Separating planetary reflex Doppler shifts from stellar variability in the wavelength domain

2021 
Stellar magnetic activity produces time-varying distortions in the photospheric line profiles of solar-type stars. The changing shape of the profile produces systematic errors in high-precision radial-velocity measurements, which limit efforts to discover and measure the masses of low-mass exoplanets with orbital periods of more than a few tens of days. We present a new data-driven method for separating Doppler shifts of dynamical origin from apparent velocity variations arising from variability-induced changes in the stellar spectrum. It uses the invariance to translation in the velocity domain of the autocorrelation function of the spectrum (and of its cross-correlation function). By projecting the measured velocity time series onto the principal components of the autocorrelation function, we isolate the velocity perturbations caused by solar magnetic activity. Dynamical shifts are preserved when we subtract the projected perturbations from the original velocity measurements. We demonstrate its effectiveness using a 5-year time sequence of 880 daily-averaged cross-correlation functions of the solar spectrum from the HARPS-N instrument and solar-telescope feed on the 3.58-m Telescopio Nazionale Galileo, reduced with a new version of the HARPS-N data-reduction pipeline. We inject synthetic low-mass planet signals with amplitude $K=40$ cm s$^{-1}$ into the solar observations at a wide range of orbital periods. We find that our method isolates these signals effectively from solar activity signals. Their semi-amplitudes are recovered with a precision of $\sim 4.4$ cm~s$^{-1}$, opening the door to Doppler detection and characterization of terrestrial-mass planets around well-observed, bright main-sequence stars across a wide range of orbital periods.
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