A new method of correcting radial velocity time series for inhomogeneous convection

Magnetic activity strongly impacts stellar RVs and the search for small planets. We showed previously that in the solar case it induces RV variations with an amplitude over the cycle on the order of 8 m/s, with signals on short and long timescales. The major component is the inhibition of the convective blueshift due to plages. We explore a new approach to correct for this major component of stellar radial velocities in the case of solar-type stars. The convective blueshift depends on line depths; we use this property to develop a method that will characterize the amplitude of this effect and to correct for this RV component. We build realistic RV time series corresponding to RVs computed using different sets of lines, including lines in different depth ranges. We characterize the performance of the method used to reconstruct the signal without the convective component and the detection limits derived from the residuals. We identified a set of lines which, combined with a global set of lines, allows us to reconstruct the convective component with a good precision and to correct for it. For the full temporal sampling, the power in the range 100-500~d significantly decreased, by a factor of 100 for a RV noise below 30 cm/s. We also studied the impact of noise contributions other than the photon noise, which lead to uncertainties on the RV computation, as well as the impact of the temporal sampling. We found that these other sources of noise do not greatly alter the quality of the correction, although they need a better noise level to reach a similar performance level. A very good correction of the convective component can be achieved providing very good RV noise levels combined with a very good instrumental stability and realistic granulation noise. Under the conditions considered in this paper, detection limits at 480~d lower than 1 MEarth could be achieved for RV noise below 15 cm/s.