coefficients after each iteration. Limb darkening is a thorny issue, with its implications discussed in detail in @prsa2016; it affects eclipse ingress and egress and is degenerate with stellar radii. We use limb darkening coefficients computed from the PHOENIX model atmospheres for the range of temperatures, surface gravities and chemical abundances applicable to our systems. We enforced consistency by interpolating the limb darkening coefficients for any explored combination of atmosphere parameters. While there are inherent limitations of using the square-root limb darkening model, the compounded systematic effects that arise from its use (compared to other limb darkening models) are below 0.5%.

### Markov Chain Monte Carlo Derived Uncertainties\[mcmcanalysis\]

Objective comparison between masses and radii measured observationally and those predicted by theory requires that realistic uncertainties be derived for the measurements. We use a Markov Chain Monte Carlo (MCMC) sampler to sample the posterior probability distribution function. At each iteration we compute the posterior log-probability distribution function:

$$\log{P(\theta|D)} = \log{P(F|\theta)} + \log{P(RV|\theta)} + \log{P(\theta)} + C,$$

where $D$ denotes the data, $F$ are the light curve measurements, $RV$ are the radial velocity measurements, $\theta$ is the parameter vector that contains the fitted parameters (specified in §\[sec:ph\_model\]) and $C$ is an arbitrary 