A new algorithm for fitting orbits of multiple-planet systems to combined RV and astrometric data

TL;DR

This paper introduces a new algorithm for fitting multiple-planet orbits using combined radial velocity and astrometric data, reducing nonlinearity and improving computational efficiency.

Contribution

The paper presents a novel algorithm that simplifies orbit fitting by using only three nonlinear parameters per planet, enhancing speed and consistency.

Findings

Algorithm validated in a double-blind simulation study.

Reduced nonlinear parameters improve computational speed.

Ensures physical consistency between RV and astrometric data.

Abstract

If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem can be partially linearized via transformation to four linear parameters (related four Thiele-Innes constants) plus three nonlinear parameters: eccentricity, period and periastron time. The RV orbit problem can be partially linearized via transformation to two additional linear parameters plus the same three nonlinear parameters. Unfortunately, the two linear parameters from RV are not linearly related to the four linear parameters from astrometry. Because of this difficulty, currently available algorithms for fitting combined RV and astrometric data to multiple-planet systems employ at least five nonlinear parameters per planet. We have developed a new algorithm for fitting orbits of multiple planet systems from combined data sets of radial velocity and astrometric measurements. The new algorithm satisfies the RV-astrometry consistency requirement, while using three nonlinear parameters per planet. We expect the reduction in nonlinearity to give the algorithm a significant advantage in computation speed over existing algorithms. In this work, we describe the algorithm, which has been validated in the context of a recent double-blind planet detection simulation study.