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

TL;DR

This paper models the impact of turbulence in accretion disks on gravitational wave signals from EMRIs, suggesting turbulence can cause detectable waveform dephasing in LISA observations.

Contribution

It introduces a Gaussian-based prescription for turbulent gas torques on EMRIs, extending previous laminar disk models to account for turbulence effects.

Findings

Turbulent gas flow can induce GW dephasing detectable by LISA.

Dephasing becomes significant for high Eddington ratios and turbulence levels.

Chaotic migration due to turbulence may produce observable waveform signatures.

Abstract

Gravitational wave (GW) detector LISA will observe near-coalescence extreme mass ratio inspirals (EMRIs), which typically form in galactic central accretion disks. Gas torques on EMRI will alter its GW-driven inspiral trajectory from the vacuum expectation, leading to potentially LISA-observable GW dephasing ($\Delta\psi_{\rm gas}$). Most studies compute $\Delta\psi_{\rm gas}$ for a thin, laminar disk, with negligible flow turbulence, where the disk exerts a fairly 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, agnostic prescription for the turbulent torque ($T_{\rm turb}$) acting on an EMRI by modeling it as a Gaussian distribution around $T_{\rm lin}$, based on recent advances from a global hydrodynamical (HD) study. We compute $\Delta\psi_{\rm gas}$ 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 Eddington ratio ${\rm f}_{\rm Edd}$, turbulence normalization $C$ ($=~360$ in the aforementioned HD study), disk aspect ratio $h_0$, and turbo-viscous coefficient $\alpha$ in a reasonable parameters space. We find that for ${\rm f}_{\rm Edd}\gtrsim0.3$, $C\gtrsim300$, $h_0\gtrsim0.03$, and $\alpha\gtrsim0.1$, gas-induced dephasings are unobservable if only considering $T_{\rm lin}$ but could become detectable ($\Delta\psi_{\rm gas}>8/$SNR) if EMRIs exhibit chaotic migration due to turbulent gas flow. Hence, this work motivates running MHD simulations of accretion disks with embedded LISA EMRIs in the early in-spiral phase over long enough timescales to understand the evolution of their orbital elements and the imprint of the turbulent environment on their gravitational waveforms.