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

Abstract

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 ($\Delta {\psi }_{\mathrm{gas}}$). So far, all studies compute $\Delta {\psi }_{\mathrm{gas}}$ for a thin, laminar disk, with negligible flow turbulence, whereby the disk exerts the well-understood linear torque ($T_{\mathrm{lin}}$). 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 ($T_{\mathrm{turb}}$) acting on an EMRI by modeling it as a Gaussian distribution around $T_{\mathrm{lin}}$, inspired by recent global simulations that study such torques. We compute $\Delta {\psi }_{\mathrm{gas}}$ for the ``golden'' circular EMRI with total source mass $M=10^6{\mathrm{M}}_{\odot }$ and mass ratio $q=5\times 10^{-5}$ 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 ${\mathrm{f}}_{\mathrm{Edd}}$, disk aspect ratio $h_0$, and turbo-viscous coefficient $\alpha$ in a reasonable parameters space. For $N_{\max }=100$ orbits, we find that for $C\gtrsim 10$, ${\mathrm{f}}_{\mathrm{Edd}}\gtrsim 0.3$, $h_0\gtrsim 0.03$, and $\alpha \gtrsim 0.1$, dephasings due to $T_{\mathrm{lin}}$ are unobservable but could become detectable ($\Delta {\psi }_{\mathrm{gas}}>8/$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.

Accepted by ApJL. 16 pages, 5 figures