Astrometric mass measurement of compact companions in binary systems with Gaia

¹ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, PR China
e-mail: wyl2013@mail.ustc.edu.cn
² School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
e-mail: jfliu@nao.cas.cn
³ Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, PR China
⁴ School of Physics and Astronomy & Institute for Gravitational Wave Astronomy, University of Birmingham, Birmingham, B15 2TT, UK
⁵ Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
⁶ Department of Astronomy, Beijing Normal University, Beijing 100871, PR China

Received: 31 March 2022
Accepted: 27 June 2022

Abstract

Context. For binary systems with an unseen primary and a luminous secondary, the astrometric wobble of the secondary could be used to study the primary. With Gaia, it is possible to measure the mass of the black hole or neutron star with a luminous companion (hereafter BH/NS-LC).

Aims. Our aim is to provide a method for predicting Gaia’s ability in measuring the mass of BH/NS-LCs. We also tried to estimate the number of solvable BH/NS-LCs using Gaia.

Methods. We used a realistic Markov chain Monte Carlo simulation of mock Gaia observations to obtain a relation between the uncertainty of mass measurement of the primary in BH/NS-LCs with the observable variables of the secondary astrometric orbit. Furthermore, we used the MOBSE code to evolve a Galactic BH/NS-LC sample with a combined Milky Way model. Our relation is applied to this sample to estimate the number of solvable BH/NS-LCs.

Results. We derived a good relation between the mass uncertainty and the binary parameters. For the first time, we show the quantitive influence of the period P, inclination i, eccentricity e, and ecliptic latitude β to the mass measurement. Our results suggest that 48₋₇⁺⁷ BH-LCs and 102₋₁₀⁺¹¹ NS-LCs are solvable during a 5 yr Gaia mission. We also give the distribution of the distance and apparent magnitude of the Gaia solvable BH/NS-LCs. This solvable sample would be increased by additional spectroscopic data or a prolonged Gaia mission.

Conclusions. The mass uncertainty relation could be used in future simulations of BH/NS-LCs observed by Gaia. The prediction of the solvable BH/NS-LCs is not only influenced by the process in generating the Galactic BH/NS-LC sample, but is also affected by our uncertainty relation. In particular, the relations of parameters such as [P, e, i,ß] are very useful to correct the selection effect in the statistic results of the future BH/NS-LC sample observed by Gaia.