2026/07/10 by Avinash Tiwari, Shasvath J. Kapadia, Aditya Vijaykumar +1
#gr-qc #astro-ph.HE
The centre of mass (CoM) of compact binary coalescences (CBCs) occurring in the vicinity of a supermassive black hole, through interaction with an arbitrary third body (e.g., of stellar mass), or in a dense stellar environment, will undergo a time-varying line-of-sight (LOS) velocity. This in turn leads to a time-varying Doppler shift and corresponding modulations in the shape of the gravitational waves (GWs). The phase and amplitude corrections arising from constant LOS acceleration and its higher-order time derivatives are already known. Specifically, these effects lead to corrections to the GW waveform at -4n post-Newtonian (PN) order, where n is the nth time derivative of the LOS velocity. In the context of a circular or eccentric outer orbit of the CoM of the CBC, these effects can be thought of as approximations to the LOS velocity in the limit: observation duration ≪ period of the outer orbit. However, this condition is not necessarily always satisfied. In this \it paper, we present phase and amplitude corrections to the GW waveforms arising from a periodic non-relativistic LOS velocity for circular and eccentric outer orbits of the CBC's CoM. Specifically, these lead to phase and amplitude modulations at 4 PN order, and reduce to the known corrections for constant kinematic parameters under appropriate limits mentioned above. We also perform a Fisher matrix analysis to forecast constraints on the environment that is sourcing the time-varying LOS velocity, for various future ground and space-based detectors. We further show that constraints acquired using GW waveforms derived in this work improve significantly in comparison to those acquired from approximate methods valid for constant kinematic parameters.