Efficient modeling of correlated noise. III. Scalable methods for jointly modeling several observables' time series with Gaussian processes

TL;DR

This paper introduces S+LEAF 2, a scalable Gaussian process framework that efficiently models multiple time series, such as stellar activity indicators and radial velocities, with linear computational cost, enabling analysis of large astronomical data sets.

Contribution

The paper presents S+LEAF 2, a novel Gaussian process method that scales linearly with data size for joint modeling of multiple observables, significantly reducing computational costs.

Findings

Successfully reanalyzed 246 radial velocity measurements with reduced computational cost

Achieved over two orders of magnitude decrease in processing time compared to previous methods

Demonstrated applicability to large astronomical data sets for exoplanet detection

Abstract

The radial velocity method is a very productive technique used to detect and confirm extrasolar planets. The most recent spectrographs, such as ESPRESSO or EXPRES, have the potential to detect Earth-like planets around Sun-like stars. However, stellar activity can induce radial velocity variations that dilute or even mimic the signature of a planet. A widely recognized method for disentangling these signals is to model the radial velocity time series, jointly with stellar activity indicators, using Gaussian processes and their derivatives. However, such modeling is prohibitive in terms of computational resources for large data sets, as the cost typically scales as the total number of measurements cubed. Here, we present S+LEAF 2, a Gaussian process framework that can be used to jointly model several time series, with a computational cost that scales linearly with the data set size. This framework thus provides a state-of-the-art Gaussian process model, with tractable computations even for large data sets. We illustrate the power of this framework by reanalyzing the 246 HARPS radial velocity measurements of the nearby K2 dwarf HD 138038, together with two activity indicators. We reproduce the results of a previous analysis of these data, but with a strongly decreased computational cost (more than two order of magnitude). The gain would be even greater for larger data sets.