Letter to the Editor

Cosmic hide and seek: The volumetric rate of X-ray quasi-periodic eruptions

¹ MIT Kavli Institute for Astrophysics and Space Research, 70 Vassar Street, Cambridge, MA 02139, USA
e-mail: rarcodia@mit.edu
² Max-Planck-Institut für extraterrestrische Physik (MPE), Gießenbachstraße 1, 85748 Garching bei München, Germany
³ INAF-Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate (LC), Italy

Received: 13 December 2023
Accepted: 22 March 2024

Abstract

Multiwavelength extragalactic nuclear transients, particularly those detectable as multi-messengers, are among the primary drivers for the next-generation observatories. X-ray quasi-periodic eruptions (QPEs) are the most recent and perhaps most peculiar addition to this group. Here, we report a first estimate of the volumetric rate of QPEs based on the first four discoveries with the eROSITA X-ray telescope onboard the Spectrum Roentgen Gamma observatory. Under the assumption, supported by a suite of simulated light curves, that these four sources sample the intrinsic population somewhat homogeneously, we correct for their detection efficiency and compute a QPE abundance of R_vol = 0.60_−0.43^+4.73 × 10⁻⁶ Mpc⁻³ above an intrinsic average log L_{0.5−2.0 keV}^peak > 41.7. Since the exact lifetime of QPEs (τ_life) is currently not better defined than between a few years or few decades, we convert this to a formation rate of ℛ_vol/τ_life ≈ 0.6 × 10⁻⁷(τ_life/10 yr)⁻¹ Mpc⁻³ yr⁻¹. As a comparison, this value is a factor ∼10 τ_life times smaller than the formation rate of tidal disruption events. The origin of QPEs is still debated, although lately most models suggest that they are the electromagnetic counterpart of extreme mass ratio inspirals (EMRIs). In this scenario, the QPE rate would thus be the first ever constraint (i.e. a lower limit) to the EMRI rate from observations alone. Future discoveries of QPEs and advances in their theoretical modeling will consolidate or rule out their use for constraining the number of EMRIs detectable by the LISA mission.