Evolution of gas disc-embedded intermediate mass ratio inspirals in the
  LISA band
  Among the potential milliHz gravitational wave (GW) sources for the upcoming
space-based interferometer LISA are extreme- or intermediate-mass ratio
inspirals (EMRI/IMRIs). These events involve the coalescence of supermassive
black holes in the mass range $10^5 M_{\odot} \lesssim M \lesssim 10^7
M_{\odot}$ with companion BHs of much lower masses. A subset of E/IMRIs are
expected to occur in the accretion discs of active galactic nuclei (AGN), where
torques exerted by the disc can interfere with the inspiral and cause a phase
shift in the GW waveform. Here we use a suite of two-dimensional hydrodynamical
simulations with the moving-mesh code DISCO to present a systematic study of
disc torques. We measure torques on an inspiraling BH and compute the
corresponding waveform deviations as a function of the binary mass ratio
$q\equiv M_2/M_1$, the disc viscosity ($\alpha$), and gas temperature (or
equivalently Mach number; $\mathcal{M}$). We find that the absolute value of
the gas torques is within an order of magnitude of previously determined
planetary migration torques, but their precise value and sign depends
non-trivially on the combination of these parameters. The gas imprint is
detectable by LISA for binaries embedded in AGN discs with surface densities
above $\Sigma_0\ge10^{4-6} \rm \, g cm^{-2}$, 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. Torques
in colder discs exhibit a noticeable dependence on the GW-driven inspiral rate
as well as strong fluctuations at late stages of the inspiral. Our results
further suggest that LISA may be able to place constraints on AGN disc
parameters and the physics of disc-satellite interaction.
