Inferring probabilistic stellar rotation periods using Gaussian processes

Abstract

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasiperiodic -spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalising over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sinefitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these 1102 Kepler objects of interest and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterising star-planet interactions. The code used to implement this method is available online.

An Ultra-short Period Rocky Super-Earth with a Secondary Eclipse and a Neptune-like Companion around K2-141

“…To understand the disagreement between the K2 light curves and the activity indices we followed the recipe of Angus et al (2018), who suggest a Gaussian process (GP) with a quasi-period covariance kernel function as a more reliable method than those mentioned above to measure rotational periods of active stars. We performed our analysis using version 5 of PyORBIT 37 (Malavolta et al 2016), a package for RV and activity indices analysis, with the implementation of the GP quasi-period kernel as described in Grunblatt et al (2015), from which we inherit the mathematical notation, through the george 38 package (Ambikasaran et al 2015).…”

APO Time-resolved Color Photometry of Highly Elongated Interstellar Object 1I/‘Oumuamua

“…This approach has recently been successfully deployed in a range of astronomical applications (e.g., Angus et al 2017;Jones et al 2017). The covariance matrix between data points is modelled by a so-called covariance function or kernel.…”

A Universal Spin–Mass Relation for Brown Dwarfs and Planets

“…We also inferred rotation periods with a GP using a methodology similar to the one presented in Angus et al (2018). This approach is slower than the ACF and the LombScargle methods, but like the ACF it allows for non-sinusoidal, evolving variability patterns, and in addition it enables us to evaluate the posterior distribution over the period, and thus to obtain meaningful error estimates.…”

“…We then analyzed the systematicscorrected light curves using a quasi-periodic GP model, fitting for the period alongside the other parameters of the model. GP regression, its application to stellar light curves, and its performance for measuring stellar rotation periods in Kepler/ K2 data, are discussed extensively in Angus et al (2018) and references therein, so we give only a brief description of the procedure here. Each normalized light curve is modeled as a GP with a mean of unity and a quasi-periodic covariance function:…”