FIRST DETECTION OF THE WHITE DWARF COOLING SEQUENCE OF THE GALACTIC BULGE^*

Stars could be in the WD region of the CMD because they are bona fide bulge or disk WDs, or because they are closer and less reddened disk MS stars. It is important then to consider a bulge sample devoid of disk stars, since some disk stars with much less reddening may appear bluer, and hence masquerade as WDs. To obtain a clean bulge sample, we estimated the proper motions (PMs) of the stars using the 2004 and 2011–13 data sets. By comparing the positions of stars in the two epochs we estimated the PMs for ≈200,000 stars down to F606W ≈ 28 mag, with an accuracy ≲0.5 mas yr⁻¹ (≲20 km s⁻¹) in both axes. PMs are then projected along the Galactic coordinates shown in Figure 1 (top right panel).

We then used the CMD to select two samples of candidate stellar populations belonging to the bulge (blue dots) and the disk (red), following a procedure similar to that adopted by CL08. The two samples were selected in different magnitude and color ranges to keep the sample sizes similar, and keep the contamination of the bulge sample by disk stars minimal. The PM histograms of the Galactic-longitude components for these two populations are shown in Figure 1 (bottom right). The two populations are clearly separated, with the bulge peaking at μ_l ≈ 0 mas yr⁻¹, and the disk peaking at μ_l ≈ 4 mas yr⁻¹. The PM distribution of disk and bulge stars is a consequence of Galactic rotation, a detailed discussion of which is given in CL08. We adopted a cut at μ_l ⩽ −2 mas yr⁻¹ to select a nearly pure bulge sample: this selection allows us to keep ≈30% of bulge members while the residual contamination of the sample by disk stars is ≲1%. Figure 2 shows the CMD of the resulting pure-bulge sample where the photometry of stars brighter than F606W = 19.8 mag (which is the saturation limit for the 2011–13 data set) is taken from the 2004 data set, while the photometry of the fainter stars is from 2011–13. About 70% of the bulge WDs were indeed rejected because of the PM selection, although most of the WDs in the selected magnitude and color range belong to the bulge. To further select candidate WDs, we individually checked each star with ROMAFOT (Buonanno & Iannicola 1989) on the F606W and the F814W median images. Some of the candidate bulge WDs turned out to be too close to or to lie on the spikes of saturated stars, and a few others were too faint to be reliably measured (F606W > 28 mag); these were rejected from the sample. We note that the PM selection has led to a reduction of the number of brighter (22 <F606W < 24 mag) WDs from eight to four objects, two of which happen to be CVs. Table 1 lists coordinates, magnitudes, and PMs for the 72 well-measured bulge WDs. Only these well-measured WDs are included in Figure 2, which clearly shows a sequence of objects ranging from 22.5 ≲ F606W ≲ 29 mag, with most of them having a color F606W − F814W ≲1.0 mag. The only known class of objects that can occupy this part of the CMD are bulge WDs and unreddened disk stars. Since almost all (≳99%) disk stars were removed by the PM selection (see Section 2.1) the only remaining possibility is bulge WDs. Furthermore, faint blue galaxies, which play the role of serious contaminants in the WD sequence observed in GGCs (Richer et al. 2008), are absent in our sample since the large reddening by the Galactic disk in this direction serves as a natural filter to remove any background galaxies.

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Theoretically, we expect to observe a WD cooling sequence in the bulge, since the bulge is old and formed over a relative short timescale, as suggested by the scarcity of younger stars (CL08). It is then natural to ask: why was this bulge WD sequence not identified until now? The reason is simple. It was essential to separate the disk stars in order to identify them as bulge WDs. Since the WDs are intrinsically faint, the PMs of this sample was not known. Our deep HST observations taken at two epochs were essential to separate the faint disk stars from the bulge WDs.

In order to characterize the bulge stellar population, we compared the PM-cleaned bulge CMD with evolutionary predictions. We used the BaSTI⁷ (Pietrinferni et al. 2004, 2006) stellar-evolution database to fit isochrones to the CMD. Evolutionary predictions were transformed to the observational plane by adopting the color–T_eff relations provided by Hauschildt et al. (1999) for T_eff ⩽ 10, 000 K, while at larger T_eff we adopted the relations published by Bedin et al. (2005). A distance modulus of DM₀ = 14.45 mag and a mean reddening of E(B − V) = 0.5 were adopted (Sahu et al. 2006). Extinction coefficients were estimated by applying the Cardelli et al. (1989) reddening relations and by adopting a standard reddening law, R_V = A_V/E(B − V) = 3.1, finding A_F606W = 0.922 A_V, A_F814W = 0.55 A_V, and E(F606W − F814W) = 1.14 E(B − V).

Solid lines in Figure 2 show isochrones for an age of t = 11 Gyr and a scaled-solar mixture with different chemical compositions. The blue line corresponds to Z = 0.03, Y = 0.288 ( [Fe/H]  = 0.26), the red to Z = 0.0198, Y = 0.273 ( [Fe/H]  = 0.06), and the green to Z = 0.008, Y = 0.256 ( [Fe/H]  = −0.35). Zero-age horizontal branches (ZAHBs) are plotted for the most metal-poor (green) and the most metal-rich chemical compositions (blue). We adopted these mixtures based on the medium-resolution spectroscopy of 93 turn-off (TO), red-giant (RG) and MS stars in the SWEEPS field, collected with FLAMES/VLT (ESO, cyan dots). The distribution spans a range of −1.0 < [M/H] < 0.8, and shows three main peaks at [M/H] ≈ -0.5, 0.0, and ≈0.25. This distribution is in fairly good agreement with the spectroscopic metallicity distributions found by Hill et al. (2011), Bensby et al. (2013), and Ness et al. (2013) for the bulge.

To fit the bulge WD cooling sequence, we adopted the BaSTI cooling tracks for DA and DB CO-core WDs and the models of Althaus et al. (2009) for He-core WDs. For t ≈ 11 Gyr, and solar metallicity, the mass of the stars at the TO is ≈0.95 M_☉ and the theoretical initial-to-final mass relationships predicts WD masses of ∼0.53–0.55M_☉ (Weiss & Ferguson 2009). This prediction is observationally supported by the spectroscopic measurements of bright WDs in the GGC M4 by Kalirai et al. (2009), for which they find a mean mass of ∼0.53 M_☉. So we used cooling tracks for DA and DB CO-core WDs with mass M = 0.54 M_☉ (Salaris et al. 2010), and He-core WD tracks for a mass of 0.23 M_☉. We applied to the cooling tracks the same distance modulus and reddening adopted for the isochrones.

The comparison between theory and observation shows that old scaled-solar isochrones spanning almost 1 dex in metallicity, −0.4 ≲  [Fe/H]  ≲ 0.3, fit the bulge MS and red giant branch (RGB) quite well over most of the color range. However, there are stars systematically bluer or redder than the most metal-poor and metal-rich isochrones. Part of this residual color spread is due to photometric errors, differential reddening and depth effects.

Figure 2 also shows that cooling tracks for DA (dashed blue line) and DB (dashed green) CO-core WDs, which are expected to be shifted up to ±0.5 mag due to the bulge depth, are unable to reproduce the entire color range of the observed WD cooling sequence. An increase in the mean mass of the WDs would move the models toward bluer colors, further increasing the discrepancy. We then assume the presence of a fraction of low-mass, M ≲ 0.45 M_☉, WDs in the bulge. The lower mass He-core cooling track for M = 0.23 M_☉ (dashed red) fits the red side of the bulge WD sequence, but it is not able to account for the reddest WDs. Note that empirical evidence shows that the lower mass limit for WDs is ≈0.2 M_☉ (Kepler et al. 2007).

To properly characterize the color spread and the completeness of the bulge WD cooling sequence, shown in the right panel of Figure 2, we performed several artificial star (AS) tests to estimate the magnitude and color dispersion of the sequence due to photometric errors and to the reduction and selection techniques adopted. We randomly added ≈160,000 artificial WDs to all images, with magnitudes and colors estimated by adopting a DA cooling track with M = 0.54 M_☉, and by adding a distance modulus of 14.45 mag and a mean reddening of E(B − V) = 0.5. Artificial stars are added and recovered on the images one at a time, not to affect the crowding, by using the same reduction procedures adopted earlier. We then estimated the magnitude and color spread of the artificial WD cooling sequence. This information was used as input to produce a synthetic sequence from the DA cooling track. After correcting the model absolute magnitudes for distance modulus and reddening, we have drawn randomly 30,000 ages with a uniform probability distribution, within the age range corresponding to the observed WD magnitude range. The resulting magnitudes were then perturbed with a Gaussian photometric error obtained from the AS tests.

Figure 3 shows the synthetic WD sequence, which also includes the effect of differential reddening. We added to the star magnitudes extinction values simulated as clumps with a maximum peak of A_V ∼ 0.6 mag on top of a uniform reddening of A_V ∼ 1.5 mag. The assumption of an extinction increase up to A_V = 1 mag for ≈30% of the WDs, which would explain the presence of the reddest WDs, must be discarded since we do not see any evidence for the presence of such differential reddening along the MS for a similar fraction of stars.

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Candidate bulge WDs are overplotted as red dots on the synthetic cooling sequence of Figure 3, together with a DA CO-core (blue line) and a He-core (red) track. Figure 3 shows that differential reddening added to photometric errors cannot account for the entire color spread of the observed WD sequence in the bulge, by assuming only a CO-core WD population with a mean mass of ∼0.54 M_☉. It is worth noting that if the spread were due only to the aforementioned factors, we would observe an equivalent number of WDs bluer than the cooling tracks.

The agreement between theory and observations improves by assuming that a fraction of the WDs have lower masses. This moves the theoretical tracks bright-ward and to the red, thus improving the agreement with our observations. These stars could be He-core WDs as described in Section 3.1, but a fraction of them could also be low-mass CO-core WDs. The recent theoretical calculations of Prada Moroni & Straniero (2009) showed indeed that CO-core WDs with masses down to ∼0.33 M_☉ can form in high-density environments, when a strong episode of mass loss occurs along the RGB, due to binary interactions. However, this theoretical scenario requires very fine-tuned initial conditions, suggesting that these stars are more likely to be He-core WDs.

It is not possible to explain the presence of He-core WDs, which are expected to have masses ≲ 0.45M_☉, as a result of single-star evolution in less than a Hubble time. As described earlier, a natural explanation for the presence of such WDs is that they result from close-binary interactions after a CE phase, or from a merger of two very low-mass He-core WDs following a second CE ejection. In this scenario, a small number of the He-core WDs are expected to show signatures of variability consistent with WD–MS and CV binaries, or ellipsoidal variables.

To look for the presence of binaries in the bulge WD sample, we checked the brightest WDs (F606W ≲ 26 mag) for variability, and we indeed identified two ellipsoidal variables (blue dots in Figure 2), two dwarf novae in outburst (magenta dots in Figures 2 and 3), and five candidate CVs in quiescence (green dots in Figures 2 and 3). These findings support the presence of He-core WDs in the bulge. Moreover, the luminosity of the accretion disk and the companion in the WD–MS systems moves the WDs toward redder colors in the optical CMD (Darnley et al. 2012), which would be consistent with our observations of the very red WDs.

The V and I light curves of one ellipsoidal variable based on the 2004 data set are shown in Figure 4. The estimated period and amplitude are P = 2.258 × 10⁻¹ ± 2 × 10⁻⁵ days and A = 5.1 × 10⁻² ± 9 × 10⁻⁴ mag. By assuming that the primary star is a WD and the companion a MS star, we estimated a semi-major axis a = 0.007 AU, and masses of ≈0.3–0.4 M_☉ and ≈0.6–0.7 M_☉ for the two components, respectively. An accurate estimate of the masses of the components of these systems needs radial velocities; we are in the process of collecting such data through spectroscopic observations with GMOS at GEMINI South. It is noteworthy that the V−I color of the variable is constant (see Figure 4), which means that we cannot be observing a reflection effect, i.e., the heated hemisphere of the MS companion as in the case of the WD–MS binary HS 1857+5144 (Aungwerojwit et al. 2007). This ellipsoidal variable is relatively bright with F606W ∼ 21.6 mag; stars belonging to the reddest WD cooling sequence could be the fainter counterparts of this object. Unfortunately, we do not have 2004 time-series photometry for the fainter candidate CVs to verify this hypothesis. The 2011–13 data set has a two-week observation cadence, so we were unable to probe all possible periods for our candidate variables. candidates for short-period variability. Population-synthesis models predict that most WD–MS systems have periods in the range 2–30 hr (Yungelson et al. 1994). Moreover, models from Iben et al. (1997) predict that ≈75% of the WDs in close binaries are low-mass He-core WDs. This scenario is observationally supported by Rebassa-Mansergas et al. (2011) who measured masses for ∼200 wide WD–MS systems and PCEBs; they find that the mass distribution of the complete sample of binaries is bimodal, with a main peak at M ∼ 0.55 M_☉ and a secondary one at M ∼ 0.40 M_☉, while the distribution of the PCEBs shows a concentration of systems toward the low-mass end, with only few binaries with M ≳ 0.55 M_☉ (see their Figure 1).

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WD–MS binaries and PCEBs might exhibit H_α excess (Rebassa-Mansergas et al. 2007). To check for the presence of H_α excess among our sample of bulge WDs, we matched the F606W, F814W-band 2011–2013 data set with the F625W-, F658-band catalog, finding ≈200,000 stars in common. Using the PMs from the 2011–2013 data set, the matched catalog was cleaned to keep only the bulge stars.

Figure 5 shows the F625W, F658N − F625W PM-cleaned CMD for the SWEEPS field. The F625W, F658N − F625W CMD is designed to specifically highlight the presence of H_α bright stars. In this plane, EHBs and the WDs are expected to be toward the right/red of the MS since they have stronger H_α absorption line. Out of 72, 48 bulge WDs and 10 out of 12 EHBs were identified in this sample and are marked as larger filled dots in the figure. The two ellipsoidal variables (blue dots), the dwarf novae (magenta) and four out of five candidate CVs (green) were identified too. WDs fainter than F606W ⩽ 27 mag were not detected either in the F625W-band or in the F658N-band. The same WD cooling tracks adopted to fit the other CMDs are overplotted. The figure shows that the WD cooling tracks agree with the observations within the uncertainties in the magnitude range 22 ≲ F625W ≲ 27 mag. However, there is a fraction of WDs that is systematically toward the left/blue of the CO-core and He-core cooling tracks. The photometric error is σ_{F606W − F814W} ≲ 0.2 mag at F625W ≈ 25.5 mag (shown by a dotted horizontal line in the figure), but some WDs are shifted toward the blue of the CMD by more than 2σ.

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For magnitudes brighter than F625W = 25.5, there are a total of 17 WDs. Six of these WDs, including both the observed dwarf novae, show H_α excess, with F658N − F625W ≲ −0.3 mag. This implies that ≈30% of the WDs show H_α excess. This result further supports the hypothesis of the presence of a fraction of PCEBs and WD–MS binaries in the bulge. For magnitudes fainter than F625W = 25.5, there is a trend of the WD cooling sequence toward bluer colors. This may be either due to blending with other stars, presence of stars with H_α excess as described above, or other yet unknown effects. It is worth noting that one of the CV candidates (F606W ∼ 24.5 mag) shows very strong H_α absorption, with F658N − F625W ≈ 0.8 mag. This object resembles the three CVs identified by (Taylor et al. 2001) in the NGC 6397, which all have F658N − F625W > 0.5 mag.

To further investigate the potential presence of a substantial fraction of He-core WDs in the bulge, we compared WD counts for F606W ⩽ 27 mag, corrected for completeness, to MS counts across the TO region (19.9 < F606W < 20.15 mag), where the evolution of the star is faster and almost independent of the initial mass function (Calamida et al. 2008).

Note that we are taking into account only 30% of bulge stars due to our PM selection, but this does not matter for a comparative analysis since the same PM selection should affect equally all evolutionary phases.

We selected the brightest PM-selected WDs (22.5 < F606W < 27 mag) in seven magnitude limits corresponding to F606W < 24, 24.5, 25, 25.5, 26, 26.5, and 27, and counted how many stars there are up to each limit. We then associated to each magnitude limit a WD cooling time, t_WD, from the BASTI DA CO-core cooling track for a mass of 0.54 M_☉. It is interesting to note that the cooling time at F606W ≈ 28 mag for this sample of WDs is ≈500 Myr, assuming most stars are 0.54 M_☉ DA CO-core WDs, and assuming a distance modulus and reddening of DM₀ = 14.45 mag and E(B − V) = 0.5 mag, respectively.

The mean MS mass at the TO magnitude range 19.9 < F606W < 20.15 mag is 0.95 M_☉, according to a BASTI scaled-solar isochrone for t = 11 Gyr and Z = 0.02, and the same distance modulus and reddening as described above. We then adopted a BASTI evolutionary track for the same composition and for a mass of 0.95 M_☉ to estimate the time that takes for MS stars to cross the magnitude range from F606W =19.9 to 20.15 as t_MS ∼ 1 × 10⁹ yr.

The comparison between observed star counts corrected for completeness, N_WD/N_MS, and the theoretical lifetime ratios, t_WD/t_MS, shows that we are observing about a factor two more WDs than predicted if all the WDs are CO core.

We now assume the presence of a fraction of ∼30% He-core WDs with a mass of 0.4 M_☉ in the sample based on the discussion above, for which the cooling times are significantly longer compared to those of CO-core WDs. We then estimate the total WD cooling time as $t_{{\rm tot}} = 0.30 \times t_{{\rm cool}}({\hbox {He-core}}) + 0.70 \times t_{{\rm cool}} (\hbox{CO-core})$ The observed and theoretical ratios then agree within the uncertainties taking into account a 10% uncertainty in the WD cooling times and MS lifetimes, and the Poisson statistics on the number counts.

This argument thus further strengthens the hypothesis of the presence of a fraction of He-core WDs in the Galactic bulge.