A statistical model of stellar variability. I. FENRIR: a physics-based model of stellar activity, and its fast Gaussian process approximation

Abstract

The detection of terrestrial planets by radial velocity and photometry is hindered by the presence of stellar signals. Those are often modeled as stationary Gaussian processes, whose kernels are based on qualitative considerations, which do not fully leverage the existing physical understanding of stars. Our aim is to build a formalism which allows to transfer the knowledge of stellar activity into practical data analysis methods. In particular, we aim at obtaining kernels with physical parameters. This has two purposes: better modelling signals of stellar origin to find smaller exoplanets, and extracting information about the star from the statistical properties of the data. We consider several observational channels such as photometry, radial velocity, activity indicators, and build a model called FENRIR to represent their stochastic variations due to stellar surface inhomogeneities. We compute analytically the covariance of this multi-channel stochastic process, and implement it in the S+LEAF framework to reduce the cost of likelihood evaluations from $O(N^3)$ to $O(N)$. We also compute analytically higher order cumulants of our FENRIR model, which quantify its non-Gaussianity. We obtain a fast Gaussian process framework with physical parameters, which we apply to the HARPS-N and SORCE observations of the Sun, and constrain a solar inclination compatible with the viewing geometry. We then discuss the application of our formalism to granulation. We exhibit non-Gaussianity in solar HARPS radial velocities, and argue that information is lost when stellar activity signals are assumed to be Gaussian. We finally discuss the origin of phase shifts between RVs and indicators, and how to build relevant activity indicators. We provide an open-source implementation of the FENRIR Gaussian process model with a Python interface.

Submitted to Astronomy \& Astrophysics

References in corpus (19)

• Planets and Stellar Activity: Hide and Seek in the CoRoT-7 system
• SOAP 2.0: A tool to estimate the photometric and radial velocity variations induced by stellar spots and plages
• The HARPS search for southern extra-solar planets. X. A m sin i = 11 Mearth planet around the nearby spotted M dwarf GJ 674
• Search for exoplanets with the radial-velocity technique: quantitative diagnostics of stellar activity
• Three years of Sun-as-a-star radial-velocity observations on the approach to solar minimum
• The HARPS search for southern extra-solar planets: XIV. Gl 176b, a super-Earth rather than a Neptune, and at a different period
• Efficient modeling of correlated noise II. A flexible noise model with fast and scalable methods
• Efficient modeling of correlated noise. III. Scalable methods for jointly modeling several observables' time series with Gaussian processes
• Statistical methods for exoplanet detection with radial velocities
• The Impact of Stellar Surface Magnetoconvection and Oscillations on the Detection of Temperate, Earth-Mass Planets Around Sun-Like Stars
• Activity time series of old stars from late F to early K. I. Simulating radial velocity, astrometry, photometry, and chromospheric emission
• Mitigating flicker noise in high-precision photometry. I -- Characterization of the noise structure, impact on the inferred transit parameters, and predictions for CHEOPS observations
• Latitude Distribution of Sunspots: Analysis Using Sunspot Data and A Dynamo Model
• The HARPS search for southern extra-solar planets XLV. Two Neptune mass planets orbiting HD 13808: a study of stellar activity modelling's impact on planet detection
• Deriving stellar inclination of slow rotators using stellar activity
• Faculae cancel out on the surfaces of active Suns
• Long-Term Variations in the Growth and Decay Rates of Sunspot Groups
• Joint Modeling of Radial Velocities and Photometry with a Gaussian Process Framework
• How do wavelength correlations affect transmission spectra? Application of a new fast and flexible 2D Gaussian process framework to transiting exoplanet spectroscopy

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• Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars
• TOI-2322: two transiting rocky planets close to the stellar rotation period and its first harmonic
• Exposure-averaged Gaussian Processes for Combining Overlapping Datasets