High-Pass Filtering and Gaussian Process Regularization: Stellar Activity Characterization Techniques Applied to the 55 Cancri Planetary System

Doppler planet searches are complicated by stellar activity, through which cyclical changes in the host star's photosphere and chromosphere can mask or mimic planetary signals. A popular technique for modeling stellar activity is to apply a quasiperiodic Gaussian process (GP) kernel, which provides a flexible model with rigorous error propagation. However, observers must guard against overfitting, as a GP may be flexible enough to subsume other signals besides the one it is intended to model. To counteract overfitting, we introduce a curvature-penalizing objective function for fitting GP models to long-term magnetic activity cycles. We also demonstrate that a Gaussian filter can be an effective method of detrending radial velocities (RVs) so that shorter-period signals can be extracted even in the absence of a mathematical model of the long-term trend. We apply our methods to the heavily studied 55 Cancri system, fitting Keplerian orbits plus the GP activity-cycle model. We show that a 4-Keplerian model that includes planets b, c, e, and f combined with a GP for the activity cycle performs at least as well as the widely agreed-upon 5-planet system with its own GP activity model. Our results suggest that the existence of planet d cannot be established from the RVs alone; additional data are required for confirmation.