ratio $\ell_{\rm Kp}$ as a constraint in the analysis of the published photometry. Another useful constraint is the surface brightness ratio in the Kepler band, $S_{\rm Kp}$, which we account for by using the empirical relation between the V-band surface brightness $S_{\rm V}$ and $(\rm
B - \rm K)$ from @2017ApJ...837....7G. The comparison between the predicted and observed values is done in terms of the surface brightness parameter $$S_i = m_{i,0} + 5\log\phi,$$ where $i$ denotes a particular band (V or Kp), $\phi$ is the angular diameter in milli-arcseconds, and $m_{i,0}$ is the de-reddened apparent magnitude in a given band, so that $S_{\rm Kp} =
S_{\rm V} + ({\rm Kp}-{\rm V})$.

We used [emcee]{} [@2013PASP..125..306F] to sample the posterior probability distribution for our model parameters. We used the reddening maps by @2011ApJ...737..103S to estimate the total line-of-sight extinction to each target, ${\rm E}({\rm B}-{\rm V})_{\rm map}$. This value is used to impose the following (unnormalized) prior on $\Delta = {\rm E}({\rm B}-{\rm
V}) - {\rm E}({\rm B}-{\rm V})_{\rm map}$: $$P(\Delta) = \left\{ 
\begin{array}{ll}
  1 & \Delta \le 0 \\ 
  \exp(-0.5(\Delta/0.034)^2) & \Delta > 0 \\ 
\end{array} \right.$$ The constant 0.034 is taken from @2014MNRAS.437.1681M and is based on a comparison 