Asteroseismology of the Double-Mode High-Amplitude $\delta$ Scuti Star VX Hydrae

Abstract

Bi-site time-series photometric and high-resolution spectroscopic observations were made for the double-mode high-amplitude $\delta$ Scuti star VX\ Hya. The fundamental frequency $f_0=4.4763\mathrm{c}\mathrm{day}{\mathrm{s}}^{-1}$, the first overtone $f_1=5.7897\mathrm{c}\mathrm{day}{\mathrm{s}}^{-1}$ and 23 harmonics and linear combinations of $f_0$ and $f_1$ are detected by pulsation analysis. From the spectroscopic data, we get $[Fe/H]=-0.2\pm 0.1\mathrm{dex}$. The period change rate of the fundamental mode is obtained by using the Fourier-phase diagram method, which gives the value of $(1/P_0)(d{P}_0/dt)=(1.81\pm 0.09)\times 10^{-7}{\mathrm{yr}}^{-1}$. With these results from the observations, we perform theoretical explorations with the stellar evolution code MESA, and constrain the models by fitting $f_0$, $f_1$, and $(1/P_0)(d{P}_0/dt)$ within $3\sigma$ deviations. The results show that the period change of VX\ Hya could be ascribed to the evolutionary effect. The stellar parameters of VX\ Hya could be derived as: the mass $2.385\pm 0.025M_{\odot }$, the luminosity $\log (L/L_{\odot })=1.93\pm 0.02$ and the age $(4.43\pm 0.13)\times 10^8$ years. VX\ Hya is found to locate at the post-main-sequence stage with a helium core and a hydrogen-burning shell on the H$-$R diagram.

arXiv comment23 pages, 9 figures, 12 tables. ApJ version

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