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The radial velocity method is one of the most successful techniques for thediscovery and characterization of exoplanets. Modern spectrographs promisemeasurement precision of ~0.2-0.5 m/s for an ideal target star. However, theintrinsic variability of stellar spectra can mimic and obscure true planetsignals at these levels. Rajpaul et al. (2015) and Jones et al. (2017) proposedapplying a physically motivated, multivariate Gaussian process (GP) to jointlymodel the apparent Doppler shift and multiple indicators of stellar activity asa function of time, so as to separate the planetary signal from various formsof stellar variability. These methods are promising, but performing thenecessary calculations can be computationally intensive and algebraicallytedious. In this work, we present a flexible and computationally efficientsoftware package, GPLinearOdeMaker.jl, for modeling multivariate time seriesusing a linear combination of univariate GPs and their derivatives. The packageallows users to easily and efficiently apply various multivariate GP models anddifferent covariance kernel functions. We demonstrate GPLinearOdeMaker.jl byapplying the Jones et al. (2017) model to fit measurements of the apparentDoppler shift and activity indicators derived from simulated active solarspectra time series affected by many evolving star spots. We show howGPLinearOdeMaker.jl makes it easy to explore the effect of different choicesfor the GP kernel. We find that local kernels could significantly increase thesensitivity and precision of Doppler planet searches relative to the widelyused quasi-periodic kernel.

Toward Extremely Precise Radial Velocities: II. A Tool For Using Multivariate Gaussian Processes to Model Stellar Activity