Constraints on White Dwarf Hydrogen Layer Masses Using Gravitational Redshifts

Abstract

The hydrogen envelope is the outermost layer of a DA white dwarf; it makes up the entirety of the stellar photosphere, and yet its typical extent is difficult to model theoretically and remains poorly observationally constrained. As a result, hydrogen envelope mass is a substantial source of systematic uncertainty in physical properties of white dwarf, including overall masses and cooling ages. In this work, we fit a Gaussian mixture model to gravitational redshifts from high-resolution spectroscopy, paired with radius measurements from Gaia BP/RP spectra, to measure the mass-radius relation for a sample of 468 white dwarfs. Our results are in excellent agreement with the predicted mass-radius relations of state-of-the-art evolutionary models, including those from the MESA Isochrones and Stellar Tracks (MIST) library. We find that mass-radius relations such as MIST which assume a thick and mass-dependent hydrogen envelope are preferred by the observed probability density function over models which assume a constant hydrogen envelope mass. Proper treatment of the evolution of white dwarf progenitors is thus important for accurately modeling the mass-radius relation. Our results indicate that gravitational redshift measurements of large samples of white dwarfs in wide binaries are promising probes of the hydrogen envelope masses of DA white dwarfs.

Figures (8)

• Figure 1: Difference between magnitude calculated from Gaia XP spectra and SDSS photometric bands for 203 stars from the isolated white dwarf sample for which both sources of data are available. Also shown is the difference between XP spectra and flux standard photometry for 27 white dwarfs in the CALSPEC database. Points are spaced uniformly along the horizontal axis in order of increasing effective temperature. Spacing along the horizontal axis is arbitrary and not linear across effective temperatures. We find that our photometric corrections produce photometry which is accurate to at least $3\%$ absolute flux.
• Figure 2: Measured radii (mean of the posterior distribution) from our work against the spectroscopic radius measurements of 2009AA...505..441K and photometric radius measurements of 2021MNRAS.508.3877G. Our results are accurate up to a $1.3\%$ bias relative to the photometric measurements. For both comparison samples we transform the reported effective temperature and surface gravity into radius via the mass-radius relation of 2020ApJ...901...93B.
• Figure 3: Kinematics of the isolated white dwarf sample. Stars with total three dimensional velocities greater than $100$ km s$^{-1}$ (indicated by the blue circle) are assumed to have kinematics inconsistent with the thin disk, and are therefore removed from the sample. This removes 13 objects from the analysis.
• Figure 4: Measured parameters for the wide binary and isolated samples, as well as on-sky distributions and ages inferred from MIST. We mark the theoretical temperature-radius curves for a cooling white dwarf of masses $0.4~M_\odot$, $0.6~M_\odot$, and $0.8~M_\odot$ using the mass-radius relation of 2020ApJ...901...93B, and the mass distributions are determined using the same relations. Those models assume a core composition of carbon and oxygen in equal ratios, meaning that the distribution masses of objects below $\approx 0.45 M_\odot$, which may have helium cores, is not necessarily accurate. Our targets are biased to the southern sky due to the location of the VLT, making our corrections to the local standard of rest important for accurate inference.
• Figure 5: Logarithm of Bayesian information criterion as a function of number of Gaussian components for deconvolution of the observed mass-radius relation (e.g. 2011AnApS...5.1657B). Component numbers which result in singular matrices are plotted marked as "x". This is a particular issue for the wide binary sample, due to its much smaller sample size. The score of the non-singular fits are similar to those of the singular fits though, indicating that the information is still captured. The isolated sample is best represented by three components, and the wide binary sample by two.