The imprint of gas on gravitational waves from LISA intermediate-mass black hole binaries

TL;DR

This paper investigates how gas torques affect gravitational wave signals from intermediate-mass black hole binaries in the LISA band, revealing potential for detecting disc-induced phase shifts and gaining insights into accretion physics.

Contribution

It provides the first detailed analysis of gas-induced waveform perturbations for IMBHBs in the LISA frequency range, highlighting their detectability and astrophysical significance.

Findings

Gas torques cause measurable phase shifts in LISA gravitational wave signals.

Detectable dephasing extends up to redshift z~7 depending on mass ratio.

Gas effects on chirp mass are too small for detection at expected SNR.

Abstract

We study the effect of torques on circular inspirals of intermediate-mass black hole binaries (IMBHBs) embedded in gas discs, wherein both BH masses are in the range $10^2$-$10^5~\rm{M}_\odot$, up to redshift $z = 10$. We focus on how torques impact the detected gravitational wave (GW) waveform in the frequency band of the Laser Interferometer Space Antenna (LISA) when the binary separation is within a few hundred Schwarzschild radii. For a sub-Eddington accretion disc with a viscosity coefficient $\alpha=0.01$, surface density $\Sigma\approx10^5$ g cm$^{-2}$, and Mach number $\mathcal{M}_{\rm a}\approx80$, a gap, or a cavity, opens when the binary is in the LISA band. Depending on the torque's strength, LISA will observe dephasing in the IMBHB's GW signal up to either $z\sim5$ for high mass ratios ($q\approx0.1$) or to $z\sim7$ for $q\approx10^{-3}$. We study the dependence of the measurable dephasing on variations of BH masses, redshift, and accretion rates. Our results suggest that phase shift is detectable even in high-redshift ($z = 10$) binaries, provided that they experience super-Eddington accretion episodes. We investigate if the disc-driven torques can result in an observable `time-dependent' chirp mass with a simplified Fisher formalism, finding that, at the expected signal-to-noise ratio, the gas-induced variation of the chirp mass is too small to be detected. This work shows how perturbations of vacuum waveforms induced by gas should be strong enough to be detected by LISA for the IMBHB in the early inspiral phase. These perturbations encode precious information on the astrophysics of accretion discs and galactic nuclei. High-accuracy waveform models which incorporate these effects will be needed to extract such information.