  Inhibition of the convective blueshift in active regions is a major
contribution to the radial velocity variations, at least for solar-like stars.
A common technique to correct for this component is to model the RV as a linear
function of chromospheric emission, because both are strongly correlated with
the coverage by plages. This correction is not perfect: the aim of the present
study is to understand the limits of this correction and to improve it. We
investigate these questions by analysing a large set of synthetic time series
corresponding to old main sequence F6-K4 stars modelled using a consistent set
of parameters. We focus here on the analysis of the correlation between time
series, in particular between RV and chromospheric emission on different
timescales. We also study the temporal variation for each time series.
Inclination strongly impacts these correlations, as well as additional signals
(granulation and supergranulation). Although RV and LogR'HK are often well
correlated, a combination of geometrical effects (butterfly diagrams related to
dynamo processes and inclination) and activity level variations over time
create an hysteresis pattern during the cycle, which produces a departure from
an excellent correlation: for a given activity level, the RV is higher or lower
during the ascending phase compared to the descending phase of the cycle
depending on inclination, with a reversal for inclinations about 60 deg from
pole-on. This hysteresis is also observed for the Sun and other stars. This
property is due to the spatio-temporal distribution of the activity pattern and
to the difference in projection effects of the RV and chromospheric emission.
These results allow us to propose a new method which significantly improves the
correction for long timescales, and could be crucial to improving detection
rates of planets in the habitable zone around F6-K4 stars.
