[Paper Review] Astrometric Identification of Nearby Binary Stars I: Predicted Astrometric Signals

Zephyr Penoyre, Vasily Belokurov+1 more|arXiv (Cornell University)|Nov 19, 2021

Stellar, planetary, and galactic studies24 references82 citations

TL;DR

This paper develops a synthetic model of nearby binary stars within 100 pc to predict astrometric signals in Gaia eDR3 data, showing that Unit Weight Error (UWE) and Proper Motion Anomaly (PMA) effectively identify binaries with periods from months to decades. It establishes UWEeDR3 > 1.25 and ∆UWE/UWEeDR3 > −0.25 as robust criteria, detecting 80–90% of stellar binaries in this range, with sensitivity sharply declining for mass ratios q ≤ 10⁻³.

ABSTRACT

We examine the capacity to identify binary systems from astrometric errors and deviations alone. Until the release of the fourth Gaia data release we lack the full astrometric time series that the satellite records, but as we show can still infer the presence of binaries from the best fit models, and their error, already available. We generate a broad catalog of simulated binary systems within 100 pc, and examine synthetic observations matching the Gaia survey's scanning law and astrometric data processing routine. We show how the Unit Weight Error (UWE) and Proper Motion Anomaly (PMA) vary as a function of period, and the properties of the binary. Both UWE and PMA peak for systems with a binary period close to the time baseline of the survey. Thus UWE can be expected to increase or remain roughly constant as we observe the same system over a longer baseline, and we suggest $UWE_{eDR3}>1.25$ and $\Delta UWE/UWE_{eDR3}>-0.25$ as criteria to select astrometric binaries. For stellar binaries we find detectable significant astrometric deviations for 80-90\% of our simulated systems in a period range from months to decades. We confirm that for systems with periods less than the survey's baseline the observed $UWE$ scales $\propto \ \varpi$ (parallax), $a$ (semi-major axis) and $\Delta =\frac{|q-l|}{(1+q)(1+l)}$ where $q$ and $l$ are the mass and light ratio respectively, with a modest dependence on viewing angle. For longer periods the signal is suppressed by a factor of roughly $\propto P^{-2}$ (period). PMA is largest in orbits with slightly longer periods but obeys the same approximate scaling relationships.

Motivation & Objective

• To predict detectable astrometric deviations in Gaia eDR3 data for nearby binary stars.
• To evaluate the effectiveness of UWE and PMA as indicators of binary systems without full orbital solutions.
• To establish quantitative criteria for identifying astrometric binaries using existing data releases.
• To assess sensitivity to binary parameters such as period, mass ratio, parallax, and viewing geometry.
• To inform future detection of low-mass companions (e.g., brown dwarfs, exoplanets) via astrometry.

Proposed method

• Simulated a synthetic population of 100 pc binary systems with varied orbital parameters and stellar properties.
• Generated synthetic Gaia-like astrometric observations matching the satellite’s scanning law and data processing pipeline.
• Fitted 5-parameter single-star models (position, proper motion, parallax) to synthetic data to compute UWE and PMA.
• Quantified signal dependence on period, parallax, mass ratio (q), luminosity ratio (l), eccentricity, and viewing angle.
• Compared UWE and PMA across DR2 and eDR3 to assess changes in fit quality over time.
• Used a simplified luminosity model (l = q³.⁵) to estimate detectability under realistic photometric conditions.

Experimental results

Research questions

• RQ1 How do UWE and PMA vary as functions of binary period and system parameters in Gaia eDR3 data?
• RQ2 What criteria based on UWE and its change between data releases can reliably identify astrometric binaries?
• RQ3 To what extent does the detectability of binaries depend on parallax, mass ratio, and viewing geometry?
• RQ4 How does the signal strength scale with orbital period, and when is it suppressed?
• RQ5 What fraction of stellar binaries with periods from months to decades are detectable via UWE > 1.25 in eDR3?

Key findings

• UWE and PMA peak for binary systems with periods near the survey’s 34-month baseline, making them most sensitive to systems with periods from months to decades.
• More than 80% of simulated stellar binaries with periods from months to decades are detectable using UWEeDR3 > 1.25.
• The UWE signal scales approximately ∝ϖ (parallax), a (semi-major axis), and ∆ = |q−l| / [(1+q)(1+l)] with modest dependence on viewing angle, and is suppressed by ∝P⁻² for longer periods.
• PMA is largest for slightly longer periods than UWE but follows similar scaling laws, confirming its utility as a complementary metric.
• The fraction of detectable systems drops sharply for mass ratios q ≤ 10⁻³, with remaining detections peaking near the 34-month baseline.
• Systems with q ≈ 1 are slightly harder to detect due to symmetric photocenter and center of mass, but real systems may show higher detectability due to natural luminosity variations.