Order-by-order Modeling of Exoplanet Radial Velocity Data

TL;DR

Exoplanet RV measurements are increasingly limited by astrophysical and instrumental chromatic noise that varies with wavelength. The authors develop two wavelength-aware approaches, Order-by-Order (OBO) and Joint Keplerian (JK), to extract orbital parameters from multi-order NEID RV data, comparing them against the standard Variance-Weighted Mean (VWM) baseline. Across three exoplanet systems, OBO and JK yield substantially tighter $M_p\sin{i}$ posteriors than VWM, with improvements up to a factor of $1.5$–$6.8$ in uncertainty and particularly strong gains for higher-amplitude signals. The work highlights chromatic noise as a key limitation of VWM, identifies JK as the more robust, principled method, and provides open-source Julia code to enable broader adoption and further exploration of multi-order RV analyses in exoplanet characterization.

Abstract

Precise radial velocity (RV) measurements are a crucial tool for exoplanet discovery and characterization. Today, the majority of these measurements are derived from Echelle spectra in the optical wavelength region using cross-correlation techniques. Although for certain stars these approaches can produce RVs with sub-1 m~s$^{-1}$ measurement errors, for many others, we are now in a regime where instrumental precision is fundamentally below the intrinsic RV variations of the star that result from astrophysical processes that can be correlated in both time and wavelength. We explore new methods for measuring exoplanet orbital parameters that take advantage of the fact that RV data sets are fundamentally multi-wavelength. By analyzing NEID extremely precise radial velocity (EPRV) data of three known exoplanet systems, we show that fitting a single Keplerian model to multi-wavelength RVs can produce a factor of 1.5 -- 6.8 better $M_p \sin i$ uncertainties compared to fitting RVs that are derived from a weighted average across wavelength.

Figures (6)

• Figure 1: Marginal posterior probability distributions of $M_p\sin i$ given the data for each system, for each of the three modeling paradigms. The blue represents the Variance-weighted-mean method, orange is the Order-by-order, green is the Joint Keplerian method, and the black lines show the mean (solid) and 1-sigma uncertainties (dashed) reported in the literature. Note in panel a), the OBO and JK methods are nearly indistinguishable, visually.
• Figure 2: Measurements of $M_p\sin{i}$ derived from each spectral order's individual MCMC analysis as a function of central wavelength. Blue points and errors are the mean and standard deviation of the posterior distributions for each order. The solid black line represents the variance weighted mean of the blue points.
• Figure 3: Mean of the photon-limited uncertainties versus the standard deviation of the $M_p\sin{i}$ posteriors for each order. Each blue point represents one spectral order. This figure shows a loose correlation between the average uncertainty in the RV time-series (for a single order) and the resulting constraint on $M_p\sin{i}$. Orders with small formal RV uncertainties can produce Keplerian orbital parameters that are poorly constrained.
• Figure 4: Joint posterior distributions for HD 217107.
• Figure 5: Joint posterior distributions for HD 3651.