Ultracool white dwarfs and the age of the Galactic disc††thanks: 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.
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
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.
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.
|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.)|
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)|
|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.|
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.
|IR photometry from UKIDSS|
|IR photometry from 2MASS|
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
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
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
where is a constant to be determined for each filter, as described below. In general,
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
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.
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.
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.
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.
|(K)||(cm s)||(M)||(R)||( He/H)||(mag)||(Gyr)||(Gyr)|