Accounting for stellar activity is a crucial component of the search for ever-smaller planets orbiting stars of all spectral types. We use Doppler imaging methods to demonstrate that starspot induced radial velocity variability can be effectively reduced for moderately rotating, fully convective stars. Using starspot distributions extrapolated from sunspot observations, we adopt typical M dwarf starspot distributions with low contrast spots to synthesise line profile distortions. The distortions are recovered using maximum entropy regularised fitting and the corresponding stellar radial velocities are measured. The procedure is demonstrated for a late-M star harbouring an orbiting planet in the habitable zone. The technique is effective for stars with vsini = 1-10 km/s, reducing the stellar noise contribution by factors of nearly an order of magnitude. With a carefully chosen observing strategy, the technique can be used to determine the stellar rotation period and is robust to uncertainties such as unknown stellar inclination. While demonstrated for late-type M stars, the procedure is applicable to all spectral types.
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