The Emerging Class of Double-Faced White Dwarfs

The surface composition of a significant fraction of white dwarfs changes with time due to gravitational settling, radiative levitation, winds, convection, and external accretion. This leads to spectral evolution; a large fraction of white dwarfs transition from one spectral type to another. For example, a recent study of the 100 pc white dwarf sample in the SDSS footprint (Kilic et al., 2024) showed that $\approx 70$% of white dwarfs retain hydrogen atmospheres throughout their evolution and 10% retain helium atmospheres. In these objects, there is no mechanism that can alter the atmosphere composition (besides trace amounts of metals that could be accreted from debris disks) given the thickness of their outer layers. Thus the dominant element in these atmospheres does not change at any point in the cooling sequence; these objects do not undergo spectral evolution. The remaining 20% consists of stars where the aforementioned processes greatly alter the composition, resulting in a transition from one atmosphere type to another.

Due to the strong gravitational settling in white dwarfs, hydrogen gradually floats up to the outermost layers as a newly formed white dwarf cools. This float-up process helps DO white dwarfs with helium atmospheres transition into DA white dwarfs, provided there is enough hydrogen in the interior (Fontaine & Wesemael, 1987; Bédard, 2024). The location on the cooling sequence where this transition occurs depends on the initial hydrogen content, with higher mass fractions leading to transitions at hotter temperatures. For example, an initial mass fraction of $X_{\mathrm{H}}=10^{-3}$ in the outer $10^{-4}~{}M_{\star}$ leads to a DO-DA transition at $T_{\rm eff}=70,000$ K, whereas $X_{\mathrm{H}}=10^{-6}$ results in a transition much later, when the star cools down to $T_{\rm eff}=35,000$ K (Bédard, 2024).

While the float-up process can change a DO into a DA, the newly formed exterior hydrogen layer is relatively thin, and thus the target will likely undergo further spectral evolution as it continues to cool. If the hydrogen layer is thinner than the outer $\sim$$10^{-14}~{}M_{\star}$, the underlying helium convective zone will erode and dilute this layer later in the cooling sequence, resulting in a helium-dominated atmosphere (DB) or a mixed atmosphere (DBA). This convective dilution process is thought to occur between $30,000$ K $\gtrsim T_{\rm eff}\gtrsim 14,000$ K depending on the hydrogen layer mass (MacDonald & Vennes, 1991; Rolland et al., 2018, 2020; Bédard et al., 2023).

Even if the hydrogen layer is massive enough to avoid convective dilution, DA white dwarfs with thin surface hydrogen layers have more chances to transition. In a hydrogen-rich white dwarf, the convection zone appears at about $T_{\rm eff}=18,000$ K (Cunningham et al., 2019), and it expands significantly below 12,000 K to include a large portion of the envelope. Hence, convective mixing can lead to further spectral evolution and increase the fraction of He-atmosphere white dwarfs at cooler temperatures (Tremblay & Bergeron, 2008; Chen & Hansen, 2011; Rolland et al., 2018; Cunningham et al., 2020; Bédard et al., 2022b; Bergeron et al., 2022).

Observational evidence for these processes manifests in how the ratio of spectral types varies across effective temperatures. Eisenstein et al. (2006) found that the ratio of DAs to DBs is 2.5 times as high at 30,000 K compared to 20,000 K due to spectral evolution. Bédard et al. (2020) analyzed 1806 white dwarfs at $T_{\rm eff}\geq 30,000$ K and found that $\sim$2/3 of DOs eventually become DAs as they cool due to the float-up process. Multiple recent studies have further confirmed the steady increase of the fraction of DBs below 20,000 K (Genest-Beaulieu & Bergeron, 2019; Ourique et al., 2019; Cunningham et al., 2020; López-Sanjuan et al., 2022; Torres et al., 2023; O’Brien et al., 2024; Vincent et al., 2024). While the details of how rapidly the fraction increases vary between studies depending on what sample is used, there is significant evidence for the transition of some DAs to DBs/DBAs due to convective dilution ($30,000$ K $\gtrsim T_{\rm eff}\gtrsim 14,000$ K) and convective mixing ($14,000$ K $\gtrsim T_{\rm eff}\gtrsim 6000$ K) .

Regardless of whether convective dilution or convective mixing occurs, the formation of mixed atmosphere white dwarfs is of particular interest for two reasons. One is that $60-75\%$ of the DB population are DBAs (Koester & Kepler, 2015; Rolland et al., 2018), which means that the majority of helium-dominated objects contain enough hydrogen for the DO-DA transition to occur. The second reason is that recent modelling has been able to reproduce the observed hydrogen abundances using the aforementioned internal transport of hydrogen to the surface (Rolland et al., 2020; Bédard et al., 2023). By treating the dilution process with a deep hydrogen reservoir, the production of DBAs can be explained via internal processes as opposed to requiring external accretion (Farihi et al., 2013; Gentile Fusillo et al., 2017).

These internal convective processes should lead to homogeneously mixed surface layers. Hence, recent discoveries of several white dwarfs with inhomogeneous atmospheres is surprising. These ‘double-faced’ white dwarfs show evidence of varying H/He abundance ratios across the stellar surface in time-resolved spectra. The most extreme example is ZTF J203349.8+322901.1 (Caiazzo et al., 2023) in which the hydrogen and helium lines completely vanish and reappear, suggesting one side is comprised of hydrogen and the other of helium. Recent modelling suggests that a stratified atmosphere where the thickness of the surface hydrogen layer varies across the surface can explain all of the observations in this relatively hot white dwarf (A. Bédard 2024, private communication).

Other examples of double-faced white dwarfs include GD 323 (Pereira et al., 2005), Feige 7 (Achilleos et al., 1992), and GALEX J071816.4+373139 (Cheng et al., 2024). The latter two are particularly noteworthy because they are magnetic, with field strengths of $B_{\rm d}=35$ MG and $B_{\rm d}=8$ MG, respectively. Achilleos et al. (1992) attributed the inhomogeneous atmosphere of Feige 7 to magnetism, where the movement of helium from the interior is constrained along the field lines, resulting in a higher He abundance at the poles. Magnetism has also been invoked to explain spectral variations in two metal-polluted white dwarfs (Bagnulo et al., 2024a, b), with polar caps containing high metal abundances compared to the equatorial regions.

Moss et al. (2024) recently discovered variations in the hydrogen line strength of the magnetic DBA white dwarf SDSS J091016.43+210554.20 with a field strength of $\sim$0.5 MG. This object is one of the 10 DA+DB white dwarf binary candidates from Genest-Beaulieu & Bergeron (2019) where homogeneous atmosphere models fail to accurately reproduce the optical spectra under the assumption of a single star (see their Figure 25.4). Moss et al. (2024) demonstrated that J0910+2105 is instead a double-faced white dwarf with a rotation period of 7.7 or 11.3 hours. The oblique rotator model (Stibbs, 1950; Monaghan, 1973) with hydrogen polar caps and a helium equatorial belt provides excellent fits to their time-resolved spectra.

Given that there are nine other unresolved DA+DB binary candidates in Genest-Beaulieu & Bergeron (2019), we initiated a time-resolved spectroscopy survey to understand their nature and the emerging class of double-faced white dwarfs. Specifically, as we find more of these double-faced objects, we can begin to understand the range of possible surface geometries (extent of the H and He caps/belts etc), their location on the cooling sequence, the impact of magnetism, and the presence or lack of photometric variability and its significance. In this paper we present our findings on six of the unresolved binary candidates listed in Genest-Beaulieu & Bergeron (2019), as well as the magnetic DBA white dwarf LB 8915. We detail our observations and target selection in Section 2, followed by the model atmosphere analysis in Section 3. In Section 4 we discuss our findings with respect to other variable mixed-atmosphere white dwarfs, and detail the properties of the emerging class of double-faced white dwarfs. We then conclude in Section 5.

Figure 1 shows our target selection in the Gaia color-magnitude diagram, along with several inhomogeneous atmosphere white dwarfs with confirmed spectral variations in the literature. We also show isotherms and evolutionary models for various masses assuming pure He atmospheres¹¹1See http://www.astro.umontreal.ca/$\sim$bergeron/CoolingModels. (Bergeron et al., 2011; Bédard et al., 2020). Seven of the candidates from Genest-Beaulieu & Bergeron (2019, black and blue symbols) are in fact overluminous; we have time-series spectra for five of these and none show spectroscopic variations over a few hours. We show in Section 3 that these five targets are likely unresolved binaries. Two of the targets however, J0847+4824 and J0856+1611, lie close together in the color-magnitude diagram, along with the double-faced white dwarf J0910+2105 (Moss et al., 2024), and we show below that they are also double-faced stars. Among the remaining three candidates from Genest-Beaulieu & Bergeron (2019) that we could not observe, one of them (J1036+1938) appears to be located close to ZTF J203349.8+322901.1 in the color-magnitude diagram, but follow-up time-series spectroscopy is required to confirm its nature.

Table 1 shows our observing summary for each target. We obtained multiple sequences for three targets at the Apache Point Observatory (APO) 3.5m telescope equipped with the Kitt Peak Ohio State Multi-Object Spectrograph (KOSMOS) over multiple nights. We used the 2" slit in the Center position with the Blue disperser and 2x2 binning. The setup covers the wavelength range 3800 - 6600 Å with a resolution of 4.7 Å.

We also obtained additional exposures for two targets at the 6.5m MMT with the Blue Channel Spectrograph. We used the 1.25" slit with the 500 l mm^-1 grating which yields a resolution of 4.5 Å.

Finally, we obtained back-to-back sequences for five targets using the 8m Gemini North telescope with the Gemini Multi-Object Spectograph (GMOS) as part of the programs GN-2024A-Q-229, GN-2024A-Q-325, and GS-2024A-Q-329. We used the B480 grating with the 1" slit and 4x4 binning, providing wavelength coverage from 3555 - 7300 Å and a resolution of 6.3 Å. All of our spectra were reduced using standard IRAF procedures.

For our variable targets, we start by fitting a Gaussian profile to both H$\beta$ and He I $\lambda$4922 using LMFIT (Newville et al., 2014) and calculate the equivalent width of these profiles for each spectrum. We then take the ratio of the equivalent widths to measure how the strength of the H lines vary as a function of time compared to the He lines. To calculate errors, we use bootstrapping to construct a distribution of values. We randomly sample the wavelength-flux pairs of a given spectrum, with replacement, while keeping only the unique pairs. This creates a new spectrum which we then fit as mentioned, repeating this process 10,000 times to generate 10,000 measurements. We then select the values at 15.9 and 84.1% in the distribution as the $1\sigma$ errors. We then generate a Lomb-Scargle periodogram with the orbital fit code MPRVFIT (De Lee et al., 2013) to constrain the rotation period using the measured equivalent widths.

Given that homogeneous atmosphere models failed to reproduce the optical spectra in Genest-Beaulieu & Bergeron (2019) for these objects, we employ a polar cap model to generate fits to our time-resolved spectra, similar to Moss et al. (2024). In this model, the polar cap is made up entirely of H and the equatorial belt of He. We denote $\theta_{\rm c}$ as the extent of the polar cap from the pole down to the equator, such that $\theta_{\rm c}=90\degree$ means the entire hemisphere is H. We also denote $\alpha$ as the angle between the magnetic axis and the plane of the sky, as defined in Schnerr et al. (2006, $\alpha=90\degree$ means pole-on). The purpose of using this geometry is to provide a physical mechanism for the observed variations. While the total amount of H and He is what determines the strength of each absorption line in our synthetic spectra, this by itself does not explain why we see varying abundances as the objects rotate. The specific use of H polar caps, positioned with respect to the magnetic axis which is misaligned with the rotation axis, accomplishes three goals: it provides excellent fits to our spectra, it explains why we see varying abundances as opposed to a constant ratio, and it fits within our framework of magnetically-inhibited convection at the poles (see Section 4.2).

We use the photometric technique described in Bergeron et al. (2019) to obtain precise $T_{\rm eff}$ and $\log{g}$ values for the variable targets. We use the Gaia DR3 parallaxes, SDSS $u$, and Pan-STARRS $grizy$ photometry to constrain the effective temperature and solid angle of each object. Since the distance is known, we directly constrain the radius and then calculate the mass using white dwarf evolutionary models.

To generate the spectroscopic fits, the emergent Eddington flux $H_{\nu}$ is calculated by numerically integrating the specific intensity $I_{\nu}$ over the visible surface of the disk given the geometry and viewing angle. We adopt pure H and pure He model atmospheres based on the surface composition of each given element, and fix the $T_{\rm eff}$ and $\log{g}$ of both sets of models to the values obtained from the photometric fits. The details of our model grid are discussed further in Bergeron et al. (2019) and Genest-Beaulieu & Bergeron (2019). This approach was successful in reproducing the time-resolved spectra for J0910+2105 (Moss et al., 2024).

With the $\alpha$ values found in our model fits, we then use the oblique rotator model (Stibbs, 1950; Monaghan, 1973) to constrain the orientation of the line of sight and magnetic axis in each target. Variations in the spectra occur if the magnetic axis is offset from the rotation axis, so this model is key for providing a physical justification of any variations we observe.

It is important to note two distinctions here. The first is that due to the degeneracies in the model fits (H caps versus He belts, and vice versa), we only use the H polar cap model. While our model only serves as a proxy for the possible geometries, this model provides excellent fits to our data.

Second, Moss et al. (2024) tested both convective and radiative atmospheres for J0910+2105, which has a magnetic field strength of $\sim$0.5 MG. While radiative atmospheres provided a noticeable improvement in the fit to the He I $\lambda$6678 line, the improvement with a radiative atmosphere is negligible outside of this line (see also the discussion in Lecavalier-Hurtubise & Bergeron, 2017). In addition, our model fits are limited to wavelengths shorter than 5150 Å. Our APO data only goes to 6600 Å, which barely covers H$\alpha$ and does not include the He I $\lambda$6678 line. To perform a uniform analysis of all of our APO, Gemini, and MMT data, we restrict our model fits to the wavelengths below 5150 Å, where the majority of the He and H lines are. Hence we use convective atmosphere models in our fits. Fits for our variable targets, as well as all observed data are provided on Zenodo via the DOI https://doi.org/10.5281/zenodo.14232043.

In summary, we present time-series spectroscopy of seven DBA white dwarfs, six of which were previously identified as unresolved DA+DB binary candidates. One of these candidates, J0847+4842, shows extreme variations in the absorption lines over the span of our exposure sequences. Hence this unresolved binary candidate is clearly a single white dwarf with an inhomogeneous atmosphere, which results in varying line strength as the object rotates. We constrained the rotation period to either 6.5 or 8.9 hours, and successfully implemented a polar cap model to obtain fits to our spectra. We fix the cap size to 40° and allow the angle between the magnetic axis and plane of the sky to vary in our fits, which lets us constrain the system geometry using the oblique rotator model. We determine that $\beta=33\degree$ and $i=33\degree$, so the angles between the magnetic axis/line-of-sight and the rotation axis are equal. Hence at certain phases, we are looking directly at the polar cap, which leads to a spectrum that looks effectively like a DA spectrum. As the target rotates, we see more of the equatorial region, which leads to the appearance of He lines.

A separate target we observed is a known variable DBAH, J0856+1611, with a rotation period of 5.7 hours. We detected variations in the strength of the weak H lines, and obtained the same previously determined rotation period. While we do obtain good fits with our polar cap model, the H lines are too weak to put a tight constraint on the cap size. Regardless, it is clear this target has a patchy atmosphere, with likely small caps and an orientation where we mostly view the equatorial region at all phases.

Given the several patchy-atmosphere objects known at this time, we are able to define the class of double-faced objects for the first time. While most objects maintain a homogeneous atmosphere throughout their evolution, this class likely forms as a result of the magnetic field influencing the motion and mixing of either H or He, creating an atmosphere with varying surface abundances. Since magnetism is quite rare in He-dominated white dwarfs, it follows that these inhomogeneous atmospheres are quite rare among the DBA population.

The targets discussed in this work are at effective temperatures where convective dilution is expected to either have already occurred or is currently ongoing. It then follows that double-faced systems could form at cooler temperatures where convective mixing should occur. We identify such a population among the cool magnetic DA white dwarf sample, where the H$\alpha$ line is shallower than expected based on pure hydrogen atmosphere models.

An important step in analyzing this class is further modelling on how the magnetic field influences convection. If modelling the transport mechanisms can indeed reproduce these atmospheres, that will further solidify the idea that magnetism is the driving force behind the creation of these objects, even if magnetism is not detected in the observations. Of course this also means better modelling of complex fields in general is needed. In our framework, the dipole field is stronger at the polar regions compared to the equatorial regions, with inefficient mixing at the poles. This framework fits well with the traditional dipole field that is used in modelling magnetic white dwarfs. However, the true field structure in these targets could be more complicated, particularly in the case of ZTF J203349.8+322901.1 since it has two opposing faces (Caiazzo et al., 2023). Nevertheless, while the exact nature of the atmosphere geometry cannot be directly confirmed due to the complexities in how magnetism affects convection, we are confident that magnetism is the source of the inhomogeneities in this class of objects.

We are grateful to Antoine Bédard for useful discussions. We thank the students of the Spring 2024 Advanced Observatory Methods class at OU for obtaining spectra of J0847+4842 and J0856+1611 during their telescope training on UT 2024 April 4 and April 5. This work is supported in part by the NSF under grant AST-2205736, the NASA under grants 80NSSC22K0479, 80NSSC24K0380, and 80NSSC24K0436, the NSERC Canada, the Fund FRQ$-$NT (Québec), and the Canadian Institute for Theoretical Astrophysics (CITA) National Fellowship Program.

Based on observations obtained with the Apache Point Observatory 3.5-meter telescope, which is owned and operated by the Astrophysical Research Consortium.

Observations reported here were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona.

Based on observations obtained at the international Gemini Observatory, a program of NSF’s NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).