  To date, the radial velocity (RV) method has been one of the most productive
techniques for detecting and confirming extrasolar planetary candidates.
Unfortunately, stellar activity can induce RV variations which can drown out or
even mimic planetary signals - and it is notoriously difficult to model and
thus mitigate the effects of these activity-induced nuisance signals. This is
expected to be a major obstacle to using next-generation spectrographs to
detect lower mass planets, planets with longer periods, and planets around more
active stars. Enter Gaussian processes (GPs) which, we note, have a number of
attractive features that make them very well suited to disentangling stellar
activity signals from planetary signals. We present here a GP framework we
developed to model RV time series jointly with ancillary activity indicators
(e.g. bisector velocity spans, line widths, chromospheric activity indices),
allowing the activity component of RV time series to be constrained and
disentangled from e.g. planetary components. We discuss the mathematical
details of our GP framework, and present results illustrating its encouraging
performance on both synthetic and real RV datasets, including the
publicly-available Alpha Centauri B dataset.
