RV$\times$TESS I : Modeling Asteroseismic Signals with Simultaneous Photometry and RVs

Detecting small planets via the radial velocity method remains challenged by signals induced by stellar variability, versus the effects of the planet(s). Here, we explore using Gaussian Process (GP) regression with Transiting Exoplanet Survey Satellite (TESS) photometry in modeling radial velocities (RVs) to help to mitigate stellar jitter from oscillations and granulation for exoplanet detection. We applied GP regression to simultaneous TESS photometric and RV data of HD 5562, a G-type subgiant ($M_\star=1.09M_{\odot}$, $R_\star=1.88R_{\odot}$) with a V magnitude of 7.17, using photometry to inform the priors for RV fitting. The RV data is obtained by the Magellan Planet Finder Spectrograph (PFS). The photometry-informed GP regression reduced the RV scatter of HD~5562 from 2.03 to 0.51 m/s. We performed injection and recovery tests to evaluate the potential of GPs for discovering small exoplanets around evolved stars, which demonstrate that the GP provides comparable noise reduction to the binning method. We also found that the necessity of photometric data depends on the quality of the RV dataset. For long baseline and high-cadence RV observations, GP regression can effectively mitigate stellar jitter without photometric data. However, for intermittent RV observations, incorporating photometric data improves GP fitting and enhances detection capabilities.