Precise Radial Velocities

TL;DR

The paper surveys the current state of Extreme Precision Radial Velocity (EPRV) science, detailing the instrumental designs, calibration sources, and data-reduction approaches that enable long-term, sub-m s$^{-1}$ precision. It integrates discussions of light-injection, spectrograph architectures, environmental stabilization, and calibrators (I$_2$ cells, hollow cathode lamps, laser frequency combs, and Fabry–Pérot etalons), with detector technologies and future directions toward diffraction-limited, single-mode delivery. A central emphasis is the mitigation of stellar variability via activity indices, Gaussian Processes, spectral-shell and line-depth proxies, and advanced data-driven methods, all within robust Bayesian and model-selection frameworks for multi-planet inferences. The authors chart a practical roadmap for reaching $ ext{cm s}^{-1}$-level precision, highlighting the need for coordinated surveys, improved calibration standards, and physics-informed stellar-variability models to enable the detection and characterization of temperate, Earth-like exoplanets and other high-precision RV applications over long timescales.

Abstract

Precise measurements of a star's radial velocity (RV) made using extremely stable, high resolution, optical or near infrared spectrographs can be used to determine the masses and orbital parameters of gravitationally-bound extra-solar planets (exoplanets). Indeed, RV surveys and follow up efforts have provided the vast majority of published exoplanet mass measurements and in doing so have enabled studies into exoplanet interior and atmospheric compositions. Here we review the current state of the RV field, with particular attention paid to: -The evolution of precise RV methodologies over the past two decades -Modern RV spectrograph designs that can be calibrated to a stability level of better than 50 cm/s over timescales of years -RV data reduction and post-processing techniques that minimize the impact of instrument systematics and stellar variability -Techniques for detecting exoplanets in RV data and disentangling planetary signals from stellar variability

Figures (10)

• Figure 1: Left: Schematic representation of the two-body Keplerian orbit of an exoplanet (in purple) and its host star (color coded with star's red/blue shift as observed from Earth), scale exaggerated for clarity. The two orbits have the same period and eccentricity, but their semi-major axes are scaled by the star-planet mass ratio. The star and planet are always on opposite sides of their barycenter (green cross) such that when the planet is moving away from an observer, the star is moving towards the observer and vice versa. Top Right: RV curve corresponding to the stellar orbit depicted on the left. Bottom Right: RV curves can exhibit a wide range of shapes based on their orbital eccentricity and longitude of periastron ($\omega$) values. Higher orbital eccentricity produces a more peaked curve and a higher maximum semi-amplitude, with most of the stellar velocity shift taking place as the star passes through periapsis. Changes in the orbit's orientation relative to the observer ($\omega$) shifts the phase in the orbit where the most significant RV variations occur.
• Figure 2: Top: Relative Doppler radial velocity (RV) information content as a function of spectral type and wavelength region normalized to $\sigma_{\mathrm{RV, total}}$ = 1 $\mathrm{m\ s^{-1}}$, following the quality-factor (Q) calculations detailed in Bouchy2001. Bluer colors indicate higher RV information content levels and correspondingly smaller contributions to the total RV uncertainty. Monochromatic color bins denote individual grating diffraction orders. Bottom: Stellar flux (transparent spectra, left-axis) and relative Doppler information content ($1/\sigma_\mathrm{RV}$, solid points and lines, right axis) as a function of wavelength for simulated Sun-like (6000 K) and M-dwarf (3300 K) spectra recorded from a notional ground-based RV system. These curves effectively represent 'slices' of the 2D map above.
• Figure 3: Major advancements in radial velocity (RV) precision over time (cyan diamonds) and the semi-amplitudes of planets discovered each year. RV-only detections are depicted as squares, while planets detected first in transit and then followed up with RV facilities are depicted as circles. The stellar activity 'barrier' has made the discovery of planets with RV semi-amplitudes below 1 $\mathrm{m\ s^{-1}}$ extremely challenging, but in recent years the combination of modern RV spectrographs, improved post-processing pipelines, and more nuanced stellar activity mitigation techniques has produced a growing number of planets in this K $\leq$ 1 $\mathrm{m\ s^{-1}}$ regime.
• Figure 4: Overview of different sources of random and systematic errors that impact Doppler radial velocity (RV) measurements. Left: The number and distribution of photons collected in the stellar spectra dictate the photon-limited Doppler measurement floor Bouchy2001. This depends on the parameters of the star being observed (brightness, spectral type, rotational velocity, etc.) and properties of the facility (aperture, atmospheric extinction, instrument efficiency). Middle: Errors associated with instabilities in the measurement system, including both the instrument and the methods used to extract velocity measurements from raw images, directly affect RV performance. Right: Stellar astrophysical noise sources span a range of amplitudes and timescales. These affects manifest at both the spectral and integrated RV level and span timescales from seconds to decades. Sub-figures in each category are inspired by figures and references in Crass2021.
• Figure 5: Typical components in a precision Doppler radial velocity (RV) single measurement error (measurement system only). Figure adapted from the Keck Planet Finder performance budget Gibson2024. Individual error terms are categorized by type and/or instrumental subsystem. Some errors are tracked by simultaneous calibration (listed as 'instrumental' in the table) and others are not. This follows similar system-level analyses from other EPRV facilities Podgorski2014Blackman2020Bechter2020bHalverson2016. Below 1 $\mathrm{m\ s^{-1}}$, a multitude of random and systematic errors begin to make measurable contributions to the RV measurement noise floor. These errors have origins ranging from the Earth's atmosphere (tellurics), to the telescope, to the spectrometer, to the methods used to extract the data and compute stellar RVs. While many of these errors are constrainable via analysis techniques or lab tests, others are active areas of research for pushing to the c$\mathrm{m\ s^{-1}}$ level Blake2017.