Asteroseismology of DAV star HS0507+0434B, including the core composition profiles

The DAV star, HS0507+0434B, was observed by Fu et al. (2013) in 2007 and from 2009 December to 2010 January. There were a total of six triplets with nearly equal split, which were identified as $l$ = 1 modes caused by rotation. In order to fit the six $l$ = 1 modes, grids of white dwarf models are generated by WDEC. For the core composition profiles, we choose the linear fittings to carbon profile of white dwarf models from MESA, which can be considered as results of real nuclear burning process. Coupled with diffusion equilibrium H/He and He/C mixtures, we make grids of models in WDEC and do asteroseismology works on HS0507+0434B. There is a total of 9.50 seconds error for our best-fitting model, which is smaller than the result (a total of 22.1 seconds error) of Fu et al. (2013), when fitting the six $l$ = 1 modes. The two other previous identified pulsation mode frequencies (286.1 s and 743.40 s) may also be well fitted by our best-fitting model. The model parameters are $T_{eff}$ = 11450 K, log$g$ = 8.088, $M_{*}$ = 0.640 $M_{\odot}$, log($M_{H}$/$M_{*}$) = -6, and log($M_{He}$/$M_{*}$) = -3.