In this paper, we present a new method for measuring the surface differential rotation of
cool stars with rotation periods of a few days, for which the sparse phase coverage achievable
from single site observations generally prevents the use of more conventional techniques.
The basic idea underlying this new analysis is to obtain the surface differential rotation
pattern that minimises the information content of the reconstructed Doppler image through
a simultaneous fit of all available data.
Simulations demonstrate that the performance of this new method in the case of cool stars
is satisfactory for a variety of observing strategies. Differential rotation parameters
can be reliably recovered
as long as the total data set spans at least 4% of the time for the
equator to lap the pole by about one complete cycle. We find in particular that these
results hold for potentially complex spot distributions (as long as they include a mixture
of low and high latitude features), as well as for various stellar inclination angles and
rotation velocities. Such measurements can be obtained from either unpolarised or polarised
data sets, provided their S/N ratio is larger than about 500 and 5000 per 2 km/s
spectral bin respectively.
This method should therefore be very useful to investigate differential rotation in a
much larger sample of objects than what has been possible up to now, and should hence
give us the opportunity of studying how differential rotation reacts to various
phenomena operating in stellar convective zones, such as tidal effects or
dynamo magnetic field generation.