Ultracool WDs

Ultracool white dwarfs and the age of the Galactic discthanks: This work is based on observations obtained at the MDM Observatory, operated by Dartmouth College, Columbia University, Ohio State University, Ohio University, and the University of Michigan.

A. Gianninas, B. Curd, John R. Thorstensen, Mukremin Kilic, P. Bergeron, Jeff J. Andrews, Paul Canton, and M. A. Agüeros
Homer L. Dodge Department of Physics & Astronomy, University of Oklahoma, 440 W. Brooks St, Norman, OK 73019, USA Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, USA Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, QC H3C 3J7, Canada Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027, USA
E-mail: alexg@nhn.ou.edu
Accepted 2015 March 8. Received 2015 March6 1; in original form 2015 February 4
Abstract

We present parallax observations and a detailed model atmosphere analysis of 54 cool and ultracool (  4000 K) white dwarfs (WDs) in the solar neighbourhood. For the first time, a large number of cool and ultracool WDs have distance and tangential velocities measurements available. Our targets have distances ranging from 21 pc to  100 pc, and include five stars within 30 pc. Contrary to expectations, all but two of them have tangential velocities smaller than 150 km s thus suggesting Galactic disc membership. The oldest WDs in this sample have WD cooling ages of 10 Gyr, providing a firm lower limit to the age of the thick disc population. Many of our targets have uncharacteristically large radii, indicating that they are low-mass WDs. It appears that we have detected the brighter population of cool and ultracool WDs near the Sun. The fainter population of ultracool CO-core WDs remain to be discovered in large numbers. The Large Synoptic Survey Telescope should find these elusive, more massive ultracool WDs in the solar neighbourhood.

keywords:
techniques: photometric – stars: atmospheres – stars: evolution – white dwarfs – Galaxy: disc
pagerange: Ultracool white dwarfs and the age of the Galactic discthanks: This work is based on observations obtained at the MDM Observatory, operated by Dartmouth College, Columbia University, Ohio State University, Ohio University, and the University of Michigan.LABEL:lastpagepubyear: 2015

1 Introduction

Given the finite age of the Universe, the first asymptotic giant branch stars that formed now live as  () = 4.5 white dwarfs (WDs; mestel52; iben84; winget87; liebert88; fontaine01). Such WDs have temperatures below 4000 K (hence classified as ultracool) and they have been observed in deep Hubble Space Telescope () images of the halo globular clusters M4 and NGC 6397 (hansen04; hansen07). The oldest WDs in these two clusters are 11.5 Gyr old.

Large-scale surveys such as the Sloan Digital Sky Survey (SDSS; gates04; harris06; harris08; kilic06a; kilic10a; vidrih07; hall08), the UKIRT Infrared Deep Sky Survey (UKIDSS; leggett11; catalan12; tremblay14) and SuperCOSMOS (hambly99; rowell08) have identified the analogues of these ultracool WDs in the field. Since these field WDs are relatively bright compared to the globular cluster WDs, optical and infrared photometry in several bands can be easily obtained from ground-based telescopes, enabling us to model their spectral energy distributions (SEDs) accurately. This is important for understanding the different opacity sources in these stars, deriving reliable temperatures and ages, and also calibrating the faint WD sequences of globular clusters that usually rely on two filter photometry.

The spectra of hydrogen-rich cool and ultracool WDs differ from those of their warmer counterparts because they show the effects of the red-wing of the Ly opacity in the blue (kowalski06) and the collision-induced absorption (CIA) due to molecular hydrogen in the near-infrared (hansen99). The latter shifts the peak of the SEDs of ultracool WDs back to the optical wavelengths. Unfortunately, there are only three ultracool WDs in the field with parallax measurements. These are WD 0346+246111We note that this object is also known as WD 0343+247., SDSS J110217.48+411315.4 (hereafter J1102; kilic12, and references therein) and LHS 3250 (bergeron02). The first two stars have SEDs that peak near 1 m. On the other hand, the LHS 3250 SED peaks at 0.6 m, representing an extreme case of CIA flux deficit in the optical and infrared. bergeron02 performed a detailed model atmosphere analysis of LHS 3250 and demonstrated that LHS 3250 has a helium-rich composition, it is overluminous, and undermassive. The best-fitting model and the parallax measurement indicate a mass of only 0.23 M (bergeron02). This is somewhat problematic as all previously known low-mass WDs are DAs with hydrogen-rich atmospheres.

gates04 and harris08 as well as several other groups have identified about a dozen stars with SEDs similar to LHS 3250. In this paper, we present parallax measurements and a model atmosphere analysis of 54 cool WDs, including half a dozen ultracool WDs and several other cool WDs with significant infrared flux deficits. Our targets were selected from the cool and ultracool WD samples of gates04, vidrih07, harris08 and kilic10a, and are biased towards WDs with significant infrared flux deficits. Parallax measurements allow us to accurately determine the distances, masses and consequently the cooling ages for these stars. Section 2 outlines our observations including a description of our Bayesian approach to estimating distances. Section 3 describes the models used in our analyses followed by our results in Section 4. In Section 5, we discuss the ages and membership of the WDs in our sample as well as the implications of our results towards our understanding of WD evolution and we conclude in Section 6.

2 Observations

2.1 Parallax

All our parallax data are from the 2.4m Hiltner telescope at Michigan-Dartmouth-MIT (MDM) Observatory on Kitt Peak, Arizona. We used a thinned SITe CCD (named ‘echelle’); at the focus, each m pixel subtended 0.275 arcsec, giving a field of view 9.4 arcmin. For all our parallax data, we used a 4-inch-square Kron–Cousins -band filter, which did not vignette the CCD. Exposure times varied with the brightness of the object, but were typically a few hundred seconds. Our data were taken on numerous observing runs between 2007 and 2011. Table LABEL:tab:obs gives the epochs that each star was observed, and the number of exposures at each epoch.

SDSS Epochs
J0045+1420 30 57 50 2007.73(4), 2007.82(3), 2008.69(11), 2008.88(16), 2008.97(8), 2009.72(8)
J01210038 15 48 115 2007.73(8), 2008.05(10), 2008.69(16), 2008.88(17), 2008.97(9), 2009.73(13), 2009.86(18),
2010.01(10), 2011.75(9), 2011.94(5)
J0146+1404 35 54 107 2007.73(8), 2008.05(8), 2008.69(12), 2008.88(18), 2008.97(8), 2009.73(12), 2009.86(16),
2010.01(12), 2011.75(3), 2011.94(10)
J02560700 15 41 149 2007.74(33), 2007.81(12), 2008.05(8), 2008.69(13), 2008.88(14), 2009.03(10), 2009.73(8),
2009.86(12), 2010.02(7), 2011.75(10), 2011.93(22)
J03010044 25 58 102 2007.73(7), 2007.82(6), 2008.06(8), 2008.69(10), 2008.88(17), 2008.97(8), 2009.73(12),
2009.86(13), 2010.01(12), 2011.75(9)
J0309+0025 17 47 126 2007.74(8), 2007.81(10), 2008.05(8), 2008.69(1), 2008.88(14), 2008.97(7), 2009.72(8),
2009.86(16), 2010.02(13), 2011.75(16), 2011.93(25)
( This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.)
Table 1: Journal of parallax observations.
Figure 1: Comparison between the proper motions measured at MDM Observatory and those from the SDSS+USNO-B catalogue (munn04) for 42 of the 54 WDs in the current sample. We compare the absolute value of the proper motion in right ascension (, top) and in declination (, bottom). The dotted line represents the 1:1 correlation. The dashed lines represent the  10 mas yr range.

Our reduction and analysis procedures differed only slightly from those described by thor03 and thor08. As in the previous work, we corrected our raw parallaxes to absolute using colour-based distance estimates for the reference stars, and estimated uncertainties using the formal errors of the fit and the scatter of the references stars. In order to correct for differential colour refraction (DCR), we need to know the colour of both the programme star and the reference stars. In previous work we measured the colours, but for this work we used SDSS colours and adjusted the DCR correction factor slightly to account for this. thor03 describes a Bayesian procedure used to estimate distances from the available data, which combines the parallax measurement with an assumed space velocity distribution and absolute magnitude range. We used a similar approach here, but modified the prior information to be appropriate to the present sample. For the velocities, we used a composite distribution consisting of 60 per cent thin disc with , 30 per cent thick disc with (chiba00), and a 10 per cent probability of a still larger dispersion . The absolute magnitudes of these WDs are likely to be in the range 11–18, so the absolute magnitudes were assumed to be drawn from a Gaussian centred on with a standard deviation of 4 mag. In most cases our parallaxes were accurate enough that the Bayesian adjustments were fairly minor. Furthermore, we have four targets in common with the USNO Parallax programme and the parallax measurements are in good agreement (Harris, private communication).

There is only one target in our parallax sample, J1547+0523 (NLTT 41210), that does not display significant parallax. This object was identified as a high proper motion target by lepine05, and included in our sample as a WD candidate. We measure relative proper motions of and mas yr in RA and DEC, respectively. These are consistent with the proper motion measurements by lepine05. We also measure a parallax of 1.9 1.4 mas, which indicates that NLTT 41210 is not a WD.

2.2 Proper Motion

In Fig. 1, we compare our measured proper motions, as listed in Table LABEL:tab:astro, for the 42 WDs in our sample that also have measured proper motions in the SDSS+USNO-B catalogue (munn04). We expect disagreement at the 10 mas yr level since our proper motions are relative to the particular reference stars used in the reduction. Fig. 1 shows that the vast majority of our WDs do indeed fall within the range of  10 mas yr when compared with the SDSS+USNO-B measurements.

This disagreement arises due to two main factors. First, we make no attempt to reduce proper motions to an inertial frame. Any systematic trend due to e.g., Galactic rotation or solar motion, is still present. Secondly, reference stars often have detectable proper motions of their own, so in  versus  space they form a cloud of points around the origin. Because there are typically only a couple of dozen reference stars, the centre of this cloud is statistically uncertain, typically of the order of 5 mas yr.

SDSS RA (J2000) Dec. (J2000)
(h:m:s) (d:m:s) (mas yr) (mas yr) (mas yr) (pc) (km s) (km s) (km s) (km s)
J0045+1420 00:45:21.89 +14:20:45.3 15.9 1.1 66 80 6 46 5 37 4 5 2
J01210038 01:21:03.00 00:38:33.6 9.6 1.9 118 69 14 46 12 4 5 27 4
J0146+1404 01:46:29.01 +14:04:38.2 11.0 1.5 90 112 14 82 13 37 8 49 6
J02560700 02:56:41.62 07:00:33.8 16.4 1.5 61 115 10 17 3 96 10 34 3
J03010044 03:01:44.09 00:44:39.5 13.4 1.3 74 192 16 83 7 155 17 60 7
J0309+0025 03:09:24.87 +00:25:25.3 21.2 1.6 49 24 1 23 2 3 3 4 2
J03100110 03:10:49.53 01:10:35.3 7.1 1.9 164 64 18 47 11 14 10 25 10
J0747+2438N 07:47:21.56 +24:38:47.7 18.4 1.0 55 40 2 29 2 13 3 32 3
J0747+2438S 07:47:23.50 +24:38:23.7 18.4 1.0 55 40 2 29 2 13 3 32 3
J0753+4230 07:53:13.28 +42:30:01.6 36.2 1.0 27 53 1 10 1 40 2 10 1
J0805+3833 08:05:57.62 +38:33:44.1 47.6 1.0 21 83 1 24 1 30 1 55 2
J0817+2822 08:17:51.52 +28:22:03.1 19.6 1.5 52 51 3 25 2 36 4 9 2
J0821+3727 08:21:08.18 +37:27:38.3 12.8 3.2 86 90 25 44 8 50 16 50 11
J0825+5049 08:25:19.70 +50:49:20.1 20.4 1.3 49 108 6 48 4 51 5 57 4
J0854+3503 08:54:43.33 +35:03:52.7 15.7 1.5 64 68 6 14 3 37 6 32 4
J0909+4700 09:09:14.56 +47:00:17.5 16.6 1.7 61 61 6 17 3 36 6 16 3
J0942+4437 09:42:44.96 +44:37:43.1 11.7 1.2 87 96 9 30 5 66 9 23 4
J1001+3903 10:01:03.42 +39:03:40.5 11.6 2.1 87 140 25 73 16 75 16 60 12
J1107+4855 11:07:31.38 +48:55:23.0 20.9 1.7 48 167 13 128 12 56 6 53 5
J1115+0033 11:15:36.97 +00:33:15.3 20.2 2.5 51 61 7 50 5 27 5 14 3
J1117+5010 11:17:08.63 +50:10:33.9 21.3 1.7 48 49 4 51 4 1 2 31 2
J1158+0004 11:58:14.52 +00:04:58.3 28.9 1.7 35 31 1 7 2 33 2 20 1
J1203+0426 12:03:28.64 +04:26:53.6 22.8 2.1 45 63 6 50 6 13 2 10 1
J1204+6222 12:04:39.54 +62:22:16.4 18.3 2.5 58 43 6 16 2 22 5 28 3
J1212+0440 12:12:07.01 +04:40:12.0 16.0 2.6 64 86 14 54 11 38 9 11 3
J1238+3502 12:38:12.85 +35:02:49.1 10.0 2.0 110 100 20 18 7 73 18 12 1
J1251+4403 12:51:06.12 +44:03:03.1 22.9 5.3 63 41 14 30 5 8 5 15 2
J1345+4200 13:45:32.92 +42:00:44.2 27.3 1.0 36 40 1 28 2 8 2 9 1
J1349+1155 13:49:02.33 +11:55:11.8 35.3 1.6 28 74 3 69 3 28 2 17 1
J1422+0459 14:22:25.73 +04:59:39.7 16.7 2.1 61 80 10 34 6 49 8 28 3
J1424+6246 14:24:29.52 +62:46:17.1 21.1 2.0 48 62 5 23 4 31 5 33 3
J1436+4332 14:36:42.78 +43:32:35.7 37.1 1.2 27 75 2 63 3 25 1 9 1
J1437+4151 14:37:18.15 +41:51:51.5 16.0 2.2 66 52 7 3 3 30 6 29 3
J1447+5427 14:47:01.85 +54:27:44.6 21.3 3.5 51 58 10 27 7 19 5 27 4
J1452+4522 14:52:39.00 +45:22:38.3 11.4 1.4 95 39 5 25 6 17 4 9 2
J1458+1146 14:58:48.52 +11:46:55.9 17.0 1.6 60 45 4 7 2 31 5 16 2
J1534+4649 15:34:51.02 +46:49:49.5 33.1 1.8 30 75 4 49 4 17 2 40 2
J1606+2547 16:06:19.81 +25:47:02.9 22.6 1.7 45 54 4 13 2 33 4 35 3
J1615+4449 16:15:44.67 +44:49:42.5 12.1 3.7 89 99 37 100 27 12 8 1 3
J1632+2426 16:32:42.23 +24:26:55.2 22.9 1.2 44 70 3 65 3 30 3 5 2
J1704+3608 17:04:47.70 +36:08:47.4 21.1 1.7 48 57 4 52 4 20 2 31 4
J1722+5752 17:22:57.78 +57:52:50.7 17.8 1.8 56 105 10 94 11 16 2 11 2
J1728+2646 17:28:07.27 +26:46:19.2 17.2 1.8 59 70 7 67 6 28 5 1 3
J20410520 20:41:28.99 05:20:27.7 15.8 1.6 65 47 5 41 4 3 3 41 4
J2042+0031 20:42:59.23 +00:31:56.6 16.0 1.3 63 75 6 60 5 42 5 8 3
J20450710 20:45:57.53 07:10:03.5 12.0 1.4 86 59 7 49 5 31 6 10 3
J21180737 21:18:05.21 07:37:29.1 14.5 2.0 72 57 8 3 3 23 6 34 6
J2147+1127 21:47:25.17 +11:27:56.1 18.9 2.0 54 69 7 26 3 28 5 45 6
J2222+1221 22:22:33.89 +12:21:43.0 24.4 1.3 41 142 6 121 7 7 1 44 3
J2239+0018A 22:39:54.12 +00:18:47.3 12.2 2.9 107 62 19 8 6 49 9 31 6
J2239+0018B 22:39:54.07 +00:18:49.2 12.2 2.9 107 62 19 8 6 49 9 31 6
J2242+0048 22:42:06.19 +00:48:22.8 14.8 1.7 70 51 5 13 4 17 4 24 4
J2254+1323 22:54:08.64 +13:23:57.2 24.2 1.6 42 75 5 24 3 28 3 44 4
J2330+0028 23:30:55.20 +00:28:52.3 18.3 2.3 59 48 6 33 6 19 2 9 1
Since we do not have any radial velocity measurements for our targets, the component has been computed assuming  = 0 km s.
For these two binary systems, a weighted mean was adopted in the determination of their astrometric measurements.
Table 2: Astrometry of cool WDs.

2.3 Optical and Infrared Photometry

We have obtained the available photometry from the SDSS Data Release 10 (DR10, ahn14) for the 54 WDs in our sample. These data are listed in columns two through six in Table LABEL:tab:phot along with their uncertainties. The majority of our targets also have near-infrared photometry available from kilic10a, and are also listed in Table LABEL:tab:phot. For the six WDs without near-infrared photometry from kilic10a, we adopt the near-infrared photometry from the UKIDSS Large Area Survey (ULAS) Catalog (lawrence07), and the Two Micron All Sky Survey (2MASS; skrut06); see the notes at the bottom of Table LABEL:tab:phot.

2.4 Optical Spectroscopy

The majority of our targets were selected from the cool WD samples of kilic06a; kilic10a, hence they have optical spectroscopy obtained at the McDonald Observatory 2.7m telescope, Hobby-Eberly Telescope, or the Multiple-Mirror Telescope. The ultracool WDs and a few other cool WDs have spectroscopy available in the SDSS or the literature (leggett11; giam12; tremblay14). There are only eight DA WDs in our sample, with the rest of the stars classified as DC due to the absence of H absorption. This overabundance of DC WDs is due to our selection bias for targeting cool and ultracool WDs.

SDSS
J0045+1420 20.64 0.08 19.20 0.03 18.45 0.03 18.20 0.03 18.10 0.03 17.24 0.04 16.99 0.04 16.89 0.04
J01210038 22.82 0.28 20.79 0.03 19.74 0.03 19.38 0.03 19.18 0.04 18.47 0.06 18.23 0.08 18.05 0.09 18.10 0.19
J0146+1404 21.37 0.11 20.00 0.03 19.39 0.02 19.27 0.03 19.79 0.11 19.56 0.05 20.07 0.12
J02560700 20.74 0.08 19.00 0.02 18.13 0.02 17.79 0.03 17.69 0.03 16.71 0.05 16.62 0.05 16.48 0.06
J03010044 22.23 0.34 20.43 0.03 19.38 0.02 18.99 0.02 18.92 0.04 17.96 0.04 17.73 0.04 17.68 0.08
J0309+0025 19.15 0.03 18.19 0.02 17.72 0.02 17.53 0.02 17.50 0.02 16.64 0.04 16.54 0.04 16.87 0.04
J03100110 22.71 0.30 20.89 0.04 20.18 0.03 19.91 0.03 19.75 0.08 18.94 0.02 18.73 0.02 18.58 0.02
J0747+2438N 21.01 0.08 19.29 0.02 18.59 0.02 18.23 0.01 18.14 0.02 17.16 0.04 16.99 0.04 16.85 0.04
J0747+2438S 19.49 0.03 18.37 0.01 17.91 0.01 17.73 0.01 17.69 0.02 16.78 0.04 16.58 0.04 16.53 0.04
J0753+4230 19.97 0.04 18.09 0.01 17.19 0.01 16.87 0.01 16.75 0.02 15.69 0.04 15.49 0.04 15.47 0.04
J0804+2239 19.73 0.03 18.30 0.02 17.59 0.01 17.39 0.01 17.33 0.02 16.71 0.04 16.92 0.04 17.29 0.06
J0805+3833 19.00 0.02 17.31 0.01 16.56 0.02 16.27 0.02 16.20 0.02 15.34 0.05 15.19 0.08 14.90 0.09
J0817+2822 21.59 0.16 19.49 0.02 18.61 0.01 18.30 0.01 18.22 0.03 17.33 0.04 17.01 0.04 16.91 0.09
J0821+3727 20.68 0.06 19.14 0.02 18.43 0.01 18.15 0.02 18.04 0.02 17.25 0.04 17.00 0.04 16.85 0.05
J0825+5049 21.09 0.09 19.34 0.02 18.43 0.02 18.09 0.02 18.00 0.03 17.08 0.04 16.83 0.04 16.74 0.04
J0845+2257 15.57 0.01 15.73 0.01 16.08 0.01 16.35 0.02 16.61 0.02 16.24 0.11 15.96 0.00 16.48 0.00
J0854+3503 23.57 0.67 20.53 0.03 19.39 0.02 19.09 0.03 18.95 0.05 18.44 0.04 18.23 0.04 17.98 0.04
J0909+4700 20.64 0.15 19.29 0.03 18.74 0.02 18.50 0.02 18.42 0.05 18.11 0.04 18.62 0.07 19.10 0.10
J0942+4437 21.37 0.09 19.47 0.02 18.58 0.01 18.22 0.02 18.05 0.02 17.15 0.04 16.97 0.04 16.86 0.04
J1001+3903 21.36 0.10 20.05 0.02 19.60 0.02 20.02 0.03 20.61 0.17 20.65 0.06 21.05 0.07
J1107+4855 21.50 0.12 19.49 0.03 18.54 0.02 18.23 0.02 18.11 0.03 17.05 0.05 16.95 0.07 16.86 0.07
J1115+0033 19.50 0.04 17.92 0.01 17.22 0.02 16.99 0.01 16.90 0.02 15.78 0.08 15.65 0.18 15.59 0.26
J1117+5010 21.17 0.10 19.34 0.03 18.57 0.03 18.30 0.02 18.16 0.03 17.24 0.04 17.07 0.04 16.97 0.05
J1158+0004 20.86 0.11 18.89 0.04 17.85 0.02 17.54 0.01 17.34 0.03 16.36 0.04 16.31 0.05 16.18 0.05
J1203+0426 19.57 0.03 18.18 0.02 17.50 0.02 17.21 0.01 17.12 0.02 16.39 0.01 16.49 0.02 16.92 0.06
J1204+6222 20.91 0.09 19.25 0.02 18.43 0.02 18.14 0.02 18.06 0.03 17.07 0.04 16.86 0.04 16.80 0.04
J1212+0440 22.07 0.21 20.04 0.03 19.09 0.02 18.79 0.02 18.66 0.04 17.67 0.04 17.50 0.04 17.50 0.05
J1238+3502 24.74 0.81 21.77 0.09 20.31 0.06 19.88 0.05 20.37 0.15 21.19 0.06
J1251+4403 21.46 0.09 20.17 0.03 20.39 0.03 20.72 0.04 20.92 0.17 21.78 0.08
J1345+4200 19.70 0.03 17.85 0.02 17.01 0.01 16.69 0.02 16.54 0.01 15.61 0.06 15.43 0.11 15.00 0.00
J1349+1155 20.55 0.06 18.64 0.02 17.84 0.01 17.42 0.02 17.20 0.02 16.43 0.01 16.29 0.02 16.26 0.02
J1422+0459 20.98 0.10 19.44 0.03 18.58 0.02 18.27 0.02 18.18 0.03 17.15 0.05 17.10 0.08 17.02 0.05
J1424+6246 20.38 0.05 18.83 0.01 18.15 0.03 17.89 0.02 17.71 0.02
J1436+4332 19.83 0.04 18.04 0.02 17.19 0.01 16.85 0.03 16.75 0.03 15.78 0.04 15.62 0.04 15.51 0.04
J1437+4151 20.06 0.04 19.03 0.01 18.45 0.02 18.23 0.03 18.12 0.02 17.43 0.04 17.76 0.05 18.42 0.08
J1447+5427 21.23 0.12 19.46 0.04 18.64 0.02 18.36 0.02 18.25 0.04 17.26 0.07 17.20 0.07 17.07 0.06
J1452+4522 21.55 0.10 20.01 0.02 19.39 0.02 19.31 0.02 19.36 0.06 18.60 0.02 18.43 0.02 18.37 0.02
J1458+1146 20.62 0.08 18.85 0.02 18.02 0.02 17.72 0.02 17.64 0.02 16.63 0.04 16.47 0.05 16.31 0.06
J1534+4649 20.90 0.08 18.76 0.02 17.74 0.02 17.36 0.02 17.19 0.02 16.17 0.04 16.12 0.04 16.04 0.05
J1547+0523 19.96 0.04 18.05 0.01 17.13 0.00 16.75 0.00 16.51 0.01 15.38 0.00 14.95 0.00 14.77 0.01
J1606+2547 20.99 0.08 19.24 0.02 18.45 0.02 18.17 0.02 18.07 0.04 17.07 0.04 17.09 0.06 16.84 0.06
J1615+4449 21.18 0.10 19.59 0.02 18.84 0.02 18.57 0.02 18.52 0.04 17.44 0.04 17.24 0.05 17.26 0.07
J1632+2426 21.47 0.10 19.60 0.02 18.73 0.02 18.49 0.02 18.40 0.03 17.67 0.02 18.10 0.02 18.04 0.02
J1704+3608 20.50 0.05 18.72 0.01 17.94 0.01 17.66 0.01 17.55 0.02 16.62 0.04 16.34 0.04 16.32 0.06
J1722+5752 20.39 0.06 19.28 0.02 18.79 0.02 18.56 0.03 18.50 0.03 17.74 0.04 17.84 0.05 18.75 0.12
J1728+2646 19.18 0.03 18.14 0.02 17.68 0.01 17.51 0.01 17.46 0.02
J20410520 20.95 0.08 19.27 0.01 18.51 0.01 18.24 0.01 18.14 0.03 17.25 0.04 16.97 0.04 16.93 0.04
J2042+0031 21.67 0.14 19.95 0.02 19.05 0.01 18.73 0.01 18.61 0.03 17.65 0.04 17.45 0.04 17.36 0.05
J20450710 21.03 0.09 19.33 0.02 18.60 0.01 18.33 0.01 18.15 0.03 17.32 0.04 17.10 0.04 17.03 0.04
J21180737 23.38 0.95 20.70 0.03 19.48 0.03 19.01 0.02 18.76 0.04 17.90 0.04 17.82 0.04 17.81 0.05
J2147+1127 20.83 0.09 19.19 0.02 18.43 0.02 18.13 0.02 18.01 0.03 17.14 0.04 16.84 0.04 16.79 0.04
J2222+1221 21.74 0.11 19.48 0.02 18.37 0.02 17.88 0.02 17.67 0.02
J2239+0018A 21.27 0.08 20.14 0.04 19.59 0.03 19.48 0.05 20.28 0.16 19.57 0.10 19.69 0.19
J2239+0018B 23.13 0.36 20.79 0.04 19.88 0.03 19.49 0.03 19.24 0.06 18.66 0.05 18.34 0.06 17.98 0.10 18.48 0.27
J2242+0048 22.11 0.22 19.63 0.02 18.65 0.02 18.28 0.01 18.16 0.03 18.06 0.04 18.72 0.07 19.16 0.10
J2254+1323 21.57 0.17 19.51 0.02 18.49 0.02 18.14 0.01 18.00 0.02 17.04 0.04 16.88 0.04 16.85 0.04
J2330+0028 21.85 0.24 19.88 0.02 18.95 0.02 18.66 0.02 18.53 0.04 17.63 0.04 17.36 0.04 17.32 0.04
IR photometry from UKIDSS
IR photometry from 2MASS
Table 3: Optical and near-infrared photometry of cool WDs.

3 Theoretical Framework

Our model atmospheres and synthetic spectra are derived from the local thermodynamic equilibrium (LTE) model atmosphere code originally described in bergeron95 and references therein, with recent improvements discussed in tb09. In particular, we now rely on their improved calculations for the Stark broadening of hydrogen lines with the inclusion of non-ideal perturbations from protons and electrons – described within the occupation probability formalism of hm88 – directly inside the line profile calculations. Convective energy transport is taken into account following the ML2/ = 0.7 prescription of the mixing length theory. Non-LTE effects are also included at higher effective temperatures but these are irrelevant for the purpose of this work. More details regarding our helium-atmosphere models are provided in bergeron11.

Our model grid covers a range of effective temperature between  = 1500 and 45,000 K in steps of 500 K for   15,000 K, 1000 K up to  = 18,000 K, 2000 K up to  = 30,000 K and by steps of 5000 K above. The  ranges from 6.5 to 9.5 by steps of 0.5 dex, with additional models at  = 7.75 and 8.25. We also calculated mixed hydrogen and helium atmosphere models with  (He/H) = 2.0 to 5.0, in steps of 1.0 dex.

Since the photometric technique described below relies heavily on the flux at the and bandpasses, we now include in our models the opacity from the red wing of Ly (kowalski06), which significantly affects the flux in the ultraviolet.

4 Photometric Analysis

4.1 General Procedure

Figure 2: Location of the WDs in our sample in a versus (left) and (right) colour-magnitude diagram. The black dots correspond to the WDs with H-rich atmospheres while the white dots represent the He-rich WDs. The red dots represent the 15 cool and ultracool WDs with mixed atmospheres. The solid and dashed black lines represent pure H and pure He tracks, respectively, for masses = 0.3, 0.6, and 0.9 M, from right to left. The solid blue lines represent the predictions from mixed model atmospheres for = 0.2 M. The mixed atmosphere model tracks are labelled with their He abundance  (He/H) = 2 and 2. LHS 3250 and J1102 are shown as a green triangle, and a blue square, respectively.

Atmospheric parameters,  and , and chemical compositions of cool WDs can be measured accurately using the photometric technique developed by brl97. We first convert optical and infrared photometric measurements into observed fluxes and compare the resulting energy distributions with those predicted from our model atmosphere calculations. To accomplish this task, we first transform every magnitude into an average flux . Since photometry is defined on the AB magnitude system, we first calculate using the equation

(1)

and then is converted to following , where is the central wavelength of the given filter. For the near-infrared photometry, we obtain using the equation

(2)

where is a constant to be determined for each filter, as described below. In general,

(3)

where is the transmission function of the corresponding bandpass, is the monochromatic flux from the star received at Earth. For the photometry, a slightly different definition of the above Equation (3) is required (see Equation (3) of hb06, for instance). The transmission functions for the system are described in hb06 and references therein. The transmission functions for the or filters on the MKO photometric system are taken from tokunaga02.

The constants in Equation (2) for each passband are determined using the improved calibration fluxes from hb06, defined with the absolute flux scale of Vega (bohlin04), and appropriate magnitudes on a given system.

For each star in Table LABEL:tab:phot, a minimum set of five average fluxes is obtained, which can be compared with model fluxes. Since the observed fluxes correspond to averages over given bandpasses, the monochromatic fluxes from the model atmospheres need to be converted into average fluxes, , by substituting in Equation (3) for the monochromatic Eddington flux, . We can then relate the average observed fluxes and the average model fluxes – which depend on , and chemical composition – by the equation

(4)

where defines the ratio of the radius of the star to its distance from Earth. We then minimize the value defined in terms of the difference between observed and model fluxes over all bandpasses, properly weighted by the photometric uncertainties. Our minimization procedure relies on the non-linear least-squares method of Levenberg–Marquardt (press86), which is based on a steepest decent method. Only  and the solid angle are considered free parameters, while the uncertainties of both parameters are obtained directly from the covariance matrix of the fit.

For stars with known trigonometric parallax measurements, we first assume a value of  = 8.0 and determine the effective temperature and the solid angle, which combined with the distance obtained from the trigonometric parallax measurement, yields directly the radius of the star . The radius is then converted into mass using evolutionary models similar to those described in fontaine01 but with CO cores, (He) and (H) = 10, which are representative of hydrogen-atmosphere WDs, and (He) = 10 and (H) = 10, which are representative of helium-atmosphere WDs. After the first iteration, if  0.406 M, we switch to the evolutionary models of althaus01, appropriate for low-mass He-core WDs. In general, the  value obtained from the inferred mass and radius will be different from our initial guess of  = 8.0, and the fitting procedure is thus repeated until an internal consistency in  is reached.

Figure 3: Fits to the observed energy distributions with pure hydrogen models (filled circles) and with pure helium models (open circles) for the eight WDs that exhibit, or potentially exhibit, absorption at H. Adopted atmospheric parameters are emphasized in red. Here and in the following figures, the photometric observations are represented by error bars while the filled and open circles represent the model fluxes for the pure H and pure He solution, respectively. In the right-hand panels we show the observed normalized spectra together with the synthetic line profiles calculated with the atmospheric parameters corresponding to the pure hydrogen solutions.

4.2 Results

Fig. 2 presents the colour-magnitude diagram for our parallax sample along with the evolutionary tracks for 0.3–0.9 M pure H, pure He, and 0.2 M mixed H/He atmosphere models. Note that all the evolutionary tracks plotted in Fig. 2 represent the evolution of CO-core WDs. Two other ultracool WDs with parallax measurements and SDSS photometry, LHS 3250 and J1102 (harris99; bergeron01; hall08; kilic12), are also included for comparison.

Interestingly, the majority of the targets in our sample fall above the evolutionary tracks for 0.6 M WDs, indicating that they are low-mass objects. Some of these WDs are even brighter than the 0.3 M WD sequence, implying masses as low as  0.2 M. A significant fraction of the stars in our sample are IR-faint WDs that suffer from CIA from molecular hydrogen. The CIA affects the redder optical bands and the infrared. Hence, most of these IR-faint objects lie to the left of the pure H and pure He model sequences. Note that our sample was selected to include as many IR-faint WDs as possible. Therefore, these are overrepresented in this figure. It is clear from this figure that the colour-magnitude distribution of our sample is well matched by WD models with masses  0.2–0.9 M with a variety of compositions, including pure H, pure He and mixed H/He atmospheres. Below we discuss the DA, DC and ultracool WD samples separately.

4.2.1 DA WDs

Fig. 3 displays the best-fitting pure-hydrogen models to the SEDs of the eight WDs classified as DA. Both the observed SEDs and the H line profiles are reproduced fairly well by our pure H models. Given our parallax measurements, the best-fitting radii for these eight targets range from 0.011 to 0.022 R (), indicating that they are relatively low-mass WDs. In fact, half of these WDs have masses below 0.45 M, and therefore are likely He-core WDs. The majority of low-mass WDs are in short-period ( 1 d) binary systems (marsh95; brown11). Therefore, J0045+1420, J0821+3727, J1115+0033, and J1728+2646 are likely unresolved binary WDs. Table 4 provides WD cooling age estimates for these DA WDs, as well as the rest of our parallax sample. For  M WDs, we provide cooling ages for both CO and He core composition based on the evolutionary tracks of fontaine01 and althaus01, respectively. Regardless of the core composition, these eight DA WDs have cooling ages of less than 8 Gyr.

It is necessary to note an important caveat regarding the four potential binaries listed above. If they are indeed unresolved binaries, then the WDs in these systems will be more massive than implied by our fits assuming a single star. Hence, their actual cooling ages will be larger for a given . Our estimates for the cooling ages of these potential binaries should therefore be regarded, at best, as lower limits.

4.2.2 DC WDs

Fig. 4 shows our model fits to the SEDs of the 31 DC WDs that are best explained by pure H or pure He atmosphere models. In all cases, the optical spectra are featureless near the H region. Hence, the choice of a pure H or pure He composition is based solely on the fits to the optical and infrared photometry. In most cases, the atmospheric parameters from both the pure H and pure He solution agree within the uncertainties. Our model fits indicate that all of these WDs have   5000 K. The ratio of the H to He atmosphere WDs is 13/18. However, all DC WDs with temperatures below  = 4530 K are best explained by H-rich atmosphere models (see also kowalski06; giam12).

Just like the DA sample discussed above, about half of the DCs in this sample are low-mass objects. The two coolest stars, J21180737 and J2222+1221, have  = 3920  60 and 4010  80 K, and  = 0.31  0.09 M and 0.37  0.03 M, respectively. Assuming He-cores, these temperatures correspond to cooling ages of 7.7 and 9.4 Gyr, respectively. If these are short-period, unresolved binary systems, then the companions would be fainter and more massive WDs. Due to the unknown prior history of such binary systems and without an estimate on their initial masses, their total ages, including the main-sequence + WD cooling ages, cannot be reliably calculated.

Figure 4: Fits to the observed energy distributions with pure hydrogen models (filled circles) and with pure helium models (open circles) for the 31 DC WDs. All objects have featureless spectra near the H region, and the SEDs are best explained with pure model atmospheres. Adopted atmospheric parameters are emphasized in red.
Figure 4: continued

4.2.3 DC WDs with Mixed H/He Atmospheres

gates04, harris08 and kilic10a have identified several IR-faint WDs that were originally thought to be ultracool WDs with   4000 K. It turns out that some of these IR-faint WDs are relatively warm. There are nine IR-faint, DC WDs in our sample that are best-fitted with   4500 K mixed H/He atmospheres models. The main opacity source in these mixed models is the H–He CIA in the infrared. Since cool He-rich WDs have lower opacities and higher atmospheric pressures, the CIA becomes effective at higher temperatures (  4000 K, bergeron02).

Fig. 5 shows the SEDs for these nine DC WDs with mixed composition. The mixed models with to 2.3 fit the observed SEDs (over the 0.3–2.2 m region) fairly well. The best-fitting parameters for some of these stars are markedly different than the parameters presented in kilic10a. However, the analysis presented in this paper is superior to earlier work since we now include all available photometry in our analysis (including the -band data) and we also have parallax measurements available. J1632+2426 is the most-massive and the oldest WD (in terms of the WD cooling age) in this sample, with a mass of 0.82  0.04 M and a cooling age of 7.7 Gyr.

Figure 5: Fits to the SEDs of the nine IR-faint, DC WDs in our sample, excluding the ultracool WDs. All objects have featureless spectra near the H region, and the SEDs are best explained with mixed model atmospheres. Note that the measured abundances are quoted relative to the dominant atmospheric constituent.
Figure 6: Fits to the SEDs of the six ultracool DC WDs in our sample. All objects have featureless spectra near the H region, and the SEDs are best explained with mixed model atmospheres. Note that the measured abundances are quoted relative to the dominant atmospheric constituent.

4.2.4 Ultracool WDs

We originally selected 12 ultracool WD candidates for follow-up parallax observations: J0854+3503 and J1001+3903 from gates04; J01210038, J03010044, J2239+0018 and J2242+0048 from vidrih07; J0146+1404, J03100110, J1238+3502, J1251+4403, J1452+4522 and J1632+2426 from harris08. Our detailed model atmosphere analysis using parallax data shows that only half of these stars are actually ultracool WDs with   4000 K. The rest of the ultracool candidates are best explained by pure H/He or mixed atmosphere models with   4000 K.

Fig. 6 shows the SEDs and our model fits to the six ultracool WDs in our sample. The best-fitting parameters are given in each panel and at the end of Table 4. Note that prior to this work, there were only three ultracool WDs with parallax observations available. Hence, the ultracool WD sample presented here is a significant addition to this sample. The six ultracool WDs presented here are best explained by mixed H/He atmospheres with  = 2710–3760 K and  = 0.65–2.96. Interestingly, all six of these ultracool WDs are too bright for average mass WDs. Instead, the observed parallaxes require relatively large radii ( = 0.015–0.023 R) and low masses ( = 0.17–0.39 M). Assuming He-cores, the WD cooling ages range from 4.5 to 9.7 Gyr. They are located within 63–110 pc of the Sun and they display tangential velocities of 40–140 km s. Hence, these ultracool WDs likely belong to the Galactic disc.

SDSS Comp.
(K) (cm s) (M) (R) ( He/H) (mag) (Gyr) (Gyr)
DA
J0045+1420 5090 60 7.73 0.15 0.43 0.07 0.015 0.001 H 15.10 0.18 2.7
J0747+2438S 5590 40 7.92 0.09 0.54 0.05 0.013 0.001 H 14.67 0.12 2.5
J0821+3727 5050 50 7.27 0.50 0.27 0.15 0.020 0.006 H 14.47 0.59 1.6 3.1
J1115+0033 4910 40 7.05 0.27 0.21 0.07 0.022 0.003 H 14.38 0.28 1.4 2.9
J1424+6246 4970 60 7.88 0.16 0.51 0.09 0.014 0.001 H 15.42 0.20 4.4
J1606+2547 4860 60 8.18 0.12 0.69 0.08 0.011 0.001 H 15.97 0.17 7.9
J1728+2646 5600 50 7.65 0.17 0.42 0.07 0.016 0.002 H 14.29 0.24 1.6 3.5
J2147+1127 4920 60 7.90 0.18 0.52 0.10 0.013 0.002 H 15.53 0.24 4.9
DC
J01210038 4560 50 7.31 0.39 0.28 0.13 0.019 0.004 He 15.43 0.46 2.2 4.6
J02560700 4780 40 7.39 0.15 0.30 0.05 0.018 0.002 He 15.07 0.20 2.2 4.6
J03010044 4530 50 7.79 0.16 0.45 0.08 0.014 0.001 He 16.08