Gaussian process regression of temperature-dependent radial velocities

Gaussian processes (GPs) described by quasi-periodic covariance functions have in recent years become a widely used tool to model the impact of stellar activity on radial velocity (RV) measurements. We perform a GP regression analysis on solar RV time series measured from spectral segments formed at different temperatures within the photosphere in order to evaluate the relation between the best-fit GP kernel hyperparameters and the observed activity signal as a function of temperature. The posterior distributions of the hyperparameters show subtle differences between high- and low-activity phases and as a function of the spectral formation temperature range, which could have implications on the characteristics of the activity signal and its optimal modelling. For the temperature-dependent RVs, we find that at high and low activity alike, the minimal RV dispersion is obtained at intermediately cool temperature ranges (4000-4750 K), for both the observed and GP model-subtracted RVs. Finally, we compare and correlate our temperature-dependent RVs with RV components derived from disk-resolved Dopplergrams of the Sun, for which we find a consistently strong correlation between RVs related to hotter temperature ranges and the dominant RV component due to the inhibition of convection.