Аңдатпа
Abstract We establish the multimessenger 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 Wentzel–Kramers–Brillouin singularities to extract the finite wave amplitudes that trigger nonlinear shock formation. These shocks produce bounded accretion bursts. We model the time-domain thermal luminosity, utilizing the Fourier shift theorem to derive an analytical power spectral density that forms an extended harmonic cascade. The superposition of the accretion streams generates a spectral beat frequency, providing a theoretical diagnostic template to estimate the binary mass ratio, though sensitive to intrinsic cavity shape. The radiative cooling of shock-accelerated electrons produces a multiwavelength spectral energy distribution from a synchrotron radio continuum to an inverse-Compton gamma-ray tail, regulated by pair-production thermostats. We identify a relativistic signature: a discontinuous, high-frequency gravitational wave sideband termed the “background gas humming.” We analytically differentiate this from steady spiral pattern speeds, showing it arises from the physical advection of highly localized, transient fluid hot spots following 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 accretion rate of the gas actively trapped within the cavity violently amplifies prior to decoupling, culminating in a terminal burst near 4 mHz (normalized to a 10 6 M ⊙ system) that serves as a multimessenger precursor to the final vacuum inspiral.