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The following repository contains the data used for the manuscript: "Searching for Low-Mass Exoplanets Amid Stellar Variability with a Fixed Effects Linear Model of Line-by-Line Shape Changes". Within line_property_files.zip there is file "line_property_files_README.md" that contains a description of each column of completeLines.csv. The important columns of this csv are date: time of observation line_order: unique identifier of a line, a combination of that line's central wavelength and order ID rv_template_0.5: the RV measure for a given line on a given day fit_gauss_a,fit_gauss_b,fit_gauss_depth,fit_gauss_sigmasq,proj_hg_coeff_0,proj_hg_coeff_2,proj_hg_coeff_3,proj_hg_coeff_4,proj_hg_coeff_5,proj_hg_coeff_6,proj_hg_coeff_7,proj_hg_coeff_8,proj_hg_coeff_9,proj_hg_coeff_10: the shape-change covariates that we use to control for stellar activity Below is a description of each of the data files completeLines.csv: this csv file contains the time series of every line's shape measurements and RVs, it is used throughout the analysis. line_property_files.zip: this directory contains .h5 files that contain all line-shape information and contaminated RVs for each line used in our analysis. The script clean_data.Rmd uses these as input and combines them all into a single csv file called completeLines.csv. project_template_deriv_onto_gh.h5: this contains the projection vector described in the paper to produce the orthogonal HG coefficients. The script clean_data.Rmd uses this as input and combines them all into a single csv file called completeLines.csv. models.zip: this directory contains the results from each model that was fit for our paper. 

Exoplanets can be detected with various observational techniques. Among them, radial velocity (RV) has the key advantages of revealing the architecture of planetary systems and measuring planetary mass and orbital eccentricities. RV observations are poised to play a key role in the detection and characterization of Earth twins. However, the detection of such small planets is not yet possible due to very complex, temporally correlated instrumental and astrophysical stochastic signals. Furthermore, exploring the large parameter space of RV models exhaustively and efficiently presents difficulties. In this review, we frame RV data analysis as a problem of detection and parameter estimation in unevenly sampled, multivariate time series. The objective of this review is two-fold: to introduce the motivation, methodological challenges, and numerical challenges of RV data analysis to nonspecialists, and to unify the existing advanced approaches in order to identify areas for improvement. 

Abstract We present the discovery of GJ 251 c, a candidate super-Earth orbiting in the habitable zone (HZ) of its M dwarf host star. Using high-precision Habitable-zone Planet Finder and NEID RVs, in conjunction with archival RVs from the Keck I High Resolution Echelle Spectrometer, the Calar Alto High-resolution Search for M dwarfs with Exoearths with Near-infrared and optical Echelle Spectrograph, and the Spectropolarimétre Infrarouge, we improve the measured parameters of the known planet, GJ 251 b (P_b= 14.2370 days; $m\sin \left(i\right)$= 3.85 ${}_{-0.33}^{+0.35}$M_⊕), and we significantly constrain the minimum mass of GJ 251 c, placing it in a plausibly terrestrial regime (P_c= 53.647 ± 0.044 days; $m\sin i_c$= 3.84 ± 0.75M_⊕). Using activity mitigation techniques that leverage chromatic information content, we perform a color-dependent analysis of the system and a detailed comparison of more than 50 models that describe the nature of the planets and stellar activity in the system. Due to GJ 251’s proximity to Earth (5.5 pc), next generation, 30 meter class telescopes will likely be able to image terrestrial planets in GJ 251’s HZ. In fact, GJ 251 c is currently the best candidate for terrestrial, HZ planet imaging in the northern sky. 

Abstract The LHS 1610 system consists of a nearby (d= 9.7 pc) M5 dwarf hosting a candidate brown dwarf companion in a 10.6 days, eccentric (e∼ 0.37) orbit. We confirm this brown dwarf designation and estimate its mass ( ${49.5}_{-3.5}^{+4.3}$M_Jup) and inclination (114.5° ${}_{-10.0}^{+7.4}$) by combining discovery radial velocities (RVs) from the Tillinghast Reflector Echelle Spectrograph and new RVs from the Habitable-zone Planet Finder with the available Gaia astrometric two-body solution. We highlight a discrepancy between the measurement of the eccentricity from the Gaia two-body solution (e= 0.52 ± 0.03) and the RV-only solution (e= 0.3702 ± 0.0003). We discuss possible reasons for this discrepancy, which can be further probed when the Gaia astrometric time series become available as part of Gaia Data Release 4. As a nearby mid-M star hosting a massive short-period companion with a well-characterized orbit, LHS 1610 b is a promising target to look for evidence of sub-Alfvénic interactions and/or auroral emission at optical and radio wavelengths. LHS 1610 has a flare rate (0.28 ± 0.07 flares per day) on the higher end for its rotation period (84 ± 8 days), similar to other mid-M dwarf systems such as Proxima Cen and YZ Ceti that have recent radio detections compatible with star–planet interactions. While available Transiting Exoplanet Survey Satellite photometry is insufficient to determine an orbital phase dependence of the flares, our complete orbital characterization of this system makes it attractive to probe star–companion interactions with additional photometric and radio observations. 

Abstract Recent discoveries of transiting giant exoplanets around M-dwarf stars (GEMS), aided by the all-sky coverage of TESS, are starting to stretch theories of planet formation through the core-accretion scenario. Recent upper limits on their occurrence suggest that they decrease with lower stellar masses, with fewer GEMS around lower-mass stars compared to solar-type. In this paper, we discuss existing GEMS both through confirmed planets, as well as protoplanetary disk observations, and a combination of tests to reconcile these with theoretical predictions. We then introduce the Searching for GEMS survey, where we utilize multidimensional nonparameteric statistics to simulate hypothetical survey scenarios to predict the required sample size of transiting GEMS with mass measurements to robustly compare their bulk-density with canonical hot Jupiters orbiting FGK stars. Our Monte Carlo simulations predict that a robust comparison requires about 40 transiting GEMS (compared to the existing sample of ∼15) with 5σmass measurements. Furthermore, we discuss the limitations of existing occurrence estimates for GEMS and provide a brief description of our planned systematic search to improve the occurrence rate estimates for GEMS. 

Abstract We revisit the long-studied radial velocity (RV) target HD 26965 using recent observations from the NASA-NSF “NEID” precision Doppler facility. Leveraging a suite of classical activity indicators, combined with line-by-line RV analyses, we demonstrate that the claimed 45-day signal previously identified as a planet candidate is most likely an activity-induced signal. Correlating the bulk (spectrally averaged) RV with canonical line activity indicators confirms a multiday “lag” between the observed activity indicator time series and the measured RV. When accounting for this lag, we show that much of the observed RV signal can be removed by a linear detrending of the data. Investigating activity at the line-by-line level, we find a depth-dependent correlation between individual line RVs and the bulk RVs, further indicative of periodic suppression of convective blueshift causing the observed RV variability, rather than an orbiting planet. We conclude that the combined evidence of the activity correlations and depth dependence is consistent with an RV signature dominated by a rotationally modulated activity signal at a period of ∼42 days. We hypothesize that this activity signature is due to a combination of spots and convective blueshift suppression. The tools applied in our analysis are broadly applicable to other stars and could help paint a more comprehensive picture of the manifestations of stellar activity in future Doppler RV surveys. 

Abstract We present the confirmation of TOI-5573 b, a Saturn-sized exoplanet on an 8.79 days orbit around an early M dwarf (3790 K, 0.59R_⊙, 0.61M_⊙, 12.30 Jmag). TOI-5573 b has a mass of $112_{-19}^{+18}$M_⊕(0.35 ± 0.06M_Jup) and a radius of 9.75 ± 0.47R_⊕(0.87 ± 0.04R_Jup), resulting in a density of $0.66_{-0.13}^{+0.16}$g cm⁻³, akin to that of Saturn. The planet was initially discovered by the Transiting Exoplanet Survey Satellite (TESS) and confirmed using a combination of 11 transits from four TESS Sectors (20, 21, 47, and 74), ground-based photometry from the Red Buttes Observatory, and high-precision radial velocity data from the Habitable-zone Planet Finder and NN-EXPLORE Exoplanet Investigations with Doppler spectrographs, achieving a 5σprecision on the planet’s mass. TOI-5573 b is one of the coolest Saturn-like exoplanets discovered around an M-dwarf, with an equilibrium temperature of only 528 ± 10 K, making it a valuable target for atmospheric characterization. Saturn-like exoplanets around M dwarfs likely form through core accretion, with increased disk opacity slowing gas accretion and limiting their mass. The host star’s supersolar metallicity supports core accretion, but uncertainties in M-dwarf metallicity estimates complicate definitive conclusions. Compared to other GEMS (Giant Exoplanets around M-dwarf Stars) orbiting metal-rich stars, TOI-5573 b aligns with the observed pattern that giant planets preferentially form around M-dwarfs with supersolar metallicity. Further high-resolution spectroscopic observations are needed to explore the role of stellar metallicity in shaping the formation and properties of giant exoplanets like TOI-5573 b. 

Theories of planet formation predict that low-mass stars should rarely host exoplanets with masses exceeding that of Neptune. We used radial velocity observations to detect a Neptune-mass exoplanet orbiting LHS 3154, a star that is nine times less massive than the Sun. The exoplanet’s orbital period is 3.7 days, and its minimum mass is 13.2 Earth masses. We used simulations to show that the high planet-to-star mass ratio (>3.5 × 10⁻⁴) is not an expected outcome of either the core accretion or gravitational instability theories of planet formation. In the core-accretion simulations, we show that close-in Neptune-mass planets are only formed if the dust mass of the protoplanetary disk is an order of magnitude greater than typically observed around very low-mass stars. 

Abstract We present an analysis of Sun-as-a-star observations from four different high-resolution, stabilized spectrographs—HARPS, HARPS-N, EXPRES, and NEID. With simultaneous observations of the Sun from four different instruments, we are able to gain insight into the radial velocity precision and accuracy delivered by each of these instruments and isolate instrumental systematics that differ from true astrophysical signals. With solar observations, we can completely characterize the expected Doppler shift contributed by orbiting Solar System bodies and remove them. This results in a data set with measured velocity variations that purely trace flows on the solar surface. Direct comparisons of the radial velocities measured by each instrument show remarkable agreement with residual intraday scatter of only 15–30 cm s⁻¹. This shows that current ultra-stabilized instruments have broken through to a new level of measurement precision that reveals stellar variability with high fidelity and detail. We end by discussing how radial velocities from different instruments can be combined to provide powerful leverage for testing techniques to mitigate stellar signals.