Few Observation Binary Orbit Solver (FOBOS) from two (or more) astrometric observations

TL;DR

FOBOS is a rapid, Monte Carlo-based method that estimates orbital parameters of binary and triple systems from as few as two astrometric observations, providing reliable confidence intervals and constraining key orbital elements.

Contribution

This paper introduces FOBOS, a novel fast method for estimating orbital properties from minimal astrometric data, significantly reducing computational time compared to traditional techniques.

Findings

Can constrain semi-major axis within a factor of 2-3

Achieves inclination accuracy of about 20 degrees

Provides statistically reliable confidence intervals

Abstract

We have developed a new, fast method of estimating the orbital properties of a binary or triple system using as few as two epochs of astrometric data. FOBOS (Few Observation Binary Orbit Solver) uses a flat prior brute force Monte Carlo method to produce probability density functions of the likely orbital parameters. We test the code on fake observations and show that it can (fairly often) constrain the semi-major axis to within a factor of 2-3, and the inclination to within $\sim$20$^{\circ}$ from only two astrometric observations. We also show that the 68 and 95 per cent confidence intervals are statistically reliable. Applying this method to triple systems allows the relative inclination of the secondary and tertiary star orbits to be constrained. FOBOS can usually find a statistically significant number of possible matches in CPU minutes for binary systems, and CPU hours for triple systems.