Identifying activity induced RV periodicities and correlations using Central Line Moments

The radial velocity (RV) method of exoplanet detection requires mitigation of nuisance signals arising from stellar activity. Using analytic cool and facular spot models, we explore the use of central line moments (CLMs) for recovering and monitoring rotation induced RV variability. Different spot distribution patterns, photosphere-spot contrast ratios and the presence or absence of the convective blueshift lead to differences in CLM signals between M dwarfs and G dwarfs. Harmonics of the rotation period are often recovered with the highest power in standard periodogram analyses. By contrast, we show the true stellar rotation may be more reliably recovered with string length minimisation. For solar minimum activity levels, recovery of the stellar rotation signal from CLMs is found to require unfeasibly high signal-to-noise observations. The stellar rotation period can be recovered at solar maximum activity levels from CLMs for reasonable cross-correlation function (CCF) signal-to-noise ratios $> 1000 - 5000$. The CLMs can be used to recover and monitor stellar activity through their mutual correlations and correlations with RV and bisector inverse span. The skewness of a CCF, a measure of asymmetry, is described by the third CLM, $M_3$. Our noise-free simulations indicate the linear RV vs $M_3$ correlation is up to 10 per cent higher than the RV vs bisector inverse span correlation. We find a corresponding $\sim 5$ per cent increase in linear correlation for CARMENES observations of the M star, AU Mic. We also assess the effectiveness of the time derivative of the second CLM, $M_2$, for monitoring stellar activity.