Supermassive black hole binaries in the multi-messenger context of ground and spaceborne VLBI
Evidence of a gravitational wave background suggests the existence of a population of sub-parsec supermassive black hole binaries (SMBHBs), with characteristic angular separations on the order of 1-10 $\mu$as. Spaceborne extensions of Very Long Baseline Interferometry (VLBI) and the next generation ground arrays introduce the possibility of directly imaging these SMBHBs. In this work, a binary Spectral Energy Distribution (SED) model is used to predict the detectability of SMBHBs with ground and spaceborne VLBI. We consider the Black Hole Explorer (BHEX), a proposal for a spaceborne VLBI mission, as our primary case study. We explore the detectable SMBHB parameter space and identify distinguishable binary signatures that could exist in the visibility domain. We find that for a flux-density-limited sample, ground array observations are more effective at detecting a wider region of the binary parameter space, with $M_\mathrm{tot} \gtrsim 10^9$ solar mass systems detectable out to redshift, $z=0.075$ and beyond. Conversely, inclusion of a spaceborne element such as BHEX, offering finer angular resolution ($\sim6\,\mu$as) and sampling of the (u,v) plane not limited by Earth rotation synthesis, will provide significant benefits in constraining binary properties, resulting in improvements in characterisation of the separation and position angle of SMBHBs by a factor of $\sim4$. Near-future ground and/or spaceborne VLBI may achieve the first direct observation of a SMBHB, contributing significantly to multi-messenger studies of such systems with pulsar timing arrays and observations across the electromagnetic spectrum.