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

TL;DR

RV×TESS I demonstrates that simultaneous TESS photometry can train Gaussian Process priors to model the asteroseismic jitter in precise RVs, improving small-planet detectability around evolved stars. Applying a six-parameter SHO GP kernel to HD 5562, informed by frequency-domain analysis of the LC, reduces RV scatter from $2.03$ to $0.51$ m s$^{-1}$ and yields robust injection-recovery gains for Earth-mass signals. The study also shows that, for long-baseline, high-cadence RV data, photometry priors are less critical, whereas intermittent RV campaigns benefit substantially from LC-informed priors. Compared with binning, GP modeling is competitive or superior in reducing jitter and provides valuable asteroseismic characterization. These results validate the RV×TESS approach and have direct implications for improving sensitivity to small planets in RV surveys under realistic observing cadences.

Abstract

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.

Figures (15)

• Figure 1: Normalized TESS 2-minute cadence PDCSAP light curve for HD 5562 from sectors 1 and 2. The large scatter during sector 1 near 1350 days originates from a misconfigured fine-pointing calibration. Note that the BJD time has an offset of 2457000 days. See Section \ref{['subsec:TESS']} for more details.
• Figure 2: Top: Stellar SED and the best-fit model. Blue points represent the photometry from the literature based on SIMBAD queries by ARIADNE, while purple diamonds denote synthetic photometry based on the best-fit stellar model (black line). Horizontal error bars indicate the filter bandpasses. Bottom: Residuals of the fit in terms of ratios between residuals and uncertainties of the photometries. See Section \ref{['subsec:sed']} for more details.
• Figure 3: Échelle diagram from the asteroseismic analyses (Section \ref{['subsec:asteroseismology']}) with the observed (colored symbols) and model (open symbols) frequencies highlighted. The frequency mod (x axis) shows the different modelled modes with the symbol sizes of $\ell=1$ and $2$ mofes inversely proportional to their mode inertia scaled to the closest $\ell=0$ modes, which indicates the mode amplitudes.
• Figure 4: Joint fitting to the RVs, Hipparcos, and Gaia astrometry. (a) RV curve of HD 5562 B. The thick black line shows the best-fit Keplerian orbit. Residuals ($O-C$) between the observation and the model are plotted underneath. (b) The best-fitting astrometric orbit of HD 5562. The black dashed line inside the orbit connects the ascending node and the descending node. The plus symbol denotes the system's barycenter, and the grey line connects it with the periapsis. The post-fit Hipparcos abscissa residuals are projected into the R.A. and decl. axes (grey dots) and have been binned into single points with colors. The brightness of these points gradually increases with observation time (the temporal baseline of each satellite is normalized to 1). The orientations of the error bars of each point denote the along-scan direction of Hipparcos. The curl at the lower left corner denotes the orientation of the orbital motion. (c) Zoom-in of the rectangular region of panel (b) which depicts the best fit to Gaia GOST data and the comparison between best-fit and catalog astrometry (positions and proper motions) at GDR2 and GDR3 reference epochs. The blue shaded regions represent the uncertainty of catalog positions and proper motions after removing the motion of the system's barycenter. The dot and slope of two lines (blue and green) indicate the best-fit position and proper motion offsets induced by the companion. (d) The residual ($O-C$) of Hipparcos abscissa.
• Figure 5: Power spectral density (PSD) of the light curve of HD 5562 from TESS Sectors 1 and 2, covering the whole frequency range (left) and a zoom-in view (right). The green line represents the smoothed spectrum for illustrative purposes, and the blue line is a Gaussian fit to the power spectrum between 700 and 1200 $\mu$Hz. The pink line represents the original, unsmoothed power spectrum. The red line is an initial guess for the SHO model in our GP regression to fit the light curve, which was derived based on the best-fit Gaussian model (blue) within 700-1200 $\mu$Hz. See Section \ref{['subsec:tradition']} for more details.