[Paper Review] Quasi-periodic eruptions from impacts between the secondary and a rigidly precessing accretion disc in an extreme mass-ratio inspiral system

Alessia Franchini, Matteo Bonetti+8 more|arXiv (Cornell University)|Apr 3, 2023

Astrophysical Phenomena and Observations4 citations

TL;DR

This paper proposes a semi-analytical model in which quasi-periodic eruptions (QPEs) in extreme mass-ratio inspiral (EMRI) systems arise from repeated impacts between a secondary object and a rigidly precessing accretion disc, producing adiabatically expanding, optically thick gas clouds that emit soft X-rays. The model successfully reproduces the diverse recurrence times, luminosities, and spectral evolution observed in four QPE sources—GSN 069, eRO-QPE1, eRO-QPE2, and RX J1301.9+2747—by tuning five system parameters, demonstrating a natural explanation for QPE variability across sources.

ABSTRACT

X-ray quasi-periodic eruptions (QPEs) represent a recently discovered example of extreme X-ray variability associated with supermassive black holes. These are high-amplitude bursts recurring every few hours that are detected in the soft X-ray band from the nuclei of nearby galaxies whose optical spectra lack the broad emission lines typically observed in unobscured active galaxies. The physical origin of this new X-ray variability phenomenon is still unknown and several theoretical models have been presented. However, no attempt has been made so far to account for the varying QPE recurrence time and luminosity in individual sources, nor for the diversity of the QPE phenomenology in the different known erupters. We present a semi-analytical model based on an extreme mass-ratio inspiral (EMRI) system where the secondary intersects, along its orbit, a rigidly precessing accretion disc surrounding the primary. We assume that QPEs result from emission from an adiabatically expanding, initially optically thick gas cloud expelled from the disc plane at each impact. We produced synthetic X-ray light curves, which we then compared with X-ray data from four QPE sources: GSN 069, eRO-QPE1, eRO-QPE2, and RX J1301.9+2747. Our model aptly reproduces the diversity of QPE properties between the considered objects and it is also able to naturally account for the varying QPE amplitudes and recurrence times in individual sources. Future implementations will enable us to refine the match with the data and to estimate the system parameters precisely, making additional use of multi-epoch QPE data. We briefly discuss the nature of the secondary object, as well as the possible implications of our findings for the EMRI population at large.

Motivation & Objective

• To explain the observed diversity in QPE recurrence times and luminosities across different sources, which no prior model has comprehensively accounted for.
• To investigate whether impacts between a secondary object and a rigidly precessing accretion disc in an EMRI system can produce the observed X-ray light curves and spectral evolution of QPEs.
• To determine whether the physical parameters of the EMRI system—such as orbital inclination, eccentricity, and disc mass—can be constrained to match multi-epoch QPE data.
• To assess the feasibility of the model in explaining the lack of broad emission lines in QPE hosts while maintaining AGN-like ionizing continua.
• To explore the implications of the model for the broader population of EMRIs and the connection between QPEs and tidal disruption events (TDEs).

Proposed method

• The model assumes that each impact between the secondary and the precessing disc ejects a transient, adiabatically expanding, optically thick gas cloud.
• X-ray emission from the cloud is modeled as thermal blackbody radiation, with temperature evolving from ~50–80 eV to ~100–250 eV during the flare.
• Synthetic X-ray light curves are generated by simulating repeated impacts along the secondary’s orbit, with luminosity and recurrence time dependent on orbital and disc parameters.
• The model incorporates disc precession and mutual inclination between the EMRI orbit and disc plane, with only prograde, low-inclination orbits (<15°) producing detectable QPEs.
• Cloud expansion is treated as adiabatic, with contrast in temperature relative to the disc set to ~1, implying expansion factors of 2–3.
• Parameter space is explored by tuning five free parameters: black hole spin, orbital eccentricity, disc mass, EMRI mass, and disc inclination, with initial values fixed for simplicity.

Experimental results

Research questions

• RQ1 Can impacts between a secondary object and a rigidly precessing accretion disc in an EMRI system naturally reproduce the observed recurrence times and luminosities of QPEs in multiple sources?
• RQ2 How do variations in orbital inclination, eccentricity, and disc mass affect the amplitude and periodicity of simulated QPEs?
• RQ3 Why do some QPE sources exhibit longer recurrence times and lower luminosities than others, and can this be explained by differences in system parameters?
• RQ4 Is the observed lack of broad emission lines in QPE hosts consistent with the proposed impact-driven cloud emission model?
• RQ5 What fraction of EMRI systems with precessing discs would be expected to produce detectable QPEs, and how does this compare to observed source counts?

Key findings

• The model successfully reproduces the diversity of QPE properties across four sources: GSN 069, eRO-QPE1, eRO-QPE2, and RX J1301.9+2747, including varying recurrence times and luminosities.
• Only prograde EMRI orbits with mutual inclinations <15° relative to the disc plane can produce detectable QPEs, implying a detection fraction of ~2% under isotropic assumptions.
• The observed X-ray spectral evolution—temperature rising from ~50–80 eV to ~100–250 eV and back—matches the adiabatic expansion of the ejected cloud.
• The model naturally accounts for varying QPE amplitudes and recurrence times in individual sources through parameter tuning, particularly disc mass and orbital eccentricity.
• Lensing effects (time delays, microlensing) are negligible except in rare, near-perfect alignment configurations, which may cause occasional magnification of a single QPE.
• Future Bayesian inference using multi-epoch QPE data will allow precise estimation of system parameters, including black hole spin, eccentricity, and disc inclination.