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The use of Gaussian processes (GPs) as models for astronomical time seriesdatasets has recently become almost ubiquitous, given their ease of use andflexibility. GPs excel in particular at marginalization over the stellar signalin cases where the variability due to starspots rotating in and out of view istreated as a nuisance, such as in exoplanet transit modeling. However, theseeffective models are less useful in cases where the starspot signal is ofprimary interest since it is not obvious how the parameters of the GP model arerelated to the physical properties of interest, such as the size, contrast, andlatitudinal distribution of the spots. Instead, it is common practice toexplicitly model the effect of individual starspots on the light curve andattempt to infer their properties via optimization or posterior inference.Unfortunately, this process is degenerate, ill-posed, and often computationallyintractable when applied to stars with more than a few spots and/or toensembles of many light curves. In this paper, we derive a closed-formexpression for the mean and covariance of a Gaussian process model thatdescribes the light curve of a rotating, evolving stellar surface conditionedon a given distribution of starspot sizes, contrasts, and latitudes. Wedemonstrate that this model is correctly calibrated, allowing one to robustlyinfer physical parameters of interest from one or more stellar light curves,including the typical radii and the mean and variance of the latitudedistribution of starspots. Our GP has far-ranging implications forunderstanding the variability and magnetic activity of stars from both lightcurves and radial velocity (RV) measurements, as well as for robustly modelingcorrelated noise in both transiting and RV exoplanet searches. Ourimplementation is efficient, user-friendly, and open source, available as thePython package starry-process.

Mapping stellar surfaces II: An interpretable Gaussian process model for light curves