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Stellar magnetic activity produces time-varying distortions in thephotospheric line profiles of solar-type stars. These lead to systematic errorsin high-precision radial-velocity measurements, which limit efforts to discoverand measure the masses of low-mass exoplanets with orbital periods of more thana few tens of days. We present a new data-driven method for separating Dopplershifts of dynamical origin from apparent velocity variations arising fromvariability-induced changes in the stellar spectrum. We show that theautocorrelation function (ACF) of the cross-correlation function used tomeasure radial velocities is effectively invariant to translation. Byprojecting the radial velocities on to a subspace labelled by the observationidentifiers and spanned by the amplitude coefficients of the ACF's principalcomponents, we can isolate and subtract velocity perturbations caused bystellar magnetic activity. We test the method on a 5-year time sequence of 853daily 15-minute observations of the solar spectrum from the HARPS-N instrumentand solar-telescope feed on the 3.58-m Telescopio Nazionale Galileo. Afterremoval of the activity signals, the heliocentric solar velocity residuals arefound to be Gaussian and nearly uncorrelated. We inject synthetic low-massplanet signals with amplitude $K=40$ cm s$^{-1}$ into the solar observations ata wide range of orbital periods. Projection into the orthogonal complement ofthe ACF subspace isolates these signals effectively from solar activitysignals. Their semi-amplitudes are recovered with a precision of $\sim~6.6$ cms$^{-1}$, opening the door to Doppler detection and characterization ofterrestrial-mass planets around well-observed, bright main-sequence starsacross a wide range of orbital periods.

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