Two-body relaxation in the EMRI-TDE disk model for Quasi Periodic Eruptions

TL;DR

This paper provides a quantitative analysis of the expected rate and abundance of Quasi Periodic Eruptions (QPEs) in galactic nuclei, based on the impact model involving TDEs and EMRIs, using simulations across various black hole masses.

Contribution

It introduces the first end-to-end calculation of QPE rates within the impact model framework, combining TDE and EMRI rates with detailed system simulations.

Findings

QPE number density ranges from 10^{-12} to 10^{-6} Mpc^{-3}.

Predicted QPE rates depend on orbital period, eccentricity, and inclination thresholds.

Simulation results are consistent with observed QPE phenomenology.

Abstract

Quasi Periodic Eruptions (QPEs) are luminous bursts of soft X-rays recently discovered in galactic nuclei. They repeat on timescales of hours to weeks, superimposed to an otherwise stable quiescent X-ray level, consistent with emission from a radiatively efficient accretion flow around relatively low-mass MBHs. Although their physical origin is still debated, their quasi-periodicity naturally arises within the 'impact model', in which the X-ray bursts are generated by the interaction between an sBH or a star in a close orbit around the central MBH and the accretion disk formed by a tidal disruption event (TDE). While this model is consistent with the phenomenology of QPEs, it remains unclear whether such specific physical configurations are sufficiently commonto explain the observed QPE number density. We present the first end-to-end quantitative calculation of the expected QPE rate and abundance within the framework of the impact model. To this purpose, we combine the rates of TDEs and extreme mass-ratio inspirals (EMRIs) around MBHs spanning a range of masses masses. We employ the public code \textsc{PhaseFlow} to simulate seven systems with MBH masses between $10^5 M_\odot$ and $10^8 M_\odot$, each sourronded by a three-component population: one composed of $1M_\odot$ stars, and two consisting of sBHs with masses of $10M_\odot$ and $40 M_\odot$. Based on the emission constraints available in the literature, we restrict to sBH EMRIs on prograde orbit with eccentricity $e<0.5$ and inclination $\iota<20^{\circ}$ with respect to the accretion disk. For stellar EMRIs the constraints instead arise from the requirement that the star avoid tidal disruption. We find that the predicted QPE number density spans the range $10^{-12} \rm Mpc^{-3}$ to $10^{-6} \rm Mpc^{-3}$, depending on the assumed orbital period interval and on the adopted eccentricity and inclination thresholds.