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

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 10²-10⁵ M_⊙, up to redshift z = 10. We focus on how torques impact the detected gravitational wave (GW) waveform in the LISA frequency band when the binary separation is within a few hundred Schwarzschild radii. For a sub-Eddington accretion disc with a viscosity coefficient α = 0.01, surface density Σ ≈ 10⁵ g cm^-2, and Mach number $\mathcal {M}_{\rm {a}}\approx 80$, 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 ~ 5 for high mass ratios (q ≈ 0.1) or to z ~ 7 for q ≈ 10^-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 if 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 gas-induced perturbations of vacuum waveforms should be strong enough to be detected by LISA for the IMBHB in the early inspiral phase. These perturbations encode precious information on accretion discs and galactic nuclei astrophysics. High-accuracy waveform models which incorporate these effects will be needed to extract such information.