Two-body relaxation in the EMRI-TDE disk model for quasi-periodic eruptions
- 1Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca
- 2INFN, Sezione di Milano-Bicocca
- 3INAF – Osservatorio Astronomico di Brera
Abstract
Quasi-periodic eruptions (QPEs) are luminous bursts of soft X-rays that were recently discovered in galactic nuclei. They repeat on timescales of hours to weeks and are superimposed on an otherwise stable quiescent X-ray level, consistent with emission from a radiatively efficient accretion flow around relatively low-mass massive black holes (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 a stellar black hole (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 common to 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. For this purpose, we combined the rates of TDEs and extreme mass-ratio inspirals (EMRIs) around MBHs spanning a range of masses. We employed the public code P HASE F LOW to simulate seven systems with MBH masses between 10 ⁵ M ⊙ and 10 ⁸ M ⊙ , each surrounded by a three-component population: one composed of 1 M ⊙ stars, and two consisting of sBHs with masses of 10 M ⊙ and 40 M ⊙ . Based on the emission constraints available in the literature, we restricted our analysis to sBH EMRIs on prograde orbits with eccentricity e < 0.5 and inclination i < 20° with respect to the accretion disk. For stellar EMRIs, we instead required the star to avoid tidal disruption, which set the constraints. We find that the predicted QPE number density spans the range 10 ⁻¹² Mpc ⁻³ to 10 ⁻⁶ Mpc ⁻³ , depending on the assumed orbital period interval and on the adopted eccentricity and inclination thresholds. Stellar EMRIs can generate QPEs with number densities comparable to those inferred from current observations. In contrast, imposing the orbital constraints required for the sBH channel significantly suppresses the number of observable events, resulting in abundances approximately three orders of magnitude lower than those in the stellar case. If the eccentricity and inclination constraints are relaxed, sBH-driven QPEs become compatible with the lower bound of the observationally inferred range.
Related
- Quasi-periodic Eruptions from Recurrent Satellite Black Hole Transits through Magnetized Galactic Nucleus Accretion Disks
- A Unified Timescale Relation for Quasi-Periodic Eruptions and Repeated Nuclear Transients
- Extreme Mass Ratio Inspirals in Light of Quasi-periodic Eruptions: Milli-Hertz Gravitational Wave Background
- The Delay Time Distribution of Quasi-Periodic Eruptions
- Quasi-periodic pulsations in solar and stellar flares
BibTeX
@article{allievi2026twobody,
title = {{Two-body relaxation in the EMRI-TDE disk model for quasi-periodic eruptions}},
author = {Chiara Maria Allievi and Luca Broggi and Alberto Sesana and Matteo Bonetti},
journal = {Astronomy \& Astrophysics},
year = {2026},
month = oct,
doi = {10.1051/0004-6361/202659702},
url = {https://www.aanda.org/10.1051/0004-6361/202659702},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Two-body relaxation in the EMRI-TDE disk model for quasi-periodic eruptions
AU - Chiara Maria Allievi
AU - Luca Broggi
AU - Alberto Sesana
AU - Matteo Bonetti
PY - 2026
DA - 2026/10/26
JO - Astronomy & Astrophysics
DO - 10.1051/0004-6361/202659702
UR - https://www.aanda.org/10.1051/0004-6361/202659702
AB - Quasi-periodic eruptions (QPEs) are luminous bursts of soft X-rays that were recently discovered in galactic nuclei. They repeat on timescales of hours to weeks and are superimposed on an otherwise stable quiescent X-ray level, consistent with emission from a radiatively efficient accretion flow around relatively low-mass massive black holes (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 a stellar black hole (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 common to 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. For this purpose, we combined the rates of TDEs and extreme mass-ratio inspirals (EMRIs) around MBHs spanning a range of masses. We employed the public code P HASE F LOW to simulate seven systems with MBH masses between 10 ⁵ M ⊙ and 10 ⁸ M ⊙ , each surrounded by a three-component population: one composed of 1 M ⊙ stars, and two consisting of sBHs with masses of 10 M ⊙ and 40 M ⊙ . Based on the emission constraints available in the literature, we restricted our analysis to sBH EMRIs on prograde orbits with eccentricity e < 0.5 and inclination i < 20° with respect to the accretion disk. For stellar EMRIs, we instead required the star to avoid tidal disruption, which set the constraints. We find that the predicted QPE number density spans the range 10 ⁻¹² Mpc ⁻³ to 10 ⁻⁶ Mpc ⁻³ , depending on the assumed orbital period interval and on the adopted eccentricity and inclination thresholds. Stellar EMRIs can generate QPEs with number densities comparable to those inferred from current observations. In contrast, imposing the orbital constraints required for the sBH channel significantly suppresses the number of observable events, resulting in abundances approximately three orders of magnitude lower than those in the stellar case. If the eccentricity and inclination constraints are relaxed, sBH-driven QPEs become compatible with the lower bound of the observationally inferred range.
SN - 0004-6361
SN - 1432-0746
ER -