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 ($Δψ_{\rm gas}$). So far, all studies compute $Δψ_{\rm gas}$ for a thin, laminar disk, with negligible flow turbulence, whereby the disk exerts the well-understood linear torque ($T_{\rm lin}$). 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 ($T_{\rm turb}$) acting on an EMRI by modeling it as a Gaussian distribution around $T_{\rm lin}$, inspired by recent global simulations that study such torques. We compute $Δψ_{\rm gas}$ for the ``golden'' circular EMRI with total source mass $M=10^6~{\rm M}_\odot$ 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 ($N_{\rm max}$), Eddington ratio ${\rm f}_{\rm Edd}$, disk aspect ratio $h_0$, and turbo-viscous coefficient $α$ in a reasonable parameters space. For $N_{\rm max}=100$ orbits, we find that for $C\gtrsim{10}$, ${\rm f}_{\rm Edd}\gtrsim0.3$, $h_0\gtrsim0.03$, and $α\gtrsim0.1$, dephasings due to $T_{\rm lin}$ are unobservable but could become detectable ($Δψ_{\rm gas}>8/$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.