  In the search for planets orbiting distant stars the presence of stellar
activity in the atmospheres of observed stars can obscure the radial velocity
signal used to detect such planets. Furthermore, this stellar activity
contamination is set by the star itself and cannot simply be avoided with
better instrumentation. Various stellar activity indicators have been developed
that may correlate with this contamination. We introduce a new stellar activity
indicator called the Stellar Activity F-statistic for Exoplanet surveys (SAFE)
that has higher statistical power (i.e., probability of detecting a true
stellar activity signal) than many traditional stellar activity indicators in a
simulation study of an active region on a Sun-like star with moderate to high
signal-to-noise. Also through simulation, the SAFE is demonstrated to be
associated with the projected area on the visible side of the star covered by
active regions. We also demonstrate that the SAFE detects statistically
significant stellar activity in most of the spectra for HD 22049, a star known
to have high stellar variability. Additionally, the SAFE is calculated for
recent observations of the three low-variability stars HD 34411, HD 10700, and
HD 3651, the latter of which is known to have a planetary companion. As
expected, the SAFE for these three only occasionally detects activity.
Furthermore, initial exploration appears to indicate that the SAFE may be
useful for disentangling stellar activity signals from planet-induced Doppler
shifts.
