Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series

Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth

doi:10.3847/1538-3881/aa9332

Cited by 792 publications

(496 citation statements)

References 102 publications

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“…It is possible to model these oscillations using sinusoidal functions or wavelets, as done by other authors (i.e., Deming et al 2012;Kovács et al 2013;von Essen et al 2014). However, we decided to use the Gaussian process code celerite (Foreman-Mackey et al 2017) to fit these pulsations nonparametrically. Gaussian processes treat the pulsations as a form of correlated noise whose properties are described by a parameterized covariance matrix fitted to our data.…”

Section: Noise Modelmentioning

confidence: 99%

Phase Curves of WASP-33b and HD 149026b and a New Correlation between Phase Curve Offset and Irradiation Temperature

Zhang

Knutson

Kataria

et al. 2018

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147

140

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We present new 3.6 and 4.5 μm Spitzer phase curves for the highly irradiated hot Jupiter WASP-33b and the unusually dense Saturn-mass planet HD 149026b. As part of this analysis, we develop a new variant of pixel-level decorrelation that is effective at removing intrapixel sensitivity variations for long observations (>10 hr) where the position of the star can vary by a significant fraction of a pixel. Using this algorithm, we measure eclipse depths, phase amplitudes, and phase offsets for both planets at 3.6 and 4.5 μm. We use a simple toy model to show that WASP-33b's phase offset, albedo, and heat recirculation efficiency are largely similar to those of other hot Jupiters despite its very high irradiation. On the other hand, our fits for HD 149026b prefer a very high albedo. We also compare our results to predictions from general circulation models, and we find that while neither planet matches the models well, the discrepancies for HD 149026b are especially large. We speculate that this may be related to its high bulk metallicity, which could lead to enhanced atmospheric opacities and the formation of reflective cloud layers in localized regions of the atmosphere. We then place these two planets in a broader context by exploring relationships between the temperatures, albedos, heat transport efficiencies, and phase offsets of all planets with published thermal phase curves. We find a striking relationship between phase offset and irradiation temperature: the former drops with increasing temperature until around 3400 K and rises thereafter. Although some aspects of this trend are mirrored in the circulation models, there are notable differences that provide important clues for future modeling efforts.

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Section: Noise Modelmentioning

confidence: 99%

Phase Curves of WASP-33b and HD 149026b and a New Correlation between Phase Curve Offset and Irradiation Temperature

Zhang

Knutson

Kataria

et al. 2018

Self Cite

147

140

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“…Our simple harmonic oscillator Gaussian process model consists of three main components: two Q 1 2 = terms, which are commonly used to model granulation in asteroseismic analyses (Harvey 1985;Huber et al 2009;Kallinger et al 2014), and one Q 1  term, which has been shown to describe stellar oscillations effectively (Foreman-Mackey et al 2017), to describe the envelope of the stellar oscillation signal. The resonant frequency 0 w of this component is thus an independent estimate of max n , and we compare our asteroseismic max n measurement made from the analysis in the frequency domain to the max n we generate here through a pure time domain analysis.…”

Section: Gaussian Process Transit Modelsmentioning

confidence: 99%

Seeing Double with K2: Testing Re-inflation with Two Remarkably Similar Planets around Red Giant Branch Stars

Grunblatt¹,

Huber²,

Gaidos³

et al. 2017

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103

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Despite more than 20 years since the discovery of the first gas giant planet with an anomalously large radius, the mechanism for planet inflation remains unknown. Here, we report the discovery of K2-132b, an inflated gas giant planet found with the NASA K2 Mission, and a revised mass for another inflated planet, K2-97b. These planets orbit on ≈9day orbits around host stars that recently evolved into red giants. We constrain the irradiation history of these planets using models constrained by asteroseismology and Keck/High Resolution Echelle Spectrometer spectroscopy and radial velocity measurements. We measure planet radii of 1.31±0.11 R J and 1.30±0.07 R J , respectively. These radii are typical for planets receiving the current irradiation, but not the former, zero age main-sequence irradiation of these planets. This suggests that the current sizes of these planets are directly correlated to their current irradiation. Our precise constraints of the masses and radii of the stars and planets in these systems allow us to constrain the planetary heating efficiency of both systems as 0.03% 0.02% 0.03% -+. These results are consistent with a planet re-inflation scenario, but suggest that the efficiency of planet re-inflation may be lower than previously theorized. Finally, we discuss the agreement within 10% of the stellar masses and radii, and the planet masses, radii, and orbital periods of both systems, and speculate that this may be due to selection bias in searching for planets around evolved stars.

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“…Furthermore, what is most interesting for our case is that some of the possible celerite kernels are well suited to describe different forms of stellar variability. According to equation 49 in Foreman-Mackey et al (2017), the kernel for a stochastically driven, damped harmonic oscillator with a quality factor (Q ) larger than 0.5 is given by…”

Section: Gaussian Process Regressionmentioning

confidence: 99%

Improving transit characterisation with Gaussian process modelling of stellar variability

Barros

Díaz

Cabrera

et al. 2020

A&A

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Context. New photometric space missions to detect and characterise transiting exoplanets are focusing on bright stars to obtain high cadence, high signal-to-noise light curves. Since these missions will be sensitive to stellar oscillations and granulation even for dwarf stars, they will be limited by stellar variability. Therefore, it is crucial and timely to develop robust methods to account for and correct for stellar variability. Aims. We tested the performance of Gaussian process (GP) regression on the characterisation of transiting planets, and in particular to determine how many components of variability are necessary to describe high cadence, high signal-to-noise light curves expected from CHEOPS and PLATO. To achieve this, we selected a sample of bright stars observed in the asteroseismology field of CoRoT at high cadence (32 sec) and high signal-to-noise ratio. Methods. We used GPs to model stellar variability including different combinations of stellar oscillations, granulation, and rotational modulation models. We preformed model comparison to find the best activity model fit to our data. We compared the best multicomponent model with the usual one-component model used for transit retrieval and with a non-GP model. Results. We found that the best GP stellar variability model contains four to five variability components: one stellar oscillation component, two to four granulation components, and/or one rotational modulation component, which is consistent with results from asteroseismology. However, this high number of components is in contrast with the one-component GP model (1GP) commonly used in the literature for transit characterisation. Therefore, we compared the performance of the best multi-component GP model with the 1GP model in the derivation of transit parameters of simulated transits. We found that for Jupiter-and Neptune-size planets the best multi-component GP model is slightly better than the 1GP model, and much better than the non-GP model that gives biased results. For Earth-size planets, the 1GP model fails to retrieve the transit because it is a poor description of stellar activity. The non-GP model gives some biased results and the best multi-component GP is capable of retrieving the correct transit model parameters.Conclusions. We conclude that when characterising transiting exoplanets with high signal-to-noise ratios and high cadence light curves, we need models that couple the description of stellar variability with the transits analysis, like GPs. Moreover, for Earth-like exoplanets a better description of stellar variability (achieved using multi-component models) improves the planetary characterisation. Our results are particularly important for the analysis of TESS, CHEOPS, and PLATO light curves.

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Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series

Cited by 792 publications

References 102 publications

Phase Curves of WASP-33b and HD 149026b and a New Correlation between Phase Curve Offset and Irradiation Temperature

Phase Curves of WASP-33b and HD 149026b and a New Correlation between Phase Curve Offset and Irradiation Temperature

Seeing Double with K2: Testing Re-inflation with Two Remarkably Similar Planets around Red Giant Branch Stars

Improving transit characterisation with Gaussian process modelling of stellar variability

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