A Gravitational Wave Background from Intermediate Mass Black Holes in AGN Disks

Abstract

Intermediate mass black holes (IMBHs) formed in active galactic nucleus (AGN) disks are expected to inspiral into their central supermassive black holes (SMBHs), generating a stochastic gravitational-wave (GW) background in the mHz--decihertz band. Using the population-agnostic energetic formalism, we treat the AGN-disk channel as a mass-flow pipeline connecting the stellar-mass black hole population observed by LIGO/Virgo/KAGRA (LVK) to the SMBH mass reservoir via IMBHs. By anchoring this estimate to the LVK merger rate densities and the cosmic SMBH mass density derived from scaling relations, we derive a limit on the background amplitude. We show that the total energy density of the background is bounded by the global mass budget of SMBH growth. For fiducial parameters consistent with the fourth Gravitational-Wave Transient Catalog (GWTC-4), this yields a characteristic strain $A_{\rm IMR} \simeq (1.2_{-0.2}^{+0.2})\times 10^{-21}$ at $3\,{\rm mHz}$. While this fiducial amplitude is subdominant to the Galactic white dwarf foreground and the stellar-mass Extreme Mass Ratio Inspiral (EMRI) background, we show it can be distinguished by its non-Gaussian statistics and higher frequency cutoff. This new background may be detectable in the decihertz band where proposed detectors such as the Big Bang Observer or long-baseline lunar interferometers can measure it cleanly. A detection would provide a direct, model-independent constraint on the efficiency with which AGN disks process stellar remnants into SMBH mass growth, linking the LVK and LISA bands.

Figures (1)

• Figure 1: Characteristic strain spectra for the AGN-IMRI background and the stellar-mass EMRI background BonettiSesana2020, highlighting the large astrophysical uncertainties in both populations. The shaded regions bracket plausible minimum-to-maximum scenarios, with fiducial models shown as thicker curves. For the AGN-IMRI background, the high-frequency cutoff is set by the ISCO of the lightest participating SMBHs. Here we plot the AGN-IMRI GWB for a spinning, $a_\bullet=0.98$, SMBH. A non-spinning SMBH would lower the cutoff frequency by a factor of $\sim$6. Also shown are representative strain sensitivities for a 4-year LISA mission AmaroSeoane2017 and for a Big Bang Observer (BBO)-like decihertz detector Harry2006. The BNS inspiral background LIGOScientific2018stochBNSEbersoldRegimbau2025 is also shown, with its shaded band reflecting uncertainties in the merger rate. The fact that both the AGN-IMRI and EMRI backgrounds can rise into the $10^{-2}$--$10^{-1}$ Hz window motivates targeted searches at higher frequencies, where the signals may become detectable even if they are subdominant near a few mHz. The Galactic white dwarf foreground appears as a bump in the LISA characteristic strain curve at around 1 mHz.