The spectral evolution of white dwarfs: where do we stand?

Abstract

White dwarfs are the dense, burnt-out remnants of the vast majority of stars, condemned to cool over billions of years as they steadily radiate away their residual thermal energy. To first order, their atmosphere is expected to be made purely of hydrogen due to the efficient gravitational settling of heavier elements. However, observations reveal a much more complex situation, as the surface of a white dwarf (1) can be dominated by helium rather than hydrogen, (2) can be polluted by trace chemical species, and (3) can undergo significant composition changes with time. This indicates that various mechanisms of element transport effectively compete against gravitational settling in the stellar envelope. This phenomenon is known as the spectral evolution of white dwarfs and has important implications for Galactic, stellar, and planetary astrophysics. This invited review provides a comprehensive picture of our current understanding of white dwarf spectral evolution. We first describe the latest observational constraints on the variations in atmospheric composition along the cooling sequence, covering both the dominant and trace constituents. We then summarise the predictions of state-of-the-art models of element transport in white dwarfs and assess their ability to explain the observed spectral evolution. Finally, we highlight remaining open questions and suggest avenues for future work.

Keywords: Atmospheric composition (2120); Stellar evolution (1599); White dwarf stars (1799).

Fig. 1

Examples of optical spectra of DA, DB, DC, DO, DQ, and DZ white dwarfs. The spectra are normalised at $\lambda =4200$ Å and shifted vertically from each other by an arbitrary amount. The data are taken from Bergeron et al. (1997), Bergeron et al. (2011), Giammichele et al. (2012), and Subasavage et al. (2017)

Fig. 2

Fraction of helium-atmosphere white dwarfs as a function of effective temperature in various post-Gaia studies. For clarity, the studies are arbitrarily divided into those that rely on SDSS spectroscopy (top panel) and those that do not (bottom panel). The curves emphasised in one panel are displayed in light grey in the other panel to allow comparison. Values at $T_{\mathrm{eff}}>90,000$ K and $T_{\mathrm{eff}}<5000$ K have been purposefully excluded because they are considered unreliable. The results of Blouin et al. (2019b), McCleery et al. (2020), and Jiménez-Esteban et al. (2023) are not shown as they have been superseded more recently by those of Caron et al. (2023), O’Brien et al. (2024), and Torres et al. (2023), respectively. For reference, the top axis gives the cooling age of a standard 0.60 $M_{\odot }$ hydrogen-rich white dwarf according to the theoretical evolutionary calculations of Bédard et al. (2020)

Fig. 3

Surface gravity as a function of effective temperature for the four main groups of hybrid-atmosphere white dwarfs: the hot homogeneous stars (blue squares, taken from Gianninas et al. and Bédard et al. 2020), the hot stratified stars (magenta diamonds, taken from Bédard et al. 2020), the classical DBA stars (cyan circles, taken from Rolland et al. and Genest-Beaulieu and Bergeron 2019b), and the helium-rich DA stars (red triangles, taken from Rolland et al. and Coutu et al. 2019). In all cases, objects suspected to be unresolved double white dwarf systems have been excluded. For the stars from Genest-Beaulieu and Bergeron (2019b) and Coutu et al. (2019), the photometric parameters are used and only the objects with a parallax error smaller than 20% are displayed. A small number of objects interpreted as DBA white dwarfs with $T_{\mathrm{eff}}>30,000$ K in Genest-Beaulieu and Bergeron (2019b) do not appear here as they have been reanalysed in Bédard et al. (2020) and found to have either pure-helium or stratified atmospheres. The cool DBA stars from Rolland et al. (2018) that suffer from the spectroscopic high-$logg$ problem have been excluded. The helium-rich DA stars from Rolland et al. (2018) were assumed to have $logg=8.0$ in that paper, hence the $logg$ values shown here are taken from other sources (Dufour et al. ; Gentile Fusillo et al. ; Caron et al. 2023). Also displayed for visual guidance are theoretical evolutionary sequences representative of hydrogen-rich (dashed curves) and helium-rich (solid curves) white dwarfs with stellar masses of 0.50, 0.60, and 0.70 $M_{\odot }$ (from top to bottom), taken from Bédard et al. (2020)

Fig. 4

Atmospheric hydrogen abundance (by number relative to helium) as a function of effective temperature for the classical DBA stars and helium-rich DA stars shown in Fig. 3. The dotted lines correspond to the optical spectroscopic detection limit for signal-to-noise ratios of $\simeq 100$ ($T_{\mathrm{eff}}>11,000$ K) and $\simeq 20$ ($T_{\mathrm{eff}}<11,000$ K), which are representative of the best-observed objects in the DBA and helium-rich DA samples, respectively

Fig. 5

Atmospheric carbon abundance (by number relative to helium) as a function of effective temperature for the three main groups of carbon-bearing white dwarfs: the classical DQ stars (cyan circles, taken from Coutu et al. and Blouin and Dufour 2019), the massive DQ stars (red triangles, taken from Koester and Kepler , Koester et al. , and Blouin and Dufour 2019), and the carbon-polluted DB stars (blue squares, taken from Petitclerc et al. and Koester et al. 2014b). An upward-pointing arrow indicates that the displayed carbon abundance is a lower limit rather than a true determination. The classical and massive DQ white dwarfs are arbitrarily defined as having stellar masses lower and higher than 0.80 $M_{\odot }$, respectively. In all cases, objects suspected to be unresolved double white dwarf systems have been excluded. Among the stars in Coutu et al. (2019) and Blouin and Dufour (2019), only those with a parallax error smaller than 20% are displayed. Among the stars in Petitclerc et al. (2005) and Koester et al. (2014b), those that also exhibit traces of other metals have been excluded. The dotted line corresponds to the optical spectroscopic detection limit for a signal-to-noise ratio of $\simeq 20$ ($T_{\mathrm{eff}}<11,000$ K), which is the average value for the cool DQ sample

Fig. 6

Gaia colour–magnitude diagram of white dwarfs located within 100 pc of the Sun (black dots, taken from the Montreal White Dwarf Database; Dufour et al. 2017). Only the objects with a parallax error smaller than 10% are displayed. Also shown are theoretical evolutionary sequences for pure-hydrogen atmosphere (red curve) and pure-helium atmosphere (blue curve) white dwarfs with a stellar mass of 0.60 $M_{\odot }$, calculated using the atmosphere models of Bergeron et al. (2011), Tremblay et al. (2011), and Blouin et al. (2019b)

Fig. 7

Vertical extent of the convection zone (hatched area) as a function of effective temperature in hydrogen-rich (top panel) and helium-rich (bottom panel) white dwarf envelope models. The position in the star is measured in terms of the fraction of the total mass located outside a given radius, such that the surface is towards the top and the core is towards the bottom. These models were computed with the STELUM code (Bédard et al. 2022b) assuming a stellar mass of 0.60 $M_{\odot }$ and the ML2 version of the mixing-length theory (Tassoul et al. 1990). In each panel, the red line shows the position of the photosphere. As a very rough indication of the expected extent of convective overshoot, the dotted lines denote two pressure scale heights above and below the formally convective region

Fig. 8

Hydrogen mass fraction profile at various effective temperatures in a typical simulation of element transport in helium-rich white dwarfs. The position in the star is measured in terms of the fraction of the total mass located outside a given radius, such that the surface is towards the right and the core is towards the left. This particular simulation is taken from Bédard et al. (2023), and assumes a stellar mass of 0.60 $M_{\odot }$ and an initial hydrogen mass fraction $X_{\mathrm{H}}={10}^{-6}$. The effective temperature decreases monotonically with time; the left panel illustrates the float-up process at high temperature, while the right panel illustrates the convective dilution process at low temperature

Fig. 9

Zoomed-in version of Fig. 4 including theoretical predictions for the convective dilution of hydrogen. These simulations assume a stellar mass of 0.60 $M_{\odot }$ and initial hydrogen mass fractions $X_{\mathrm{H}}={10}^{-7.0}$, ${10}^{-6.5}$, ${10}^{-6.0}$, ${10}^{-5.5}$, and ${10}^{-5.0}$ (from bottom to top). For each simulation, the transition temperature (dashed part of the curve) is based on the approximate method of Rolland et al. (2020), while the resulting hydrogen abundance (solid part of the curve) is taken from Bédard et al. (2023)

Fig. 10

Zoomed-in version of Fig. 6 including theoretical evolutionary sequences for helium-rich white dwarfs contaminated by hydrogen due to convective dilution (left panel) and contaminated by carbon due to convective dredge-up (right panel). These sequences were calculated using the atmosphere models of Blouin et al. (2023a), assuming a stellar mass of 0.60 $M_{\odot }$ and the hydrogen (left panel) and carbon (right panel) abundances predicted by the simulations shown in Figs. 9 and 12, respectively

Fig. 11

Carbon mass fraction profile at various effective temperatures in a typical simulation of element transport in helium-rich white dwarfs. The position in the star is measured in terms of the fraction of the total mass located outside a given radius, such that the surface is towards the right and the core is towards the left. This particular simulation is taken from Blouin et al. (2023a), and assumes a stellar mass of 0.55 $M_{\odot }$ and an initial carbon mass fraction $X_{\mathrm{C}}=0.60$. The effective temperature decreases monotonically with time; the left panel illustrates the settling process at high temperature, while the right panel illustrates the convective dredge-up process at low temperature. In the latter case, notice the non-monotonic behaviour of the surface carbon abundance, which first increases (cyan, yellow, and brown curves) and then decreases (dark green curve)

Fig. 12

Zoomed-in version of Fig. 5 including theoretical predictions for the convective dredge-up of carbon. These simulations are taken from Blouin et al. (2023a), and assume stellar masses of 0.55 $M_{\odot }$ (dashed curves) and 0.60 $M_{\odot }$ (solid curves) and initial carbon mass fractions $X_{\mathrm{C}}=0.20$, 0.40, and 0.60 (from bottom to top)

Fig. 13

Schematic summary of the main white dwarf spectral evolution channels. For clarity, only internal element transport is considered, and it is implied that external accretion may at any time add metals to the atmosphere and thus add a “Z” to the spectral type. Some intermediate phases are also omitted for simplicity, most notably the hot stratified white dwarfs (amidst the DO-to-DA transition) and the cool helium-rich DA white dwarfs (amidst the DBA-to-DC/DQ transition)