Asteroseismology of RRab variable star EZ Cnc from K2 photometry and LAMOST spectroscopy

EZ Cnc, or EPIC 212182292, is a non-Blazhko RRab variable star located in the field of K2 Campaign 16. Its atmospheric parameters ($T_{\rm eff}$, $\log{g}$, [M/H]) and radial velocities are measured from the 55 high-quality LAMOST medium-resolution spectra. The fundamental frequency of pulsation is derived as $f=1.8323(17)$ d$^{-1}$ from the K2 light curves. The amplitude ratios $R_{21} = 0.5115(15), 0.490(8)$, $R_{31} = 0.3249(20), 0.279(7)$ and Fourier phase differences $\varphi_{21}=2.7550(20), 2.764(16)$, $\varphi_{31}=5.7194(25), 5.719(31)$ are determined from the Fourier decomposition of K2 light curve and LAMOST radial velocity curve, respectively. Through the constraints of the parameters, four optimal models are obtained in a time-dependent turbulent convection model survey for EPIC 212182292. The parameters of EPIC 212182292 are derived as $M=0.48\pm0.03$ M$_{\odot}$, $L = 42\pm2$ L$_{\odot}$, $T_{\rm eff}=6846\pm50$ K, $\log{g}=2.79\pm0.01$ dex, and $Z = 0.006\pm0.002$, respectively. The precisely determined parameters for RRab variable stars like EPIC 212180092 might help to better understand the period-luminosity relationship of RR Lyrae stars.