correlations in the data that are poorly understood by specifying only the high-level properties of a covariance kernel. We elected to use GPs to address the issues associated with stellar variations due to spots, correlated noise and instrumental systematics that are present in the light curves for both objects. We further incorporated a white noise kernel to assess our computed uncertainties.

Prior to the application of Gaussian processes, we create a combined binary star light and radial velocity curve model using  and . We then apply Gaussian processes to the light curve model, which removes the need to associate the systematics in the light curve with an explicit functional form. That way, we are able to model a wide range of systematics with a small number of tunable parameters.

The kernel, or covariance function, describes the similarity between two adjacent data points. For our kernel, we elected to use a term that approximates a Matern 3/2 function, which has a slowly and a rapidly varying component:

$$\label{eqn:matern}
k(\tau) = \sigma^2 \left[ (1+1/\epsilon)e^{-(1-\epsilon)\sqrt{3}\tau/\rho} (1+1/\epsilon)e^{-(1+\epsilon)\sqrt{3}\tau/\rho}\right]$$

Parameter $\epsilon$ controls the quality of the approximation since, in the limit as ${\epsilon \to 0}$, this becomes the Matern-3/2 function. For our computations, we set $\epsilon$ 