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

TL;DR

This work assesses the prospect of directly imaging sub-parsec SMBHBs with space VLBI by developing a post-Newtonian orbital model up to $3.5\mathrm{PN}$, and a Bayesian orbit-fitting pipeline to detect and estimate orbital parameters from multi-epoch astrometric data. Using the Black Hole Explorer (BHEX) as a primary case, the authors simulate observations, establish a binary-confirmation criterion, and demonstrate parameter retrieval for several representative binaries, showing that $M$, $a$, and $e$ can be constrained and curved orbital motion detected for periods up to $P_{obs}\lesssim 23$ years with a few epochs. The study also discusses strategies to identify candidates from multi-messenger data and outlines the requirements for future spaceborne VLBI (THEZA) to achieve a statistically significant SMBHB survey, including an angular resolution near $1\ \mu\mathrm{as}$ and sub-mJy sensitivity. Collectively, the results provide a concrete pathway for imaging SMBHBs, constraining their demographics and evolution, and informing the design of next-generation space VLBI facilities that complement GW observations.

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 $μ$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.

Figures (21)

• Figure 1: Minimum number of observations required to detect curved motion of secondary black hole as a function of observed orbital period and semi-major axis in angular units. Face-on orbit with no inclination. Observations performed annually. (Solid lines) BHEX with angular resolution of 6 $\mu$as. (Dashed lines) ngEHT with angular resolution of 15 $\mu$as.
• Figure 2: Predicted number of observable SMBHB systems as a function of array angular resolution ($\theta_{r}$) and flux density sensitivity ($S_{\nu}$) out to $z$ = 2. $P_{\text{obs}} \leq$ 10 years and $q \geq$ 0.01. Figure generated using the assumptions made by dorazio_repeated_2018 in the generation of their results.
• Figure 3: BHEX capabilities of binary system detection. Depicts the total flux density of the source required to distinguish a binary from a single Gaussian source, assuming a brightness thermal noise of $5$ mJy/beam. $w_1$ is the angular diameter of the primary black hole. The y-axis describes the ratio between the primary and secondary component flux densities and solid angles. For illustrative purposes, we assume the same brightness for both components of the binary system. The positions of the 7 test cases presented below are illustrated in this parameter space. Subscript $A$ indicates the largest angular separation of the orbit from the observer's perspective and $P$ is the smallest observed separation.
• Figure 4: Stokes I image of the binary toy model for Case 1 in Mar 2032, 2033, and 2034. Primary source fixed to origin and first position of secondary illustrated. Subsequent observed positions of secondary depicted with yellow crosses.
• Figure 5: (Top) Best-fit solution for Case 1. Observed positions of secondary relative to the primary are indicated by red markers with 1$\sigma$ error bars. (Bottom) Relative right ascension and declination.