Environmental Effects in Stellar Mass Gravitational-wave Sources. I. Expected Fraction of Signals with Significant Dephasing in the Dynamical and Active Galactic Nucleus Channels

Abstract We present the first overview of the expected quantity of signals that will showcase significant gravitational-wave phase shifts caused by astrophysical environments, considering the upcoming A+ and A# LIGO/Virgo/KAGRA, Cosmic Explorer, and Einstein Telescope detectors. We construct and analyze two general families of dephasing prescriptions with extensions to eccentric sources, as well as collect five specific prescriptions for the fundamental smoking gun physical mechanisms at play in the dynamical and active galactic nucleus formation channel for stellar mass binary black holes: Roemer delays, tidal forces, and hydrodynamical interactions. We compute the expected fraction of signals containing astrophysical dephasing, as a function of environmental properties and based on observed distributions of binary parameters. We find that next generation detectors can expect to find environmental effects in hundreds of detected signals.