Simulation and analysis of sub-{\mu}as precision astrometric data for planet-finding

TL;DR

This paper develops a detailed vector model for interferometric astrometry to detect Earth-mass planets, demonstrating the limitations of linear approximations and proposing a more accurate expansion method.

Contribution

It introduces a comprehensive vector formulation for astrometric measurements and a novel expansion approach that accurately captures signals from Earth-mass planets.

Findings

Linear models are insufficient for Earth-mass planet signals.

The proposed expansion reduces residuals by orders of magnitude.

Numerical issues in simulation are discussed.

Abstract

We present a vector formulation of an interferometric observation of a star, including the effects of the barycentric motion of the observatory, the proper motions of the star, and the reflex motions of the star due to orbiting planets. We use this model to empirically determine the magnitude and form of the signal due to a single Earth-mass planet orbiting about a sun-mass star. Using bounding values for the known components of the model, we perform a series of expansions, comparing the residuals to this signal. We demonstrate why commonly used first order linearizations of similar measurement models are insufficient for signals of the magnitude of the one due to an Earth-mass planet, and present a consistent expansion which is linear in the unknown quantities, with residuals multiple orders of magnitude below the Earth-mass planet signal. We also discuss numerical issues that can arise when simulating or analyzing these measurements.