COOL WHITE DWARFS FOUND IN THE UKIRT INFRARED DEEP SKY SURVEY

UKIDSS consists of five survey components, one of which is the LAS (Lawrence et al. 2007). The LAS is the sub-survey most likely to contain faint and rare sources of the local Galaxy, such as the cool white dwarfs and brown dwarfs. The LAS aims to survey 4000 deg² in YJHK (Hewett et al. 2006) with a second epoch at J, to reach J ∼ 20. The 5σ photometric depths are Y = 20.2, J = 19.6, H = 18.8, and K = 18.2 (Dye et al. 2006). The data and catalogs generated by the automatic pipeline processing can be retrieved through the WFCAM Science Archive (WSA; Hambly et al. 2008). All data are pipeline-processed by the Cambridge Astronomical Survey Unit (CASU) following a standard procedure for infrared images (Irwin et al. 2004). An extensive description of each step involved in the processing of the Wide-Field Camera (WFCAM) data is available on the CASU Web site.⁵

The work presented here involves spectroscopic follow-up during Gemini Observatory semesters 2008B and 2010A (see Section 3). Our selection of candidates evolved over time, as LAS DRs became available, and as we obtained spectra for the candidates. The Observatory was flexible in allowing us to replace targets listed in the proposals with better candidates as they were found in new DRs. The LAS Releases used were DR3 (2007 December, 809 deg²), DR4 (2008 July, 984 deg²), DR5 (2009 April, 1270 deg²), and DR6 (2009 October, 1434 deg²).

We have cross-correlated the LAS with the SDSS database, using Structured Query Language and the WSA. SDSS DRs 6 and 7 were used, as available (Adelman-McCarthy et al. 2008; Abazajian et al. 2009). The area surveyed by the LAS was designed to overlap with the SDSS, divided up into three blocks (Dye et al. 2006; Lawrence et al. 2007; Warren et al. 2007). The equatorial block with right ascension 22 to 04 hr and declination between −1.5 and +1.5 deg overlaps SDSS stripes 9 to 16. The southern block covers 8 to 16 hr and (approximately) −3 to +15 deg, and includes SDSS stripe 82. The northern block covers 8 to 17 hr and (approximately) +30 to +50 deg, and provides an overlap with SDSS stripes 26 to 33.

Sources were matched by requiring the presence of a "primary" SDSS source within 5'' of the LAS coordinates (increasing the search radius led to erroneous pairings). The WFCAM astrometry is tied to the Two Micron All Sky Survey point-source catalog (Skrutskie et al. 2006) and has a systematic accuracy of <01 rms (Dye et al. 2006). Lodieu et al. (2009b) plot the rms of the difference between the coordinates of all point sources in the LAS DR2 and SDSS DR5 as a function of J magnitude; for the sources in this sample with 17.5 ⩽ J ⩽ 19.2 the implied astrometric uncertainty is 0025 to 0035 for the brighter to fainter sources, respectively.

We have restricted our queries of the LAS database to detections classified as point sources, and imposed color criteria and lower limits on the g-band RPM, H_g. The queries return coordinates, photometry, and errors from both surveys, as well as the proper motion, computed from the difference between the LAS J-band coordinates and the SDSS z-band coordinates. For the sample presented here, the SDSS epoch ranges from 1999 to 2006, and the LAS from 2005 to 2008. The average time period between the LAS and SDSS astrometry is 4.5 ± 2.0 years. Given the astrometric uncertainty, the uncertainty in proper motion is ≲ 14 mas. For one source, ULAS J1323+12, the LAS and SDSS epochs are separated by only 0.89 years and the proper-motion uncertainty is 30 mas.

Table 1 gives astrometric information for the candidate white dwarfs studied here, and Table 2 gives the SDSS ugriz and the LAS YJHK photometry. Note that the photometry is taken from the eighth DRs for both the LAS and SDSS, and not the releases used for our initial source identification. The proper motion in Table 1 is similarly an updated value, and has been calculated from the coordinates and epochs given in the DR8 releases.

With the exception of the close binary ULAS J1234+06, Table 1 also lists proper motions derived from alternative catalog matching. For 10 of the 16 sources, proper motion derived by matching the USNO-B catalog (Monet et al. 2003) to the SDSS catalog is available via DR8 of the SDSS. Of these 10, there is good agreement for six objects. For two the differences are at the ∼2σ level (ULAS J0121−00 and ULAS J1142+00). For the remaining two objects the discrepancies are large, and we rederived the proper motions using the digitized sky images, as well as the USNO-B, SDSS, and LAS astrometry, in order to obtain the motion over a large timeline. For ULAS J1323+12, which has a small SDSS-LAS epoch difference, the derived motion is close to the USNO-SDSS value, and significantly smaller than the SDSS-LAS value. For ULAS J2246−00, the derived value is close to the SDSS-LAS value but significantly different from the USNO-SDSS value in direction. For the six objects without USNO-SDSS proper motions, three show good agreement between the SDSS-LAS proper motions and new measurements derived from the imaging and catalog data listed above. Three objects differ by ∼2σ (ULAS J0840+05, ULAS J1345+15, ULAS J1454−01). Table 1 gives the RPM values derived from both proper-motion measurement sets.

Figures 1 and 2 illustrate the selection criteria imposed to arrive at the candidate list of Table 1. For all queries, we selected 14 ⩽ J ⩽ 19.6 to avoid saturated sources, and to ensure a good (5σ) J-band detection, in the LAS. We also restricted the targets to r_AB < 20.7, so that the spectroscopic observations were of reasonable duration (see Section 3.1). To select for faint high proper motion sources, we restricted sources to H_g > 20.5 (see Figure 1). This last selection greatly reduced the number of objects returned from a query. Figure 3 shows the red to far-red colors of various samples, for completeness.

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Most sources, 9 of the 17 listed in Table 1, were found in the search identified as region A in Figures 1 and 2, and in Table 1. The cuts imposed, in addition to those listed above, were H < 18.9, 0.8 ⩽ g − r ⩽ 1.6, 0.2 ⩽ r − i ⩽ 0.6, 0.6 ⩽ i − J ⩽ 1.4, J − H ⩽ 0.2. This selection is designed to produce hydrogen-rich white dwarfs with T_eff ∼ 4000 K (Figure 2), with a good detection in the H band. Early on in this work an additional source on the blue side of this cut with g − r = 0.63 was followed up; later we prioritized redder (in g − r) sources in order to find white dwarfs cooler than 5000 K. This bluer source is identified as found in region Ab in Table 1. An additional six sources were found in search B, defined as 0.2 ⩽ g − r ⩽ 1.2, −0.6 ⩽ r − i ⩽ +0.6, J − H ⩽ −0.1, H − K ⩽ −0.1. This search is designed to find bluer sources where H₂ opacity is impacting the red as well as the near-infrared, due to either lower T_eff, or a higher-pressure-mixed H–He atmosphere (Figure 2). Finally, one more source was found by selecting for extreme sources in the RPM diagram (Figure 1): H_g > 22.5, −0.5 ⩽ g − i ⩽ 1.0, 0.0 ⩽ r − i ⩽ 0.6, H < 18.8, J − H ⩽ 0.1, H − K ⩽ 0. This source is identified as found in region C in Table 1 (later the RPM value was found to be erroneous).

Our spectroscopic follow-up is complete for the pairing of the 1270 deg² of the LAS DR5 and the SDSS DR7 with the following selection: H_g > 20.5, r < 20.7, 14 ⩽ J ⩽ 19.6, H < 18.9, 0.9 ⩽ g − r ⩽ 1.6, 0.2 ⩽ r − i ⩽ 0.6, 0.6 ⩽ i − J ⩽ 1.4, $J-H +(\sqrt{{\rm err}(J)^2 + {\rm err}(H)^2}) < 0.2$. This search of the 1270 deg² of LAS DR5 produced six new white dwarfs with 4120 K ⩽T_eff ⩽ 4380 K (see Section 4) and recovered a known white dwarf with T_eff = 4390 K (SDSS J115814.52+000458.3; Kilic et al. 2010a). Kilic et al. (2010a) perform a detailed analysis of 113 white dwarfs with v_tan ⩾ 20 km s⁻¹ found using an RPM search of the 5282 deg² footprint of the SDSS DR3 (Harris et al. 2006). We can compare our results to those of Kilic et al., neglecting the additional 13 white dwarfs in the Kilic et al. sample that were found through a search of SDSS spectral data, in order to compare similarly determined samples. Kilic et al. find six white dwarfs with 4100 K ⩽T_eff ⩽ 4400 K out to a distance of about 55 pc. The implied space density of 4200 K white dwarfs, with cooling age ≈8 Gyr (Section 4), is 2 × 10⁻⁵ pc⁻³. The r-, J-, and H-band cuts imposed for our LAS search indicate that we should be sensitive to 4200 K white dwarfs at distances of 10–95 pc, based on the models. The H_g selection combined with a faint limit of g ≈ 21 implies that our lower limit on proper motion is 008 yr⁻¹. Our upper limit is determined by the 5'' matching radius and the difference between the SDSS and LAS epochs; the typical difference is four years, implying an upper limit to the proper motion of ∼13 year⁻¹. Excluding ULAS J1142+00 and ULAS J1234+06AB for which erroneously high proper motions were initially derived, the sample has a range in proper motion of 009 to 03 yr⁻¹. The density of 4200 K white dwarfs implied by the Kilic et al. sample suggests that we would expect to find around seven 4200 K white dwarfs. However, two of the six Kilic et al. white dwarfs have H_g < 20.5, suggesting that our selection would find around five 4200 K white dwarfs, very close to the number found.

We note in passing that we have applied this last selection to the 48 deg² overlap area of the UKIDSS Galactic Cluster Survey (GCS) DR8 and SDSS DR7, and found no candidates. The GCS will survey 10 open star clusters in the ZYJHK filters to a similar depth in YJHK as the LAS. It has been successfully used to find field brown dwarfs (Lodieu et al. 2009a), as well as to study open clusters (Lodieu et al. 2007), but a larger area in common with the SDSS is required before cool white dwarfs will be found.

We obtained optical spectra of the candidate cool white dwarfs listed in Table 1, selected as described in the previous section, excluding SDSS J1247+06 for which Kilic et al. (2010a) present an optical spectrum (a spectrum is also available in the SDSS database). The Gemini Multi-Object Spectrographs (GMOS; Hook et al. 2004) at both Gemini North and South were used, through queue time granted under programs GS-2008B-Q-35, GN-2008B-Q-111, and GS-2010A-Q-58. For all observations the R400 grating was used with the GG455 blocking filter. The central wavelength was 680 nm, with wavelength coverage of 460–890 nm. Detector fringing affected the spectra longward of about 800 nm. We did not correct for the fringing as this wavelength region is not necessary for target classification. The 075 slit was used with 2 × 2 binning and the resulting resolution was R ≈ 1280 or 6 Å. An observing log is given in Table 3.

Flat fielding and wavelength calibration were achieved using lamps in the on-telescope calibration unit. Spectrophotometric DA white dwarf standards were used to determine the instrument response curve and flux calibrate the spectra; for program GS-2008B-Q-35, LTT 7987 was used, for GN-2008B-Q-111, G191-B2B was used, and for GS-2010A-Q-58, LTT 3218 was used. The data were reduced using routines supplied in the IRAF Gemini package.

Figure 4 shows the GMOS spectra of the three non-white dwarf objects in our sample, as well as G- and K-type stellar spectra taken from the spectral atlas of Le Borgne et al. (2003) for reference, for a wavelength range that contains the features useful for classification. The narrow metal lines seen in the spectra exclude the possibility that these are white dwarfs. The three objects (ULAS J1142+00, ULAS J1234+06N, and ULAS J2246−00) are early-G to early-K dwarfs or subdwarfs. For two of these, ULAS J1142+00 and ULAS J1234+06N, we initially derived too high a proper motion, the revised smaller H_g value places them near the subdwarf region of the RPM (Figure 1). Our true contamination is therefore small—one in fifteen, or 7%.

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Figure 5 shows the spectra for the 13 newly confirmed white dwarfs. Two of these show weak pressure-broadened Hα (ULAS J1323+12 and ULAS J2331+15), and 11 are featureless.

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When carrying out our analysis by fitting models to the observed photometry (Section 4), we found several instances where the infrared photometry appeared to be in error, in particular for the H band. To trace the source of the discrepancies, we obtained repeat photometry for a subset of the sample.

H and K photometry for five of our targets was obtained using the WFCAM (Casali et al. 2007) on UKIRT, through the UKIRT Service program, via program USERV1876. Single-pointing WFCAM "paw-print" observations were defined to place the target in one of the four cameras: camera number 2. Exposure times of 10 s were used, with an eight-position telescope dither pattern and a four-position microstep pattern. These 32 exposures were repeated three times, for a total on-source time of 16 minutes, in each filter. An observing log is given in Table 4, together with the derived photometry. The "flat-file" FITS images and catalogs produced by the CASU pipeline were accessed through the WSA (Section 2). The 2'' diameter aperture photometry, provided in counts, were converted to magnitudes using the air mass and zero points provided for each of the three reduced groups of observations for each filter and each object. We derived the weighted mean (using the uncertainties provided in the catalog) and the uncertainty in the mean for these measurements. Subsequently, the merged catalog data were released for the three objects observed on 2010 June 13, and the photometry from this catalog, database USERV1876v20101104, is given in the table for ULAS J1206+03, ULAS J1351+12, and ULAS J1404+13. The merged catalog photometry agreed with the flat-file photometry to within 0.02 mag for the two brighter sources, within 3% at H for the fainter ULAS J1404+13, and within 12% at K for ULAS J1404+13, which has K ≈ 19.7. These differences are well within the quoted uncertainties.

Additional H, or H and K, photometry was obtained for five more white dwarfs using NIRI (Hodapp et al. 2003) on Gemini North, via program GN-2011A-Q-59. Exposure times of 15 s or 30 s were used, with a five- or nine-position telescope dither pattern. The total integration time is given in Table 4, together with the derived photometry. The data were reduced using routines supplied in the IRAF Gemini package. UKIRT Faint Standards were used for calibration (FS 16, FS 33, FS 126, FS 136; Leggett et al. 2006).

Comparing Table 4 to the LAS photometry in Table 2 shows that typically, for the sources fainter than H ≈ 18, the LAS H-band magnitude is too faint by about 2σ. In selecting faint sources near the LAS detection limit, with blue J − H colors, objects have been scattered into the sample with H magnitudes too faint by twice the estimated uncertainty. A similar effect is seen in searches for faint brown dwarfs that are also blue in J − H (B. Burningham 2010, private communication).

The pure-hydrogen, pure-helium, and mixed composition model atmospheres used in this analysis are described in detail in Kilic et al. (2010a). These models are in local thermodynamic equilibrium, they allow energy transport by convection, and they can be calculated with arbitrary amounts of hydrogen and helium. For the sample considered here, the mixed composition atmospheres had ratios of He to H by number ranging from low values of 10⁻² to high values of 10¹⁰. The method used to fit the photometric data is described at length in Bergeron et al. (2001). Briefly, we convert the magnitudes into observed fluxes using the method of Holberg & Bergeron (2006) and the appropriate filters. We use the SDSS to AB system corrections for u, i, and z given in Eisenstein et al. (2006; Section 2). Then we fit the resulting energy distributions with those derived from model atmosphere calculations, using a nonlinear least-squares method. Only T_eff and the solid angle π(R/D)², where R is the radius of the star and D is its distance from Earth, are considered free parameters. Since no parallax measurements are available, we assume a surface gravity of log g = 8 which determines the value of R for a given value of T_eff (Bergeron et al. 2001). White dwarfs have been shown to have a very strongly peaked mass and surface gravity distribution (e.g., Bergeron et al. 1992; Liebert et al. 2005; Kepler et al. 2007). DA white dwarfs have a mean mass of 0.6 ± 0.1 M_☉ while DBs are slightly more massive with 0.7 ± 0.1 M_☉; these ranges infer a likely range in gravity for our sample of 7.7 ⩽ log g ⩽ 8.3. The photometric variance uncertainties in T_eff and the solid angle are obtained directly from the covariance matrix of the fit.

Since our models do not include the red wing opacity from Lyα calculated by Kowalski & Saumon (2006), we neglect here the u bandpass in our fitting procedure as well as the g bandpass for white dwarfs cooler than 4600 K in hydrogen-rich solutions (as the missing Lyα opacity has a larger impact at lower temperatures). The Lyα opacity affects a wavelength region where there is very little flux; hence, the atmospheric structure is not affected significantly by a change of the opacity in the ultraviolet, although the blue colors calculated by the models are.

As described in Section 3.2, we have found that in selecting faint sources near the LAS detection limit, with blue J − H colors, objects have been scattered into the sample with H magnitudes too faint by twice the estimated uncertainty. In our fits to the data we use the NIRI and WFCAM photometry where available (Table 4), and where LAS photometry is used we exclude data with uncertainties ⩾0.15 mag. The fits use the DR8 releases of both the SDSS and LAS photometry, the most recent at the time of writing.

We use the energy distributions together with the optical spectra at Hα to constrain the surface composition. Only two of the white dwarfs show Hα (Figure 5); however, this does not necessarily imply that the remaining objects are helium-rich, as Hα absorption is not seen in hydrogen-rich white dwarfs cooler than ∼5000 K. Figures 6 through 11 show the model fits to the observational data, assuming log g = 8.0.

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The energy distributions are somewhat sensitive to log g in the temperature range considered here. A variation of ±0.3 dex in log g yields differences in effective temperature between 40 K and 80 K. The uncertainty due to the photometric variations is between 40 K and 150 K. Another error estimate is provided by fitting the observed Hα line profile for the two DAs: the derived T_eff differs from that derived from the energy distribution by 100–200 K (for ULAS J1323+12 5400 K cf. 5260 K, for ULAS J2331+15 5200 K cf. 4970 K). This is consistent with our other error estimates.

Table 5 lists the derived atmospheric properties of the 13 new white dwarfs in our sample, together with the SDSS white dwarf recovered here. Using the composition and temperature, and assuming that these stars have the canonical white dwarf mass of 0.6 M_☉, we can use the synthetic colors of Holberg & Bergeron (2006; an extension of Bergeron et al. 1995) and the evolutionary sequences of Fontaine et al. (2001) to derive both a cooling age and distance, and hence tangential velocity. These values are also given in Table 5. The derived tangential velocities, H_g and g − i, are consistent with the 40–150 km s⁻¹ region indicated in Figure 1. The uncertainty in the implied cooling age, distance, and velocity is primarily due to the uncertainty in gravity (or mass). The sense of the gravity effect is that more massive white dwarfs will have a longer cooling age and be closer and slower, and vice versa.

Four of the thirteen newly identified white dwarfs (∼ 30%) are best fit with pure-hydrogen atmospheres (Figures 6 and 7; ULAS J0826−00, ULAS J1323+12, ULAS J1345+15, ULAS J2331+15), and four (∼ 30%) are best fit with pure-helium atmospheres (Figure 8; ULAS J1006+09, ULAS J1206+03, ULAS J1351+12, ULAS J1454−01). An additional white dwarf (ULAS J1320+08) is fit with either pure-helium or a helium-rich atmosphere, where the latter fit, with H/He =10^−4.4, is superior (Figure 9). Two sources (ULAS J0840+05, ULAS J1404+13) have mixed atmospheres with large flux deficits in the infrared, due to pressure-induced H₂ absorption (Figure 10). As described in Kilic et al. (2010a), there are generally two solutions to such objects. The H₂ opacity peaks around H/He =10⁻² and there is usually a good solution both above and below this peak with slightly different temperatures. This is demonstrated by the fits shown in Figure 10, where ULAS J0840+05 is fit with H/He =10^−4.5 or 10^−0.6 and ULAS J1404+13 is fit with H/He =10^−2.8 or 10^−2.1. Thus, three white dwarfs (∼ 25%) have mixed atmospheres and are similar to the mixed composition white dwarfs found by Kilic et al. (2010a, their Figure 14). There are seven white dwarfs (∼55%) that have pure-helium or helium-dominated atmospheres. Finally, there are two white dwarfs (∼15% of the sample) for which we cannot constrain the atmospheric composition: ULAS J0121−00 and ULAS J1436+05 (Figure 11). ULAS J1436+05 is particularly puzzling—it appears to be much too bright at zYJ. A binary solution does not seem likely given the flux distribution, and the photometric uncertainties are small.

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Typically, studies of samples of cool white dwarfs find a much larger fraction of pure-hydrogen atmospheres: 50%–60% (Bergeron et al. 2001; Kilic et al. 2010a). However, Kilic et al. (2010a) find that ∼ 60% of their sample of white dwarfs (25 of 40) in the temperature range 4500–5000 K have pure-helium atmospheres while only ∼ 20% have pure-hydrogen, consistent with our findings. As Kilic et al. state, further work is required to understand if the observed overabundance of helium-rich atmosphere white dwarfs at this temperature range is real, or if Lyα or H₂ opacity uncertainties or photometric errors have biased the results.

Seven white dwarfs, half of our sample, have 4120 K ⩽T_eff ⩽ 4480 K and cooling ages between 7.3 Gyr and 8.7 Gyr. Their distances are 60–80 pc, and their tangential velocities are 40–85 km s⁻¹. The main-sequence lifetime of these remnants is likely to have been ∼2 Gyr (e.g., Catalán et al. 2008); hence, these white dwarfs are most likely to be thick disk 10–11 Gyr-old objects. Of these seven, we could not constrain the atmospheric composition for two, two have mixed atmospheres, two pure hydrogen, and one pure helium. We note that there are no pure-helium atmosphere white dwarfs cooler than 4400 K in the Kilic et al. (2010a) sample. The uncertainty in the photometry would allow ULAS J1006+09 to be hydrogen-rich, in which case it is slightly cooler, with T_eff = 4230 K, and older, with a cooling age of 8.4 Gyr.

Four of the white dwarfs have 4610 K ⩽T_eff ⩽ 4810 K and cooling ages between 6.5 Gyr and 6.9 Gyr. Their distances are 65–100 pc and velocities are 60–95 km s⁻¹. The remaining three white dwarfs have 4970 K ⩽T_eff ⩽ 5260 K and cooling ages between 4.3 Gyr and 5.8 Gyr. Their distances are 60–100 pc and velocities are 70–100 km s⁻¹. This half of our sample may consist of thin disk remnants with unusually high velocities (e.g., Bergeron 2003; Tetzlaff et al. 2011), or lower-mass remnants of thick disk or halo late-F or G stars.