The Asteroseismology of ZZ Ceti star GD1212

TL;DR

This study analyzes the pulsation modes of the ZZ Ceti star GD 1212 using Kepler data, identifying rotation modes, deriving stellar parameters, and linking internal composition gradients to observed pulsation features.

Contribution

It provides a detailed asteroseismic analysis of GD 1212, including mode identification, rotation period estimation, and modeling of internal structure, which advances understanding of white dwarf evolution.

Findings

Identified multiple pulsation modes and rotation modes in GD 1212.

Derived a mean rotation period of approximately 6.65 hours.

Linked internal C/O gradient to observed period spacings.

Abstract

The ZZ Ceti star GD 1212 was detected to have 19 independent modes from the two-wheel-controlled Kepler Spacecraft in 2014. By asymptotic analysis, we identify most of pulsation modes. We find out two set of complete triplets, and four sets of doublet which are interpreted as rotation modes with $l=1$. For the other five modes, the four modes $f_{13}$, $f_{15}$, $f_{16}$ and $f_{4}$ are identified as ones with $l=2$; and the mode $f_{7}$ is identified to be the one with $l=1$. Meanwhile we derive a mean rotation period of $6.65\pm0.21$ h for GD 1212 according to the rotation splitting. Using the method of matching the observed periods to theoretical ones, we obtain the best-fitting model with the four parameters as $M_{\rm{*}}/M_{\rm{\odot}} = 0.775$, $T_{\rm{eff}} = 11400$ K, $\log (M_{\rm{H}}/M_{\rm{*}}) = -5.0$, $\log (M_{\rm{He}}/M_{\rm{*}})=-2.5$ for GD 1212. We find that due to the gradient of C/O abundance in the interior of white dwarf, some modes can not propagate to the stellar interior, which leads to the period spacing of the adjacent modes to become large. This feature is just proven by the observational data from GD 1212. All of these imply that GD 1212 may be evolved from an intermediate mass star.