Observable signatures of extreme mass-ratio inspiral black hole binaries embedded in thin accretion disks

We examine the electromagnetic and gravitational wave (GW) signatures of stellar-mass compact objects (COs) spiraling into a supermassive black hole (extreme mass-ratio inspirals), embedded in a thin, radiation-pressure dominated, accretion disk. At large separations, the tidal effect of the secondary CO clears a gap. We derive the conditions necessary for gap opening in a radiation-pressure dominated disk and show that the gap refills during the late GW-driven phase of the inspiral, leading to a sudden electromagnetic brightening of the source. The accretion disk leaves an imprint on the GW through its angular momentum exchange with the binary, the mass increase of the binary members due to accretion, and its gravity. We compute the disk-modified GWs both in an analytical Newtonian approximation and in a numerical effective-one-body approach. We find that disk-induced migration provides the dominant perturbation to the inspiral, with weaker effects from the mass accretion onto the CO and hydrodynamic drag. Depending on whether a gap is present, the perturbation of the GW phase is between 10 and 1000 rad per year, detectable with the future Laser Interferometer Space Antenna at high significance. The perturbation is significant for disk models with an effective viscosity proportional to gas pressure but much less so if proportional to the total pressure. The Fourier transform of the disk-modified GW in the stationary phase approximation is sensitive to disk parameters with a frequency trend different from post-Newtonian vacuum corrections. Our results suggest that observations of extreme mass-ratio inspirals may place new sensitive constraints on the physics of accretion disks.