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 $f_{0}=4.4763 rm{c days^{-1}}$, the first overtone $f_{1}=5.7897 rm{c days^{-1}}$ and 23 harmonics and linear combinations of $f_{0}$ and $f_{1}$ are detected by pulsation analysis. From the spectroscopic data, we get $rm{[Fe/H] = -0.2pm0.1 dex}$. The period change rate of the fundamental mode is obtained by using the Fourier-phase diagram method, which gives the value of $(1/P_{0})(dP_{0}/dt)=(1.81pm0.09) times 10^{-7} rm{yr}^{-1}$. 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 $(1/P_{0})(dP_{0}/dt)$ within $3sigma$ 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 $2.385pm0.025 M_{odot}$, the luminosity $log(L/L_{odot})=1.93pm0.02$ and the age $(4.43pm0.13)times 10^8$ 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.
تحميل البحث