Likelihood for Detection of Sub-parsec Supermassive Black Hole Binaries in Spectroscopic Surveys

TL;DR

This paper presents an analytic model to estimate the likelihood of detecting sub-parsec supermassive black hole binaries in spectroscopic surveys, considering orbital evolution, survey selection effects, and emission line signatures.

Contribution

It introduces a modular analytic framework combining orbital evolution and survey effects to predict detection probabilities of SBHBs in spectroscopic data.

Findings

Detection likelihood depends on orbital evolution speed and survey cadence.

Spectroscopic surveys are sensitive to binaries with separations less than a few times 10^4 r_g.

For every detected SBHB, there are over 200 similar systems at larger separations.

Abstract

Motivated by observational searches for sub-parsec supermassive black hole binaries (SBHBs) we develop a modular analytic model to determine the likelihood for detection of SBHBs by ongoing spectroscopic surveys. The model combines the parametrized rate of orbital evolution of SBHBs in circumbinary disks with the selection effects of spectroscopic surveys and returns a multivariate likelihood for SBHB detection. Based on this model we find that in order to evolve into the detection window of the spectroscopic searches from larger separations in less than a Hubble time, $10^8M_\odot$ SBHBs must, on average, experience angular momentum transport faster than that provided by a disk with accretion rate $0.06\,\dot{M}_E$. Spectroscopic searches with yearly cadence of observations are in principle sensitive to binaries with orbital separations $< {\rm few}\times 10^4\, r_g$ ($r_g = GM/c^2$ and $M$ is the binary mass), and for every one SBHB in this range there should be over 200 more gravitationally bound systems with similar properties, at larger separations. Furthermore, if spectra of all SBHBs in this separation range exhibit the AGN-like emission lines utilized by spectroscopic searches, the projection factors imply five undetected binaries for each observed $10^8M_\odot$ SBHB with mass ratio $0.3$ and orbital separation $10^4\,r_g$ (and more if some fraction of SBHBs is inactive). This model can be used to infer the most likely orbital parameters for observed SBHB candidates and to provide constraints on the rate of orbital evolution of SBHBs, if observed candidates are shown to be genuine binaries.