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We study the effects of a thin gaseous accretion disk on the inspiral of astellar--mass black hole into a supermassive black hole. We construct aphenomenological angular momentum transport equation that reproduces known diskeffects. Disk torques modify the gravitational wave phase evolution todetectable levels with LISA for reasonable disk parameters. The Fouriertransform of disk-modified waveforms acquires a correction with a differentfrequency trend than post-Newtonian vacuum terms. Such inspirals could be usedto detect accretion disks with LISA and to probe their physical parameters.

Imprint of Accretion Disk-Induced Migration on Gravitational Waves from Extreme Mass Ratio Inspirals