Into the Depths: a new activity metric for high-precision radial velocity measurements based on line depth variations

Abstract: The discovery and characterization of extrasolar planets using radial velocity (RV) measurements is limited by noise sources from the surfaces of host stars. Current techniques to suppress stellar magnetic activity rely on decorrelation using an activity indicator (e.g., strength of the Ca II lines, width of the cross-correlation function, broadband photometry) or measurement of the RVs using only a subset of spectral lines that have been shown to be insensitive to activity. Here, we combine the above techniques by constructing a high signal-to-noise activity indicator, the depth metric $\mathcal{D}(t)$, from the most activity-sensitive spectral lines using the "line-by-line" method of Dumusque (2018). Analogous to photometric decorrelation of RVs or Gaussian progress regression modeling of activity indices, time series modeling of $\mathcal{D}(t)$ reduces the amplitude of magnetic activity in RV measurements; in an $\alpha$CenB RV time series from HARPS, the RV RMS was reduced from 2.67 to 1.02 m s$^{-1}$. $\mathcal{D}(t)$ modeling enabled us to characterize injected planetary signals as small as 1 m s$^{-1}$. In terms of noise reduction and injected signal recovery, $\mathcal{D}(t)$ modeling outperforms activity mitigation via the selection of activity-insensitive spectral lines. For Sun-like stars with activity signals on the m s$^{-1}$ level, the depth metric independently tracks rotationally modulated and multiyear stellar activity with a level of quality similar to that of the FWHM of the CCF and log$R^{\prime}_{HK}$. The depth metric and its elaborations will be a powerful tool in the mitigation of stellar magnetic activity, particularly as a means of connecting stellar activity to physical processes within host stars.