Toward Extremely Precise Radial Velocities: II. A Tool For Using Multivariate Gaussian Processes to Model Stellar Activity. (arXiv:2009.01085v2 [astro-ph.IM] UPDATED)

Toward Extremely Precise Radial Velocities: II. A Tool For Using Multivariate Gaussian Processes to Model Stellar Activity. (arXiv:2009.01085v2 [astro-ph.IM] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Gilbertson_C/0/1/0/all/0/1">Christian Gilbertson</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ford_E/0/1/0/all/0/1">Eric B. Ford</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Jones_D/0/1/0/all/0/1">David E. Jones</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Stenning_D/0/1/0/all/0/1">David C. Stenning</a>

The radial velocity method is one of the most successful techniques for the
discovery and characterization of exoplanets. Modern spectrographs promise
measurement precision of ~0.2-0.5 m/s for an ideal target star. However, the
intrinsic variability of stellar spectra can mimic and obscure true planet
signals at these levels. Rajpaul et al. (2015) and Jones et al. (2017) proposed
applying a physically motivated, multivariate Gaussian process (GP) to jointly
model the apparent Doppler shift and multiple indicators of stellar activity as
a function of time, so as to separate the planetary signal from various forms
of stellar variability. These methods are promising, but performing the
necessary calculations can be computationally intensive and algebraically
tedious. In this work, we present a flexible and computationally efficient
software package, GPLinearOdeMaker.jl, for modeling multivariate time series
using a linear combination of univariate GPs and their derivatives. The package
allows users to easily and efficiently apply various multivariate GP models and
different covariance kernel functions. We demonstrate GPLinearOdeMaker.jl by
applying the Jones et al. (2017) model to fit measurements of the apparent
Doppler shift and activity indicators derived from simulated active solar
spectra time series affected by many evolving star spots. We show how
GPLinearOdeMaker.jl makes it easy to explore the effect of different choices
for the GP kernel. We find that local kernels could significantly increase the
sensitivity and precision of Doppler planet searches relative to the widely
used quasi-periodic kernel.

The radial velocity method is one of the most successful techniques for the
discovery and characterization of exoplanets. Modern spectrographs promise
measurement precision of ~0.2-0.5 m/s for an ideal target star. However, the
intrinsic variability of stellar spectra can mimic and obscure true planet
signals at these levels. Rajpaul et al. (2015) and Jones et al. (2017) proposed
applying a physically motivated, multivariate Gaussian process (GP) to jointly
model the apparent Doppler shift and multiple indicators of stellar activity as
a function of time, so as to separate the planetary signal from various forms
of stellar variability. These methods are promising, but performing the
necessary calculations can be computationally intensive and algebraically
tedious. In this work, we present a flexible and computationally efficient
software package, GPLinearOdeMaker.jl, for modeling multivariate time series
using a linear combination of univariate GPs and their derivatives. The package
allows users to easily and efficiently apply various multivariate GP models and
different covariance kernel functions. We demonstrate GPLinearOdeMaker.jl by
applying the Jones et al. (2017) model to fit measurements of the apparent
Doppler shift and activity indicators derived from simulated active solar
spectra time series affected by many evolving star spots. We show how
GPLinearOdeMaker.jl makes it easy to explore the effect of different choices
for the GP kernel. We find that local kernels could significantly increase the
sensitivity and precision of Doppler planet searches relative to the widely
used quasi-periodic kernel.

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