differential rotation that can be modeled as $$P_{\beta} = P_{EQ}/(1 - k \sin^{2}\beta)$$ where $P_{\beta}$ is the rotation period at latitude $\beta$ and $P_{EQ}$ is the equatorial rotation period. Observations of spots on the Sun yield $k = 0.19$ while surface radial velocity measurements give $k = 0.12$ [@Kitchatinov.05]. Theoretical simulations of turbulent convection predict that $k$ should decrease with increasing rotation rate [@Brown.04], this has been confirmed by observations of starspots on $\kappa^{1}$ Ceti by the MOST satellite which yield $k = 0.09$ for this solar-like star rotating with $P = 8.77~{\rm days}$ [@Walker.07]. While sunspots are rarely seen with $|\beta| > 30^{\circ}$, there are indications that younger stars may have spots at any latitude. For example, the aforementioned observations of $\kappa^{1}$ Ceti found 7 spots over the range $10^{\circ} < |\beta| < 80^{\circ}$. Assuming spots may be uniformly distributed over the surface of a star (i.e. uniformly distributed in $\sin\beta$), a value of $k = 0.09$ will yield an RMS spread in detected periods of $\sim 3\%$. We adopt this as an estimate for the expected contribution of differential rotation to the period uncertainty for stars in M37.

### Color Uncertainties

There are several effects that contribute to 