Towards direct imaging and orbital parameter estimation of supermassive black hole binaries with spaceborne VLBI

TL;DR

This paper evaluates the potential of spaceborne VLBI, specifically the BHEX mission, to directly image and estimate orbital parameters of supermassive black hole binaries, which are key to understanding galaxy evolution and gravitational wave sources.

Contribution

It introduces a novel observational approach using BHEX for detecting and characterizing SMBHBs, including a Bayesian orbit fitting method and mission design considerations.

Findings

BHEX can detect binaries with flux density >0.04 Jy and separation ~2 μas.

Orbital parameters can be constrained within 13% for periods ≤10 years.

Curved trajectories are detectable for binaries with periods ≤23 years.

Abstract

Direct electromagnetic observation of the orbital motion of a sub-parsec, supermassive black hole binary (SMBHB) would provide the first conclusive proof of such systems existing. Widely considered to be the sources of gravitational waves, binaries are expected to form as a natural consequence of galactic mergers and determining the processes that drive their evolution is essential for understanding cosmological evolution. In this work, we evaluate the prospects of using ground and spaceborne Very Long Baseline Interferometry (VLBI) to observe supermassive black hole binaries and estimate their orbital parameters. The Black Hole Explorer (BHEX) is considered as the primary case study. Achieving unprecedented resolution, BHEX will provide access to a new volume of binary parameter space, potentially enabling the first, confident detection of an SMBHB. A binary toy model using a post-Newtonian orbit propagation is developed and simulated observations by BHEX and a ground array of telescopes are performed. An orbit fitting approach using Bayesian dynamic nested sampling is presented and its efficacy is demonstrated on the simulated observational data for a set of example binary systems. It is found that for BHEX, binary detection requires a total flux density of 0.04 Jy with a minimum separation of ~2 $\mu$as and an observable mass ratio dependent on the total flux. With three annual observations, BHEX could constrain semi-major axis and eccentricity of binaries with orbital periods $\leq$10 years to within 13% of the true values. A curved trajectory could confidently be detected in binaries with period $\leq$23 years. Proposals for how candidate sources could be identified in time for the BHEX mission are also provided. Finally, we constrain the requirements of a future spaceborne VLBI system, capable of performing a statistically significant survey of supermassive black hole binaries.