Barycentric Corrections at 1 cm/s for precise Doppler velocities

TL;DR

This paper establishes the stringent requirements for barycentric corrections at 1 cm/s precision, detailing the theory, implementation, and validation of an algorithm crucial for detecting Earth-like exoplanets via Doppler spectroscopy.

Contribution

It introduces a minimal, accurate algorithm for barycentric correction at 1 cm/s, validated against TEMPO2, and discusses the effects of relativistic and observational uncertainties.

Findings

Achieved barycentric correction accuracy of ≤1 cm/s RMS.

Validated the correction algorithm against pulsar timing software.

Identified key sources of error, including relativistic and chromatic effects.

Abstract

The goal of this paper is to establish the requirements of a barycentric correction with an RMS of $\lesssim 1$ cm/s, which is an order of magnitude better than necessary for the Doppler detection of true Earth analogs ($\sim9$ cm/s). We describe the theory and implementation of accounting for the effects on precise Doppler measurements of motion of the telescope through space, primarily from rotational and orbital motion of the Earth, and the motion of the solar system with respect to target star (i.e. the "barycentric correction"). We describe the minimal algorithm necessary to accomplish this and how it differs from a na\"ive subtraction of velocities (i.e. a Galilean transformation). We demonstrate the validity of code we have developed from the California Planet Survey code via comparison with the pulsar timing package, TEMPO2. We estimate the magnitude of various terms and effects, including relativistic effects, and the errors associated with incomplete knowledge of telescope position, timing, and stellar position and motion. We note that chromatic aberration will create uncertainties in the time of observation, which will complicate efforts to detect true Earth analogs. Our code is available for public use and validation.