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Stellar active regions like spots and faculae can distort the shapes of spectral lines, inducing variations in the radial velocities that are often orders of magnitude larger than the signals from Earth-like planets. Efforts to mitigate these activity signals have hitherto focused on either the time or the velocity (wavelength) domains. We present a physics-driven Gaussian process (GP) framework to model activity signals directly in time series of line profiles or cross-correlation functions (CCFs). Unlike existing methods that correct activity signals in line profile time series, our approach exploits the time correlation between velocity (wavelength) bins in the line profile variations, and is based on a simplified but physically motivated model for the origin of these variations. When tested on both synthetic and real data sets with signal-to-noise ratios down to ∼100, our method was able to separate the planetary signal from the activity signal, even when their periods were identical. We also conducted injection/recovery tests using two years of realistically sampled HARPS-N solar data, demonstrating the ability of the method to accurately recover a signal induced by a 1.5-Earth mass planet with a semi-amplitude of 0.3 m s−1 and a period of 33 d during high solar activity. [ABSTRACT FROM AUTHOR]

Stellar magnetic activity induces both distortions and Doppler-shifts in the absorption line profiles of Sun-like stars. Those effects produce apparent radial velocity (RV) signals which greatly hamper the search for potentially habitable, Earth-like planets. In this work, we investigate these distortions in the Sun using cross-correlation functions (CCFs), derived from intensive monitoring with the high-precision spectrograph HARPS-N. We show that the RV signal arising from line-shape variations on time-scales associated with the Sun's rotation and activity cycle can be robustly extracted from the data, reducing the RV dispersion by half. Once these have been corrected, activity-induced Doppler-shifts remain, that are modulated at the solar rotation period, and that are most effectively modelled in the time domain, using Gaussian processes (GPs). Planet signatures are still best retrieved with multidimensonal GPs, when activity is jointly modelled from the raw RVs and indicators of the line width or of the Ca  ii H & K emission. After GP modelling, the residual RVs exhibit a dispersion of 0.6–0.8 m s−1, likely to be dominated by signals induced by supergranulation. Finally, we find that the statistical properties of the RVs evolve significantly over time, and that this evolution is primarily driven by sunspots, which control the smoothness of the signal. Such evolution, which reduces the sensitivity to long-period planet signatures, is no longer seen in the activity-induced Doppler-shifts, which is promising for long term RV monitoring surveys such as the Terra Hunting Experiment or the PLATO follow-up campaign. [ABSTRACT FROM AUTHOR]

Although instruments for measuring the radial velocities (RVs) of stars now routinely reach sub-metre per second accuracy, the detection of low-mass planets is still very challenging. The rotational modulation and evolution of spots and/or faculae can induce variations in the RVs at the level of a few m s–1 in Sun-like stars. To overcome this, a multidimensional Gaussian Process framework has been developed to model the stellar activity signal using spectroscopic activity indicators together with the RVs. A recently published computationally efficient implementation of this framework, S + LEAF 2 , enables the rapid analysis of large samples of targets with sizeable data sets. In this work, we apply this framework to HARPS observations of 268 well-observed targets with precisely determined stellar parameters. Our long-term goal is to quantify the effectiveness of this framework to model and mitigate activity signals for stars of different spectral types and activity levels. In this first paper in the series, we initially focus on the activity indicators (S-index and Bisector Inverse Slope), and use them to (a) measure rotation periods for 49 slow rotators in our sample, (b) explore the impact of these results on the spin-down of middle-aged late F, G, and K stars, and (c) explore indirectly how the spot to facular ratio varies across our sample. Our results should provide valuable clues for planning future RV planet surveys such as the Terra Hunting Experiment or the PLATO ground-based follow-up observations programme, and help fine-tune current stellar structure and evolution models. [ABSTRACT FROM AUTHOR]

Detecting planetary signatures in radial velocity time-series of young stars is challenging due to their inherently strong stellar activity. However, it is possible to learn information about the properties of the stellar signal by using activity indicators measured from the same stellar spectra used to extract radial velocities. In this manuscript, we present a reanalysis of spectroscopic High Accuracy Radial Velocity Planet Searcher data of the young star K2-233, which hosts three transiting planets. We perform a multidimensional Gaussian process regression on the radial velocity and the activity indicators to characterize the planetary Doppler signals. We demonstrate, for the first time on a real data set, that the use of a multidimensional Gaussian process can boost the precision with which we measure the planetary signals compared to a one-dimensional Gaussian process applied to the radial velocities alone. We measure the semi-amplitudes of K2-233 b, c, and d as |$1.31_{-0.74}^{+0.81}$| , |$1.81_{-0.67}^{+0.71}$| ,  and |$2.72_{-0.70}^{+0.66}$| |${\rm m\, s^{-1}}$| , which translate into planetary masses of |$2.4_{-1.3}^{+1.5}$| , |$4.6_{-1.7}^{+1.8}$| , and |$10.3_{-2.6}^{+2.4}$| M⊕, respectively. These new mass measurements make K2-233 d a valuable target for transmission spectroscopy observations with JWST. K2-233 is the only young system with two detected inner planets below the radius valley and a third outer planet above it. This makes it an excellent target to perform comparative studies, to inform our theories of planet evolution, formation, migration, and atmospheric evolution. [ABSTRACT FROM AUTHOR]