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Among the potential milliHz gravitational wave (GW) sources for the upcomingspace-based interferometer LISA are extreme- or intermediate-mass ratioinspirals (EMRI/IMRIs). These events involve the coalescence of supermassiveblack holes in the mass range $10^5 M_{\odot} \lesssim M \lesssim 10^7M_{\odot}$ with companion BHs of much lower masses. A subset of E/IMRIs areexpected to occur in the accretion discs of active galactic nuclei (AGN), wheretorques exerted by the disc can interfere with the inspiral and cause a phaseshift in the GW waveform. Here we use a suite of two-dimensional hydrodynamicalsimulations with the moving-mesh code DISCO to present a systematic study ofdisc torques. We measure torques on an inspiraling BH and compute thecorresponding waveform deviations as a function of the binary mass ratio$q\equiv M_2/M_1$, the disc viscosity ($\alpha$), and gas temperature (orequivalently Mach number; $\mathcal{M}$). We find that the absolute value ofthe gas torques is within an order of magnitude of previously determinedplanetary migration torques, but their precise value and sign dependsnon-trivially on the combination of these parameters. The gas imprint isdetectable by LISA for binaries embedded in AGN discs with surface densitiesabove $\Sigma_0\ge10^{4-6} \rm \, g cm^{-2}$, depending on $q$, $\alpha$ and$\mathcal{M}$. Deviations are most pronounced in discs with higher viscosities,and for E/IMRIs detected at frequencies where LISA is most sensitive. Torquesin colder discs exhibit a noticeable dependence on the GW-driven inspiral rateas well as strong fluctuations at late stages of the inspiral. Our resultsfurther suggest that LISA may be able to place constraints on AGN discparameters and the physics of disc-satellite interaction.

Evolution of gas disc-embedded intermediate mass ratio inspirals in the LISA band