Title: A new method of correcting radial velocity time series for inhomogeneous convection,
Abstract: 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.