# Accounting for Chromatic Atmospheric Effects on Barycentric Corrections

## TL;DR

This paper investigates how atmospheric effects influence barycentric corrections in stellar radial velocity measurements, emphasizing the importance of wavelength-dependent adjustments for achieving extreme precision in exoplanet detection.

## Contribution

It introduces a method to account for atmospheric wavelength dependence in barycentric corrections, including the implementation of a multi-channel exposure meter for high-precision spectrographs.

## Key findings

- Wavelength dependence can cause several cm/s errors in radial velocity measurements.
- At least four wavelength channels are needed to correct at the 10 cm/s level.
- A multi-channel exposure meter is proposed for the EXPRES spectrograph.

## Abstract

Atmospheric effects on stellar radial velocity measurements for exoplanet discovery and characterization have not yet been fully investigated for extreme precision levels. We carry out calculations to determine the wavelength dependence of barycentric corrections across optical wavelengths, due to the ubiquitous variations in air mass during observations. We demonstrate that radial velocity errors of at least several cm/s can be incurred if the wavelength dependence is not included in the photon-weighted barycentric corrections. A minimum of four wavelength channels across optical spectra (380-680 nm) are required to account for this effect at the 10 cm/s level, with polynomial fits of the barycentric corrections applied to cover all wavelengths. Additional channels may be required in poor observing conditions or to avoid strong telluric absorption features. Furthermore, consistent flux sampling on the order of seconds throughout the observation is necessary to ensure that accurate photon weights are obtained. Finally, we describe how a multiple-channel exposure meter will be implemented in the EXtreme PREcision Spectrograph (EXPRES).