counterparts lying within the NLTT rectangle but without previous 2MASS matches. To also allow for a substantial error in the NLTT value for the amplitude of the proper motion, µ NLTT, we set the inner and outer and outer radii of the 47

70 annulus at θ ± =(T 2MASS T USNO )(µ NLTT ± 100 mas yr 1 ). Here T 2MASS and T USNO are the respective epochs of the 2MASS and USNO observations. Queries of the 2MASS database allow one to ask for the nearest USNO star within 5. We accept 2MASS stars only if they do not have a plausible USNO counterpart as determined from the consistency of the optical/ir colors of the two catalog objects relative to the predictions of equation (2.6) and their relative position offset. We also check that the USNO rectangle star does not have a plausible 2MASS counterpart at small separation, which would also indicate that it is not a proper motion star. Occasionally we find a 2MASS counterpart to the USNO star near the outer edge of the 5 search radius which, given the 45 year baseline, could only be a real counterpart if the proper motion were µ < 100 mas yr 1.Inthiscasewepermitthe identification provided that the position angle is reasonably consistent with NLTT. In total, we find 50 stars in the annulus, or 0.2%, substantially smaller than the 1% (18/1800) that were identified in the overlap with Tycho-2+Starnet. This may be because the PPM search was more aggressive than the one we have conducted here (since it could make use of additional proper-motion information). When no USNO/2MASS match is found either in the circle or the rectangle, and when there is no USNO candidate within the rectangle, we hypothesize that the NLTT position is correct to within the precision of the rectangle, but that the star is absent from USNO. We therefore predict the position of the star at 48

71 the 2MASS epoch assuming that the NLTT 1950 position and proper motion are correct. We then search for 2MASS counterparts of the NLTT star in a radius of 12 around this position to allow for NLTT PPM errors. As in the annulus search, we reject 2MASS stars that have plausible USNO counterparts. Of course, the result of this search yields only a position and IR photometry, but not a new proper motion. In all, this search yields 862 2MASS-only identifications. When a valid USNO counterpart (one without an associated 2MASS star having consistent optical/ir colors and lying within a few arcsec) of the NLTT star is found within the rectangle, but it is not matched with a 2MASS star either in the original search or the annulus search, we assume that the star is absent from 2MASS and accept the USNO/NLTT identification, provided that the USNO/NLTT magnitudes are consistent. In these cases, we obtain a new position and new optical photometry, but no new proper motion. In all, this search yields 409 USNO-only identifications. Based on the USNO reduced proper motion diagram we conclude that most of these stars are WDs. The notes to NLTT contain references to more than 2400 pairs that Luyten considered to be CPM binaries or possible binaries. Unfortunately, it is not straightforward to extract all of this information in a completely automated way. The biggest single problem is that, for some reason, Luyten did not name a large numbers of the objects in his catalog. In these cases, he will have a note to one 49

72 star such as comp. to prec. star. Sometimes the companion will be the preceding star, but very often it will be several preceding, or occasionally following. Often, when there is a reference to a named star, the meaning of the reference is clear only from context. In brief, it seemed impossible to make sense of these references in an automated way. Fortunately, for stellar pairs that Luyten believed to be CPM binaries, he almost always recorded the same proper motion for both components, even when (as we will show in 2.3.5) he was able to measure the difference. This permitted us to adopt a different approach. First, we create our own naming system: each NLTT star is named for its sequential number in the electronic version of the catalog, from 1 to 58,845. Next, we run a program to find all notes that might plausibly be interpreted as indicating that the star is a component of a binary or multiple system. Normally, these contain a separation and position angle relative to a primary, but sometimes they are more ambiguous. We then find all NLTT stars within one degree of the noted star that have identical NLTT proper motions (magnitude and position angle). If any of these stars had been identified in either the PPM or USNO/2MASS searches, we print out the catalog entries as well as all the notes that are associated with all of these stars. If two or more of these stars have been identified, we also print out the separations and position angles of all pairs. We then review this output, tracking down discrepancies when we have two or more identifications and our relative 50

73 astrometry is in conflict with NLTT s, and we interactively query the 2MASS data base to search for additional matches when the companion is not already in our data base. After updating our catalog with these results, we run a second program that finds only those notes that it can parse well enough to determine a predicted separation and position angle. It assumes that this vector separation applies to all pairs of NLTT stars with the same proper motion and lying within 1 degree. If our catalog contains entry pairs that disagree with this separation by more than 20% or with the position angle by more than 20, or if we do not have an entry for one component but do have an entry with 2MASS identification for the other, it flags this system. All such flagged systems are reviewed and the 2MASS data base is searched for unmatched companions. This search yields 137 CPM companion identifications, of which 59 are corrections to previously incorrect 2MASS identifications. Of these 59, 47 are components of binaries for which our USNO/2MASS search found the same star for both components. Our algorithm is prone to such errors because it treats each component separately, and we intended to sort out these discrepancies at the time we reviewed all binary matches. They therefore do not represent real mismatches. However, the remaining 12 are genuine misidentifications: if these stars, which were treated by our algorithm as individuals, did not happen to belong to CPM binaries, we would never have recognized the error. Since, there are a total of 51

74 1235 stars in CPM binaries that were matched to USNO/2MASS, this represents a false-identification rate of about 1%. Alternatively, one might want to consider only those stars in CPM binaries with separations greater than 10 in order to probe a sample that is not severely affected by confusion with a nearby high-proper motion source. This would be a fairer proxy to the conditions that the algorithm faced for the majority of single stars. In this case, we get 6 misidentifications out of 784 stars. Or, for a more conservative 30, we get 4 misidentifications out of 442 stars. That is, our estimated misidentification rate is consistently 1%. This rate is about three times higher than the 0.3% rate we estimated from comparison with PPM stars. Most likely, this is because brighter stars are rarer, and hence the possibility that a random unrelated USNO/2MASS pair will mimic a given high-proper star is smaller. In any event, we consider a 1% misidentification rate to be quite good. Since the CPM search was conducted after the search for 2MASS-only stars, we can use it to check the reliability of the 2MASS-only identifications. There are 34 2MASS-only stars that lie in CPM binaries in addition to the 137 companion identifications discussed above. The relative positions of all 34 stars are consistent with the values in NLTT, and in this sense all 34 pass the test. However, of these 34, 26 are from 13 CPM pairs both components of which are identified only in 2MASS. Since we processed both stars from a pair simultaneously, we had knowledge of their CPM nature and offsets, and so these 26 do not constitute the a 52

75 fair test. The remaining 8 stars are companions of independently identified NLTT stars, and so are a good proxy for single stars. The statistical significance of this test is modest because of small number statistics, but at least it has the right sign. One of the 8 is a companion to a USNO-only star, which does not have an independent proper motion. The remaining 7 are additional CPM companions each of whose proper motions can be inferred from that of its companion. This brings the total of such CPM companions to Positional Errors of Faint NLTT Stars Here we use our improved measurements of NLTT stars to characterize the precision of its positions. Figure 2.4 shows the differences between the 1950 epoch positions of NLTT and those predicted based on the 2000 positions and proper motions in our catalog. It is restricted to faint (V > 11) stars to maximize the potential contrast with Figures 2.2 and 2.1, which show the same quantities for bright NLTT stars found in Tycho-2. In fact, there is no qualitative difference between the bright and faint position errors. The majority of the residuals are roughly uniformly distributed in a rectangle whose dimensions are set by the decimal truncation of the NLTT entries. The fuzziness of the rectangle edges gives an estimate of the underlying measurement errors. As was true of the bright sample,thisisabout1. Figure 2.4b shows that the heavily populated rectangle 53

76 is surrounded by a diffuse halo extending out to at least 2, which was the limit of our faint search in most cases. Nevertheless, taken as a whole, the positions are extremely good. These good positions played a critical role in our ability to identify the vast majority of NLTT stars in USNO and 2MASS in an automatic fashion. Note that the claim by Bakos, Sahu, & Németh (2002) that the typical LHS (subset of NLTT) position errors are larger than 10 is manifestly not true. We further investigate the magnitude dependence of the NLTT position errors in Figure 2.5, which shows the fraction of NLTT stars whose actual position lies within a rectangle of dimensions (15 cos δ +2 ) (6 +2 ) and centered on the NLTT recorded position. The first term in each dimension is the imprecision created by decimal truncation and the second allows for 1 measurement errors at each edge of the rectangle. The fraction remains mostly constant at about 80% over 19 magnitudes, except for a pronounced feature suddenly dipping to 45% at V = 10 and then gradually climbing back to 80% at V = 15. We speculate that the brighter stars V 9 were already well studied and that Luyten made use of literature data on these. For the remainder of the stars he made his own measurements from plates. Saturation badly affects such measurements at V = 10, but gradually ameliorates at fainter mags. Figure 2.6 shows the rectangle fraction as a function of declination. This figure has a number of important features. Over most of the sky, 30 <δ<50, 54

77 the fraction is roughly 80%. As expected, it drops to essentially zero for δ< 45 where NLTT records positions only to 6 seconds of time and 1 of arc. Less expected, however, are the rapid dropoffs for δ< 30 and δ>50. The former dropoff has significant negative consequences for the prospects of extending our catalog to the south, δ< 33, Proper Motion Errors of NLTT Stars Figure 2.7 shows the differences between proper motions in the α direction as given by NLTT and our values. The diagram for the δ direction looks extremely similar and is not shown. Binaries with separations closer than 10 are excluded from this plot because our measurements, at least, can be corrupted due to blending. The bracketing lines show the 1σ scatter (with 3 σ outliers excluded). At bright magnitudes, NLTT errors are extremely small, then rise typically to 20 mas yr 1. However, there is a curious bump of higher errors at V 10, which is reminiscent of the degradation in positions (see 2.3.3) and which may have the same cause. At the very faintest mags, V > 18, the errors deteriorate toward 30 mas yr 1. The fraction of 3 σ outliers excluded from the fit is fairly constant at 3%, which is much higher that would be characteristic Gaussian noise. These outliers may be due to transcription errors in NLTT, misidentifications of NLTT stars by 55

78 us, or possibly other causes. Whatever the cause, the reader should not apply Gaussian norms to the interpretation of the tails of this error distribution Common Proper Motion Binaries Figure 2.8 shows the difference in 339 separation vectors between binary components as given by NLTT versus our astrometry. The sample is restricted to separations θ >10 to avoid problems in our astrometry due to confusion, and θ <57 to avoid the regime in which NLTT errors induced by truncation of the position angle (given to integer degree) become larger than the errors induced by the truncation of the separation (given to integer arcsec). The inset shows that this relative astrometry is usually very good, better than 1. A number of the large outliers are due to transcription errors in NLTT. This highly precise relative astrometry permitted us to reliably identify NLTT CPM components even when USNO data were missing. Our improved proper motions permit us to better determine the reality of the CPM binaries listed in the NLTT notes. Figure 2.9 shows the differences in component proper motions for 468 NLTT binaries with separations θ >10 (again, to avoid problems with our astrometry due to confusion). 56

79 Of course, one does not expect the components of CPM binaries to have exactly the same proper motion. First they have orbital motion, which for face-on circular orbits induces a relative motion µ =2π(M/D 3 θ) 1/2,whereD is the distance, M is the total mass, θ is the angular separation, with units of pc, M, arcsec, and years. Even if they had the same physical velocity, their proper motions would differ because the components are at different distances and because we see different components of motion projected on the sky. The order of these differences combined is µ/µ θ, in radians. We add these orbital and projection effects in quadrature and show them as error bars in Figure 2.9. We estimate distances using the brighter (but non-wd) component. We classify it as a SD or MS star according to position in the reduced proper motion diagram (see 2.5.2), and then assign it an absolute magnitude M V =2.7(V J)+2.1 orm V =2.09(V J)+2.33 in the respective cases. In addition, there is a 6 mas yr 1 error (see 2.4.2) in our relative proper-motion measurements that must be added in quadrature to the errors shown in the figure. We have not done this to avoid overwhelming the intrinsic scatter. Also, we have not placed any error bars on the points lying below 12 mas yr 1 (i.e., 2 σ) to avoid clutter and because in our view these CPM identifications can be accepted with good confidence. The figure shows that the overwhelming majority of NLTT CPM binaries with separations θ <50 are real, but that close to half of those with θ >100 are 57

80 unrelated optical pairs. In fact, a number of these with proper motion differences µ >100 mas yr 1 could have been excluded by Luyten at the 2.5 σ level given his 20 mas yr 1 precision in each direction and for each component. However, he evidently decided to err on the side of not missing potential CPM binaries Revised NLTT Catalog Format of the Revised NLTT The Revised NLTT catalog contains information grouped in six sections, 1) summary, 2) NLTT, 3) source identifications, 4) USNO, 5) 2MASS, and 6) binaries. The catalog is available online from The summary section contains 11 entries: 1) the NLTT number (drawn consecutively from 1 to 58,845), 2) a letter code A, B, or C if the NLTT star has been resolved into several sources, 3) α (2000, epoch and equinox), 4) δ (2000), 5) µ α,6)µ δ,7)σ(µ α ), 8) σ(µ δ ) (all four in arcsec yr 1 ), 9) V, 10) V J, 11) 3-digit source code. The three digits of the source code refer to the sources of the position, proper motion, and V photometry. 1 = Hipparcos, 2 = Tycho-2, 3 = Tycho Double Star 58

81 Catalog (TDSC, Fabricius et al. 2002), 4 = Starnet, 5 = USNO/2MASS, 6 = NLTT, 7 = USNO (for position) or common proper motion companion (for proper motion). More specifically, 555 means 2MASS based position, USNO based V photometry, and USNO/2MASS based proper motion. The (2000) position has been evolved forward from whatever epoch it was measured using the adopted proper motion. When the position source is Hipparcos, Tycho-2, or TDSC, the position is given in degrees to 6 digits, otherwise to 5 digits. For proper motions derived from a PPM catalog, the errors are adopted from that catalog. Proper motions from USNO/2MASS determinations have an estimated error of 5.5masyr 1 is accordance with the results from NLTT proper motions are 20 mas yr 1 as found in CPM binary companions (without other astrometry) are not assigned an error, and zeros are entered into the error fields. V refers to the Johnson V entry for Hipparcos, Tycho V for Tycho-2 and TDSC, and Guide-star catalog R for Starnet. The conversion from USNO photometry can be obtained from 3.6, V = R USNO (B R) USNO. (2.7) We remind the reader that for USNO-A1 photometry, we first convert to USNO-A2 using equation (2.3) before applying equation (2.7). When NLTT photometry is 59

82 used, V is evaluated using equations (2.4) and (2.5) to convert to USNO mags, and then applying equation (2.7). In the rare cases for which NLTT photometry is employed and one of the two bands is not reported, a color of (B R) NLTT =1 is assumed. No effort has been made to de-combine photometry in the case of unresolved binaries. For example, if a binary is resolved into two stars in 2MASS, but is unresolved in USNO, then different J band measurements will be reported for the two stars, but both with have the same, combined-light V photometry. The V J color reported in field 10 will be the simple difference of these two numbers. Similarly, if the NLTT star is resolved by TDSC but not 2MASS, then the V light will be partitioned between the two stars but not the J light. Finally, note that if no J band photometry is available (whether because of saturation, faintness, or the star being in an area outside the second incremental 2MASS release) V J is given as 9. When multiple sources of information are available, the priority for what is presented in the summary is as follows. Positions: 3,1,2,5,4,7,6; Proper Motions: 3,2,1,5,4,7,6; Photometry: 3,1,2,5,4,6. Tycho-2 proper motions are given precedence over Hipparcos primarily because they better reflect the long-term motion when the stars are affected by internal binary motions, but also because at faint magnitudes they are generally more precise. When Hipparcos proper motions are given, it is often because the 60

83 star is so faint that it does not show up in Tycho. In this case, the nominal Hipparcos errors are often quite large and true errors can be even larger. We found a handful of cases by chance in which the Hipparcos proper motion was grossly in error and we removed the Hipparcos entry and substituted the USNO/2MASS value. However, we made no systematic effort to identify bad Hipparcos proper motions. Only stars for which we are providing additional information are recorded in the catalog. There are 36,020 entries for 35,662 NLTT stars including a total of 723 entries for 361 NLTT stars that have been resolved in TDSC. The next 6 columns give information taken from NLTT, namely 12) α (2000), 13) δ (2000), 14) µ α, 15) µ δ, 16) B NLTT, 17) R NLTT. The coordinates and proper motions are precessed from the original 1950 equinox to 2000, and the position is updated to 2000 epoch using the NLTT proper motion. The next 2 columns give source information. Column 18 is the Hipparcos number (0 if not in Hipparcos). Column 19 is the identifier from TDSC, Tycho-2, or Starnet, whichever was used to determine the position in columns 3 and 4. When the position comes from Hipparcos, 2MASS, or USNO, or NLTT, null is entered in this field with one exception: when a Starnet measurement has been superseded by a 2MASS measurement, the Starnet identifier has been retained 61

84 for ease of recovery of this source. It can easily be determined that the summary information comes from 2MASS because the first digit in field 11 will be a 5. The next six fields give USNO information: 20) Integer RA, 21) Integer DEC, 22) B A1 or A2, 23) R A1 or A2, 24) USNO Epoch, 25) 3-digit search-history code. The Integer RA and DEC together serve as a unique USNO identifier since that is the form RA and DEC are given in the original USNO-A1 and USNO-A2 releases. They can also be converted into degree α and δ (at the USNO epoch) using the formulae: α = (Integer RA)/360000, δ = (Integer DEC)/ Regarding the 3-digit search history code, the first digit tells which USNO catalog the entry is from: 1 = USNO-A1, 2 = USNO-A2. The second tells whether the USNO source was found in the rectangle (1) or the circle (2). The third tells whether it was a unique match (1), or had to be resolved by hand from among several possible matches (2). If there is no USNO information, all of these fields are set to zero. The next six fields contain 2MASS information: 26) α, 27) δ (both at 2MASS Epoch), 28) J, 29) H, 30) K s, 31) 2MASS Epoch. If no 2MASS data are available, all fields are replaced by zeros. If there are 2MASS data, but not for a particular magnitude measurement, that value is replaced by 9. The next six fields contain information about binarity: 31) binarity indicator, 32) NLTT number of binary companion, 33) NLTT estimated separation, 34) 62

85 NLTT estimated position angle, 35) our estimated separation, 36) our estimated position angle. Regarding the binarity indicator, 0 means NLTT does not regard this as a binary. Otherwise, it is a NLTT binary and the indicator is set according to whether the companion is (2) or is not (1) in our catalog. The NLTT estimates of the separation position angle come from the NLTT Notes. Our estimates come from the difference of the 2000 positions of the two stars. In cases for which the companion is not in our catalog, the fields with our separation and position angle are replaced by values found from the difference of the NLTT coordinates (i.e., fields 12 and 13). As discussed in 2.3.5, the companion numbers are based on what we think is obviously what Luyten intended, rather than what was literally written down. However, no effort has been made to clean up any other transcription errors, even when these are equally obvious. No binary information is recorded in these fields about NLTT stars that were resolved by TDSC. Rather, the reader should recognize each of those binaries from the upper case letter appended to its NLTT number (column 2) Proper Motion Errors of the Revised NLTT Once bright stars are identified with PPM catalog stars, they acquire the proper motions, and with them the proper motion errors, given in those catalogs. These vary but are generally of order a few mas yr 1. Faint-star proper motions 63

86 are obtained by taking the difference of 2MASS and USNO positions. Again, these vary in quality but typically have errors of order 130 and 250 mas respectively. Given the 45 year baseline, we expect proper motion errors of order 6 mas yr 1. Nevertheless, one would like an independent experimental confirmation of this estimate. To obtain this, we compare in Figure 2.10 our USNO/2MASS proper motions with Tycho-2 proper motions for 1179 stars for which we have measurements from both. We exclude for this purpose binaries closer than 10 because, as we have emphasized several times, they can be corrupted by blending. The scatter, which is dominated by USNO/2MASS errors, is high at bright magnitudes and then plateaus at V 10 at about 6 mas yr 1 in each component. The poorer quality for bright stars is due to the problems that USNO astrometry has in dealing with saturated stars. Because we do not use USNO/2MASS proper motions for bright stars, our primary interest is in the asymptotic behavior of the error envelope toward faint magnitudes. Taking an average over the bins V > 10 and taking account of the small contribution to the scatter due to Tycho-2 errors, we find average errors of σ µ =5.5masyr 1, (wide angle), (2.8) 64

87 in each direction. These error bars are calculated excluding 3 σ outliers, which constitute almost 5% of the points. Thus, as in the case of NLTT, these proper-motion errors have strong non-gaussian tails. USNO astrometry, which dominates the proper-motion error budget, is more accurate on small scales than large scales. On scales of several degrees it suffers from errors in the plate solutions while on smaller scales it is limited by centroiding errors. For some applications, notably studying the reality of binaries or their internal motions (see 2.3.5), it is the small scale errors that are relevant. To determine these narrow-angle errors, we plot in Figure 2.11 the difference in the proper motions of the two components of 52 SD binaries (based on the position in the reduced proper motion diagram, Figure 2.13) with separations θ >10. We choose SDs because they are more distant, which in turn implies that these binaries will have wide physical separations (and so be relatively unaffected by internal motions) without being widely separated on the sky (and so prone to contamination by optical binaries see Fig. 2.9). In a proper-motion selected sample, the mean distance is proportional to the mean transverse speed, which is of order five times larger for SDs than MS stars. The figure shows a tight clustering of points with two outliers at > 10 σ, which are either not physical binaries or have extremely bad proper-motion measurements. After excluding these, we obtain a scatter in the two directions of 4.4masyr 1 and 4.2masyr 1. 65

88 Since each results from the combination of two proper motions measurements, we derive a narrow-angle proper-motion error of σ µ =3.0masyr 1, (narrow angle). (2.9) Hence, the RMS error in the magnitude of the proper motion difference of a binary is 6 mas yr 1, which was the value we adopted in analyzing Figure Classification of NLTT Stars Classification with the Original NLTT One of the principal motivations for undertaking a proper-motion survey is to construct a reduced proper motion (RPM) diagram, in which the RPM (= m + 5log µ), is plotted against color. Here m is the apparent magnitude and µ is the proper motion measured in arcsec per year. The RPM serves as a rough proxy for the absolute magnitude M = m +5logπ +5, whereπ is the parallax measured in arcsec. Indeed, if all stars had the same transverse speed, the RPM diagram would be identical to a conventional color-magnitude diagram (CMD) up to a zero-point offset. 66

89 Hence, one can hope to roughly classify stars using a RPM diagram, even when one has no parallax or spectroscopic information. In particular, subdwarfs (SDs) should be especially easy to distinguish from main-sequence (MS) stars, since they are several magnitudes dimmer at the same color, and are generally moving several times faster. Each of these effects tends to move SDs several magnitudes below the MS on a RPM diagram. White dwarfs (WDs) should also be easily distinguished from MS stars, since they are typically 10 magnitudes fainter at the same color, and are generally moving at similar velocities. Although WDs are closer to SDs on an RPM than they are to the MS, they still should be distinguishable. The combination of NLTT photometry and astrometry permits the construction of a RPM diagram. See Figure Unfortunately, this diagram is almost devoid of features that could be used to isolate individual populations. There is a clump of stars off to the lower left that one might plausibly identify with WDs. However, there is no obvious separation between SDs and MS stars. Moreover, it is common knowledge that reddish WDs are mixed in with the SDs at intermediate colors, so that WDs must be spectroscopically culled from relatively large samples drawn from the lower reaches of this diagram (e.g., Liebert, Dahn, Gresham, & Strittmatter 1979). There are three reasons for this mixing of populations. First, photographic B and R do not provide a very broad color baseline. Second, photographic photometry has intrinsically large errors. Third, 67

90 NLTT does not reach even the relatively limited precision that is in principle achievable with photography. Given the steepness of the color-magnitude relations of individual populations, the short color baseline and large errors combine to seriously smear out the diagram Classification with the Revised NLTT In Figure 2.13 we show the RPM based on optical-infrared V J color from the Revised NLTT. Note that the SDs and MS stars are clearly separated into two tracks, at least for V +5logµ > 9. The WDs are also clearly separated from the other stars. Going towards the bright end, the SD track becomes vertical at V +5logµ 10 and then turns to the right at V +5logµ 9. For a star having a transverse speed of v 250 km s 1, this latter value corresponds to M V 5, i.e., roughly a mag below the subdwarf turnoff. In any event, the bright end is dominated by Hipparcos counterparts of NLTT stars (shown in yellow). Hipparcos stars generally have excellent parallaxes, so for them RPMs are superfluous. We therefore remove these stars from further consideration. Using superior color-color plots of NLTT stars based on Sloan Digital Sky Survey (SDSS, York et al. 2000) photometry, we have checked that the scheme shown in Figure 2.13 indeed properly classifies NLTT stars that lie in the SDSS Early Data Release (Stoughton et al. 2002) area. 68

91 Panels in Figure 2.14 show respectively where the stars classified as WDs, SDs, and MS stars in Figure 2.13, lie in the original NLTT RPM. The points representing the WDs are enlarged for emphasis. Note that while the region to the lower left is indeed dominated by WDs, the red WDs are sprinkled among a much higher density of other faint red stars. From the distribution of SDs and MS stars it is clear that while the SDs do tend on average to be bluer and fainter than the MS stars, the two populations are severely mixed in the original NLTT RPM diagram Candidate Nearby White Dwarfs Once stars are classified using the RPM diagram, it is possible to estimate their distances photometrically. Using this technique, in Table 2.4 we have tentatively identified 23 WD candidates that lie within 20 pc and are not listed in the online edition of the Gliese Catalog of Nearby Stars 2. These WD candidates are also not listed in McCook & Sion (1999) catalog of spectroscopically confirmed WDs. We determine photometric distances from J, V J, and a CMR calibrated using Bergeron, Leggett, & Ruiz (2001) data. Stars with low values of (V J) lie close to the SD/WD discriminator line shown in Figure 2.13, and could therefore be extreme SDs stars interesting in their own right. Spectroscopy will be ultimately required to confirm the nature of these objects. If confirmed, these WDs would

92 represent a significant addition to 109 WDs known to be closer than 20 pc (Holberg, Oswalt, & Sion 2002). In fact, since for 10 of our candidate WDs we calculate d<13 pc, they could raise the local density derived by Holberg, Oswalt, & Sion (2002) using a 13 pc sample (which they believe is complete) by as much as 20% (but note that we do not cover the entire sky) Completeness of NLTT Completeness at Bright Magnitudes We study the completeness of NLTT at the bright end by comparing it to Hipparcos and Tycho-2. (Starnet cannot be used for this purpose because it contains spurious high proper-motion stars). That is, we count the fraction of Hipparcos/Tycho-2 stars that were detected by NLTT as a function of various parameters. Before doing this, however, we first ask the opposite question: what fraction of NLTT stars were detected by Hipparcos/Tycho-2 as a function of R NLTT (i.e., NLTT s proxy for V )? The answer to this question, which is given by Figure 2.15, delineates the NLTT magnitude range to which our subsequent completeness tests apply. 70

93 The bold curve in Figure 2.15 shows the Hipparcos/Tycho-2 completeness as a function of R NLTT, i.e. it is the ratio of Hipparcos/Tycho-2 detections (shown by the upper of the two thin-line histograms) to NLTT detections (bold histogram). This completeness falls to 50% at R NLTT =11.6, as a result of the Tycho-2 magnitude limit. Hence, our subsequent completeness tests apply approximately to NLTT stars with V < Figure 2.15 has several other features of note. First, there is a peak in NLTT detections at R NLTT 8.7, which is then reproduced by the histogram of Hipparcos/Tycho-2 matches, as well as that of the Hipparcos-only matches just below it. This turns out to be an artifact of systematic bunching of NLTT magnitudes: a histogram of Hipparcos/NLTT matches as a function of Hipparcos V (not shown in the figure to avoid clutter) exhibits no such premature peak, but rather has a single, relatively broad peak at V 9.5. Note that Hipparcos/Tycho-2 completeness is 100% only to about R NLTT 8.5, falls to 95% at R NLTT 9.5, and then plummets rather sharply. Given that Hipparcos/Tycho-2 is itself quite incomplete significantly below R NLTT =11.6, one might ask whether it can be used to reliably probe NLTT completeness all the way to this threshold. It can be so used if the reasons for NLTT non-detections are independent of the reasons for Tycho-2 non-detections. It is clear from the form of the completeness curve in Figure 2.15 that Hipparcos/Tycho-2 71

94 loses sensitivity with faintness. We will argue below that the NLTT non-detections are due to crowding, and not due to faintness, since NLTT goes much fainter than the limits of the modern catalogs. However, since crowding can exacerbate problems with detection of fainter objects, there could be some interplay between these two effects. We will comment on the role of this interplay in Figure 2.16 shows the fraction of Hipparcos/Tycho-2 recovered by NLTT as a function of proper motion µ (as measured by Hipparcos or Tycho-2). The solid vertical line is at µ lim = 180 mas yr 1, the proper motion limit of NLTT. One expects completeness to fall by 50% at this point because half the stars that actually have this proper motion will scatter to lower values due to measurement error, and so will be excluded from the NLTT catalog. One therefore expects completeness to achieve its asymptotic value a few σ above this threshold. The two dashed vertical lines are at µ lim ± 40 mas yr 1, which corresponds to ±2 σ for the better-precision NLTT stars, and about ±1.5 σ for the others. The completeness curve does indeed reach an asymptotic value of 90% just beyond this point. Hence, at µ = µ lim we expect the completeness to be % = 45%. The actual value is 42%. To avoid this threshold effect, we will restrict future completeness tests to stars with true (i.e., Hipparcos/Tycho-2) proper motions µ>250 mas yr 1. 72

95 Bright-end Completeness as a Function of Galactic Coordinates Figure 2.17 (bold curve) shows the fraction of Hipparcos/Tycho-2 propermotion (µ >250 mas yr 1 ) stars recovered by NLTT as a function of sin b, whereb is Galactic latitude. NLTT is virtually 100% complete away from the Galactic plane, but its completeness falls to about 75% close to the plane. This incompleteness is not symmetric: it is somewhat worse in the south. We will discuss the reasons for this in the following paragraph. The histogram shows the underlying distribution of proper-motion stars, from Hipparcos/Tycho-2, as a function of sin b. If these stars were distributed uniformly over the sky, then this histogram would be a horizontal line. One expects halo stars to be over-represented near the poles because the reflex of the Sun s motion is most pronounced in those directions. One also expects disk stars to be over-represented near the plane because their density does not fall off with distance in these directions. Plausibly, one can see both effects in the Hipparcos/Tycho-2 histogram. We will return to this conjecture in Figure 2.18 (bold curve) shows the fraction of Hipparcos/Tycho-2 propermotion stars lying in the Galactic plane ( b < 15 ) that are recovered by NLTT as a function of Galactic longitude. While the curve is somewhat noisy, there is a clear increase in incompleteness over the interval 80 <l < 20. Thisisthe 73

96 brightest contiguous region of the Milky Way, which lends credence to the idea that NLTT incompleteness is traceable to crowding-induced confusion. The areas just south of the Galactic equator are on average brighter than the corresponding areas just to the north, so the asymmetric behavior seen in Figure 2.17 also lends credence to this hypothesis. In 2.6.1, we entertained the possibility that detection failures in NLTT and Hipparcos/Tycho-2 might be correlated which, if it were the case, would undermine the completeness estimates obtained from the fraction of Hipparcos/Tycho-2 stars recovered in NLTT. Figure 2.18 shows that this effect cannot be very strong, if it exists at all. The expected number of high proper-motion stars as a function of Galactic longitude need not be uniform, and will in general depend on the model of the Galaxy. However, in any plausible model, the number should be the same looking in directions separated by 180 because NLTT stars are not at sufficiently large distances to probe the Galactic density gradients. Consequently, the distribution is a result of bulk kinematic effects, which should be identical in antipodal directions. Hence, if there were a correlation, one would expect that pairs of antipodal points with a positive difference in NLTT completeness would also have a positive difference in Hipparcos/Tycho-2 counts. No such pattern is seen in Figure

97 In any event, the primary implication of Figure 2.17, namely that NLTT is essentially 100% complete away from the Galactic plane remains true, independent of these more subtle considerations Completeness at Faint Magnitudes Here we perform a statistical test to investigate the completeness of the faint end of NLTT down to its nominal cutoff of µ = 200 mas yr 1, and additionally to µ = 500 mas yr 1, which is the cutoff of LHS. It should be noted that the data in LHS is a subset of data present in NLTT. In this test we assume that the local luminosity function is constant, and that the number density of stars does not change appreciably within the volume occupied by the majority of proper motion stars. We will discuss the validity of this assumption later on. Consider two spheres centered around the Sun, the volumes of which stand in ratio 2:1. This is equivalent to radii being in relation r 1 /r 2 =1.259, or distance modulus difference of 0.5 mag. If we define the outer edge of the bigger sphere as the distance at which a star of apparent magnitude R L,1 produces a proper motion µ 1 = 200 mas yr 1, then this same star, if placed at distance r 2,wouldhaveaproper motion of µ 2 = r 1 r 2 µ 1 = 252 mas yr 1. Also, it would be 0.5 mag brighter. Therefore, µ 2 defines a proper motion limit at the distance r 2 that is equivalent to proper motion limit µ 1 at r 1. These are the lower limits. For the upper proper-motion 75

98 limit we adopt µ lim 2 = 2500 mas yr 1, below which we know the sky was searched homogeneously. NLTT does contain stars with µ>2500 mas yr 1, possibly all that exist, but these were found by methods other than automated plate scanning. Anyway, because of the small relative number of these stars, our statistical test is not very sensitive to the choice of upper proper-motion limit. So, if we take µ lim 2 = 2500 mas yr 1 as a limit below which we want to check for completeness, than this corresponds to some inner boundary of the smaller sphere (which we can now call a shell). Everything closer than this inner boundary would have µ>µ lim 2 and would not be included in NLTT. Now, in order to keep volumes of both shells in appropriate ratio, the outer shell has to have an inner edge corresponding to apropermotionofµ lim 1 = r 2 r 1 µ lim 2 = 1986 mas yr 1. Thistestisperformedinthe same way when investigating completeness of LHS subset of NLTT, but with µ 1 = 500 mas yr 1, and corresponding µ 2. Now that we have defined the two shells in terms of the limiting proper motions, the statistical test consists of comparing the number of stars N 1 of a given magnitude R NLTT (in a R NLTT =0.5 mag bin) in the outer shell (µ 1 <µ<1986 mas yr 1 ), with the number of stars N 2 of a magnitude R NLTT (R NLTT,1 R NLTT,2 )=R NLTT R NLTT = R NLTT 0.5 in the inner shell (µ 2 <µ<2500 mas yr 1 ). The 0.5 mag shift (equal to one bin) brings the absolute 76

99 magnitudes of stars in the outer shell to that of the inner shell. The measure of completeness at magnitude R NLTT is given by the ratio f(r NLTT )= N 1 (R NLTT ) N 2 (R NLTT 0.5). (2.10) If the sample of stars of apparent magnitude R NLTT is 100% complete with respect to those of R NLTT 0.5, then f(r NLTT ) (r 1 /r 2 ) 3 = 2. Now we can define the completeness function F (R NLTT ) for the stars of apparent magnitude R NLTT,in the following way R NLTT =R NLTT F (R NLTT )= f(r R NLTT =R NLTT,comp+ R NLTT 2 NLTT), (2.11) where R NLTT,comp is some bright apparent magnitude at which we believe the catalogue is complete. In Figure 2.19 we show the completeness function F (R NLTT ) for the faint end of NLTT (dotted line) and LHS (solid line). More specifically, the test was performed on the subsample of NLTT that is believed to be spatially complete, that is, the part called the Completed Palomar Region (CPR) by Dawson (1986). This region covers northern declinations (δ > 33 ), and avoids the galactic plane ( b > 10 ). We take R NLTT,comp = 13. The choice is somewhat arbitrary, but we have reasons to believe that NLTT is complete at this magnitude. First, 77

100 when we plot f(r NLTT ) against R NLTT, we get a flat region around R L = 13. Going to still brighter magnitudes might bring us into the part of NLTT that was not compiled from the photographic plates. Therefore, Figure 2.19 shows the completeness at R NLTT with respect to R L = 13. Dashed lines represent 100%, 75% and 50% completeness levels. The completeness of NLTT drops gradually from 90% at R NLTT =13.5 to 60% at R NLTT =18.5. Although one would not a priori expect the completeness to be the function of proper motion, for the stars with µ>500 mas yr 1, i.e., those that are present in LHS, the completeness is much higher - in fact, it seems to be 100% complete to R NLTT = 18, and becomes incomplete at one magnitude fainter. (The solid line is much less smooth than the dotted one, because of the smaller number of stars that produced it.) The reason for differing completeness of lower and higher proper motion stars might have to do with possibly better detection techniques used in LHS part of the catalog. As mentioned, this test depends on number density being roughly constant in the volume investigated. Is this volume small enough for this condition to be valid, i.e. how far above the plane do we get? In a proper motion selected catalog the mean transverse velocity of stars is couple of times higher than the transverse velocity of the population itself, i.e. v t 90 km s 1. This means that the stars moving at µ>200 mas yr 1 will all be closer than 95 pc. Such stars will have disk scale height greater than that of normal population, so the distance of 95 pc is not 78

101 significant compared to that scale height. As for stars that move more slowly, they have to be placed even closer to make their way into NLTT, which means that they will be affected even less. We tested this by comparing completeness of the subsamples of NLTT and LHS from low (10 < b 36 ) and high ( b > 36 ) galactic latitudes. We see no significant difference Completeness of Different Star Populations as a Function of Galactic Latitude Our revised catalog recovers 95 97% of NLTT stars in areas that it covers. This allows investigation of relative completeness of various types of stars (as determined using RPM diagram) as a function of Galactic latitude. We showed in by direct comparison with Hipparcos and Tycho-2, that at bright (V < 11) magnitudes NLTT is close to 100% complete for b > 15, but that its completeness falls to 75% close to the plane, even for these bright stars. For the faint stars we do not have an independent compilation of proper motions, so we cannot directly establish the absolute completeness of the catalog. (We will carry out an indirect absolute measurement in forthcoming work.) However, by making use of both the RPM classification the much greater dynamic range of the 79

102 full catalog presented here, we can give a much more detailed picture of the relative completeness as a function of various variables. Figure 2.20 shows the number of WDs, SDs, and MS stars per square degree as a function of Galactic latitude, for three different magnitude ranges. To determine the surface density (stars deg 2 ), we calculate the fraction of each latitude bin that is covered by the 2MASS release and that lies to the north of our cutoff in declination. (To allow for the somewhat ragged boundary of USNO-A1/POSS I coverage near δ 33, we set this cutoff at δ> ) However, we do not attempt to compensate for stars that fail to appear in 2MASS due either to saturation, faintness, or other causes. For 10 <V < 17.5 the fraction of these is only 1%. On the other hand, bright stars V < 6 are virtually absent from these plots due to saturation, and saturation remains to some detectable degree until V 10. This effect should not influence the relative number of stars as a function of Galactic latitude, which is the main point of Figure In any event, completeness questions at the bright end are more effectively investigated by the techniques described in They are included here mainly as a point of reference. The very faintest blue stars from NLTT will be missing from these plots because of the 2MASS flux threshold. The results shown in Figure 2.20 are quite unexpected. One often hears of the severe incompleteness of NLTT close to the Galactic plane, but the real story 80

103 is more complex: NLTT is substantially less complete in the plane, but only for MS stars. By contrast, NLTT coverage of SDs is near uniform over the sky and its coverage of WDs appears to be completely uniform. For MS stars, there is an evident dropoff in counts over the interval 0.2 < sin b<0.3 in all three magnitude ranges. It is not very pronounced for bright stars, but one already knows that NLTT is more than 85% complete averaged over this range. However, it is quite pronounced in the other two ranges, falling by a factor 10 over only 15 in each case. One also notices a more gradual decline in the MS density going from high to low latitudes. For example, in the faintest bin, it falls by a factor 2 between the poles and b ±15. A priori, one does not know if this is due to a genuine change in density or to an extension of the obvious incompleteness near the plane to higher latitudes. In our further analysis, we will adopt the former explanation for two reasons. First, one does expect a general trend of this sort because a large fraction of the fainter MS stars entering a proper-motion limited sample are from the old disk. These have on average substantially higher transverse speeds seen towards the poles than in the plane because of asymmetric drift, and are therefore selected over a larger volume. Second, as we now discuss, this trend is also seen in SDs where it is expected on similar grounds, but this time without the problem of contamination from a slower population. 81

104 There are too few SDs in the bright bin to draw any meaningful conclusion. In the middle bin 11 <V <15, the SD distribution appears to be almost completely flat, in very striking contrast to the MS distribution in the same magnitude range. In particular, near the plane where the MS density suffers a factor 10 decline, the SD distribution is virtually flat and if it declines, does so by at most a few tens of percent. The fact that the MS counts gradually rise toward the poles while the SD counts do not is easily explained. For a population of characteristic transverse speed v, a survey will saturate its proper-motion limit µ lim only for stars with M V brighter than, M V <V 5log v 10 pc µ lim (2.12) For SDs with v 300 km s 1 surveyed at V = 15 to the NLTT limit µ lim = 180 mas yr 1, this corresponds to M V < 7.3. There are very few subdwarfs at these bright magnitudes that could take advantage of the higher transverse velocities seen toward the poles. On the other hand, for typical MS speeds, v 50 km s 1, the limit is M V < Since this is close to the peak of the MS luminosity function (LF), a large fraction of MS stars are seen more readily toward the poles than the plane. The same effect explains the patterns seen in the faintest bin. The limit imposed by equation (2.12) for subdwarfs at this magnitude is M V < 10.3, which includes a large fraction of the SD LF. Similarly, we expect 82

105 the effect to be even stronger for MS stars in the faintest bin than the middle bin, because now the whole peak of the MS LF is included. On the other hand, in the brightest bin, the limit for MS stars is M V < 7.1 which includes a very small fraction of the MS LF. We therefore expect the slope to be small, and it is. There are significant numbers of WDs only in the faintest bin. Since WDs in NLTT mostly have the same kinematics as the MS, the limit imposed by equation (2.12) is M V < Many WDs satisfy this constraint, so we expect to find more WDs near the poles, which is actually the case. Note that in the faintest bin, neither the WDs nor the SDs show any significant tendency to drop off close to the plane. Thus, a consistent picture emerges from Figure 2.20: MS completeness is very severely affected by proximity to the plane but SD and WD completeness are barely affected at all. The most plausible explanation for this is that while Galactic-plane fields are extremely crowded and therefore in general subject to confusion, blue stars are no more common in the plane than anywhere else. Hence, by focusing on blue objects in the plane, Luyten was able to recover most high-proper motion SDs and WDs, even while he lost the overwhelming majority ( 90%) of the MS stars. 83

106 2.7. Discussion and Conclusion Once the full 2MASS catalog is released, it will be relatively straightforward to extend our catalog to the other 33% of the sky that lies north of δ = 33. However, the prospects for extending it to the south are less promising. First, as we discussed in 2.3.1, the great majority of NLTT stars are missing from USNO-A. In the north, even when a NLTT star was missing from USNO-A, we were frequently able to recover it by looking for the 2MASS counterpart at the position predicted by assuming that the star was inside the NLTT rectangle and that the NLTT proper motion was approximately correct. See However, the reason that this method was effective is that over most of the northern sky, the star does actually lie in the rectangle about 80% of the time. From Figure 2.6, one sees that progressively fewer stars are in the rectangle in the south, and virtually none are for δ< 45. Moreover, a 2MASS-only identification yields a position and infrared photometry, which are useful for many applications, but not a proper motion. At present only 13% of the area δ< 33 is covered by the 2MASS release, but the above factors lead us to believe that after full release, our technique will not be very effective in this region. In any event, NLTT is generally limited to V < 15 in the South and the brighter stars among these are already covered by our PPM search. 84

107 The catalog presented here gives improved astrometry and photometry for the great majority of stars in the NLTT that lie in the overlap of the areas covered by the second incremental 2MASS release and those covered by POSS I (basically δ> 33 ). In addition, essentially all bright NLTT stars over the whole sky have been located in PPM catalogs and, whenever possible, the close binaries among them have been resolved using TDSC. We recover essentially 100% of NLTT stars V < 10, about 97% for 10 <V <18, and a declining fraction thereafter. Most of the faint stars that we do not recover are WDs, which are too faint and too blue to show up in one or both of USNO-A or 2MASS, the two catalogs that we combine to obtain our astrometry and photometry. The catalog contains a total of 36,020 entries for 35,662 NLTT stars including a total of 723 entries for 361 NLTT stars that have been resolved in TDSC. Of these 36,020 entries, 1353 ( 4%) contain new positions and photometry but not new proper motions because they have been identified in only USNO-A or 2MASS, but not both. The new positions are accurate to 130 mas. The new proper motions are accurate to 5.5masyr 1, more than a 3-fold improvement over NLTT. Narrow angle proper motions are accurate to 3 mas yr 1. The catalog provides a powerful powerful means to investigate SDs, WDs, faint MS stars as well as CPM binaries. 85

108 Table 2.1. Bright NLTT stars position precisions fit σ 1 σ 2 c q N N 1 RA s DEC

109 Table 2.2. Bright NLTT stars proper motion precisions Catalog Rectangle Position Number σ( µ ) σ(µ α ) σ(µ δ ) quality mas yr 1 mas yr 1 mas yr 1 Hipparcos In Better Out Better All Worse Tycho-2 In Better Out Better All Worse Starnet In Better Out Better All Worse

110 Table 2.3. Number of USNO/2MASS matches rectangles circles total unique resolved unique resolved USNO-A USNO-A total

111 Table 2.4. New candidate white dwarfs closer than 20 pc NLTT R.A. Decl. V B V V J (V J) d (pc) Notes a b c b b b b b d e (continued) 89

112 Table 2.4 Continued NLTT R.A. Decl. V B V V J (V J) d (pc) Notes f g h i Note. NLTT numbers follow the record number in the electronic version of NLTT (ADC/CDS catalog I/98A). Positions are given for epoch and equinox V and B V are calibrated from USNO photographic magnitudes, except for NLTT (GSC red magnitude). (V J) gives horizontal separation from the SD/WD discriminator line. Distances are photometric, based on Bergeron, Leggett, & Ruiz (2001) data. a USNO photometry blended with NLTT b NLTT magnitudes fainter. c 2MASS photometry possibly affected by crowding. d LHS e USNO photometry blended with NLTT f Giclas, Burnham, & Thomas (1965) : Suspected WD (GD 5). g Beers et al. (1992) : V =15.09, B V =0.23, composite spectrum. h Green, Schmidt, & Liebert (1986) : Spectral type sdb (PG ). i Eggen (1968) : V =15.07, B V =0.24 (WD ). 90

113 10 5 DEC (arcsec) RA (seconds) Fig Differences between stellar positions as reported in NLTT and the very accurate positions of the same stars from Tycho-2, both evaluated in the NLTT epoch of The (1 s 6 ) rectangle that dominates this plot is caused by the fact that Luyten measured a majority of his stellar positions to a precision of 1, but reported them only to 1 second of time and 6 of arc. 91

114 100 DEC (arcsec) RA (arcsec) Fig Same as Fig. 2.1 except that first, RA is now plotted in arcsec rather than in seconds of time, and second, the scale is much larger. Although most NLTT positions are quite accurate (see Fig. 2.1), there is a substantial halo of outliers, some that go well beyond the dimensions of this plot. 92

115 2 R NLTT R USNO (B R) NLTT (B R) USNO R NLTT Fig Differences between photographic photometry from NLTT and USNO for stars in our catalog. Upper panel shows the difference in R magnitude and bottom panel shows the difference in (B R) color. The bold curves give the mean difference and the solid lines give the 1 σ scatter (with 3 σ outliers removed from the fit) in 1 mag bins. This scatter ranges from 0.4 to 0.5 mag over most of the plot and is dominated by errors in NLTT. Note that errors in B and R are highly correlated in both NLTT and USNO. 93

116 10 5 DEC (arcsec) RA (time) 100 DEC (arcsec) RA (arcsec) Fig Differences between NLTT listed position and true position (as determined by propagating the star back to its 1950 position using the 2000 position and proper motion from our catalog) for all faint, V > 11, stars. The rectangle in the upper panel arises because, for most of his catalog, Luyten actually measured positions to about 1 but only recorded them to 1 s of time and 6 of arc. However, the lower panel shows that there is a substantial halo of outliers at least out to our search radius of 2. Compare to Figs. 2.2 and

117 1.8 Fraction in Rectangle V Fig Fraction of NLTT stars found in a rectangle centered on the NLTT position and with dimensions (15 cos δ+2 ) (6 +2 ) as a function of V magnitude. The size is set to allow for 1 errors in addition to error caused by decimal truncation of the catalog entries. The feature at V 10 is probably caused by difficulty doing astrometry for stars saturated on plates. 95

118 Fraction in Rectangle sin δ Fig Fraction of NLTT stars found in a rectangle centered on the NLTT position and with dimensions (15 cos δ+2 ) (6 +2 ) as a function of of declination. The fraction is very high over most of our catalog area, δ> 33, but deteriorates drastically to the south. 96

119 100 µ α (NLTT) µ α (Catalog) V Fig Differences between proper motions in the α direction as given by NLTT and our catalog. The bold line shows the mean difference, which is consistent with 0. The solid lines indicate the 1 σ scatter (with 3σ outliers removed from the fit) in 0.5 mag bins. The NLTT errors are typically 20 mas yr 1 in the range 11 <V <18. The pronounced scatter at V 10 may be related to the feature seen at the same place in Fig

120 20 Tangential (arcsec) Radial (arcsec) Fig Difference between separation vectors of 339 binaries with separations 10 < θ <57 as given by NLTT and our catalog. The x-coordinateisalongthe direction of the separation and the y-coordinate is perpendicular to it. The great majority of NLTT separation vectors are accurate to 1.Seeinset. 98

121 µ tot (mas/yr) log( θ/") Fig Magnitude of the difference in the relative vector proper motion of binary members as given in our catalog. Error bars reflect the effects of internal binary motion at small separations, θ, and projection effects at large separations. They do not include our measurement error of 6 mas yr 1.Pointswith µ<12 mas yr 1 are likely to be genuine pairs and do not have error bars to avoid clutter. At large separations, many NLTT CPM binaries are actually optical pairs. 99

122 40 µ α,u2m µ α,tyc2 (mas/yr) µ δ,u2m µ δ,tyc2 (mas/yr) V Fig Differences between proper motions as given by Tycho-2 and our measurements based on identifying the stars in USNO and 2MASS. Most of the difference is due to errors in the USNO/2MASS measurement, which are thereby evaluated to be 5.5masyr 1 for V>10. The bold curve shows the mean difference (consistent with 0) and the solid curves show the 1 σ scatter (with 3 σ outliers omitted from the fit) in 0.5 mag bins. Errors are more severe at bright magnitudes because saturation adversely affects USNO astrometry. 100

123 µ δ (mas/yr) µ α (mas/yr) Fig Difference in the vector relative proper motion of the components of 52 subdwarf binaries with separations θ >10. For physical pairs the real relative proper motion is very close to 0, so these differences provide an estimate of our narrow-angle proper-motion errors, 3 mas yr 1 (with the two outliers omitted). 101

124 5 R L + 5 log(µ) (B R) L Fig Original reduced proper motion (RPM) diagram for NLTT stars. Both the proper motions, µ, and the photographic magnitudes, B NLTT and R NLTT,are taken from NLTT. However, since the magnitudes are originally given only to one decimal place, the color has been randomized by 0.1 mag to show the density of points. The apparent stripes result from discretization of color in the original NLTT data. 102

125 5 V + 5 log(µ) V J Fig Optical-infrared RPM diagram for NLTT stars having 2MASS and Hipparcos counterparts (yellow), as identified in 2.2, or 2MASS and USNO-A counterparts (black), as identified in 2.3. For RPM V +5logµ > 9, subdwarfs (SDs) and main-sequence (MS) stars clearly lie on different tracks. White dwarfs (WDs) are also clearly separated from SDs and MS stars. In the subsequent figure, the NLTT stars with 2MASS/USNO-A counterparts will be identified as MS (red), SD (green), or WD (cyan), depending on whether they lie to the right, between, or to the left of the two dashed lines shown in this figure. 103

126 5 5 5 R L + 5 log(µ) (B R) L (B R) L (B R) L Fig Left panel: Original NLTT RPM diagram (see Fig. 2.12) but with the stars identified in Fig as WDs shown as large cyan dots. While the region to the lower left is strongly dominated by WDs, many WDs lie further to the red where they are heavily contaminated by other stars. SDs are shown as small green dots in the middle panel, and MS stars are shown as small red dots in right panel. Comparison of SD and MS distribution shows that they strongly overlap in NLTT RPM. In all cases the other types of stars with 2MASS/USNO-A counterparts are shown as smaller black dots. 104

127 Completeness.6.4 NLTT.2 Hip+T2 Hipparcos Only R NLTT Fig The completeness of the combined Hipparcos and Tycho-2 catalogs as a function of R NLTT (roughly Johnson V ) magnitude, measured from the fraction of NLTT stars (bold histogram) that are matched to one of these two catalogs (upper thin-line histogram). Also shown are the Hipparcos-only matches. The bump in NLTT detections at R NLTT 8.7 is an artifact of NLTT mags. See text. Completeness falls to 50% at R NLTT =11.6. Hence, the subsequent tests on completeness of NLTT apply directly to its brighter stars, V < (All histograms are divided by The bin size is 0.1 mag.) 105

128 1.2 1 Completeness log µ (arcsec/yr) Fig Completeness of NLTT (i.e., the fraction of Hipparcos/Tycho-2 stars recovered by NLTT) as a function of Hipparcos/Tycho-2 proper motion, µ. The solid vertical line shows the proper-motion limit of NLTT, µ lim = 180 mas yr 1,and the two dashed lines show µ lim ± 40 mas yr 1, i.e., roughly the 1.5 to 2 σ errors in NLTT. The effect of this proper-motion threshold disappears by µ 250 mas yr 1. Hence, subsequent completeness tests will be restricted to stars moving faster than this value. 106

129 Completeness.6.4 Hipparcos/Tycho 2 Counts sin(b) Fig Completeness of NLTT (bold curve) as a function of sin b where b is Galactic latitude, i.e., the fraction of stars with µ>250 mas yr 1 in Hipparcos and Tycho-2 (whose distribution is shown by the histogram) that are recovered in NLTT. (The histogram has been divided by 200. The bin size is 0.04) Incompleteness is significant only close to the plane, where it is somewhat skewed toward the south. 107

130 Completeness.6.4 Hipparcos/Tycho 2 Counts Galactic Longitude Fig Completeness of NLTT (bold curve) as a function of Galactic longitude for the subset of stars lying close to the plane ( b < 15 ). Also shown is a histogram (counts divided by 200, 20 bins) of Hipparcos and Tycho-2 stars with µ>250 mas yr 1 and b <

131 Fig Completeness relative to R NLTT = 13, in the Completed Palomar Region (δ > 33, b > 10 ). Solid line is the completeness of the LHS subset of NLTT, while the dotted one is the completeness of the entire NLTT. Dashed lines show 100%,75% and 50% completeness levels. 109

132 0 log(number/deg 2 ) log(number/deg 2 ) Main Sequence Subdwarfs White Dwarfs V > < V < 15 log(number/deg 2 ) V < sin b Fig Surface density of stars in our catalog as a function of Galactic latitude for three different stellar populations and three different magnitude bins. Only stars with J photometry (needed for star classification with the RPM diagram) are included. Main sequence stars show a drop of a factor 10 in density close to the plane, but subdwarfs and white dwarfs do not. The tendency for the counts of all populations to rise at high latitudes in the faintest bin compared to the flat behavior of the subdwarfs in the mid bin and the main sequence stars in the bright bin is easily explained from simple kinematic arguments. 110

133 Chapter 3 Precise Masses of Nearby Stars 3.1. Introduction The mass of a star is a single most important parameter determining many of its other physical parameters, its structure, and the course of its evolution. This is why the knowledge of mass is important by itself. However, since the advances in the theoretical understanding of stellar structure and evolution are today profound enough to be able to predict many of the stellar characteristics, the knowledge of a precise mass is also the best way to check the validity of the stellar theory, or to pose challenges for the refinement of the stellar models. We can illustrate this with a well known relation between mass and luminosity of stars on the main sequence. The bold line in Figure 3.1 shows the theoretical M L relation for solar-metallicity stars (Baraffe, Chabrier, Allard, & Hauschildt 111

134 1998), while the thin line shows the relation for metal-poor star with [Fe/H] = 1 (Baraffe, Chabrier, Allard, & Hauschildt 1997). The current mass measurements with their error bars are shown as circles (astrometric and spectroscopic binaries) and as triangles (eclipsing binaries). It is obvious that the observations offer very weak constraints on the theoretical models. This is especially true for low-metallicity stars for which there are few measurements to begin with. With precise mass measurements one would be able to map the mass-luminosity relation as a function of metallicity, or perhaps some other parameters that currently do not figure in the models (like the onset of full convection for low-mass stars). In addition to this, all currently used methods measure masses of stars in binary systems. Although we have no reason to believe that the masses of isolated stars would be different, this has never been actually tested Astrometric Microlensing with Space Interferometry Mission One is used to thinking of microlensing events as taking place towards the Magellanic Clouds or the Galactic bulge. In both of these cases the lens is a faraway object, either a star belonging to the same system as the source star (self-lensing), a distant star in the Milky Way s disk, or a member of Milky Way s 112

135 halo (whatever its nature might be). The effect that is routinely observed in such cases is the change in source s brightness, but also present is an additional effect of the deflection of the source apparent position (Boden, Shao, & van Buren 1998). The astrometric effect scales as the inverse of lens-source separation ( β 1 ), while the photometric effect decreases more severely ( β 4 ). This means that for the nearby lenses (d < 100 pc), where lens-source separations are likely to be large, the only observable effect will be astrometric deflection. The amount of this deflection is directly proportional to the lens mass, allowing it to be measured in principle. Initially proposed by Refsdal (1964), this idea was later examined by Paczyński (1995, 1998) and Miralda-Escudé (1996) in the context of rapid developments in space-based astrometry. Obtaining masses using astrometric lensing has several advantages. First, it allows achievement of a greater precision than the one routinely achieved by measuring binary systems. Second, it is the only known method to obtain the masses of stars not residing in binary systems. Finally, the selection bias favors fast moving lenses, which are often low-metallicity halo subdwarfs, the masses of which are rarely measured. The deflection is so small ( 100µas) as to be unobservable with presentday facilities. However the unprecedented astrometric precision of the Space Interferometry Mission (SIM) of 4µas will enable such measurements. 113

136 We plan to measure some 20 stars using 200 hr of SIM time alloted to the SIM Microlensing Key Project 3.3. Selection of Microlensing Candidates Principles of Selection Here we describe the original selection of candidate microlensing events. Later improvements for the part of the selection process came most notably from the use of 2MASS catalog, as described in Chapter 2. The impact of 2MASS on the selection process will be discussed in Our overall plan is to search for astrometric microlensing events (or events, for short) and rank these by the amount of SIM time required to measure the lens mass to a fixed fractional error of 1%. To this end, we would like to consult a catalog containing the positions, parallaxes, proper motions, and magnitudes of all stellar sources in the sky. Unfortunately, there is no such catalog. To understand how to make use of existing catalogs, we review the basic requirements of the search. First, while in principle the event depends on the relative proper motion of the source and lens, the lenses, being closer, almost always move much faster in 114

137 the sky than the sources. Hence, no proper-motion information is required for the sources in order to select candidate events. The probability p that any individual lens will deflect light from a more distant star enough to measure the lens mass M to fixed fractional accuracy is p N s πµm, (3.1) where N s is the surface density of sources, and π and µ are the parallax and proper motion of the lens. One therefore expects events to be clustered near the Galactic plane, and for nearby, fast-moving stars to be over-represented as lenses. However, there are a greater number of distant than nearby stars and consequently more stars with low than high proper motions. The net of these two competing effects is that for parallax-limited and proper-motion-limited catalogs, the total number of events scales as (Gould 2000a) N events π 1 min, N events µ 1 min, (3.2) where π min and µ min are the limits of the respective types of catalogs of lenses. Of course, the total number of potential lenses that one must examine scales as π 3 min or µ 3 min. Thus it is most efficient to start with high π or high µ stars and move progressively to more distant or slower ones. In practice, one has available 115

138 magnitude-limited and not distance-limited catalogs, but for stars of fixed absolute magnitude these are effectively distance-limited Catalogs Used in Selection The USNO-A2.0 all sky astrometric catalog, which is constructed from two photographic surveys [Palomar Observatory Sky Survey I (POSS I) for δ> ( north celestial hemisphere) and UK Science Research Council SRC-J survey plates and European Southern Observatory ESO-R survey plates (SERC/ESO) for δ< ( south celestial hemisphere)] is a nearly ideal catalog for sources, containing 526 million entries. To be included in the catalog, a star had to be detected on both the blue and red plates within a 2 coincidence radius aperture. Hence the catalog begins to lose completeness at V 19 as stars fall below the detection threshold on one plate or the other. The catalog is also incomplete at bright magnitudes (V < 11) because of poor astrometry of saturated stars, although for these stars USNO-A2.0 contains inserted entries from the ACT (Urban, Corbin, & Wycoff 1998b) or Tycho (ESA 1997) catalog. However, the epoch of these additional entries is and respectively, unlike the epoch of the other sources which is the mean epoch of the blue and the red plates (1950s for POSS I, and 1980s for SERC/ESO). In addition, USNO-A2.0 is by and large missing the stars with proper motions µ > 250 mas yr 1 in the south, because the blue and 116

139 red plates of the SERC/ESO survey were on average taken 8 years apart, and so stars with µ>250 mas yr 1 moved outside the 2 error circle between the blue and red exposures. In reality, the time elapsed between the two plates varies from 0 to 15 years, leading to different proper-motion cutoffs for each plate. This problem does not affect POSS I because its blue and red plates were taken on the same night. Neither the incompleteness at bright magnitudes nor the incompleteness at high proper motions has any significant effect on USNO-A2.0 as a catalog for microlensing sources, since they are usually faint and move very slowly. However, both have substantial impact on our efforts to obtain critical information from this catalog about the lenses (see below). The relative position errors, important for NLTT events, for USNO-A2.0 are about 150 mas. For Hipparcos and ACT events, it is the absolute errors [USNO-A2.0 uses ICRS (International Celestial Reference System) as its reference frame] of about 250 mas that are relevant. There is, of course, an additional error in the position of the source in 2010 due to 60 years of proper motion in the case of POSS I and 30 years for the SERC/ESO plates. Since typical sources are on average 3 kpc distant and are moving at 25 km s 1 in each direction, this gives a proper motion of 2masyr 1. This proper motion adds about 100 mas in the north and 50 mas in the south to the total positional error. Hence, the total error on average is about 170 mas (260 mas in the absolute system). Note that this 117

140 will not be improved significantly by the release of the USNO-B all-sky position and proper motion catalog (D. Monet 1998, private communication), since its proper-motion errors will be of the same order as the proper motions of typical source stars. Similar limitations will hold true in the case of GSC II (Guide Star Catalog Two) (see Lasker et al. 1998, for example). USNO-B and GSC II will be compiled by comparing first generation sky surveys with the second generation. The absolute photometry errors in USNO-A2.0 are said to be about 0.25 mag for the stars that are not saturated. USNO-A2.0 lists photographic blue and red magnitudes. The equinox of the coordinates is ICRS J2000. We search for lenses in three catalogs: Hipparcos, the ACT Reference Catalog (ACT) and the New Luyten Catalogue of Stars with Proper Motions Larger than Two Tenths of an Arcsecond and First Supplement (NLTT). The three catalogs have substantially different characteristics. Hipparcos is a heterogeneous catalog with 118,000 entries. However, it has two approximate completeness characteristics that are very useful for understanding its role in the present study. First, it is approximately complete for V<8, with 41,000 stars to this limit. Second, it contains essentially all the NLTT stars brighter than its operational limit of V 12. As we mention below, NLTT is nominally complete for µ>180 mas yr 1. Based on statistical tests of the Hipparcos catalog, we find that it (and thus presumably NLTT) is essentially complete for µ>220 mas yr 1 118

141 and V < 11. In its last magnitude (11 <V <12), Hipparcos shows some evidence for incompleteness, perhaps because of the difficulty of making precise conversions from NLTT s photographic magnitudes to the near-johnson system used by Hipparcos. There are 6500 Hipparcos stars with µ>200 mas yr 1 and 15,000 with µ>100 mas yr 1. Hipparcos stars have trigonometric parallaxes with typical precisions of 1 mas. As we discuss in 3.3.3, uncertainty in the distance to the lens is the main problem in estimating the amount of SIM time required for a lens mass measurement. This uncertainty is virtually eliminated for Hipparcos stars. In addition, we use Hipparcos parallaxes to calibrate our method for estimating distances of stars in the other two catalogs which lack trigonometric parallaxes. Hipparcos positions are accurate to 1 mas, while the proper motions have errors of order 1 mas yr 1, implying an error of about 20 mas in the star s 2010 position. This is negligible compared to the error in the source position given in USNO-A2.0. Finally, most Hipparcos stars have Tycho photometry which is accurate to of order 0.01 mag. Even those stars lacking Tycho photometry usually have ground-based photometry of similar quality. Tycho photometry is far better than the minimum precision required for the present search. The ACT catalog is constructed by matching stars common to both the Astrographic Catalogue 2000 (AC 2000, Urban et al. 1998a) and Tycho, with 119

142 epochs circa 1910 and 1990 respectively. Such a long baseline combined with Tycho s precise positions, permits the proper motion accuracy of ACT to be 3masyr 1 (ten times better than Tycho itself). ACT is presently the largest (nearly 1 million stars) all-sky catalog containing proper motions. It is limited at the faint end by incompleteness of the Tycho catalog which sets in over the range 11 <V < 11.5, and at the bright end by incompleteness (due to saturation) of plates that produce AC Completeness of ACT with respect to Tycho (entries that have proper motion) is about 95% in the 6 <V <12 range, and drops to 50% for V 3. There is also a cutoff at high proper motions (µ > 1. 5yr 1 ), which results from the lack of proper-motion information about these stars in the Tycho catalog. Typical errors of ACT proper motions imply an uncertainty in 2010 position of about 60 mas. This is still small compared to the uncertainty of the source position and so can be ignored. Tycho photometry is available for the great majority of ACT stars and, as stated above, this has much higher precision than is required for the present study. As we discuss in 3.3.3, we are able to estimate the distances to ACT stars with 30% accuracy which is quite adequate for our purposes. The characteristics of NLTT are investigated in detail in Chapter 2, and here we present just the details relevant to lens selection. NLTT is nominally complete to µ>180 mas yr 1 and V < 19 in the northern part of the sky (δ > 33 ), and 120

143 away from the galactic plane ( b > 10 ). In the south and near the plane, the incompleteness sets in at brighter magnitudes. NLTT α and δ are given only to 1 s and 0. 1 respectively (in some cases to 0.1 min and 1 respectively) and so are not sufficiently accurate to predict lens-source encounters which typically have impact parameters β 1. Hence to obtain improved positions of NLTT stars we search for the corresponding entries in USNO-A2.0. Recall that USNO-A2.0 entries have position errors of 250 mas. However, recall also that in the south (δ < 17. 5), USNO-A2.0 is missing a large fraction of the NLTT stars. To recover this part of the NLTT catalog, it would be necessary to make new position measurements for the majority of NLTT stars in the south, or at least for all that pass within 6 (position error of NLTT) of some source star. This would be a major project which we do not attempt. The proper motion error present in NLTT ( 2.3.4), propagated over the 50 year baseline implies errors of 1. 2 in 2010 position. This is the dominant astrometric error for these stars and has important consequences as we discuss in Because NLTT stars must be found in USNO-A2.0 in order to be used, they automatically have available two sources of photometry, both photographic. As we discuss in 3.3.3, it is necessary to transform these photographic systems to the Johnson-like system used by Tycho in order to estimate distances. We find that the transformation from USNO-A2.0 colors to Johnson B V has somewhat 121

144 smaller scatter than the transformation from NLTT colors, and we therefore use the former. This scatter (0.25 mag) is still substantially larger than we would like. As we discuss in 3.3.3, it leads to a factor 1.7 uncertainty in distance estimates for NLTT stars. There is one important additional source of incompleteness that affects all searches based on USNO-A2.0. Suppose that a lens will pass close to a source in 2010 with a relative proper motion µ. The source must be identified from USNO-A2.0 which is based on plates taken δt 60 yr earlier in the north and δt 20 yr earlier in (the later of the two plates) the south. At that time, the lens and source were separated by µδt. If the lens is sufficiently bright, it will appear as a blob on the photographic plates and will therefore blot out the source at the epoch of the plate, and so the source will not appear in USNO-A2.0. The exact blot-out radius depends on the magnitude of both the lens and the source (fainter stars will get blotted-out farther from the lens). However, the great majority of sources are relatively faint (V 17). For simplicity, we therefore identify this radius as a function of lens magnitude, θ(v ), the point where 50% of V 17 stars are lost. We find for V =2, 5, 8, 11, 15 that θ(v ) = 350, 80, 21, 11, 4 arcseconds respectively. Thus, for example, for a V = 8 lens (i.e., θ =21 ), the minimum proper motion it is required to have to allow an event to be detected is µ min = θ(v )/δt = 350 mas yr 1 in the north or 1000 mas yr 1 in the south. 122

145 Estimates of Errors The basic requirement for constructing a list of astrometric microlensing events is to rank order the events by the amount of telescope time (here specifically SIM time) needed to make a mass measurement of a specified precision. At a later stage, one might decide to eliminate events with short observation times because of some difficulty in carrying out the observations, and one might choose to skip down the list to include an event with a long observation time because the lens in question is exceptionally interesting. However, for now we will be concerned primarily with the fundamental requirement of rank ordering the events. 2000a) The observation time needed for a 1% mass measurement is given by (Gould τ = T 0 α 2 0 ( rβc 2 4GM ) 2 ( (V s 17) µt0 γ β, µ t ), (3.3) β where r is the distance to the lens, β is the impact parameter of the event (the projected angular separation at the time t 0 of closest approach), M is the mass of the lens, V s is the apparent magnitude of the source, µ is the relative lens-source proper motion, t(= 5 yr) is the duration of the experiment, γ is a known function which is discussed in detail by Gould (2000a), T 0 =27hours,andα 0 = 100 µas. 123

146 In order to estimate τ, one must first measure or estimate r, β, M, V s,µ, and t 0. Of course, there will be errors in all of these quantities, and these will in turn generate errors in τ. In most cases, these errors can be reduced by making additional observations (as will be done in 3.4.2) or carrying out additional investigations of various types. However, these refinements often require substantial legwork. Therefore, one should first decide what is an acceptable level of error in τ and what are the main contributors to it. The list of events will be constructed in three stages. Stage 1 is an automated search of a pair of star catalogs (sources and lenses) for events with estimated observation times τ τ max,1. Stage 2 is a simple (but potentially very time consuming) check of this list to eliminate spurious candidates. In stage 3, additional observations are made of the remaining candidates. The estimate of τ is refined and the final list is constructed with a more restrictive maximum observation time τ τ max,3,andτ max,3 <τ max,1. What level of errors are acceptable at stage 1 and stage 3? At the outset it should be emphasized that errors in the estimate of τ do not cause errors in the final mass measurement by SIM. The cost of errors in stage 3 is that the SIM observations will be too short (causing larger than desired statistical errors in the mass measurement) or too long (wasting valuable SIM time pushing down the mass measurement errors below what is actually desired). Hence, a factor of two error is 124

147 acceptable. That is, if the SIM time were underestimated by a factor of 2, then the mass-measurement error would be 1.4% instead of 1%. This would be a bit worse than desired but on the other hand there would be a saving of SIM time that could be applied to other stars. If the SIM times were overestimated by a factor of 2, then one would waste some SIM time on the event, but one would reduce the error to 0.7% which is not completely without value. On the other hand, factor of 10 errors are not acceptable. Either one would waste a huge amount of SIM time, or one would obtain a mass measurement with an error much larger than desired. As a corollary, errors that are small compared to a factor of 2 can be ignored at any stage. Much larger errors can be tolerated at stage 1 than stage 3. For example, if the stage-1 estimates could be in error by a factor of 10, then one must set τ max,1 =10τ max,3 to avoid losing viable candidates. The cost is that the candidate list is increased by a factor (τ max,1 /τ max,3 ) 1/2 3 (Gould 2000a), and one must then sift through this larger list in stages 2 and 3. Clearly, however, this work load can become prohibitive for sufficiently large errors. We now show that of all the input parameters, only the distance r and the impact parameter β can induce sufficiently large uncertainties in τ to warrant special attention. We examine the various parameters in turn. 125

148 If the lens is taken from the Hipparcos catalog, it will have a trigonometric parallax. In virtually all cases of interest, the lens will be close enough (r < 200 pc) that the distance error will be less than 20%, which is quite adequate for present purposes. If the lens does not have a trigonometric parallax, its distance must be estimated from its measured flux (in say V band) F V together with an estimate of its intrinsic luminosity, L V : τ r 2 = L V 4πF V. (3.4) Equation (3.4) makes it appear as though the uncertainty in τ will be enormous. For example, a star with a measured color V I = 1 could plausibly be a clump giant with M V = 1, a main-sequence star with M V = 6, a subdwarf with M V =8, or a white dwarf with M V = 14. This covers a range of in luminosity and implies an uncertainty in τ of the same magnitude. Nevertheless, we will show below that with good two-band photometry, r can be determined with 30% accuracy which implies an error in τ of less than a factor of 2. Stars in the ACT catalog have good (Tycho) photometry. For stars in NLTT only photographic photometry is generally available. We will later show that for NLTT the 1 σ errors in L V (and so τ) are a factor of 3. The first step in estimating the distance to the lens is to determine its luminosity class (e.g., white dwarf, subdwarf, main-sequence, or giant star). If this 126

149 is properly determined, then the lens mass can be estimated quite accurately from the color. For the cases where the luminosity class is not correctly determined, the error induced in the distance is much greater than the error induced in the mass. Thus, in either case, the error in the mass can be ignored. The geometry of the event (µ, β, andt 0 ) is determined from the astrometry. These quantities affect the estimate of τ through the β 2 factor and the γ factor in equation (3.3). We focus first on the β 2 factor. As discussed in 3.3.2, the relative source-lens position error (and hence the error in β) is about 260 mas for lenses in Hipparcos and ACT and about 1. 2 for NLTT. In 3.3.4, we discuss how these errors are incorporated into the search procedure. According to equation (3.3) the 0.25 mag error in the source magnitude from USNO-A2.0 induces a 25% error in τ. We ignore this. Finally, since the launch date of SIM is not fixed, we do not attempt to calculate γ based on the time of closest approach t 0 relative to the midpoint of the mission, γ(µt 0 /β, µ t/β). Rather, we calculate γ for the optimal possible launch date for the given event when the midpoint of the mission coincides with the time of closest approach, i.e., t 0 = 0. That is, we use γ(0,µ t/β). Some representative values are γ(0,x) = 10 for x 4, γ(0, 2) = 19, and γ(0, 1) = 99. When the launch date is fixed and the time of minimum separation is better determined in the case 127

150 of NLTT events, one can substitute the correct first argument in place of 0. In some cases, γ may rise significantly but in others (particularly when µ t 4β) it will hardly be affected. In any event, because we are suppressing consideration of the first argument, any uncertainty in t 0 does not enter our calculation. Now we describe our method for estimating the distances to the lenses and evaluate the accuracy of these estimates. Our method has three distinct steps. First, we assign a luminosity class (type) to each star based on its position in a reduced proper-motion diagram. Second, we assign a V band luminosity L V (equivalently M V ) to each star based on its luminosity class and color. Third, we combine the L V with the measured flux from the star F V (equivalently V )to obtain a distance. We apply this method to both the ACT and NLTT catalogs. However, to calibrate and describe the method, we first apply it to Hipparcos stars with parallax errors smaller than 20%. After the method is calibrated, we use it to predict the distances to these stars and then compare the results to the measured Hipparcos parallaxes. Figure 3.2 is a reduced proper motion diagram of Hipparcos stars with parallax errors smaller than 20% (dots) and NLTT stars not present in Hipparcos (crosses). (Please note that throughout this Chapter we will use V magnitudes in Tycho system, and B V colors in Johnson system. To get Johnson V magnitude, use the transformation (ESA 1997): V J = V 0.090(B V ). Consequently 128

151 M V is in Tycho system as well.) If all stars had identical transverse speeds v, then this diagram would look exactly like a color-magnitude diagram (CMD), but with the vertical axis shifted by 5 log(v /47.4kms 1 ). This means that disk stars (i.e., white dwarfs, main-sequence stars, and giants) which have typical v 30 km s 1 are shifted upward by 1 mag, while halo stars (i.e., subdwarfs) which have typical v 240 km s 1 are shifted downward by 3.5 mag. That is, the 2 mag separation between the main sequence and the subdwarfs in a normal CMD is here augmented to 6.5 mag. (But note that in a proper motion selected sample, like that from NLTT, there is a bias which makes the mean transverse speed of disk stars several times greater than their true speed v.) We separate luminosity classes according to the bold lines shown in the diagram. Once these classes are chosen, we use color-magnitude relations for each class (white dwarfs, subdwarfs, main-sequence stars, and giants) to determine the absolute magnitude, and therefore the distance. Inevitably, stars of different class have some overlap in the reduced proper motion diagram, especially in the red end of the diagram. In those cases our classification is conservative, i.e. places a star in a class that will make it closer, and therefore producing smaller τ. Figure 3.3 compares the distances of Hipparcos stars derived from these luminosity estimates (together with the measured V mags) to the true distances based on parallax. For the typical lens distance moduli of less than 2.7 (r =35pc), 129

152 the dispersion (excluding outliers) is 0.53 mag. This is equivalent to a distance uncertainty of 28%, and an error in the estimate of τ of 63%. For distance moduli greater than 2.7, the dispersion is larger, but this is dominated by giants which are of little practical interest in the present search. We directly apply this technique to the ACT catalog for which there is generally excellent photometry from Tycho. For NLTT, generally only photographic photometry is available. Because of the large position errors in the NLTT catalog, we can search for astrometric lensing events only if we can identify the NLTT star with the corresponding object in USNO-A2.0. Thus, in all cases we have photometry from USNO-A2.0. We convert from USNO-A2.0 mags to Johnson color and Tycho V using the relations: B V = (B R) USNO, (3.5) V = R USNO (B R) USNO. (3.6) The transformations were derived by comparing USNO-A2.0 photographic magnitudes to ground-based Johnson magnitudes of some sixty faint M dwarfs and white dwarfs. Here, B USNO and R USNO are blue and red photographic magnitudes, respectively. The scatter in the predicted versus actual B V is 0.25 mag. Since the slope of the main sequence is V/ (B V ) 5, the error in distance modulus 130

153 of NLTT stars is 1.2 mag or about a factor of 1.7 in distance. This corresponds to a factor 3 error (1 σ) insim time τ. In the case of ACT and NLTT, the distance is also used to find the luminosity, that in turn (using mass-luminosity relations) determines the masses of main sequence stars and subdwarfs. For giants and white dwarfs we adopt masses of 1M and 0.6M respectively. With Hipparcos, the mass is found directly because their distances, and therefore luminosities are known from trigonometric parallax. Thus, we only need to correctly determine the luminosity type based on luminosity and color (CMD). This is fairly straightforward for giants and white dwarfs, but can be ambiguous for main sequence stars vs. subdwarfs since they occupy not too different regions of CMD. We differentiate them by their transverse velocities, calling stars with v>85 km s 1 subdwarfs. Exact classification is only possible with additional information, such as a spectrum. In any case, as noted previously, the mass determination is not critical for the estimate of τ. Next we explore the uncertainty in the predicted impact parameter. At first sight these uncertainties appear so high (in the case of NLTT events 1. 2) to make the estimate of τ impossible. For example, any source whose calculated impact parameter with respect to an NLTT lens is less than 2 might actually pass within 131

154 50 mas or even closer, thus reducing its SIM time by a factor of 1600 or more. In essence, one would seem to be forced to do follow-up observations of all encounters in this catalog having apparent impact parameters β<2 in order to find the small subset with very close encounters. In fact, the situation is not quite so severe. The size of the aperture stop for SIM has not yet been fixed, but is likely to be at least 300 mas. This is about the size of the envelope of the SIM fringe pattern (set by the 25 cm size of the mirrors). Hence, if the lens is as bright as the source then it would be difficult to obtain reliable astrometry while the source is within 300 mas of the lens. Typically, the lens will be much brighter than the source so the problem will be even more severe. For events with β<300 mas, observations can be carried out during most of the event, but must be suspended during the period of closest approach. The precision of the mass measurement will then be approximately the same as for an event with β = 300 mas. That is, there is an effective minimum impact parameter, β min = 300 mas. We account for the errors in distance and impact parameters as follows. We aim for a final catalog with τ max,3 = 100 hrs. For the Hipparcos and ACT lenses, we accept the lens distances and impact parameters at face value, but set τ max,1 = 300 hrs to allow for errors, primarily overestimation of the impact 132

155 parameter. For NLTT we set τ max,1 = 1000 hrs to allow for 1 σ photometry errors. In addition, we calculate the τ (the best-case τ) by reducing β so that β max(β 1. 8, 0 ). (3.7) We always use the reduced β to calculate the corresponding γ factorthatenters τ, but in cases when β < 300 mas, we use β = 300 mas for the value of the impact parameter, because of the discussed aperture stop. Finally, we allow all events where the lens is fainter than the source and the nominal impact parameter is β<1. 8 on the off chance that the true impact parameter is very small. It is this best-case τ on which we impose the 1000 hr limit. These three adjustments to the NLTT-based catalog mean that it will contain a large number of spurious candidates. These must be eliminated by follow-up observations to obtain better photometry (which in some cases is available from the literature) and astrometry ( 3.4.2). 133

156 Searching for the Candidate Events Although the basic strategy for searching for the candidate events is the same for all three catalogs (Hipparcos, ACT and NLTT) there are some specific details that apply to each of them. Also, there were certain problems associated with the raw lists of events produced by these catalogs. That is, each catalog s initial list had its own set of events that turned out not to be real. The catalog of sources, USNO-A2.0, is written on 11 CD-ROMs, and the sky is divided into 24 zones each corresponding to 7. 5 in declination. Each zone is written as one file. Our search program processes one zone at a time, checking every lens star that lies within that zone. First, the initial position of the lens in J coordinates is needed. In the case of Hipparcos and ACT this is straightforward as they both list coordinates in the ICRS J system, the one used by USNO-A2.0. One only needs to apply proper motion in order to change the epoch of the coordinates from and (Hipparcos and ACT, respectively) to that of the search period ( ). In the case of NLTT, the procedure is much more involved, and is described in detail We made a special effort not to search NLTT stars that were included in Hipparcos or ACT: as discussed in 3.3.2, the NLTT data are of much lower quality and would generate many spurious events that are 134

157 eliminated by the better Hipparcos and ACT data. We screen for these duplicates by looking for Hipparcos stars around NLTT positions that have similar proper motions ( µ α, µ δ < 40mas yr 1 ), and not too different magnitudes. We find 6233 matches, i.e., most of the Hipparcos stars with µ>200 mas yr 1. These matches are then flagged and skipped when identifying NLTT stars in USNO-A2.0. Also, if the match in USNO-A2.0 is associated with an ACT star, such NLTT star is also skipped. Occasionally, no match for an NLTT star is found because the input position was completely wrong [most likely a typo, since a machine-readable NLTT was produced by Optical Character Recognition (OCR)]. Identification efficiency is much worse in the south (SERC/ESO) for reasons discussed in Only 20% of NLTT stars are found within 10 of the expected position. Next, the basic search strategy for events is to produce a box, the diagonal of which represents the lens s proper motion from 2005 to 2015, the time span during which an event should take place. The size of the box is further increased by 5 years worth of proper motion (i.e, the largest possible impact parameter) to allow for events that take place near the starting and final years. We then find all the stars in USNO-A2.0 that are located within this box. A moving star, i.e. the lens, will pass by these stars, but not every encounter will produce a microlensing event. As discussed in and this depends on the physical parameters of the lens and on the brightness of the source star. Therefore, for each encounter we 135

158 calculate the required SIM time and keep only events with τ<τ max,1.inthecase of NLTT, we use the reduced impact parameter β, as described in 3.3.3, to find τ. Additionally, when searching ACT we discard encounters with stars that were labeled in USNO-A2.0 as being associated with ACT, in order to avoid finding encounters of an ACT star with itself. It might not sound logical to find an ACT star approaching its USNO-A2.0 entry in the future, but this happens with some slowly moving ACT stars because the astrometry of bright USNO-A2.0 stars is poor. A similar problem is present with bright Hipparcos stars, for which USNO-A2.0 sometimes contains multiple spurious entries. We discard these based on brightness and proximity of the Hipparcos star to the USNO-A2.0 entry at the epoch of the plate. Despite these automated rejection criteria, some events that are nothing other than the lens and its entry in USN0-A2.0, make their way into a final list. This most often happens because bright stars, having bad astrometry in USNO-A2.0, produce multiple entries if located in overlapping regions of the plates. These events are characterized by very short SIM observing times (because the source magnitude is bright). We check them by hand, by looking at the sky survey images themselves and making sure that there is only one star present. Once an event satisfying all criteria is found, the output list containing all the information about the lens, the source, and the geometry of an event is produced. 136

159 We present these results in However, the computer generated list is still far from containing only genuine events. One source of spurious entries affecting searches with Hipparcos and ACT catalogs is discussed in the preceding paragraph. Another problem is that since stars in these two catalogs are bright, their images in sky surveys have conspicuous diffraction spikes. These spikes in turn produce spurious entries in USNO-A2.0. Thus, sometimes an encounter will be reported in cases when the source is just an artifact from a diffraction spike. When we checked all of the Hipparcos and ACT events by comparing the sky survey images with USNO-A2.0 generated star charts ( we were able to identify such occurrences. Also, since the diffraction spikes run along right ascension and declination, it was always the stars that had their proper motion along these directions that turned out to produce spurious events. When it comes to NLTT, the most serious problem is with the encounters in the south, because the lens identification is often spurious. These are checked by calculating how much the lens has moved between the two plates. If that distance is less than the 2 error circle the chances are greater that the lens identification, and therefore the event, are real. Since there are not many of them, we check the south NLTT events by hand. Finally, since the NLTT position is sometimes completely off, it could lead to the wrong USNO star be identified as a match for NLTT star. Such a misidentified star might even produce an event. Since we do 137

160 not check entries in NLTT list by hand, a possibility exists that some entries might not be real. As previously discussed, we try to eliminate doing NLTT stars that are present in either the Hipparcos or ACT catalogs. However, some survive our automated procedures. Therefore we check all NLTT events up to the Hipparcos/ACT detection limit and eliminate repetitions by hand. Thus, the NLTT list should contain only stars not present in the other two catalogs Candidate Events The events produced by stars in the Hipparcos and ACT catalogs are presented in Tables Tables 3.1 and 3.2 list the properties of the lens stars, while Table 3.3 lists those of the source stars and of the events themselves. Details about specific columns are given in the table notes. The events are ordered by the required SIM time. There are 32 events taking place between years 2005 and Eight of them are found using both the Hipparcos and ACT catalogs (in which case the results presented are from the Hipparcos catalog), as indicated by the last column in Table 3.3. There was only one event (associated with the star AC368588) that was found in ACT and not in Hipparcos. However, inspection of POSS I and POSS II plates lead us to conclude that its proper motion is much smaller than that reported in ACT, and that no event will be taking place. One 138

161 would expect all events detected by Hipparcos to be found in ACT, but this not the case. This is because in many cases of high-proper motion stars, the proper motion was not listed in Tycho, and therefore it is not listed in ACT either. In other cases, ACT was missing photometry because it was not available in Tycho. These 32 events are produced by 25 different stars. Therefore, seven entries in Tables 3.1 and 3.2 are repetitions, but we keep them in order to preserve compatibility with Table 3.3, i.e., the Event #.There are some notable stars among the lenses, such as Proxima Centauri (the closest star), Barnard Star (the highest proper motion), and the bright binary 61 Cyg A/B. They, together with the only white dwarf in the list (GJ 440), undergo multiple events that will both enable a more precise mass measurement and provide a check on systematics. We classify 10 stars as subdwarfs, although some of them might be main sequence stars, and vice versa. A convenient way of presenting the types of Hipparcos stars that will undergo microlensing is given in Figure 3.4. Plotted is the classical CMD of Hipparcos catalog stars with distances known to better than 10%. Superimposed as big dots are the Hipparcos/ACT stars that produce events listed in Tables As we see, except for a single white dwarf, the rest of the stars are uniformly distributed within the faint (M V > 5) portion of the main sequence, with subdwarfs located mostly below the densest concentration of stars. 139

162 The absence of stars with M V < 5 is the result of blotting out, as discussed in Although the table includes events up to τ max = 300 hrs, they are concentrated towards shorter times. For example, 1/3 ofeventshaveτ<20 hrs, and 1/2 less than 70 hrs. In fact, when we investigate the number of events as a function of τ we see a behavior that is in line with the theoretical predictions of Gould (2000a). As an example, in Figure 3.5 we show the 8 8 field surrounding 61 Cyg A/B as it appeared in 1951 (DSS 1/POSS I) and in 1991 (DSS 2/POSS II) (upper left and lower left panels, respectively). We can see that the pair has moved some 3. 5 across the field. In a 2 2 blow-up we show the region that the pair will transverse in the period (from DSS 2/POSS II). The star chart (created from USNO-A2.0 data), corresponds to the 2 2 field and has the lensed stars labeled with the number of the corresponding event from Tables Additional features of the set of events found with Hipparcos and ACT will be discussed later in this section, together with the events from NLTT. Tables 3.4 and 3.5 contain data about the 146 events found in NLTT, ordered by their nominal SIM observing time τ. Details about the columns are given in the table notes. These tables have many more entries than the Hipparcos/ACT tables partly because of the τmax = 1000 hr limit compared to τ max = 300 hrs 140

163 for Hipparcos/ACT. In fact, there are just 34 events with τ<300 hrs. That means that if we had perfect knowledge about the NLTT stars there would be approximately 34 events in such a perfect list with τ<300 hrs, but those, of course, would not necessarily be the first 34 from our present list. However, it should be noted that out of 146 events only 8 (5%) are detected in the SERC/ESO part of USNO-A2.0 which comprises 35% of the sky. Again, the nominal SIM observing times are concentrated toward the lower values, and the trend of the number of events vs. τ basically agrees with Gould (2000a) predictions. NLTT events are produced evenly by stars that we classify as white dwarfs, subdwarfs, and late-type main-sequence stars. Such representation is not surprising having in mind that most intrinsically bright, fast-moving stars are also apparently bright and therefore already covered by Hipparcos and ACT, so the ones covered by NLTT represent a sample of relatively nearby, intrinsically faint stars. One should keep in mind that our classification is conservative as not to miss a possible candidate, in the direction that some of our white dwarfs are actually subdwarfs or main-sequence stars, and some subdwarfs are main-sequence stars. This issue can be resolved in the stage 3 of list refinement, when better photometry and astrometry is obtained, supplemented by what is known about these stars from previous studies. 141

164 Finally, both the Hipparcos/ACT and NLTT events can be investigated in the V µ plane. This allows us to see the characteristics of the catalogs and events combined. Figure 3.6 covers a wide range of visual magnitudes (2 <V <19.5) exhibited by high proper motion stars. It shows a range of proper motions from µ =0. 1yr 1 to that of Barnard s star. The two long-dashed vertical lines show the nominal limit of the Hipparcos catalog of survey stars (V = 8), and the detection limit of Hipparcos non-survey stars, Tycho, and therefore of ACT (V = 12). The horizontal long-dashed line is the lower limit of µ =0. 18 yr 1 for the NLTT. The lenses found only in Hipparcos are designated with, and those found in both Hipparcos and ACT look like asterisks. In order to present a more realistic relative number of NLTT lenses, we plot only those with nominal τ<300 hrs (circles). As discussed in 3.3.2, the blotting out of images in USNO-A2.0 limits our ability to find events moving slower than a specific value for the given lens magnitude. We plot this function θ(v ) as a short-dashed line. Because of different epochs of POSS I and SERC/ESO, these cutoffs will be different in the two parts of the sky. The lower line corresponds to north (POSS I). The region below these two lines is therefore excluded, and we can see that none of the lens stars is found there. The exclusion due to blot-out approximately follows the diagonal line corresponding toastarwithm V =6,v = 75km s 1. This shows that our survey cannot find disk-star lenses with M V < 6, unless they are moving faster than average. Indeed, as shown in Figure 3.4, we find no lenses with M V < 5. However, halo stars with 142

165 M V =6,v = 240km s 1 (upper diagonal line), are comfortably away from this limit Confirmation of Candidate Events Refining Estimates Using 2MASS Currently 47% of the sky has been released in the 2MASS infrared survey. These data, and more specifically, its Point Source Catalog, can be used in two ways to refine the selection procedure outlined in 3.3. First, as shown in 2.5.2, 2MASS can be combined with USNO-A to produce optical-infrared reduced proper motion diagram of NLTT stars, allowing more secure classification, and therefore the correct assignment of luminosity for a given color. Also, with a wider baseline for color, the distance estimates of NLTT stars becomes much more secure (σ d /d 20%), especially so for late dwarfs for which the optical color becomes degenerate with absolute magnitude. Second, the benefit of using 2MASS, where available, is its 2000 epoch positions, given with an adequate precision of 130 mas. This allows for a manifold refinement of the impact parameter of NLTT lensing candidates by fixing the position at the current epoch, and by refining the proper motion vector ( 2.4.2). 143

166 Taken together, there are two ways we can put 2MASS to use. First, confirm the quality of events already selected in 3.3, and discard those that do not pass 2MASS criteria, thus reducing the observational burden needed to confirm these events by 50 75%. Alternatively, use distances and proper motion vectors derived with 2MASS to predict additional events, but this time allowing for more than 1σ errors in astrometry. Both of these strategies where used to produce the list of events for the observing campaign Observing Campaign The observation of microlensing candidates was performed on four observing runs March, June and December 2001, and October Observations were carried out for a total of 8 photometric nights on a 2.4-m Hiltner telescope at the MDM Observatory at Kitt Peak, Arizona. The detector used was 2k 2k CCD Echelle, although due to the small lens-source separation, and in order to expedite the observing, only the central pixels where read out. On the first two runs the observations where performed in BV I filters, but the B filter was excluded in the subsequent runs since it offered little additional information. Exposures where adjusted not to saturate the lens star (which is usually the brighter of the two stars), or not to exceed 30 s, whichever is shorter. A number of photometric standards was observed each night. 144

167 After the reduction of the CCD images and calibration of photometric standards, each image was checked against a finder chart in order to identify the candidate lens-source pair, and their photometry and relative astrometry where measured. Fields with good seeing and a sufficient number of stars where used to establish the orientation and scale of the CCD frame by fitting the chip coordinates to celestial coordinates of the stars (taken from USNO-A2). This was done for each night separately. In a certain number of cases ( 10%) no event was taking place. This was either due to incorrect identification of NLTT star, or in some more bizarre instances when the lens and the source actually belonged to a CPM binary, the separation vector of which happened to be parallel with the proper motion vector. By measuring the separation vector today, and comparing it with the separation at POSS epoch, we obtained precise relative proper motion and therefore very accurate estimates of the projected impact parameter and the time of the event. The V I color was used to determine accurate photometric distance after the star was classified as being WD, SD, or MS star. This finally allowed a new estimate of SIM observing time τ. More than 400 candidate events where observed, including the Hipparcos events where we wanted to confirm the assumed stationarity of the source. At the 145

168 moment 1/2 of the observations have been analyzed. Hipparcos events that were considered good (Tables ) were almost always confirmed. As expected, the estimates of τ for NLTT events in some cases differ substantially from those given in Table Discussion and Conclusion If precise stellar masses are to be obtained using astrometric microlensing with SIM, there is a necessity of finding microlensing candidates, as soon as possible, since the separation between the lens and the source is steadily getting closer, and it will become harder to produce a valid estimate of the likelihood of an event the longer we wait. With the currently available catalogs, we were able to produce a fairly reliable list of candidates from Hipparcos and ACT catalogs. Obtaining a list of similar quality of NLTT candidates required additional astrometric and photometric observations of the candidates in our list. Another issue is getting more candidates. This can be assured with new catalogs of proper motions, having lower proper motion cutoffs and going to fainter magnitudes. The biggest such projects are USNO-B and GSC II which should list the proper motions of basically all the stars in POSS I/SERC/ESO. Others are discussed in 2.1. Having a lower proper motion limit is particularly 146

169 important in V > 12 range, where the blotting of stellar images no longer presents a limitation (at least not in the northern hemisphere), and where NLTT goes only to µ = 180 mas yr 1. USNO-B will also push the detection limit 1 mag fainter compared to NLTT. Since in USNO-B all the stars will have proper motions, the uncertainty of the source star s position will also be reduced. There is also an issue of NLTT incompleteness at faint magnitudes, as discussed in This is even more severe in the south and close to the galactic plane, where the incompleteness sets already at V 14. With USNO-B and GSC II this matter will most probably be resolved. 147

170 Table 3.1. Hipparcos and ACT events - lens star properties (astrometry and photometry) Event HIP # RA DEC V B V Other name # h m s Cyg A HD GJ V774 Her GJ Cyg B HD Ross GJ Cyg A Proxima Cen Ross GJ 440 (continued) 148

171 Table 3.1 Continued Event HIP # RA DEC V B V Other name # h m s Barnard s Star HD GJ V1513 Cyg GJ HD HD HD BD Proxima Cen Proxima Cen Cyg B AX Mic (continued) 149

172 Table 3.1 Continued Event HIP # RA DEC V B V Other name # h m s BD Cyg A Barnard s Star HD SAO HD Rows are ordered by increasing τ (see Table 3). HIP # is the Hipparcos catalog number. Right ascension and declination are taken from Hipparcos catalog. Equinox J2000, epoch Visual magnitude is in Tycho system if available, or Johnson (italics). Johnson colors are from Hipparcos catalog as well. Multiple entries arise from the fact that a single lens can produce multiple events. 150

173 Table 3.2. Hipparcos and ACT events - lens star properties (distance, kinematic and physical properties) Event µ p.a. vrad MV r M Class Sp # / yr km s 1 pc M SD K5V MS G8V WD DC: MS K4V MS M SD K7V MS K MS M: MS K SD K5V MS M5Ve SD K WD DC: (continued) 151

174 Table 3.2 Continued Event µ p.a. vrad MV r M Class Sp # / yr km s 1 pc M SD sdm SD K0V: MS M SD M MS M SD G MS K3Vvar MS K0V MS MS M5Ve MS M5Ve SD K7V MS M1/M2V (continued) 152

175 Table 3.2 Continued Event µ p.a. vrad MV r M Class Sp # / yr km s 1 pc M SD K SD K5V SD sdm SD K0V SD M MS M1V Proper motions are given as intensity and position angle (from Hipparcos). Radial velocities are taken from SIMBAD. Absolute magnitude is in the same system as the corresponding visual magnitude. Distances come from Hipparcos trigonometric parallaxes. For mass estimate and class determination see (MS - main sequence star, SD - subdwarf, WD - white dwarf). Spectral class is taken from Hipparcos catalog. 153

176 Table 3.3. Hipparcos and ACT events - source star and event properties Event RA DEC V B V τ d2000 t0 β # h m s hr yr mas H H/A H H/A H H H/A H H H H H H (continued) 154

177 Table 3.3 Continued Event RA DEC V B V τ d2000 t0 β # h m s hr yr mas H H H H H/A H/A H H/A H/A H H H H (continued) 155

178 Table 3.3 Continued Event RA DEC V B V τ d2000 t0 β # h m s hr yr mas H/A H H H H H Numeration follows the numbers in tables 1 and 2. Source star s right ascension and declination are from USNO-A2.0, at plate epoch, equinox J2000. Visual magnitude is in Tycho, and color in Johnson system, as calibrated from photographic magnitudes (see 3.3.3). Event is described by τ (SIM observing time), d2000 lens-source separation in year , t0 time of closest approach and β, the minimum impact parameter. If β<300 mas, τ is calculated using β = 300 mas. The last column designates whether the event was detected only using the Hipparcos catalog (H), or in both the Hipparcos and the ACT catalogs (H/A). 156

179 Table 3.4. NLTT events - lens star properties Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M MS MS MS WD SD WD MS 8 R WD WD SD 11 R WD * WD 13 R MS WD WD (cnt.) 157

180 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M WD WD WD MS SD WD MS * SD 24 * MS 25 W MS MS MS 28 R MS 29 R MS WD (cnt.) 158

181 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M SD WD MS MS WD WD WD 38 W WD MS SD MS WD MS SD 45 St2051B WD (cnt.) 159

182 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M MS WD SD MS SD WD 52 W 359* MS MS 54 T MS SD 56 15:4074B SD SD SD WD 60 R MS (cnt.) 160

183 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M MS MS SD 64 53:2911* SD MS WD WD WD * WD SD WD MS 73 R MS MS WD (cnt.) 161

184 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M WD MS MS WD MS WD SD 83 L WD SD SD 86 * SD MS 88 R SD 89 * SD WD (cnt.) 162

185 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M * SD SD SD WD 95 R MS WD MS * WD WD MS SD MS WD WD SD (cnt.) 163

186 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M SD SD MS SD MS WD MS WD SD WD SD 117-3: SD WD MS * SD (cnt.) 164

187 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M SD 122 R SD MS SD WD MS MS MS WD MS MS SD SD MS MS (cnt.) 165

188 Table 3.4 Continued Name RA DEC epoch V B-V µ p.a. MV r M Cl. # h m s / yr pc M SD SD WD WD SD SD SD SD MS SD WD Events are given in the order of increasing τ (see Table 5). Names are taken from NLTT. Right ascension and declination come from USNO-A2.0. Equinox J2000, epoch is that of the plate and is given in a separate column. Visual magnitude is in Tycho system, transformed from USNO-A2.0 photographic magnitudes. Color is in Johnson system, also transformed from photographic magnitudes. Proper motions are from NLTT, but in equinox J2000. For distance, physical parameters and class, see (MS - main sequence star, SD - subdwarf, WD - white dwarf). 166

189 Table 3.5. NLTT - source star and event properties Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 167

190 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 168

191 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 169

192 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 170

193 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 171

194 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 172

195 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 173

196 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas (continued) 174

197 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas > > > > > > (continued) 175

198 Table 3.5 Continued Event RA DEC V B V τ τ d2000 t0 β # h m s hr hr yr mas > > > > > > > > > > > Numeration follows the numbers in table 4. Source star s right ascension and declination are at plate epoch, equinox J2000. Visual magnitude is in Tycho, and color in Johnson system (see 3.3.3). Event is described by τ (SIM observing time), τ (SIM observing time with reduced impact parameter), d2000 lens-source separation in year , t0 time of closest approach and β, the impact parameter. 176

199 0 log M M bol Fig Mass-luminosity relation for main sequence stars. The bold line shows the theoretical M L relation for solar-metallicity stars, while the thin line shows the relation for metal-poor star with [Fe/H] = 1. The current mass measurements with their error bars are shown as circles (astrometric and spectroscopic binaries) and as triangles (eclipsing binaries). 177

200 Fig Reduced proper motion diagram for Hipparcos and NLTT stars. For Hipparcos, only stars with σ π /π < 20% are plotted (dots). From NLTT, only stars that are not in Hipparcos are plotted (crosses). In both cases, every 10th star is plotted. For Hipparcos data, abscissa is B V color as usually determined from Tycho photometry but sometimes from ground-based photometry, while for NLTT it is calibrated from photographic magnitudes, and then randomized to correctly show regions of different density. If all stars had the same transverse speed, this figure would look like an ordinary CMD. Solid lines indicate the boundaries of our assignment of stars to classes: red giants are in the upper right corner, white dwarfs in the lower part, and subdwarfs between white dwarfs and the main sequence. 178

201 Fig Distance-modulus errors versus distance modulus for the Hipparcos stars shown in Fig The distance-modulus of each star is estimated by first classifying it according to the bold-line divisions in Fig. 3.2 and then assigning it an absolute magnitude using color-magnitude relations appropriate for each class. The distancemodulus error is then the difference between this estimate and the value based on the measured trigonometric parallax. For distance moduli less than 2.7 (35 pc), the typical errors are only 0.53 mag. Errors are larger for more distant stars, but these are dominated by giants which are not relevant in the present study. 179

202 Fig A color-magnitude diagram of Hipparcos stars with distances measured to better than 10%. The event-producing stars (lenses) from the Hipparcos and ACT catalogs are superimposed as filled dots, some of which are labeled. 180

203 Fig fields around 61 Cyg A/B in 1951 (upper left panel) and 1991 (lower left panel). Shown magnified is a 2 2 region where events will take place during period. The chart corresponds to the 2 2 field with source stars labeled with the numbers corresponding to Event # in Tables Events 6 and 25 are produced by 61 Cyg B, and the other three by 61 Cyg A. 181