Inferring probabilistic stellar rotation periods using Gaussian processes

Abstract

Variability in the light curves of spotted, rotating stars is often\nnon-sinusoidal and quasi-periodic --- spots move on the stellar surface and\nhave finite lifetimes, causing stellar flux variations to slowly shift in\nphase. A strictly periodic sinusoid therefore cannot accurately model a\nrotationally modulated stellar light curve. Physical models of stellar surfaces\nhave many drawbacks preventing effective inference, such as highly degenerate\nor high-dimensional parameter spaces. In this work, we test an appropriate\neffective model: a Gaussian Process with a quasi-periodic covariance kernel\nfunction. This highly flexible model allows sampling of the posterior\nprobability density function of the periodic parameter, marginalising over the\nother kernel hyperparameters using a Markov Chain Monte Carlo approach. To test\nthe effectiveness of this method, we infer rotation periods from 333 simulated\nstellar light curves, demonstrating that the Gaussian process method produces\nperiods that are more accurate than both a sine-fitting periodogram and an\nautocorrelation function method. We also demonstrate that it works well on real\ndata, by inferring rotation periods for 275 Kepler stars with previously\nmeasured periods. We provide a table of rotation periods for these 1132 Kepler\nobjects of interest and their posterior probability density function samples.\nBecause this method delivers posterior probability density functions, it will\nenable hierarchical studies involving stellar rotation, particularly those\ninvolving population modelling, such as inferring stellar ages, obliquities in\nexoplanet systems, or characterising star-planet interactions. The code used to\nimplement this method is available online.\n