TESS Asteroseismology of the known red-giant host stars HD 212771 and HD 203949

The Transiting Exoplanet Survey Satellite (TESS) is performing a near all-sky survey for planets that transit bright stars. In addition, its excellent photometric precision enables asteroseismology of solar-type and red-giant stars, which exhibit convection-driven, solar-like oscillations. Simulations predict that TESS will detect solar-like oscillations in nearly 100 stars already known to host planets. In this paper, we present an asteroseismic analysis of the known red-giant host stars HD 212771 and HD 203949, both systems having a long-period planet detected through radial velocities. These are the first detections of oscillations in previously known exoplanet-host stars by TESS, further showcasing the mission's potential to conduct asteroseismology of red-giant stars. We estimate the fundamental properties of both stars through a grid-based modeling approach that uses global asteroseismic parameters as input. We discuss the evolutionary state of HD 203949 in depth and note the large discrepancy between its asteroseismic mass ($M_\ast = 1.23 \pm 0.15\,{\rm M}_\odot$ if on the red-giant branch or $M_\ast = 1.00 \pm 0.16\,{\rm M}_\odot$ if in the clump) and the mass quoted in the discovery paper ($M_\ast = 2.1 \pm 0.1\,{\rm M}_\odot$), implying a change $>30\,\%$ in the planet's mass. Assuming HD 203949 to be in the clump, we investigate the planet's past orbital evolution and discuss how it could have avoided engulfment at the tip of the red-giant branch. Finally, HD 212771 was observed by K2 during its Campaign 3, thus allowing for a preliminary comparison of the asteroseismic performances of TESS and K2. We estimate the ratio of the observed oscillation amplitudes for this star to be $A_{\rm max}^{\rm TESS}/A_{\rm max}^{\rm K2} = 0.75 \pm 0.14$, consistent with the expected ratio of $\sim0.85$ due to the redder bandpass of TESS.