i.e. the number of iterations required for the chain to “forget” where it started. We require a minimum of 30 auto-correlation time-scales to achieve convergence.

Eclipse depths are related to the temperature ratio. To obtain an accurate uncertainty for the temperature ratios, and thus secondary component temperatures, we marginalized over the primary and secondary effective temperatures, and report the posterior probability of the temperature ratio. From this, we calculate the secondary temperature and its uncertainty. The minimal rotational radial velocity that can be derived from APOGEE spectra is limited by the resolving power, allowing us to measure $v_\mathrm{rot} \gtrsim 10$km/s. We do not detect any broadening for any component in the studied systems, implying that all measured rotational velocities are below the $10$km/s detection threshold.

### **[Gaussian Process Regression]{}** {#sec:gp}

A Gaussian process (GP) is used to model noise, both instrumental and astrophysical; it is defined as a collection of random variables for which any finite number have a Gaussian distribution with a specified covariance structure. When using GPs, we use the data to condition the GP prior so that the GPs are normally distributed with respect to the data. A significant advantage of GP modeling is that it handles 