Orbit Tomography of Binary Supermassive Black Holes with Very Long Baseline Interferometry

TL;DR

This paper demonstrates that VLBI observations, like those from the EHT, can be used over several years to infer the orbital parameters of supermassive black hole binaries, aiding in gravitational wave and cosmological measurements.

Contribution

It introduces a method to recover SMBHB orbital parameters from time-dependent VLBI measurements, even with periods longer than the observation duration.

Findings

Orbital parameters can be recovered from VLBI data over multiple years.

The method enables mass and Hubble constant measurements when combined with other observations.

Applicable to binaries with periods longer than the observation span.

Abstract

In this work, we study how to infer the orbit of a supermassive black hole binary (SMBHB) by time-dependent measurements with Very Long Baseline Interferometry (VLBI), such as the Event Horizon Telescope (EHT). Assuming a point-like luminosity image model, we show that with multiple years of observations by EHT, it is possible to recover the SMBHB orbital parameters -- eccentricity, (rescaled) semi-major axis, orbital frequency, and orbital angles -- from their time-varying visibilities even if the binaries orbital period is a few times longer than the duration of observation. Together with the future gravitational wave detections of resolved sources of SMBHBs with Pulsar Timing Array, and/or the detections of optical-band light curves, we will be able to further measure the individual mass of the binary, and also determine the Hubble constant if the total mass of the binary is measured through the light curves of the two black holes or by alternative methods.