Measuring precise radial velocities and cross-correlation function line-profile variations using a Skew Normal density

Abstract

Stellar activity is one of the primary limitations to the detection of low-mass exoplanets using the radial-velocity (RV) technique. We propose to estimate the variations in shape of the CCF by fitting a Skew Normal (SN) density which, unlike the commonly employed Normal density, includes a skewness parameter to capture the asymmetry of the CCF induced by stellar activity and the convective blueshift. The performances of the proposed method are compared to the commonly employed Normal density using both simulations and real observations, with different levels of activity and signal-to-noise ratio. When considering real observations, the correlation between the RV and the asymmetry of the CCF and between the RV and the width of the CCF are stronger when using the parameters estimated with the SN density rather than the ones obtained with the commonly employed Normal density. Using the proposed SN approach, the uncertainties estimated on the RV defined as the median of the SN are on average 10% smaller than the uncertainties calculated on the mean of the Normal. The uncertainties estimated on the asymmetry parameter of the SN are on average 15% smaller than the uncertainties measured on the Bisector Inverse Slope Span (BIS SPAN), which is the commonly used parameter to evaluate the asymmetry of the CCF. We also propose a new model to account for stellar activity when fitting a planetary signal to RV data. Based on simple simulations, we were able to demonstrate that this new model improves the planetary detection limits by 12% compared to the model commonly used to account for stellar activity. The SN density is a better model than the Normal density for characterizing the CCF since the correlations used to probe stellar activity are stronger and the uncertainties of the RV estimate and the asymmetry of the CCF are both smaller.