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Register a new userMapping stellar surfaces II: An interpretable Gaussian process model for light curves
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The use of Gaussian processes (GPs) as models for astronomical time series datasets has recently become almost ubiquitous, given their ease of use and flexibility. GPs excel in particular at marginalization over the stellar signal in cases where the variability due to starspots rotating in and out of view is treated as a nuisance, such as in exoplanet transit modeling. However, these effective models are less useful in cases where the starspot signal is of primary interest since it is not obvious how the parameters of the GP model are related to the physical properties of interest, such as the size, contrast, and latitudinal distribution of the spots. Instead, it is common practice to explicitly model the effect of individual starspots on the light curve and attempt to infer their properties via optimization or posterior inference. Unfortunately, this process is degenerate, ill-posed, and often computationally intractable when applied to stars with more than a few spots and/or to ensembles of many light curves. In this paper, we derive a closed-form expression for the mean and covariance of a Gaussian process model that describes the light curve of a rotating, evolving stellar surface conditioned on a given distribution of starspot sizes, contrasts, and latitudes. We demonstrate that this model is correctly calibrated, allowing one to robustly infer physical parameters of interest from one or more stellar light curves, including the typical radii and the mean and variance of the latitude distribution of starspots. Our GP has far-ranging implications for understanding the variability and magnetic activity of stars from both light curves and radial velocity (RV) measurements, as well as for robustly modeling correlated noise in both transiting and RV exoplanet searches. Our implementation is efficient, user-friendly, and open source, available as the Python package starry-process.
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In this note we present the starry_process code, which implements an interpretable Gaussian process (GP) for modeling variability in stellar light curves. As dark starspots rotate in and out of view, the total flux received from a distant star will change over time. Unresolved flux time series therefore encode information about the spatial structure of features on the stellar surface. The starry_process software package allows one to easily model the flux variability due to starspots, whether one is interested in understanding the properties of these spots or marginalizing over the stellar variability when it is treated as a nuisance signal. The main difference between the GP implemented here and typical GPs used to model stellar variability is the explicit dependence of our GP on physical properties of the star, such as its period, inclination, and limb darkening coefficients, and on properties of the spots, such as their radius and latitude distributions. This code is the Python implementation of the interpretable GP algorithm developed in Luger, Foreman-Mackey, and Hedges (2021).
We present K2SC (K2 Systematics Correction), a Python pipeline to model instrumental systematics and astrophysical variability in light curves from the K2 mission. K2SC uses Gaussian process regression to model position-dependent systematics and time-dependent variability simultaneously, enabling the user to remove both (e.g., for transit searches) or to remove systematics while preserving variability (for variability studies). For periodic variables, K2SC automatically computes estimates of the period, amplitude and evolution timescale of the variability. We apply K2SC to publicly available K2 data from campaigns 3--5, showing that we obtain photometric precision approaching that of the original Kepler mission. We compare our results to other publicly available K2 pipelines, showing that we obtain similar or better results, on average. We use transit injection and recovery tests to evaluate the impact of K2SC on planetary transit searches in K2 PDC (Pre-search Data Conditioning) data, for planet-to-star radius ratios down Rp/Rstar = 0.01 and periods up to P = 40 d, and show that K2SC significantly improves the ability to distinguish between correct and false detections, particularly for small planets. K2SC can be run automatically on many light curves, or manually tailored for specific objects such as pulsating stars or large amplitude eclipsing binaries. It can be run on ASCII and FITS light curve files, regardless of their origin. Both the code and the processed light curves are publicly available, and we provide instructions for downloading and using them. The methodology used by K2SC will be applicable to future transit search missions such as TESS and PLATO.
We present the first data release of the Kepler Smear Campaign, using collateral smear data obtained in the Kepler four-year mission to reconstruct light curves of 102 stars too bright to have been otherwise targeted. We describe the pipeline developed to extract and calibrate these light curves, and show that we attain photometric precision comparable to stars analyzed by the standard pipeline in the nominal Kepler mission. In this paper, aside from publishing the light curves of these stars, we focus on 66 red giants for which we detect solar-like oscillations, characterizing 33 of these in detail with spectroscopic chemical abundances and asteroseismic masses as benchmark stars. We also classify the whole sample, finding nearly all to be variable, with classical pulsations and binary effects. All source code, light curves, TRES spectra, and asteroseismic and stellar parameters are publicly available as a Kepler legacy sample.
Thanks to missions like Kepler and TESS, we now have access to tens of thousands of high precision, fast cadence, and long baseline stellar photometric observations. In principle, these light curves encode a vast amount of information about stellar variability and, in particular, about the distribution of starspots and other features on their surfaces. Unfortunately, the problem of inferring stellar surface properties from a rotational light curve is famously ill-posed, as it often does not admit a unique solution. Inference about the number, size, contrast, and location of spots can therefore depend very strongly on the assumptions of the model, the regularization scheme, or the prior. The goal of this paper is twofold: (1) to explore the various degeneracies affecting the stellar light curve inversion problem and their effect on what can and cannot be learned from a stellar surface given unresolved photometric measurements; and (2) to motivate ensemble analyses of the light curves of many stars at once as a powerful data-driven alternative to common priors adopted in the literature. We further derive novel results on the dependence of the null space on stellar inclination and limb darkening and show that single-band photometric measurements cannot uniquely constrain quantities like the total spot coverage without the use of strong priors. This is the first in a series of papers devoted to the development of novel algorithms and tools for the analysis of stellar light curves and spectral time series, with the explicit goal of enabling statistically robust inference about their surface properties.
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