TESS Asteroseismic Analysis of the Known Exoplanet Host Star HD 222076

The Transiting Exoplanet Survey Satellite (TESS) is an all-sky survey mission aiming to search for exoplanets that transit bright stars. The high-quality photometric data of TESS are excellent for the asteroseismic study of solar-like stars. In this work, we present an asteroseismic analysis of the red-giant star HD~222076 hosting a long-period (2.4 yr) giant planet discovered through radial velocities. Solar-like oscillations of HD~222076 are detected around $203\mu$Hz by TESS for the first time. Asteroseismic modeling, using global asteroseismic parameters as input, yields a determination of the stellar mass ($M_{\star }=1.12\pm 0.12M_{\odot }$), radius ($R_\star = 4.34 \pm 0.21,R_\odot$),andage($7.4 \pm 2.7,$Gyr), with precisions greatly improved from previous studies. The period spacing of the dipolar mixed modes extracted from the observed power spectrum reveals that the star is on the red-giant branch burning hydrogen in a shell surrounding the core. We find that the planet will not escape the tidal pull of the star and be engulfed into it within about $800$Myr, before the tip of the red-giant branch is reached.