WHITE DWARFS IN THE UKIRT INFRARED DEEP SKY SURVEY DATA RELEASE 9

The LAS is a sub-survey of UKIDSS aimed at identifying cool and faint galactic sources in the YJHK bands (Hewett et al. 2006) with a large photometric depth. In Paper I, target white dwarfs were selected in the 280 deg² sky area of the LAS DR2, producing a sample of seven new white dwarfs with T_eff ∼ 6000 K, confirmed with optical spectroscopy obtained at Gemini Observatory. Paper II used the larger 1400 deg² area covered by the LAS DR6 and refined the color selection to identify 13 more white dwarfs, including 7 objects with T_eff < 4500 K.

Near-infrared photometry is essential to characterize cool white dwarfs since the CIA due to H₂ molecules is observed in this wavelength range. It is also crucial to have a broad wavelength coverage in order to determine precise T_eff values. The LAS and SDSS databases were therefore cross-correlated in order to add ugriz photometric information. Furthermore, proper motions were derived using the target coordinates and the epochs of the SDSS and UKIDSS images. Sources were matched by requiring the presence of a primary SDSS source within 5'' of one LAS point source coordinate.

The color and reduced proper motion (RPM) selection of the published LAS white dwarf candidates is discussed in Paper I (Section 3) and Paper II (Section 2.3). In brief, the search was restricted to high proper-motion sources with RPM values of H_g = g + (5log (μ) + 5) > 20.5 (20.35 in Paper I), where g is the SDSS magnitude and μ the proper motion. The near-infrared flux was limited to 14 ⩽ J ⩽ 19.6 to ensure non-saturation and a good detection while the restriction r_AB < 20.7 was employed to allow for spectroscopic observations of the candidates. In Figures 1 and 2, we present the sample of Paper I and Paper II in the H_g versus g − i RPM diagram, and r − i versus g − r and J − H versus i − J color versus color diagrams, respectively.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In Paper I, sources as faint as 19.7 in H were selected, although it was found that LAS uncertainties were significantly underestimated for such large H magnitudes. In particular, many of the objects selected as probable very cool white dwarfs with J − H < −0.1 were in fact warmer degenerates with H-line spectra (DA) that were scattered into the color selection because H was too faint. This led to a more stringent color selection and the acquisition of repeat JHK photometry, using the WFCAM on UKIRT and NIRI on Gemini North, for most candidates in Paper II. It was confirmed that for H ≳ 18, LAS H-band magnitudes are too faint by about 2σ.

We updated the photometry presented in Paper I and Paper II by relying on the improved data reduction from the Data Release 10 of both the SDSS and LAS surveys. We employ this improved data set to derive updated atmospheric parameters in Section 4.

In this work, we have employed the LAS DR9 combined with the SDSS DR9 (Ahn et al. 2012) to identify 18 new cool white dwarf candidates. The LAS DR9 covers 3176 deg², most of which is also covered in SDSS DR9 since UKIDSS was originally designed to provide a near-infrared counterpart to the SDSS survey. This suggests that we can significantly enhance the size of the sample compared to the earlier studies. We refer to Paper II for a review of the derivation of the proper motions from the combined SDSS/LAS data.

Table 1 gives the astrometric information for the new candidates, and Table 2 presents the observed photometry and associated uncertainties. While the sample was identified and selected from the SDSS and LAS DR9, the photometric and astrometric data used for our analysis and presented in Tables 1 and 2 is drawn from the DR10 of both surveys. It was found that the new SDSS/LAS astrometry implies much smaller proper motions for four objects, which led us to discard J0349−00 and J0838+24 since they are likely to be G- to K-type (sub)dwarfs (H_g < 20).

Table 1 identifies the three different RPM and color regions where white dwarf candidates were selected in this work. Region A corresponds to cool T_eff ∼ 4000 K pure-H atmospheres, and this is where most white dwarfs were detected in earlier studies. Out of 10 candidates in this area, 8 were confirmed spectroscopically as white dwarfs (see Section 2.3), 1 is a likely white dwarf with no spectrum, and 1 was found to be a G- to K-type (sub)dwarf. Region B aims at recovering mixed H/He objects with near-infrared CIA absorption, and we extend this search area compared to Paper II. This selection did not result in any new confirmed white dwarf as all four candidates with H_g > 20 were found to be either subdwarfs or extragalactic sources. We also created a third search criterion to identify objects with no H or K detection although it only resulted in one more object (J0916+30) as a likely white dwarf, while one other was confirmed as a main-sequence star. As also concluded in Paper II, the region A selection robustly identifies white dwarfs with T_eff = 4100–4700 K, and cooling ages of 7–9 Gyr.

Two of our candidates, J1240+25E and J1240+25W, have a close projected position on the sky. Over the period of 5.12 yr covered between the SDSS DR10 and UKIDSS DR10 detections, the east component shows a proper motion of +1338 in R.A. and +0103 in decl. Over this same period the west component moves +1348 in R.A. and +0120 in decl. Given the close projected proximity, the movement in the same direction across the sky, and the agreement in the measured motion to within 4 mas yr⁻¹, we can identify the pair as a binary.

We obtained additional near-infrared photometry for a subset of the sample where LAS data were missing. Repeat photometry was also secured for objects where LAS uncertainties are larger than ∼0.1 mag since the errors are likely to be underestimated in those cases (see Paper II). The additional YJHK photometry was obtained for 12 targets using NIRI (Hodapp et al. 2003) on Gemini North. In Table 3, we present the observation log and the data are given in Table 4.

Optical spectroscopic observations were obtained for 13 objects and 8 of them turned out to be genuine white dwarfs. The Gemini Multi-Object Spectrographs (GMOS; Hook et al. 2004) at both Gemini North and South were used for all new observations. The R400 grating was employed with the GG455 blocking filter and the central wavelength was 680 nm, with wavelength coverage of 460–890 nm. As in Paper II, the 075 slit was used with 2 × 2 binning and the resulting resolution is R ∼ 1280 or 5.5 Å.

Figure 3 shows the GMOS spectra of the new white dwarfs. All of them are featureless and consistent with the DC classification except for J1240+25E which shows a weak pressure-broadened Hα. In the following, we add two objects without spectra in our sample (J0100+11 and J0916+30) since the photometric fits and tangential velocities suggest they could be white dwarfs (see Section 4.2). We also rely on the white dwarf spectra presented in Paper I and Paper II for objects found in earlier LAS data releases.

Zoom In Zoom Out Reset image size

The eight new spectroscopically confirmed white dwarfs and two degenerate candidates are presented in the RPM and color versus color diagrams of Figures 1 and 2 along with white dwarfs discovered in earlier LAS data releases. We also illustrate the search regions A, B, and C. There is a significant number of new objects outside of the search regions since we rely on the updated DR10 samples and NIRI photometry instead of the DR9 used in the initial selection. As in our earlier studies, some objects were scattered into the color selection because LAS H was too faint.

We rely on pure-H, pure-He, and mixed composition 1D model atmospheres that are similar to those described and used in Paper I, Paper II, Kilic et al. (2010), Giammichele et al. (2012), and Catalán et al. (2012). Contrary to earlier studies of LAS white dwarfs, the pure-H models now include the Lyα red wing opacity from Kowalski & Saumon (2006), while the pure-He and mixed composition models are identical to those described in Kilic et al. (2010). The mixed composition atmospheres have ratios of He to H by number ranging from values of 10⁻² to high values of 10¹⁰. All models rely on the mixing-length theory (MLT; under the ML2/α = 0.8 parameterization) to treat convective energy transfer.

For the coolest DA white dwarfs, there is no change in the predicted spectra when the mixing-length parameterization of the MLT is varied in the model atmospheres (Bergeron et al. 1995). The source of this behavior is that the MLT predicts that convection is essentially adiabatic throughout the atmosphere (i.e., there is no significant entropy jump), in which case the thermodynamic structure only depends on the value of the adiabatic gradient and not on the properties of convective granules, such as the horizontal extent and lifetime.

It is desirable to confirm the robustness of the 1D approximation for cool white dwarfs. For that purpose, we have computed CO⁵BOLD multi-dimensional simulations for T_eff = 3770 and 4520 K, in both cases at log g = 8. We present the properties of these simulations in Table 5. The two-dimensional (2D) models use the same numerical setup as the one described in Tremblay et al. (2013b) where the coolest simulations are at T_eff = 6000 K. On the other hand, the 3D simulations rely on a new version of CO⁵BOLD with advances for low-Mach-number flows (Freytag 2013). The improved numerical schemes are less diffusive and provide proper granulation in brown dwarfs (i.e., similar to models at higher Mach numbers). In brief, we rely on an equation of state and opacities that are the same as those of our 1D model atmospheres described above. We employ an eight opacity bin scheme to describe the band-integrated radiative transfer. The wavelength dependent opacities are sorted based on the Rosseland optical depth (τ_R) at which τ_λ = 1 and we take 150 × 150 × 150 grid points to solve the radiative transfer and hydrodynamical equations. We have derived T_eff from the temporally and spatially averaged emergent stellar flux.

Figure 4 demonstrates that the convective turnover timescale is rather similar in very cool DC white dwarfs and hotter DAs, with a value below one second. On the other hand, the radiative relaxation timescale is more than 30 s in all layers at T_eff = 4520 K which is rather long compared to DAs. It implies that radiative transfer will have little impact on the structure of the convectively unstable layers. This decoupling between the two timescales is also unfortunate for 3D simulations, since one must use small time steps to solve the dynamical equations and have a long total time to cover the radiative relaxation time. This problem is similar to the one encountered in Tremblay et al. (2013b, see Section 3.3) for cool DA white dwarfs (T_eff ≲ 8000 K). As in Tremblay et al. we instead perform non-gray 2D simulations where it is possible to cover a few radiative relaxation timescales. Tremblay et al. (2013b) have shown that most of the multi-dimensional effects are already in the 2D simulations, and that 3D mean structures are only slightly different from their 2D counterparts.

Zoom In Zoom Out Reset image size

We find that both our models at T_eff = 3770 and 4520 K reach an almost completely adiabatic structure in all layers. This outcome is similar to the coolest DA models in Tremblay et al. (2013b). The convective overshoot causes the entropy gradient in the upper layers to relax to an adiabatic structure even in regions that are stable to convection in 1D. In Figure 5, we compare 1D and 〈2D〉 structures for the simulation at 3770 K. The spatial and temporal averages are performed over surfaces of constant Rosseland optical depth and for 12 random snapshots. We observe that both structures are nearly identical, except for the very top layers. The results are very similar for the 4520 K case. In these cool objects, H₂ molecule formation causes a strong CIA, and even the 1D model atmospheres are unstable to convection up to τ_R ∼ 10⁻³. In the convective layers, the structure is adiabatic and identical for 1D and 2D models since they rely on the same equation of state. Therefore, we conclude that 1D model atmospheres relying on the MLT are appropriate to model current observations of cool DC white dwarfs.

Zoom In Zoom Out Reset image size

We have used our 2D simulations as initial conditions to compute 3D atmospheres for 10 s in stellar time. Since radiative relaxation timescales are much longer, we expect that the mean structure will remain adiabatic and there is little interest in using the mean properties of the 3D simulations. However, the 3D simulations allow the study of the granulation properties, which is impossible in 1D and rather limited in 2D.

Cool DC white dwarfs reach photospheric densities that are seen otherwise in cool M dwarfs and brown dwarfs. However, the latter objects contain metals in their atmospheres and are subject to molecule, grain, and cloud formation in and above their photosphere (Freytag et al. 2010). In Figure 6, we present intensity snapshots for our 3D simulations. The relative intensity contrast (see Equation (73) of Freytag et al. 2012) is given on the top of each snapshot in Figure 6. For our coolest simulation at T_eff = 3770 K, the intensity contrast is remarkably small at 0.03%, although it is following the trend observed in Tremblay et al. (2013a) given the low Mach number value in Table 5. In the same table, we also give the characteristic horizontal size of the granulation, which is roughly a factor of three to four times the pressure scale height at τ_R = 1, in very good agreement with the trend found for cool DA white dwarfs where the characteristic size reaches a plateau at around that value for photospheric densities larger than ∼10⁻⁵ g cm⁻³.

Zoom In Zoom Out Reset image size

In order to determine the atmospheric parameters of our observed targets, we first converted the magnitudes into observed fluxes using the method of Holberg & Bergeron (2006) and the appropriate filters. The SDSS magnitudes are converted to the AB system employing the u, i, and z corrections given in Eisenstein et al. (2006, see their Section 2). We fit the resulting energy distributions with those derived from model spectra, integrated over the same filters, using a nonlinear least-squares method (Bergeron et al. 2001). Given our result that 3D effects are negligible, in the following we rely only on the 1D spectra described in Section 3.

From the fit of the observed energy distribution we constrain 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. Since predicted energy distributions depend only weakly on gravity and no parallax measurements are available, it is not possible to constrain the gravity of our objects. We therefore assume a surface gravity of log g = 8. Most white dwarfs are found in a rather narrow range of gravity (Bergeron et al. 1992; Kleinman et al. 2013) and we employ, as in Paper II, a gravity uncertainty of ±0.3 dex. The photometric variance uncertainties are obtained from the covariance matrix of the fit.

We rely on the mass–radius relation from the evolutionary models of Fontaine et al. (2001) with carbon–oxygen cores (50/50 by mass fraction mixed uniformly) to determine the radius, mass, and cooling age. We assume thick H layers (M_H/M_total = 10⁻⁴) for H-atmosphere white dwarfs and thin layers (M_H/M_total = 10⁻¹⁰) for He and mixed atmospheres. We also derive the distance to our targets by combining the mass–radius relation and the best-fit solid angle. The log g = 8.0  ±  0.3 assumption dominates the uncertainties on our derived masses and cooling ages. On the other hand, it has little impact on the T_eff determinations for which the uncertainty is dominated by the photometric variance. Compared to Paper II, we include the SDSS u and g filters for all fits since our model spectra rely on the Lyα red wing opacity. We use NIRI instead of LAS near-infrared photometry when available, and neglect LAS photometry with uncertainties larger than 0.15 mag since it was found in earlier studies that errors were significantly underestimated in those cases.

Finally, the surface composition is constrained from both the optical spectra at Hα and the photometry. Since Hα absorption is not seen in H-rich white dwarfs cooler than ∼5000 K, we can only rely on the photometric fit in those cases. When possible, we also estimate effective temperatures from a fit of the Hα equivalent width (T_Hα).

The best-fit atmospheric parameters for the 10 new white dwarfs drawn from the LAS DR9 and the 20 white dwarfs identified in Paper I and Paper II are given in Table 6. We also derive distances and cooling ages from evolutionary models as discussed in Section 4.1. The distances and proper motions, given in Table 1, are then used to compute the tangential velocity v_tan.

Table 6. Derived Properties of the LAS Sample

Short Name	Spectral	Composition	Teff	THα	Cool. Age	Distance	vtan
	Type		(K)	(K)	(Gyr)	(pc)	(km s−1)
ULAS J0024−00	DC	Unconstrained	4610 ± 130	⋅⋅⋅	7.1$^{+2.3}_{-3.5}$	98 ± 21	78 ± 17
ULAS J0049−00	DA	H	6290 ± 90	5700	2.0$^{+1.8}_{-0.6}$	141 ± 26	83 ± 15
ULAS J0100+11	⋅⋅⋅	He	4140 ± 80	⋅⋅⋅	8.0$^{+0.2}_{-3.0}$	88 ± 19	49 ± 11
ULAS J0121−00	DC	H	4320 ± 100	⋅⋅⋅	8.2$^{+1.6}_{-2.8}$	71 ± 10	33 ± 5
ULAS J0142+00	DA	H	6010 ± 100	5650	2.2$^{+2.0}_{-0.7}$	149 ± 27	74 ± 13
ULAS J0226−00	DA	H	5620 ± 120	5550	2.8$^{+2.4}_{-1.1}$	157 ± 28	82 ± 15
ULAS J0302+00	DC	He	5630 ± 150	⋅⋅⋅	3.5$^{+2.2}_{-1.5}$	171 ± 34	99 ± 20
ULAS J0815+24	DC	H	4150 ± 100	⋅⋅⋅	8.6$^{+1.4}_{-2.7}$	72 ± 11	42 ± 7
ULAS J0826−00	DC	H	4100 ± 130	⋅⋅⋅	8.8$^{+1.3}_{-2.6}$	76 ± 9	33 ± 4
ULAS J0840+05	DC	Mixed	4360 ± 140	⋅⋅⋅	7.5$^{+0.4}_{-3.0}$	82 ± 16	44 ± 9
ULAS J0916+30	⋅⋅⋅	Unconstrained	5630 ± 240	⋅⋅⋅	3.3$^{+2.7}_{-1.6}$	168 ± 42	58 ± 15
ULAS J1006+09	DC	He	4250 ± 110	⋅⋅⋅	7.8$^{+0.4}_{-3.2}$	72 ± 17	50 ± 12
ULAS J1206+03	DC	He	4570 ± 70	⋅⋅⋅	7.0$^{+0.7}_{-3.2}$	92 ± 19	72 ± 15
ULAS J1240+25E	DA	H	5570 ± 50	5250	3.0$^{+2.6}_{-1.2}$	130 ± 25	163 ± 31
ULAS J1240+25W	DA?	H	5130 ± 50	⋅⋅⋅	5.0$^{+2.8}_{-2.5}$	124 ± 24	154 ± 30
ULAS J1320+08	DC	Mixed	4810 ± 130	⋅⋅⋅	6.5$^{+0.8}_{-3.1}$	103 ± 19	96 ± 18
ULAS J1323+12	DA	H	5270 ± 70	5300	4.3$^{+2.8}_{-2.1}$	107 ± 19	106 ± 19
ULAS J1345+15	DC	H	3990 ± 80	⋅⋅⋅	9.0$^{+1.4}_{-2.7}$	57 ± 9	71 ± 11
ULAS J1351+12	DC	He	4780 ± 60	⋅⋅⋅	6.5$^{+0.9}_{-3.2}$	101 ± 20	58 ± 12
ULAS J1404+13	DC	Mixed	4350 ± 140	⋅⋅⋅	7.5$^{+0.4}_{-2.7}$	59 ± 9	43 ± 7
ULAS J1409+07	DC	H	4710 ± 30	⋅⋅⋅	6.9$^{+2.1}_{-3.2}$	60 ± 11	64 ± 12
ULAS J1436+05	DC	Unconstrained	4320 ± 170	⋅⋅⋅	7.9$^{+2.1}_{-3.7}$	56 ± 13	84 ± 19
ULAS J1454−01	DC	Unconstrained	4700 ± 80	⋅⋅⋅	6.8$^{+2.4}_{-3.4}$	63 ± 13	63 ± 13
ULAS J1522+08	DA	H	5370 ± 130	5450	3.7$^{+2.9}_{-1.7}$	151 ± 28	75 ± 14
ULAS J1607+26	DC	H	4450 ± 50	⋅⋅⋅	7.7$^{+1.9}_{-3.3}$	64 ± 12	49 ± 9
ULAS J2206+02	DC	H	4120 ± 70	⋅⋅⋅	8.7$^{+1.6}_{-2.9}$	58 ± 10	58 ± 10
ULAS J2330+05	DC	Unconstrained	4465 ± 380	⋅⋅⋅	7.6$^{+2.4}_{-4.1}$	74 ± 23	61 ± 19
ULAS J2331−00	DA	H	6310 ± 130	5550	2.0$^{+1.8}_{-0.6}$	183 ± 34	119 ± 22
ULAS J2331+15	DA	H	5030 ± 60	5100	5.5$^{+2.7}_{-2.8}$	99 ± 20	75 ± 15
ULAS J2339−00	DA	H	6450 ± 200	5900	1.9$^{+1.7}_{-0.6}$	189 ± 35	92 ± 17

Notes. We assume log g = 8 and uncertainties are computed from the photometric scatter and an allowed range in gravity of 7.7 ⩽log g ⩽ 8.3. The tangential velocity is calculated from the distance and proper motion given in Table 1 and Paper I and Paper II. For J1323+12 we rely on the alternative proper motion given in Paper II. We do not include ULAS J1528+06 and J1554+08 from Paper I which were found to be subdwarfs. We also exclude LAS white dwarfs that were previously discovered in the SDSS (SDSS J2242+00; Kilic et al. 2006, and SDSS J1247+06; Kilic et al. 2010).

Download table as:  ASCIITypeset image

Among the newly identified white dwarfs, the fits shown in Figure 7 for the resolved binary ULAS J1240+25E/W are particularly interesting since we can compare the derived distance and age of both components. J1240+25E is clearly H-rich given the Hα observation. However, while the photometric fit gives a temperature of ∼5570 K, the equivalent width of Hα is consistent with a ∼300 K lower T_eff value, which is significantly larger than the variance allowed by the photometric uncertainties. The photometric and T_Hα temperatures can be brought into agreement if the mass is very large (>1 M_☉). The other component, J1240+25W, does not show a clear Hα absorption feature, and it is either a cooler H atmosphere or an He-rich object. The fit quality is average for both the pure-H (filled circles) and pure-He (open circles) cases, hence it is difficult to constrain the composition only from the photometric fit. However, the u − g color has a large positive value which is consistent with a Lyα red wing absorption. We therefore select the pure-H composition, also noticing that the spectrum shows a hint of a faint Hα line. The cooling age of the system is 3.0 and 5.0 Gyr based on the east and west component, respectively. We look at this apparent discrepancy and compare the parameters of both components of the system under different assumptions in Section 4.3. Nevertheless, it is clear that both white dwarfs have a relatively low cooling age, and have a large velocity of v_tan ∼ 155 km s⁻¹, which could suggest disk remnants with a very high velocity or former halo G stars.

Zoom In Zoom Out Reset image size

Figure 8 displays four new white dwarfs that are best fit with pure-H atmospheres. For J0815+24 and J2206+02, the cooling ages of 8.5–9.0 Gyr and the tangential velocities in the range 40 km s⁻¹ ⩽v_tan ⩽ 60 km s⁻¹ suggest they are thick disk stars with a total age of 10–11 Gyr. Figure 9 exhibits two more new white dwarfs for which we could not constrain the composition based on the photometric fits and featureless DC spectra (J0024−00 and J2330+05). Finally, Figure 10 shows two objects for which we do not have spectra to confirm their degenerate nature. J0100+11 has a similar temperature to the coolest pure-H objects in our sample in Figure 8, but a significantly larger near-infrared flux that is better fitted with a pure-He model. This would be one of the coolest known white dwarfs with a derived pure-He composition if the nature of this object is confirmed.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We have also performed a new analysis of the 20 LAS white dwarfs from Paper I and Paper II, with the main difference being that the pure-H models now include the Lyα red wing absorption. Furthermore, we rely on the more recently released SDSS and LAS DR10 photometry. The derived atmospheric parameters are similar to those presented in earlier works. This is in part because the u and g observations were not included in the fitting procedure in earlier studies. We show three examples of cool pure-H degenerates in Figure 11 where the fit in the blue region is very good for the pure-H solution, even though there is only a moderate change in the atmospheric parameters compared to Paper II.

Zoom In Zoom Out Reset image size

The fits for pure-He and mixed objects are very similar to those of Paper I and Paper II. However, it was necessary to review the composition assigned to the DC white dwarfs because of the improved pure-H fits. Recent studies relying on the Lyα red wing opacity have found that most DC white dwarfs below T_eff ∼ 5000 K have an H-rich atmosphere (Kowalski & Saumon 2006; Kilic et al. 2009; Giammichele et al. 2012). In Figure 12, we present the observed r − i versus u − g color versus color diagram for our sample compared with theoretical sequences for pure-H and pure-He atmospheres. The observed scatter is relatively large, although this may be due to a scatter in the unknown surface gravities. We remark that most objects identified as pure-He white dwarfs in Paper I and Paper II (blue filled circles) actually follow the pure-He sequence (blue dashed lines) in Figure 12 and show no significant blue absorption. Hence, even by adding the blue filters neglected in previous works, this does not impact the derived composition for the three cool pure-He DC white dwarfs J1006+09, J1206+03, and J1351+12. However, we have updated the pure-He classification for J1454−01 which is now unconstrained since the pure-H fit is comparable to the pure-He fit, both shown in Figure 10. Furthermore, J0121−00, which previously had an unconstrained composition, is now better fit with a pure-H atmosphere (displayed in Figure 11 and with a black triangle in Figure 12).

Zoom In Zoom Out Reset image size

We have derived T_eff values based on the equivalent width of the Hα line, when observed, that can be compared with the photometric results. Since the strength of Hα depends on the unknown gravities, our values should be considered as estimates only. For most of the DAs observed in Paper I, T_Hα is significantly lower than the photometric temperature. We note that only ugrizYJ was used in the photometric fit since the faint LAS H for those objects was found to be unreliable. One explanation is that the objects could be very massive white dwarfs, which would explain a weaker Hα. Alternatively, it is possible that even the uncertainties for the ugrizYJ photometry have been underestimated. We note that some of the objects with LAS photometry, such as J0226−00, J1323+12, and J1522+08, reveal a good agreement between photometric and Hα temperatures.

In this section, we compare the stellar parameters of the two cool white dwarfs found in the resolved double degenerate system J1240+25E/W. The objective is to better constrain the properties of the system considering the fact that the total age and distance should be the same for both objects. We have attempted to vary the gravity of the components in order to match both the total ages and distances. To compute the total age, we use the initial–final mass relation of Kalirai et al. (2008) with a third-order polynomial fit, and the main-sequence lifetimes of Hurley et al. (2000). We reject solutions for which the total age is larger than 13 Gyr. We only consider the photometric variance in the uncertainties, hence we neglect the effects of varying the initial–final mass relation. We therefore consider that an agreement at the 3σ level is acceptable.

In Figure 13, we display the log g couples for which both total ages and distances are in agreement. Different combinations are shown in terms of the uncertain T_eff value of J1240+25E and composition of J1240+25W. The photometric T_eff solution for J1240+25E and pure-H composition for J1240+25W (top-left panel) do not allow the ages and distances to both match within 1σ (black) although there are possible solutions within 2σ (blue) or 3σ (cyan). The bottom-left panel demonstrates that when relying on the spectroscopic T_eff for J1240+25E, the agreement is much better, and multiple solutions are possible including the log g ∼ 8 canonical value for both components. The pure-He solution for J1240+25W also provides matching ages and distances, although only for higher gravities. Our results do not provide strong constraints on the composition or atmospheric parameters, but demonstrate that the apparent age discrepancy assuming log g = 8 can be resolved if we allow the gravities to vary. Parallax measurements for the system will be necessary to determine the distance and total age. The analysis also suggests that the spectroscopic solution for J1240+25E is preferred, and that underestimated photometric uncertainties are causing the discrepancy between the spectroscopic and photometric T_eff solutions. We note from Figure 7 that the shape of the energy distributions between i and Y are fairly different between the observations and predictions. Since the problem is not generally observed in other data sets (see, e.g., Bergeron et al. 2001), it is likely an issue with the observations.

Zoom In Zoom Out Reset image size

In view of our results and those of similar recent studies, we review the status of the spectral evolution of white dwarf atmospheres below T_eff ∼ 6000 K. In order to have all studies on an equal footing, we have refitted the ugrizJHK photometry for the 126 cool white dwarfs in Kilic et al. (2010) with models including the Lyα opacity. In Figure 14, we compare the observed u − g colors for their sample with predictions from model atmospheres. Most objects with a pure-He composition assigned in Kilic et al. (2010) are actually in better agreement with the new pure-H sequence. However, most of the pure-He objects are relatively warm (T_eff > 4600 K) and in a regime where the predicted differences between the pure-H and pure-He colors are close to the photometric uncertainties. We have inspected the individual fits (not shown here), and the new pure-H fits do not always provide an obvious better match to the observations. We refrain from assigning new compositions to the objects for the time being, although Figure 14 demonstrates that it is a likely possibility that most derived pure-He atmospheres with T_eff < 5000 K in Kilic et al. (2010) are actually H-rich atmospheres. In the following we consider both possibilities.

Zoom In Zoom Out Reset image size

In Table 7, we present the fraction of He-dominated atmospheres (N_He-dom/N_total) found in this work, as well as in the similar studies of Giammichele et al. (2012), Kilic et al. (2009), and Kilic et al. (2010), respectively. We take the value of He/H = 1 in number as the break point between the two compositions in cases of mixed atmospheres. For the local sample of Giammichele et al. (2012), we only include objects within 20 pc, allowing for a nearly volume complete sample and a better representation of the local population.

The so-called non-DA gap in the range 5000 < T_eff (K) < 6000 was first discussed in Bergeron et al. (1997), where they found very few pure-He atmosphere white dwarfs in that temperature range. In this regime, it is fairly straightforward to define the main constituent of the atmosphere, since the detection of Hα and the agreement of its observed equivalent width with predictions using the photometric T_eff allows the confirmation of the pure-H interpretation. On average, recent studies from Table 7 suggest that only ∼25% of the white dwarfs in that T_eff range possess He-dominated atmospheres. This confirms a deficit in He atmospheres since for slightly warmer objects (6000 < T_eff (K) < 8000), the ratio is in the range 40%–50% (Tremblay & Bergeron 2008; Giammichele et al. 2012).

It was understood early that He atmospheres are found in the non-DA gap (see the discussion in Bergeron et al. 2001), although in most cases they are peculiar white dwarfs with pressure shifted C₂ bands (spectral type DQpec; see Kowalski 2010) or metals (DZ). Furthermore, a significant fraction of cool He-dominated atmospheres have a derived mixed He/H composition due to the presence of near-infrared CIA H₂-He absorption. Indeed, for the local white dwarf sample within 20 pc, Giammichele et al. (2012) find 25% of He-dominated atmospheres in the non-DA gap, and in the six identified He atmospheres, four are DQpec stars. The LAS sample is smaller and does not allow for a statistically significant characterization of the He-rich population in the non-DA gap, although our results are in agreement with those of Giammichele et al. (2012), with a non-DA fraction of 25% and one of the two He-rich objects is a DQpec (SDSS J1247+06; Kilic et al. 2006). The survey of Kilic et al. (2010) is also in agreement with a non-DA gap, and more than half of the He-dominated atmospheres (with spectroscopic observations) are DQpec, DZs, or mixed He/H DCs with significant near-infrared absorption. Finally, the sample of Kilic et al. (2009) is drawn from Bergeron et al. (2001) and they did not include any of the DQpec stars. Therefore, we believe that their low He-atmosphere fraction is due to their target selection and we do not discuss further this sample.

The non-DA gap described in Bergeron et al. (2001) has a red edge at T_eff ∼ 5000 K. It is, however, difficult to differentiate between pure-He and pure-H atmospheres at cooler temperatures since both compositions have the DC spectral type. We exclude objects with a derived T_eff below 4000 K since we lose the thin disk contribution in this range, and most ultracool objects have peculiar colors which are likely to lead to strong selection biases in magnitude-limited samples.

Giammichele et al. (2012) find that N_He-dom/N_total = 24% in the range 4000 < T_eff (K) < 5000 when employing the Lyα opacity. All He-rich objects are DQpec, DZs, or mixed He/H DCs, hence they find a white dwarf population that is very similar to that found in the non-DA gap. This suggests that the non-DA gap is not actually a gap but a one-time chemical evolution near T_eff ∼ 6000 K. The sample of Kilic et al. (2010) includes seven He-rich mixed DC white dwarfs and one DZA in the range 4000 < T_eff (K) < 5000, which implies a minimum ratio of N_He-dom/N_total = 14% even if we consider that all derived pure-He atmospheres are actually H-rich. Based on our new fits with models including the Lyα opacity and the fact that the u − g colors in Figure 14 show little evidence of pure-He compositions, it is unlikely that the number of He-dominated atmospheres is much larger than the minimum fraction. Our sample has a higher fraction of He atmospheres in the same range, with a minimum of 18% based on the fraction of mixed objects, but a value of 46% if we include the three DC white dwarfs that are better fitted with pure-He models and if we exclude unconstrained compositions. This result is certainly at odds with the other samples, although our sample is fairly small and the color selections favor the detection of mixed objects. It is also possible that the discrepancy described in Sections 4.2 and 4.3 between the observed photometry and predictions has an impact on the derived compositions at low T_eff. All in all, there is no clear evidence with the most recent models and observations, compared to the picture presented in Bergeron et al. (2001), that the number of He-dominated atmospheres increases below T_eff = 5000 K.

In the following, we review the possible explanations for the spectral evolution of He atmospheres toward H atmospheres at T_eff ∼ 6000 K. First of all, it could be caused by events in the interior, perhaps in a way analogous to the convective mixing that is observed from DA to DB between 30,000 and 20,000 K and from DA to DC at around 8000 K (Bergeron et al. 2011; Tremblay & Bergeron 2008). The turnover timescales in white dwarf convective zones, even in the deepest layers, are less than a few hours (Van Grootel et al. 2012), hence many orders of magnitude shorter than the characteristic cooling times. It appears improbable that H could float on the surface due to incomplete mixing. However, if the microscopic diffusion timescale of H in the He-rich plasma dominates over the turnover timescale somewhere within the convective zone, it might be possible to create an abundance gradient.

According to Tassoul et al. (1990), the convective zone in pure-He DC white dwarfs stops growing at M_He/M_tot ∼ 10⁻⁶ once it reaches the degenerate core at around 10,000 K. In the highly degenerate parts, conduction becomes the dominant energy transfer mechanism, although convection is still predicted to take place in layers with a relatively high level of degeneracy. Below T_eff ∼ 10, 000 K, the size of the convective zone slowly decreases due to the growing degenerate core, although between 7000 and 5000 K, the total mass included in the convective zone only decreases by ∼0.4 dex according to Table 4 of Fontaine & van Horn (1976). This slow evolution is in part because the level of degeneracy increases very slowly with depth for adiabatic convection (see Equation (13) of Böhm 1968). It is therefore unlikely that changes in the composition of the atmosphere would be linked to changes in the size of the convective zone. We note that since the internal core is directly linked to the convective zone in that regime, chemical evolution will lead to a change in the relation between the surface and core temperatures. At a given initial T_eff, an He-atmosphere white dwarf turning into an H atmosphere would result in an object with a slightly lower T_eff due to the larger difference between the core and atmospheric temperatures in a DA white dwarf (Chen & Hansen 2011). This has to be taken into account in a spectral evolution model.

Chen & Hansen (2012) put forward a scenario where a significant fraction of H atmospheres turn into He-dominated atmospheres at T_eff ∼ 6000 K, and the resulting DC objects are shifted to ∼500 K higher T_eff by conservation of the core temperature. The larger cooling rates for the post-mixing objects would create a deficit of He atmospheres below 6000 K. In their scenario, He atmospheres would still be found in large number at T_eff < 5000 K. We do not support this interpretation from the observational evidences presented here. Furthermore, there is no strong constraint on the total mass of H in DA white dwarfs to suggest a DA to DC transformation around 6000 K and M_H/M_tot ∼ 10⁻⁷. Instead, we propose a DC to DA evolution from a yet unknown mechanism.

Finally, the transition could be caused by an external factor, such as the accretion of H from disrupted circumstellar material. Some relatively warm (T_eff ∼ 10,000 K) He-dominated white dwarfs have already accreted a significant amount of H (see, e.g., Zuckerman et al. 2007). From an extrapolation of the accreted H masses from Jura et al. (2009) to cooler temperatures, very cool DC white dwarfs with a history of accretion may have H masses of the order of M_H/M_tot ∼ 10⁻⁸–10⁻⁶. The upper limit gives a mass of H similar to the mass of He within the convective zone at T_eff ∼ 6000 K. While this could be the explanation for the presence of mixed objects, this is insufficient to create a pure-H atmosphere, and especially it would be very difficult to explain a rather abrupt chemical evolution at T_eff ∼ 6000 K which corresponds to a cooling age of ∼2 Gyr.

The difficulties in defining a theoretical scenario for the chemical evolution of very cool white dwarfs suggest that we may need to further define the observed populations in larger samples and identify the nature of the mixed, DQpec, and DZ degenerates as the first step.