The background gas humming and multi-messenger transients of stalled supermassive black hole binaries

TL;DR

This paper investigates the complex multi-messenger signals from stalled supermassive black hole binaries, revealing novel gas dynamics, shock-induced emissions, and a unique gravitational wave signature called 'background gas humming' that precedes black hole merger.

Contribution

It introduces a new analytical framework for modeling episodic accretion and shock phenomena in black hole binaries, including the discovery of the 'background gas humming' gravitational wave signature.

Findings

Identification of the 'background gas humming' as a high-frequency gravitational wave sideband.

Derivation of an analytical power spectral density revealing harmonic cascades.

Prediction of a terminal burst serving as a precursor to black hole merger.

Abstract

We establish the multi-messenger mechanics of episodic mass transfer in supermassive black hole binaries stalled within circumbinary discs. Utilizing continuous wavelet transforms, we isolate localized gas clumps at the cavity edge and track their evolution. By regularizing the forced fluid equations at Lindblad resonances via the inhomogeneous Airy differential equation, we bypass linear singularities to extract the finite wave amplitudes that trigger non-linear shock formation. These shocks produce bounded accretion bursts. We model the time-domain thermal luminosity, deriving an analytical power spectral density that forms a harmonic cascade. The superposition of the accretion streams generates a spectral beat frequency, providing an exact mathematical extraction of the binary mass ratio. The radiative cooling of shock-accelerated electrons produces a multi-wavelength spectral energy distribution from a synchrotron radio continuum to an inverse-Compton gamma-ray tail. We identify a relativistic signature: a discontinuous, high-frequency gravitational wave sideband termed the ``background gas humming''. This emission arises from the highly asymmetric, transient fluid geometry of the accretion shocks. Evaluating the asymptotic properties of the Airy regularization, we show that this humming manifests as a sequence of discrete high-frequency bursts with temporal quiescence gaps that systematically compress as the cavity shrinks. We show that the instantaneous mass of the gas actively trapped within the cavity violently amplifies prior to decoupling, culminating in a terminal burst near 4.0 mHz that serves as a multi-messenger precursor to the final vacuum inspiral.