PASJ: Publ. Astron. Soc. Japan , 1–??,

\begin{matrix}c \\ ◯ \end{matrix} 2008. Astronomical Society of Japan.

Proper motions with Subaru I. Methods and a first sample in the Subaru Deep Field

Michael W. Richmond

Physics Department, Rochester Institute of Technology, Rochester, NY 14623, USA mwrsps@rit.edu

Tomoki Morokuma

Optical and Infrared Astronomy Division, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan tomoki.morokuma@nao.ac.jp

Mamoru Doi

Institute of Astronomy, Graduate School of Science, University of Tokyo, 2-21-1, Osawa, Mitaka, Tokyo 181-0015, Japan doi@ioa.s.u-tokyo.ac.jp

Yutaka Komiyama

Optical and Infrared Astronomy Division, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan komiyama@subaru.naoj.org

Naoki Yasuda

Institute for Cosmic Ray Research, University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa, Chiba 277-8582, Japan yasuda@icrr.u-tokyo.ac.jp

Sadanori Okamura

Department of Astronomy and Research Center for the Early Universe, School of Science, University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan okamura@astron.s.u-tokyo.ac.jp

and Avishay Gal-Yam

Benoziyo Center for Astrophysics, Weizmann Institute of Science, 76100 Rehovot, Israel avishay.gal-yam@weizmann.ac.il

(Received ; accepted )

Abstract

We search for stars with proper motions in a set of twenty deep Subaru images, covering about 0.28 square degrees to a depth of i′ ≃ 25, taken over a span of six years. In this paper, we describe in detail our reduction and techniques to identify moving objects. We present a first sample of 99 stars with motions of high significance, and discuss briefly the populations from which they are likely drawn. Based on photometry and motions alone, we expect that 9 of the candidates may be white dwarfs. We also find a group of stars which may be extremely metal-poor subdwarfs in the halo.

Key words: stars: kinematics — Galaxy: kinematics and dynamics — Galaxy: structure

1. Introduction

The basic structure of our Milky Way galaxy seems clear: a thin disk of young stars, gas and dust circles the center quietly, immersed within a thicker disk of older stars. Both disks sit inside a nearly spherical halo of very old, metal-poor stars which do not share the overall rotation of the disks. Surrounding everything is an extended distribution of dark matter. Our knowledge of the details within this big picture, on the other hand, is not so clear. Recent large-scale projects, such as the Sloan Digital Sky Survey, have measured the properties of high-luminosity stars throughout the halo (see, for example, Yanny et al. 2000, and Juric et al. 2008), while the rapid development of infrared detectors has allowed projects such as the Two Micron All Sky Survey (Skrutskie et al. 2006) and Spitzer Space Telescope (Patel & Spath 2004) to pierce the dusty disks and measure the properties of their stars. Nonetheless, some portions of the Milky Way remain largely unexplored.

In particular, we know little of the low-mass, low-luminosity stars of the halo. The white dwarfs and metal-poor subdwarfs of the halo glow so faintly, from so great a distance, that they are rarely seen and more rarely recognized. As a recent review (Reid 2005) points out, however, these shy and elusive stars may dominate the microlensing events observed towards the Galactic bulge and the Magellanic Clouds.

There are two ways to search for these stars: cover a very large area on the sky to a shallow depth, or use a “pencilbeam” survey to examine a tiny region much more deeply.

The first approach (see, for example, Oppenheimer et al. 2001 and Carollo et al. 2006) will find objects in many directions, but only out to a small distance from the Sun; the second approach (see, for example, Mendez 2002, Nelson et al. 2002, and Kalirai et al. 2004) probes farther into the halo, but only in a specific direction. One way to characterize surveys is to combine their area with the distance out to which they would detect some specific star to generate an “effective volume” for that type of star. In Table 1, we compare the projects mentioned above by this metric, using a star of absolute magnitude M_{V} = 16.5, appropriate for a cool white dwarf. We assumed a color (V − R) = 0.5 to convert limiting magnitudes for Rbased surveys to V -band.

Our project could be described as a “pencil-beam” survey, but it uses a very thick pencil. We examine images in the area of the Subaru Deep Field (SDF) (Kashikawa et al. 2004) acquired over a period of six years to search for moving objects. These images were acquired primarily to study high-redshift galaxies (Nagao et al. 2004, Shimasaku et al. 2006), but have also been used to find high-redshift supernovae (Poznanski et al. 2007). The images are nearly as deep as those in some HST-based surveys, but cover a significantly wider area, yielding a large effective volume. We can refer to the SDF catalogs compiled by Kashikawa et al. (2004) and Richmond (2005) for information on our candidates in multiple passbands (B, V, R_{c}, i′ and z′). Unlike most other pencil-beam surveys, we have measurements at many epochs: our dataset contains images taken on 20 nights. We can therefore measure the proper motion of our candidates very well, and place strong constraints on the uncertainties in our measurements.

This paper is the first in a series on proper motions in several small fields studied with Subaru. We will concentrate on techniques, leaving detailed analysis of the results for later papers. In Section 2, we describe the observations, their reductions, and the combination of individual frames into a single combined image for each night. In Section 3, we walk through our procedure for finding moving objects, and discuss our criteria for separating good candidates from bogus ones; we end up with a first sample of stars which have very well measured proper motions. In Section 4, we compute the reduced proper motions for objects in this sample, and compare their properties to those of objects drawn from a simulated survey of our field. Finally, in Section 5, we list our plans for future work on this dataset, and in other fields with multiple epochs of deep Subaru imaging.

Astronomers at the Observatoire de Besançon have created a model of the stellar populations in the Milky Way (Robin et al. 2003) with a very convenient web-based interface^{1}. The model consists of four populations of stars – thin disk, thick disk, spheroid, outer bulge (the innermost portions of the Milky Way are poorly constrained) – plus white dwarfs added to each component separately. The parameters of each component are adjusted to produce the best fit to the observed stellar populations and their dynamics. Recent work by Ibata et al. (2007) finds that the Besançon model does a very good job of reproducing observed star counts in two of three deep fields down to i_{0} = 24. Those authors criticized the Besançon populations for being too sharply defined, forcing them to smooth the model colors by small amounts (∼ 0.10 mag) in order to match observed color-magnitude diagrams. However, since our main concern is to classify objects very broadly using a mixture of kinematics, magnitudes and colors, we will adopt the Besançon model and use it as a reference throughout this paper to help us interpret properties of our sample.

2. Observations

The SDF is a region at high galactic latitude (l = 37_{.}^{∘}6,b = +82_{.}^{∘}6) roughly half a degree on a side. Kashikawa et al. (2004) describe very deep optical images taken with the Subaru 8.2-meter telescope and Suprime-Cam camera (Miyazaki et al. 2002). We investigated this region using a set of i′-band images with shorter exposure times. Table 2 lists the date for all nights used in our analysis. Note that our images taken on 2003 April 30 had a shorter exposure time than the rest; since these images also had some of the worst seeing, we gave those measurements very little weight in the final proper motion calculations. We split the images taken on the night of 2006 May 3 into two sets and treated each independently, as if taken on different nights. Since the data taken on 2007 Feb 15 had the best seeing and the largest number of detected objects, we adopted it as the fiducial set for matching (see Section 3).

During each night of observing, we took a series of short (typically 180-second to 360-second) exposures, shifting the telescope position slightly to fill in small gaps between the ten CCDs on the focal plane. Using the SDFRED package (Ouchi et al. 2004) and NEKO software (Yagi et al. 2002), we followed the procedures described in section 4 of Kashikawa et al. (2004) to turn all the raw frames taken during the night into a single, large mosaic. Briefly, we cleaned the raw images by subtracting a bias deduced from the overscan regions and dividing by a normalized flatfield frame made from a median of many night-time target images. Using the parameters derived in Miyazaki et al. (2002), we corrected for optical distortions in the focal plane. Images from all chips were convolved to form a uniform point-spread function (PSF) across the entire array. We determined a sky background by calculating the local sky at a series of grid points spaced at intervals of roughly 51 arcseconds and using bi-linear interpolation between the grid points; we then subtracted this sky background from each image. We used stars shared by adjacent CCDs to determine the weights to use when combining data from individual images to make the final mosaic. The result for each night is one (or, in the case of 2006 May 3, two) large image covering the entire SDF.

The quality of final combined images varied from night to night. The Full Width at Half Maximum (FWHM) ranged from 0.′′75 to 1.′′30, but, since the plate scale was 0.′′202 per pixel, no data was undersampled. The limiting magnitude also varied with the conditions, but was usually i′ ∼ 25.5.

3. Searching for candidates with proper motion

Selecting objects with proper motions from a set of images requires several steps: finding and measuring the properties of stars in individual images, matching stars found at differ-

1 http://bison.obs-besancon.fr/modele

Table 1. Effective volumes, for M_{V} = +16.5

Survey  Area (sq.deg.) limiting mag V volume (pc^{3})
Oppenheimer et al. 4165  19.8  80000
Carollo et al.  1150  20  15000
Nelson et al.  0.021  26.5  2100
Mendez  0.0013  26.0  64
Kalirai et al.  0.0031  29  9800
this work  0.28  26  14000

Table 2. Observations of the SDF in i′-band

UT Date  Julian Date - 2,450,000 Exptime (seconds)
2001 April 25  2024.34  3600
2001 May 20  2049.44  3240
2002 April 12  2376.44  9780
2002 May 7  2401.52  5670
2003 April 1  2730.43  12330
2003 April 3  2732.29  2730
2003 April 25  2754.42  4800
2003 April 26  2755.36  4680
2003 April 30  2759.60  964
2003 May 1  2760.39  4583
2005 March 5  3434.54  5100
2005 March 6  3435.54  5400
2006 May 3(a)  3858.41  3000
2006 May 3(b)  3858.52  2400
2007 February 13  4144.59  2700
2007 February 14  4145.59  4200
2007 February 15  4146.59  4500
2007 February 16  4147.60  3600
2007 May 16  4236.32  4180
2007 May 17  4237.27  3780

ent epochs, computing the change in position of each star over time, and deciding which changes are due to real movement. We will now describe these steps in detail.

In order to find star-like objects in each image, we used the “stars” program within the XVista package (Treffers & Richmond 1989)^{2}. The position of each object was calculated by fitting a gaussian to the background-subtracted, intensityweighted marginal sums in each direction (see Stone (1989) for details).

It is not crucial to separate stars from galaxies at this early stage, since we will later discard any objects which do not move significantly; therefore, we accepted any object with a sharp core, 0.′′6 < FWHM < 1.′′4, as a “star.” The number of “stars” found each night ranged from about 20,000 to about 100,000, depending on the exposure time and seeing.

The Suprime-Cam field is wide enough that even small uncorrected distortions near the edge of the field might move the apparent position of a star enough from one epoch to the next to hide real, but small, proper motions. In order to reduce any residual distortions, we broke the field into smaller units we will call “sectors.” Each sector is a square 1000 × 1000 pixels, or 202×202 arcseconds, on a side. We allowed a small overlap of 10 arcseconds between adjacent sectors so that stars near the edges would not be missed.

We designated one epoch, 2007 February 15, as “fiducial,” to serve as the basis of our matching procedure. For every other image, we used the match package (Droege et al. 2006)^{3} to match the objects in each sector to objects in the corresponding sector of the fiducial image. In order to count as an initial match to the fiducial image, a star had to lie within 1.′′0 of the position of an object in the fiducial frame; we imposed this limit in order to avoid spurious matches between unrelated objects. Given the six-year span of our survey, this places an upper limit of about 0.′′17 per year on our proper motion candidates. We may increase this limit to look for fast-moving objects in the future. We will demonstrate later (see Figure 6) that this requirement does not have a strong effect on the results. There were typically three hundred to eight hundred pairs of matching items found within each sector. We transformed the (pixel) coordinates of each star to the (pixel) coordinates of the fiducial image in the following iterative manner. First, we used all the matched pairs in the sector to find the coefficients of a linear transformation

x′ = A + Bx + Cy  (1)
y′ = D + Ex + F y  (2)

2 http://spiff.rit.edu/tass/xvista

3 http://spiff.rit.edu/match

via a least-squares technique. Next, we computed the residuals between the positions of the members of each pair in the fiducial coordinate system. We discarded pairs with large residuals; specifically, any pair with a residual more than 10 times the 35th percentile. We then went back to compute new coefficients of the linear transformation with the surviving pairs. We repeated this procedure three times in each sector. Ignoring a few sectors with very few objects, the mean residual difference in position for surviving items matched to the fiducial frame was 0.′′071. However, most of the objects contributing to this residual, like most of the objects in each image, are faint, and some of the matches are spurious. The uncertainties in the positions of bright objects are considerably smaller, as we will show below.

We performed trials using a cubic transformation between the two coordinate systems, but found that the residuals were not significantly smaller than those based on a linear transformation.

The final steps in our matching procedure were to discard duplicate entries for objects in the overlapping areas between sectors, and to discard any objects which appeared in fewer than five epochs. The result was a set of positions in the fiducial coordinate system for objects appearing in at least five epochs. In order to estimate the uncertainty in the calculated positions, we computed the mean position of each objects in each coordinate (row and col) and its standard deviation; we then discarded measurements more than two standard deviations from the mean and recalculated mean and standard deviation. As shown in the first two rows of Table 3, the typical clipped standard deviation rose from 0.′′007 for bright, unsaturated objects to 0.′′047 for faint objects.

In order to create a sample of objects for which proper motions could be measured accurately, we selected all objects which appeared in the fiducial image and at least four others. A total of 79605 objects satisfied this requirement. Faint objects were less likely to be selected, since they might not be detected on nights with poor seeing. In order to check the completeness of this sample as a function of magnitude, we inserted a set of 1000 artificial stars with magnitudes ranging from 21 < i′ < 27 into the images. We then re-analyzed the entire set of images as before. Figure 1 shows the fraction of artificial stars which were detected and placed into the sample for further study. Since the fraction falls to 50% at i′ ≃ 25.5, we estimate that our search may be considered complete to that magnitude.

We subjected this sample to a round of tests. For each coordinate, row and column, we made a linear fit to position as a function of Julian Date. Our fitting routine, following Press et al. (1992), provides values for the the slope b of this line, the 95 percent confidence interval ci in the value of the slope, and the scatter s_{x} around the line. The scatter is another estimate of the one-dimensional uncertainty in the position of a single measurement; we show its values in the lower rows of Table 3.

In order to verify that our fitting method yields both the correct motion and an appropriate uncertainty, we ran a Monte Carlo simulation. For each integer magnitude between 21 < i′ < 25, and for each value of 1-D annual proper motion μ = 0.′′01,0.′′02,...,0.′′20, we created 100 artificial stars. For

Fig. 1. Fraction of artificial stars added to the images which were detected and matched in at least 5 epochs.

each star, we drew 15 epochs randomly from our list of observations (see Table 2), and computed a set of positions, using the true proper motion plus some random error in each direction drawn from a gaussian distribution consistent with our measurements of s_{x} for the given magnitude. We then submitted this list of simulated positions to our fitting routines, and compared their results to the true proper motions. We found that over this entire range of magnitudes and motions, our estimates for the proper motion and its uncertainty were accurate.

Next, we computed a significance of the slope for each coordinate:

S_{row} ≡ \frac{b_{row}}{ci_{row}}  (3)
S_{col} ≡ \frac{b_{col}}{ci_{col}}  (4)

Choosing objects based on the significance of their motion in one direction alone would discriminate against objects moving diagonally across the CCD, which was aligned with the equatorial coordinate system. Therefore, we combined the significance values to create an unbiased measure of motion, S_{tot} = \sqrt{S_{row}^{2} + S_{col}^{2}}.

We expect that real proper motions should show an asymmetry, due to the relative motions around the galactic center of the Sun and the stars in the SDF, while spurious motions due to random errors in position measurements should be the same in all directions. In the upper panel of Figure 2, we plot the observed motions of objects with motions of low significance; they are distributed around zero with circular symmetry. On the other hand, objects with highly significant motions (shown in the lower panel of Figure 2) are biased towards the south-east. The observed asymmetry matches that of the stars in a simulation made with the Besançon model (the motions of which we have scaled appropriately).

For the sample discussed below, we selected objects with S_{tot} ≥ 5.0. Note that since our definition of S is based on a 95-percent confidence interval, corresponding to two standard deviations for a normal distribution, our criterion could be described as “motion at the 10-sigma level.” Selecting objects based on the S_{tot} statistic introduces a bias against objects with

Table 3. Estimates of uncertainty in position (arcsec) as function of i′-band mag

Sample, method  direction 19 − 20 20 − 21 21 − 22 22 − 23 23 − 24 24 − 25 25 − 26
All objects, clipped  row  0.010  0.006  0.006  0.007  0.012  0.028  0.047
stdev from mean pos  col  0.011  0.007  0.007  0.008  0.013  0.028  0.047
Moving candidates,  row  0.007  0.007  0.007  0.009  0.022  0.036  0.052
scatter from fit  col  0.008  0.008  0.009  0.011  0.023  0.036  0.052

Fig. 2. Proper motions of objects with motions of small significance (top panel) and large significance (large circles in the bottom panel).

Fig. 3. Completeness test of the proper-motion sample using artificial stars.

small proper motions. We investigated the nature of this bias by adding artificial stars with a range of proper motions into our images, analyzing the images as before, and comparing the output properties of the artificial stars to their input values. In Figure 3, we show the fraction of artificial stars which had measured motions of high enough significance to be included in our proper motion sample. For bright stars, the fraction drops to 50% at a total proper motion of about μ = 0.′′025 per year.

We found that 110 objects passed this test. However, upon visually inspecting each candidate, we discovered that in five cases, the motions were due to a blend of two nearby stars, or a star mixed with the light of a background galaxy. That left a set of 105 candidates with real motions at a high significance. The median number of epochs of measurement for these objects was 19, and only 2 stars had fewer than 15 epochs. We show an example of the motions for one of these candidates in Figure 4.

How accurate are the derived motions? Using our set of artificial stars again, we computed a fractional error E based on the one-dimensional motion of stars in row and column directions separately.

E ≡ \frac{(measured μ) − (input μ)}{|input μ| + Q} (5)

We included a constant Q = 0.′′001 per year to prevent division by zero. Figure 5 shows the median value of E as a function of input proper motion for stars of different magnitudes. The fractional error reaches 10% for proper motions of about μ = 0.′′025 per year.

Let us turn back to the real stars in the SDF. Figure 6 shows that the distribution of proper motions among stars in our sam-

Fig. 4. An example of the motions for one of the candidates with high significance.

Fig. 5. Fractional errors in derived one-dimensional proper motions using artificial stars.

Fig. 6. Distribution of proper motions for candidates with high significance.

ple has a peak at μ = 0.′′025 per year, which is (not coincidentally) the point at which the efficiency of detecting motion falls to 50%. The largest motions we found are about 0.′′09 per year, which is far less than the limit of 0.′′17 per year set by our matching procedure. We conclude that our matching requirement – that each measurement lie within 1.′′0 of its match in the fiducial epoch – does not have a strong effect on the resulting proper motions.

Some of the analysis described below requires the color of an object, in order to distinguish different types of star. We chose the (V − I) color for several reasons: it samples a wide range of wavelengths, avoids B-band measurements which are hard to make for cool stars, is often used in studies of galactic structure, and is commonly tabulated in models of stellar properties. Since we used i′-band images to search for motions, all the candidates had good i′-band magnitudes; we will convert them to the standard Cousins I system in the next paragraph. However, many of the candidates grow faint in images taken at shorter wavelengths. We inspected each candidate in deep SDF images (Kashikawa et al. 2004) taken in B, V and R_{C} passbands, and compared its appearance in those images to the B, V and R_{C} magnitudes listed for each object in the SDF catalogs. In six cases, the V -band measurement was clearly incorrect, sometimes due to confusion with a brighter object nearby; the number of improper magnitudes was much larger in B-band. Removing these six objects from our sample, we are left with a set of 99 stars which have well measured proper motions and good magnitudes in V, R_{C}, i′ and z′. We call this our “first sample.” We list these candidates in Table 4.

Before we can compare our measurements to models of galactic structure, we need to convert the Suprime-Cam i′ magnitudes, which are calibrated on the AB system ( Fukugita et al. 1996; Miyazaki et al. 2002; Kashikawa et al. 2004), to I magnitudes, which are on the standard Johnson-Cousins system. We used synthetic photometry to find the relationship between the Suprime-Cam (V_{s} − i′) and Johnson-Cousins (V − I), taking bandpasses from Miyazaki et al. (2002) and Bessell (1990), respectively. We selected main sequence stars, O5V to M6V, from the library of Pickles (1998), stars ranging in metallicity −2 ≤ [Fe/H] ≤ 0 from models of Lejeune et al.

(1997), and flux-calibrated spectra of white dwarfs observed by the SDSS (Adelman-McCarthy et al. 2008). We convolved each spectrum with the Suprime-Cam passbands and with the Johnson-Cousins passbands to compute synthetic magnitudes, and used the spectrum of Vega from Bohlin & Gilliland (2004) to set the zeropoints to the values given in Fukugita et al. (1996). We found that the following linear relationship fit the data well, yielding a scatter of less than 0.03 mag across the range of colors −0.3 < (V − I) < 3.5:

(V − I) = 0.391 + 1.1145(V_{s} − i′) (6)

We use this equation to convert the observed colors for stars in the SDF to Johnson-Cousins (V − I) when comparing our results to stellar models.

4. Simple analysis of the first sample

We begin with the Besançon model. We generated 10 simulated catalogs of objects in the area of the SDF, using the parameters found by Robin et al. (2003) and including stars down to an apparent magnitude of V = 30. We applied cuts to the synthetic catalogs to match the combined limits of the i′-band proper motion images and the SDF catalogs.

V ≤ 26.0  (7)
I ≤ 25.4  (8)
0.′′014 ≤ μ ≤ 0.′′17  (9)

The result should be a set of stars similar to those in the actual SDF, though ten times more numerous. The large size of this synthetic sample will make it easier to delineate sparsely populated regions in the reduced proper motion diagram, to which we now turn.

Reduced proper motion was introduced by Luyten (1922) as a way to separate stars of different luminosities using only the observable apparent magnitude, m, and proper motion, μ, in units of arcseconds per year. We will base our reduced proper motion on V -band magnitudes, so that

H_{V} = m_{V} + 5log(μ) + 5 (10)

It is also possible to express this quantity in terms of a star’s absolute magnitude, M, and tangential velocity, v_{t}, expressed in units of km/s,

H_{V} = M_{V} + 5log(v_{t}) − 3.378 (11)

Using this version of the formula, we compute H_{V} for stars in the simulated catalogs produced from the Besançon model. Figure 7 shows the reduced proper motion as a function of (V − I) color. We assigned objects in the simulation to three populations based on their metallicity and the component of their space velocity in the direction of galactic rotation, which we denote as vgr to avoid confusion with the passband V.

• if vgr < −130 km/s and [F e/H] < −1.20, we assign the star to the halo

• if vgr > −60 km/s and [F e/H] > −0.50, we assign the star to the thin disk

• otherwise, we assign the star to the thick disk Stars from different populations appear in distinct regions in this diagram. We have drawn rough outlines by hand to aid the reader in recognizing the populations.

Note that there is a clear “red edge” in the distribution of WDs, at a color of (V −I)∼1.4. Theoretical models of cooling WDs (Richer et al. 2000; Chabrier et al. 2000) indicate that at an age of about 10 Gyr and a temperature of T_{eff} ∼ 5000 K, an increase in opacity due to molecular hydrogen causes the (V − I) color to shift back to the blue as the star continues to cool. WDs with atmospheres dominated by other elements, such as helium or carbon, would continue to grow redder as they cool. Objects near the bottom of the WD region are likely to be members of the halo.

In Figure 8, we present the reduced proper motions for the real stars in our first sample. We must switch to the first form of reduced proper motion, Equation 7, to compute H_{V} for the observed stars. To facilitate comparison with the Besançon model, we include the hand-drawn regions from Figure 7 as well as all objects from the simulated catalogs as tiny points. Note that the saturation of very bright stars V < ∼ 20 in the Subaru images, plus our limited ability to measure proper motions μ < ∼ 0.′′02 per year, combine to eliminate any candidates with reduced proper motions H < ∼ 16.5. In the discussion which follows, please recall that the boundaries of the regions drawn in the diagram are only approximations intended to provide rough classifications; the number of items within each region could change by ten or twenty percent if one shifted the boundaries slightly.

Our 99 proper motion (PM) candidates divide into four groups: 9 fall inside the WD region, 43 inside the halo region, 23 in the disk region, and 24 lie in an area which had no stars in the Besançon model. Let us discuss the WD candidates first, and then consider the objects in the “empty” area.

The PM candidates falling into the WD region are concentrated near the red edge of the region, just as models of WD cooling predict. We take the combined results for ten simulated catalogs generated from the Besançon model, correct for completeness as a function of magnitude and proper motion, based on our tests with artificial stars (see Figure 3), and divide by 10 to find predictions of 2.2 WDs in the halo, 5.9 in the thick disk and 0.7 in the thin disk, for a total of 8.8 WDs satisfying our selection criteria in the SDF. Our sample yields 9 candidates in this region, consistent with the model. Note that several candidates lie just outside the WD region; we must make additional measurements of these objects before we can make any confident claim about the exact number of WDs. Which of our candidates are most likely to be members of the halo? As a young WD cools, it slides diagonally down and to the right on this diagram, parallel to the lower envelope of the simulation’s objects. Due to their high velocities, halo WDs should lie near the bottom of the distribution. There are several candidates at some distance below the main locus of simulation objects; we believe the two at H_{V} = 23.0 and H_{V} = 24.2 are the most likely of our candidates to be halo dwars.

Roughly one-quarter of our PM candidates lie in an “empty” region between the simulation’s WD and halo stars. Since we drew the boundaries by hand, they may certainly be shifted by small amounts; that would cause a number of the anamolous

8  Richmond et al.  [Vol. ,

Fig. 7. Reduced proper motion diagram for objects in simulated catalogs created with the Besançon model

Fig. 8. Reduced proper motion diagram for real objects observed in the SDF. The regions are identical to those in Figure 7. Each measurement has errorbars in both directions, though some are too small to see.

objects to fall within the halo or WD regions. However, some of our candidates are more than one magnitude away from any population in the simulations. Is it possible that they may be ordinary stars reddened by dust? According to Schlegel et al. (1998), dust along the line of sight through the SDF should produce E(B −V) = 0.015 mag; the corresponding extinction, A_{V} = 0.051 and A_{I} = 0.030, is too small to shift candidates a significant distance in the reduced PM diagram. We suggest that these objects may be metal-poor subdwarfs in the halo, a class of star which is not included in the Besançon model. If we make an HR diagram using M_{V} and (V − I), we find that the halo stars in the Besançon model cross the disk main sequence in the range 1.5 < (V − I) < 3.0, and are slightly more luminous in the redder portion of this range. However, as Reid & Gizis (1998) show, extremely metal-poor subdwarfs are much fainter than disk stars in this color range, by up to 4 magnitudes. Stars with these photometric properties and halo kinematics would lie several magnitudes below the halo region drawn in our diagrams. We therefore tentatively identify as extremely metal-poor halo stars the PM candidates which fall far from the WD and halo regions.

5. Future work

Our first step will be to acquire spectra of some of our PM candidates to verify their identity as WDs and metal-poor subdwarfs. After we have spectra for a good fraction of our candidates, we can assign types to the candidates with more confidence. At that point, we will make a more detailed and quantitative comparison of the WDs in our sample with those expected from models of the Milky Way.

We can also look at candidates with motions of somewhat lower significance. In this paper, we examined the 110 stars which had S_{tot} > 5.0. There were 72 stars with 4.0 ≤ S_{tot} < 5.0, and they show nearly the same degree of asymmetry in their motions as our first sample. It is likely that a significant number of these stars have real proper motions. However, it will take extra effort to distinguish them from the growing number of false detections, and to check their photometry (many of them are fainter than the stars in our sample). As we sift through this set of stars with less significant motions, we can also try to improve the B and V measurements of our stars, so that we will not discard so many candidates due to their uncertain colors.

Finally, we can apply the same techniques to find stars with large proper motions in other deep fields with multiple visits by Subaru. Our next target will be the area of the Subaru/XMM-Newton Deep Survey (Sekiguchi et al. 2004, Furusawa et al. 2008), which is roughly in the opposite direction from the SDF. We can use it to check our results in the SDF, but also to look for differences predicted by models of galactic populations.

We thank the staff at the Subaru Telescope for their assistance with the observations used in this project. MWR gratefully acknowledges grant S-03031 from the JSPS Invitation Fellowship for Research in Japan. This work is supported in part by a JSPS core-to-core program “International Research Network for Dark Energy” and by a JSPS research grant (17104002). Long ago, Charles Alcock suggested that we use Suprime-Cam to search for white dwarfs; we are glad to be putting his idea into practice at last. A.G. acknowledges support by the Benoziyo Center for Astrophysics and the William Z. and Eda Bess Novick New Scientists Fund at the Weizmann Institute.

Funding for the Sloan Digital Sky Survey (SDSS) and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, and the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web site is http://www.sdss.org/.

The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, The University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

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Table 4. First sample of proper motion candidates in the SDF

ID  RA^{∗}  Dec^{∗}  V^{∗∗} R_{c}^{∗∗}  i′^{∗∗}  z′^{∗∗}  RA PM^{†}  Dec PM^{†}
SDFPM J132339.4+271916 200.91424 27.32130 21.784 21.025 20.164 19.607 -0.049 ± 0.004 -0.024 ± 0.004
SDFPM J132343.5+272230 200.93138 27.37519 20.889 20.198 19.501 18.853 -0.034 ± 0.004 -0.003 ± 0.006
SDFPM J132343.6+272753 200.93170 27.46494 22.821 21.995 20.868 20.265 -0.017 ± 0.002 0.001 ± 0.004
SDFPM J132346.9+274556 200.94582 27.76573 21.810 20.993 20.003 19.425 -0.073 ± 0.004 -0.018 ± 0.004
SDFPM J132347.5+271829 200.94827 27.30829 21.711 21.005 20.505 20.139 -0.037 ± 0.004 -0.023 ± 0.004
SDFPM J132348.0+273232 200.95033 27.54234 24.208 23.350 22.209 21.615 -0.053 ± 0.002 0.018 ± 0.002
SDFPM J132348.0+273702 200.95029 27.61729 23.585 22.739 21.520 20.867 -0.022 ± 0.002 -0.002 ± 0.002
SDFPM J132350.2+272744 200.95944 27.46232 19.051 19.110 19.193 19.141 0.030 ± 0.004 -0.036 ± 0.004
SDFPM J132351.0+273453 200.96275 27.58148 21.617 20.713 19.596 18.739 0.017 ± 0.002 -0.027 ± 0.004
SDFPM J132353.1+272759 200.97157 27.46647 23.648 22.870 22.073 21.626 -0.006 ± 0.002 -0.018 ± 0.002
SDFPM J132353.4+272207 200.97253 27.36882 20.417 19.870 19.564 19.130 -0.034 ± 0.004 -0.035 ± 0.002
SDFPM J132354.0+272806 200.97518 27.46843 24.444 23.488 21.818 20.910 -0.012 ± 0.000 -0.009 ± 0.002
SDFPM J132354.3+273016 200.97647 27.50454 23.857 23.334 22.733 22.322 -0.032 ± 0.004 0.001 ± 0.004
SDFPM J132354.5+273356 200.97722 27.56561 22.793 22.390 22.199 22.029 -0.056 ± 0.004 -0.042 ± 0.002
SDFPM J132356.7+274445 200.98637 27.74593 22.248 21.560 21.150 20.835 -0.024 ± 0.004 -0.025 ± 0.002
SDFPM J132357.5+271458 200.98977 27.24948 23.025 22.144 20.812 20.046 -0.019 ± 0.002 -0.007 ± 0.002
SDFPM J132400.0+273750 201.00007 27.63083 21.997 21.169 20.115 19.443 -0.009 ± 0.000 -0.021 ± 0.004
SDFPM J132401.1+273613 201.00494 27.60384 23.932 23.034 21.688 20.989 -0.036 ± 0.002 -0.002 ± 0.002
SDFPM J132402.5+272639 201.01074 27.44421 25.483 24.796 23.022 22.008 0.003 ± 0.002 -0.025 ± 0.002
SDFPM J132403.6+271314 201.01540 27.22081 24.830 24.027 23.312 22.843 -0.024 ± 0.004 -0.027 ± 0.006
SDFPM J132403.6+273833 201.01540 27.64265 22.152 21.247 19.998 19.174 -0.022 ± 0.004 -0.011 ± 0.002
SDFPM J132404.5+272557 201.01911 27.43275 24.593 23.464 21.534 20.563 -0.033 ± 0.004 -0.006 ± 0.002
SDFPM J132404.5+273829 201.01897 27.64141 23.774 23.016 22.452 22.084 -0.023 ± 0.002 -0.026 ± 0.002
SDFPM J132407.4+272751 201.03110 27.46440 23.326 22.556 22.030 21.693 -0.032 ± 0.002 0.009 ± 0.002
SDFPM J132407.4+272924 201.03107 27.49026 20.825 20.089 19.268 18.488 0.008 ± 0.002 -0.036 ± 0.004
SDFPM J132407.8+273621 201.03275 27.60605 20.992 20.211 19.334 18.498 -0.011 ± 0.002 -0.028 ± 0.002
SDFPM J132408.0+274455 201.03344 27.74886 23.205 23.035 23.011 22.952 -0.031 ± 0.004 -0.005 ± 0.002
SDFPM J132409.7+273406 201.04050 27.56846 22.629 21.914 21.501 21.195 -0.018 ± 0.002 -0.032 ± 0.002
SDFPM J132411.1+271310 201.04634 27.21970 21.478 20.735 19.868 19.261 0.001 ± 0.002 -0.036 ± 0.004
SDFPM J132412.6+272220 201.05261 27.37244 21.385 20.713 20.279 19.940 -0.005 ± 0.002 -0.039 ± 0.002
SDFPM J132413.0+272651 201.05433 27.44771 21.211 20.568 20.195 19.890 0.007 ± 0.002 -0.048 ± 0.002
SDFPM J132413.2+273139 201.05511 27.52759 24.476 23.966 23.694 23.519 0.024 ± 0.004 -0.047 ± 0.002
SDFPM J132413.5+271547 201.05657 27.26317 23.270 22.586 22.068 21.668 -0.010 ± 0.002 -0.024 ± 0.002
SDFPM J132415.4+271328 201.06428 27.22462 23.341 22.562 21.837 21.368 -0.024 ± 0.004 -0.013 ± 0.002
SDFPM J132415.9+271624 201.06654 27.27336 21.285 21.492 21.654 21.798 -0.037 ± 0.002 0.004 ± 0.004
SDFPM J132418.0+271902 201.07534 27.31740 20.754 20.099 19.576 19.011 -0.029 ± 0.004 0.001 ± 0.004
SDFPM J132419.4+273411 201.08115 27.56974 23.404 22.691 22.296 21.994 -0.013 ± 0.002 -0.026 ± 0.004
SDFPM J132423.6+274031 201.09851 27.67550 24.878 24.092 22.810 22.094 -0.008 ± 0.002 -0.030 ± 0.002
SDFPM J132423.7+274425 201.09904 27.74048 24.684 23.560 21.358 20.143 -0.023 ± 0.002 0.026 ± 0.004
SDFPM J132425.8+272415 201.10777 27.40424 22.134 21.348 20.242 19.579 0.015 ± 0.004 -0.018 ± 0.002
SDFPM J132427.4+271919 201.11456 27.32220 21.667 20.920 19.939 19.277 -0.016 ± 0.002 -0.006 ± 0.002
SDFPM J132427.5+274302 201.11464 27.71747 21.899 21.050 19.979 19.326 -0.004 ± 0.000 -0.029 ± 0.004
SDFPM J132429.2+273817 201.12177 27.63832 22.417 21.510 20.291 19.581 -0.031 ± 0.002 0.008 ± 0.002
SDFPM J132429.7+273932 201.12378 27.65908 23.801 23.352 23.149 22.980 -0.019 ± 0.002 -0.011 ± 0.002
SDFPM J132429.8+274304 201.12447 27.71788 24.576 23.709 22.521 21.894 -0.002 ± 0.002 -0.026 ± 0.002
SDFPM J132430.6+272406 201.12789 27.40185 25.066 24.034 22.769 22.151 -0.026 ± 0.002 -0.014 ± 0.004
SDFPM J132430.9+273624 201.12897 27.60693 23.844 23.145 22.437 22.015 -0.001 ± 0.002 -0.036 ± 0.002
SDFPM J132431.3+271528 201.13047 27.25786 23.296 22.392 21.111 20.377 -0.008 ± 0.002 -0.028 ± 0.002
SDFPM J132431.9+272236 201.13305 27.37668 20.942 20.325 19.957 19.596 -0.007 ± 0.002 -0.039 ± 0.004
SDFPM J132432.0+273510 201.13343 27.58623 26.614 25.586 23.635 22.704 -0.005 ± 0.002 -0.027 ± 0.002
SDFPM J132432.9+274301 201.13713 27.71701 21.809 21.082 20.626 20.313 0.012 ± 0.004 -0.053 ± 0.002
SDFPM J132434.5+271432 201.14385 27.24230 21.333 20.533 19.396 18.506 -0.074 ± 0.006 0.042 ± 0.006
SDFPM J132435.0+271638 201.14597 27.27749 24.078 23.314 22.761 22.360 -0.022 ± 0.002 -0.010 ± 0.002
SDFPM J132436.5+272345 201.15221 27.39585 25.624 24.331 22.079 20.895 0.022 ± 0.004 -0.027 ± 0.002
SDFPM J132438.0+273622 201.15867 27.60634 20.594 20.088 19.836 19.525 -0.048 ± 0.002 -0.054 ± 0.002

Table 4. (Continued.)

SDFPM J132438.4+273433 201.16001 27.57608 25.234 24.507 23.642 23.123 -0.037 ± 0.004 -0.007 ± 0.006
SDFPM J132438.8+272847 201.16168 27.47980 21.242 20.387 19.401 18.580 0.019 ± 0.004 -0.017 ± 0.002
SDFPM J132439.0+272413 201.16284 27.40377 21.748 20.978 20.063 19.473 -0.029 ± 0.004 -0.021 ± 0.004
SDFPM J132439.2+273949 201.16367 27.66381 25.890 25.991 23.708 22.493 -0.025 ± 0.002 0.006 ± 0.002
SDFPM J132440.4+272911 201.16870 27.48653 20.569 20.101 19.872 19.567 -0.010 ± 0.002 -0.012 ± 0.002
SDFPM J132440.6+272548 201.16954 27.43018 25.902 25.050 23.210 22.293 0.002 ± 0.002 -0.033 ± 0.004
SDFPM J132440.7+271501 201.16992 27.25041 20.436 20.017 19.781 19.510 0.000 ± 0.002 -0.024 ± 0.002
SDFPM J132444.4+273945 201.18514 27.66254 23.530 22.957 22.607 22.279 -0.016 ± 0.002 -0.011 ± 0.002
SDFPM J132444.9+272709 201.18741 27.45264 22.431 21.622 20.613 20.051 0.013 ± 0.004 -0.023 ± 0.002
SDFPM J132446.0+272605 201.19208 27.43499 22.250 21.553 21.112 20.813 -0.026 ± 0.002 -0.004 ± 0.002
SDFPM J132446.8+274114 201.19519 27.68733 24.778 23.590 21.544 20.448 -0.040 ± 0.002 0.012 ± 0.004
SDFPM J132447.0+272814 201.19610 27.47077 23.045 22.143 20.783 20.064 0.008 ± 0.000 -0.025 ± 0.002
SDFPM J132447.8+272157 201.19930 27.36586 23.236 22.290 20.836 19.993 -0.025 ± 0.002 0.002 ± 0.002
SDFPM J132448.1+272803 201.20046 27.46761 21.790 21.173 20.812 20.554 -0.025 ± 0.002 -0.004 ± 0.002
SDFPM J132448.6+272747 201.20255 27.46314 25.725 24.967 23.319 22.436 -0.022 ± 0.002 -0.010 ± 0.002
SDFPM J132448.8+273205 201.20361 27.53479 21.771 20.993 20.036 19.427 -0.081 ± 0.004 0.007 ± 0.002
SDFPM J132449.7+274510 201.20714 27.75295 25.447 24.324 22.278 21.207 -0.043 ± 0.002 -0.042 ± 0.002
SDFPM J132451.7+273110 201.21556 27.51972 25.980 25.510 25.241 24.948 -0.021 ± 0.008 -0.042 ± 0.004
SDFPM J132452.1+271813 201.21743 27.30386 24.103 23.165 21.596 20.792 -0.025 ± 0.002 -0.007 ± 0.004
SDFPM J132453.1+271821 201.22154 27.30592 22.338 21.642 21.242 20.944 -0.035 ± 0.002 -0.029 ± 0.004
SDFPM J132454.0+274226 201.22508 27.70739 23.462 22.682 21.698 21.148 -0.012 ± 0.002 -0.013 ± 0.002
SDFPM J132455.3+272957 201.23056 27.49939 25.095 24.307 23.423 22.968 -0.022 ± 0.002 -0.004 ± 0.004
SDFPM J132456.0+274126 201.23345 27.69078 25.805 24.801 22.578 21.065 -0.060 ± 0.002 0.020 ± 0.002
SDFPM J132456.1+272807 201.23412 27.46872 22.942 22.059 20.673 19.936 -0.030 ± 0.004 -0.011 ± 0.000
SDFPM J132458.1+272326 201.24241 27.39072 23.633 22.700 21.372 20.676 -0.022 ± 0.002 0.011 ± 0.002
SDFPM J132459.8+271251 201.24932 27.21436 23.548 22.849 22.374 21.961 -0.022 ± 0.002 -0.006 ± 0.006
SDFPM J132500.3+272357 201.25147 27.39927 22.401 21.675 21.122 20.775 -0.015 ± 0.002 -0.010 ± 0.002
SDFPM J132503.8+273938 201.26620 27.66072 21.497 20.741 19.999 19.479 -0.018 ± 0.002 -0.006 ± 0.002
SDFPM J132504.6+273028 201.26917 27.50779 21.614 20.808 19.792 19.074 -0.021 ± 0.002 -0.011 ± 0.000
SDFPM J132505.4+273731 201.27253 27.62530 22.684 21.943 21.160 20.728 -0.017 ± 0.002 -0.024 ± 0.002
SDFPM J132505.3+271440 201.27212 27.24446 22.854 22.143 21.642 21.233 -0.007 ± 0.002 -0.029 ± 0.002
SDFPM J132505.5+273401 201.27318 27.56696 22.398 21.772 21.336 21.058 -0.021 ± 0.002 -0.011 ± 0.002
SDFPM J132506.1+273816 201.27567 27.63800 21.999 21.309 20.880 20.594 -0.007 ± 0.002 -0.034 ± 0.002
SDFPM J132508.4+273553 201.28501 27.59830 20.672 20.018 19.546 19.011 -0.003 ± 0.002 -0.029 ± 0.004
SDFPM J132512.6+271620 201.30271 27.27244 22.398 21.731 21.362 21.034 -0.009 ± 0.000 -0.011 ± 0.000
SDFPM J132512.9+274045 201.30410 27.67940 25.443 24.610 23.500 22.863 -0.015 ± 0.002 -0.009 ± 0.002
SDFPM J132514.3+272421 201.30981 27.40588 21.422 20.499 19.379 18.486 -0.007 ± 0.002 -0.018 ± 0.002
SDFPM J132514.7+272642 201.31146 27.44522 23.121 22.559 22.187 21.881 -0.025 ± 0.004 -0.018 ± 0.006
SDFPM J132514.7+271707 201.31146 27.28543 22.993 22.180 21.211 20.640 -0.027 ± 0.002 -0.046 ± 0.004
SDFPM J132515.3+274212 201.31400 27.70335 22.304 22.297 22.357 22.406 -0.004 ± 0.004 -0.089 ± 0.002
SDFPM J132515.7+272708 201.31560 27.45226 24.696 23.629 21.645 20.570 -0.031 ± 0.002 -0.012 ± 0.002
SDFPM J132516.9+274518 201.32065 27.75507 23.660 22.886 22.281 21.891 0.008 ± 0.004 -0.032 ± 0.004
SDFPM J132521.1+271927 201.33814 27.32435 25.853 25.090 24.331 23.887 -0.018 ± 0.004 -0.031 ± 0.006
SDFPM J132525.4+273755 201.35591 27.63220 22.179 21.330 20.105 19.355 -0.031 ± 0.002 -0.004 ± 0.002
SDFPM J132527.7+274407 201.36559 27.73528 25.738 24.934 23.663 22.972 -0.016 ± 0.002 -0.043 ± 0.004
SDFPM J132527.7+272350 201.36576 27.39737 22.596 21.898 21.498 21.218 -0.010 ± 0.002 -0.019 ± 0.002
SDFPM J132528.3+274355 201.36796 27.73214 25.676 24.699 22.785 21.825 -0.043 ± 0.002 0.003 ± 0.002
SDFPM J132528.3+272012 201.36811 27.33679 22.163 21.424 20.568 20.040 -0.031 ± 0.004 -0.002 ± 0.002
SDFPM J132533.6+274708 201.39036 27.78563 23.894 22.665 20.660 19.533 -0.061 ± 0.008 0.041 ± 0.006
SDFPM J132533.9+272808 201.39152 27.46905 23.653 22.925 22.398 22.030 -0.029 ± 0.002 -0.026 ± 0.002

∗ Equinox J2000, epoch 2007.13. ∗∗ Corrected isophotal magnitudes from catalogs of Kashikawa et al. (2004). † Proper motions in arcseconds per year.