Seismic test of the mass-radius relationship of hydrogen-atmospheric white dwarf stars

TL;DR

This work compiles a comprehensive ZZ Ceti catalog to test the empirical mass-radius relation for hydrogen-atmosphere white dwarfs using GAIA DR3 parallaxes and asteroseismic masses. It confirms a linear relation between effective temperature and the amplitude-weighted mean pulsation period and reveals a bimodal WMP distribution, enabling a semi-empirical mass-radius test. Radii inferred from seismic masses are larger than theoretical MRR predictions by up to about 15%, especially at higher masses, suggesting systematic differences in mass determinations or core composition effects. The findings highlight the need for unified modeling and updated evolutionary tracks to resolve MRR discrepancies and improve constraints on white dwarf interiors and progenitor evolution.

Abstract

The pulsation of white dwarfs provides crucial information on stellar parameters for understanding the atmosphere and interior structure of these stars. In this study, we present a comprehensive statistical analysis of known ZZ Ceti stars from historical literature. Our dataset includes stellar parameters and oscillation properties from 339 samples, with 194 of them having undergone asteroseismological analysis. We investigated the empirical instability strip of ZZ Ceti stars and confirmed the linear relationship between temperature and weighted mean pulsation periods (WMP). We found that the WMP distribution is well-described with two groups of stars with peak values at $\sim254$ s and $\sim719$ s. Using seismic mass and trigonometrical radii derived from GAIA DR3 parallaxes, we tested the mass-radius relationship of white dwarfs through observational and seismic analysis of ZZ Cetis. They are generally larger than the theoretical values, with the discrepancy reaching up to $\sim15\%$ for massive stars with a mass estimated by seismology.

Figures (6)

• Figure 1: Comparison of observational effective temperature and mass between K25 and V24. The red dashed lines give the reference when the value from the two sources is equal.
• Figure 2: Distribution of ZZ Ceti stars on the $T_\mathrm{eff}$ - $\log g$ plane. Circles are known ZZ Ceti stars with parameters taken from 2025ApJ...979..157K (Blue), 2024AA...682A...5V (Red), 2011ApJ...730..128T (Green), and values collected from the original paper (Purple), respectively. The size of the points shows the amplitude-weighted mean periods of each star. Small blue triangles are pure DA white dwarfs collected from 2025ApJ...979..157K except known DAVs. Blue and red dashed lines show the theoretical instability strip from 2015ApJ...809..148T. Horizontal gray dashed lines present the La Plate models of white dwarfs.
• Figure 3: Mean weighted pulsating period (WMP) as a function of effective temperature (left) and stellar mass (right) for ZZ Ceti, as well as the distributions of observational parameters (grey). In comparison, green points show the seismology results. A two-gaussian model is used to fit the distribution of WMP, with peaks of $\sim241$s and $\sim707$s. The red line shows a linear relationship of $\mathit{WMP} \propto -0.92T_\mathrm{eff}$, fitted by linear regression.
• Figure 4: (Upper) Eperical mass-radius relationship (MRR) of ZZ Ceti. Radii are taken from trigonometrical radii $R_\pi$. Color points are derived from K25, V24, T11, and others, respectively, as described in Sect. \ref{['sec:data']}. Orange circles are derived from the seismology results, which include over six observed modes. Solid lines show the theoretical blue and red edge MRR of ZZ Ceti. (Lower) Residuals between $R_\pi$ and the theoretical radius as a fraction of $R_\pi$.
• Figure 5: Comparison between observational (squares) and seismological (circles) results in MRR diagram. Three panels show the samples with $<3$, $3-7$, $>7$ observed modes, respectively. Observational and seismological results of one star are linked with solid lines.