within, instead of two large individual spots (Fig. \[fig:stellar\_surface\]).

When considering these complexes of smaller star spots, it is useful to consider the area ratio of spots to uncontaminated photosphere within each of these regions, which we define here as the filling factor, $f$. This quantity can be related to the spot’s contrast, $\rho$, through

$$\label{eq:filling_factor}
\rho = \frac{f F_{\bullet}(\lambda) +  (1-f)F_{*}(\lambda)}{F_{*}(\lambda)}$$

where $F_{\bullet}$ is the flux of the spot and $F_{*}$ is the flux of the star.

[@Berdyugina2005] plotted the observed temperature differences of spots for several different stellar effective temperatures. For K stars, the spot temperature differences ($\Delta$T) lie in the region of 1250 – 1500K.

Due to the degeneracy between spot size and contrast the spot contrasts have large error bars in Fig. \[fig:stellar\_surface\] (right panel). However, by fixing the spot sizes and positions at the best fitting values from the first MCMC run, the second run gave the relative uncertainty in the spot contrasts across the bands rather than the absolute uncertainty, as with the planetary radii. When considering the relative spot contrasts (Fig. \[fig:stellar\_surface\], right panel, solid error bars) it can be seen that the contrasts and colour dependences of these active regions are consistent 