Application of a screened Coulomb potential in fitting the DAV star HS 0507+0434B

Abstract: We use \texttt{WDEC} to evolve grids of DAV star models adopting the element diffusion scheme with pure and screened Coulomb potential effect. The core compositions are thermonuclear burning results which are derived from \texttt{MESA}. \texttt{MESA} yields composition profiles that the version of WDEC used in this work could not accommodate (most notably the presence of helium in the core of the model). According to the theory of rotational splitting, Fu et al. identified 6 triplets for a DAV star HS 0507+0434B based on 206\,h photometric data. The grids of DAV star models are used to fit the 6 reliable $m$ = 0 modes. When adopting the screened Coulomb potential, we obtain a best fitting model of log($M_{\rm He}/M_{\rm *}$) = -3.0, log($M_{\rm H}/M_{\rm *}$) = -6.1, $T_{\rm eff}$ = 11790\,K, $M_{\rm *}$ = 0.625\,$M_{\odot}$, log$g$ = 8.066, and $\sigma_{RMS}$ = 2.08\,s. Compared with adopting the pure Coulomb potential, the value of $\sigma_{RMS}$ is improved by 34\%. The study may provide a new method for the research of mode trapping properties.