  We present the results of numerical experiments to assess degeneracies in
lightcurve models of starspots. Using synthetic lightcurves generated with the
Cheetah starspot modeling code, we explore the extent to which photometric
light curves constrain spot model parameters, including spot latitudes and
stellar inclination. We also investigate the effects of spot parameters and
differential rotation on one's ability to correctly recover rotation periods
and differential rotation in the Kepler lightcurves. We confirm that in the
absence of additional constraints on the stellar inclination, such as
spectroscopic measurements of vsini or occultations of starspots by planetary
transits, the spot latitude and stellar inclination are difficult to determine
uniquely from the photometry alone. We find that for models with no
differential rotation, spots that appear on opposite hemispheres of the star
may cause one to interpret the rotation period to be half of the true period.
When differential rotation is included, the changing longitude separation
between spots breaks the symmetry of the hemispheres and the correct rotation
period is more likely to be found. The dominant period found via periodogram
analysis is typically that of the largest spot. Even when multiple spots with
periods representative of the star's differential rotation exist, if one spot
dominates the lightcurve the signal of differential rotation may not be
detectable from the periodogram alone. Starspot modeling is applicable to stars
with a wider range of rotation rates than other surface imaging techniques
(such as Doppler imaging), allows subtle signatures of differential rotation to
be measured, and may provide valuable information on the distribution of
stellar spots. However, given the inherent degeneracies and uncertainty present
in starspot models, caution should be exercised in their interpretation.
