Chaotic migration of LISA Extreme Mass Ratio Inspirals in a turbulent accretion disk: effect on waveform de-phasing

Gravitational wave (GW) detector LISA will observe near-coalescence extreme mass ratio inspirals (EMRIs), which typically form in galactic central accretion disks. Torques from the disk can alter the GW-driven inspiral trajectory of an embedded EMRI from the vacuum expectation, leading to potentially observable GW dephasing (Δψ gas). So far, all studies compute Δψ gas for a thin, laminar disk, with negligible flow turbulence, whereby the disk exerts the well-understood linear torque (T lin). However, these disks must be turbulent due to magneto-rotational instability in the inner regions. Hence, we present a proof-of-concept general prescription for the turbulent torque (T turb) acting on an EMRI by modeling it as a Gaussian distribution around T lin, inspired by recent global simulations that study such torques. We compute Δψ gas for the ``golden'' circular EMRI with total source mass M=10 6 M and mass ratio q=5 times10-5 in its final four-year evolution at redshift z=0.276 and signal-to-noise ratio (SNR) =50 by varying turbulence amplitude C (=1 in the aforementioned study), maximum correlation timescale (N max), Eddington ratio f Edd, disk aspect ratio h 0, and turbo-viscous coefficient α in a reasonable parameters space. For N max=100 orbits, we find that for C, f Edd 0.3, h 0 0.03, and α 0.1, dephasings due to T lin are unobservable but could become detectable (Δψ gas>8/ SNR) if EMRIs experience turbulent torques. Hence, this work motivates running MHD simulations of accretion disks with embedded early-inspiral LISA EMRIs over long timescales to understand the imprint of the turbulent environment on their orbital parameters and gravitational waveforms.