2025MNRAS.543.1816Z

Quasi-periodic eruptions (QPEs) are intense repeating soft X-ray bursts with recurrence times about a few hours to a few weeks from galactic nuclei. More and more analyses show that (at least a fraction of) QPEs are the result of collisions between a stellar mass object (SMO, a stellar mass black hole or a main-sequence star) and an accretion disc around a supermassive black hole (SMBH) in galactic nuclei. Previous studies have shown the possibility of reconstructing the SMO trajectory from QPE timing data, consequently measuring the SMBH mass from tracing a single SMO. In this paper, we construct a comprehensive Bayesian framework for implementing the QPE timing method, explore the optimal QPE observation strategy for measuring SMBH masses, and forecast the measurement precision expected in the era of multitarget X-ray telescope, Chasing All Transients Constellation Hunters (CATCH). Simulations of CATCH observations of GSN 069 and eRO-QPE2 like QPEs confirm the possible applications of the QPE timing method in precise measurement of SMBH masses (and spins), especially in the lower mass end ($\lesssim 10^7 \, \mathrm{M}_\odot$) where QPEs prevail and relevant dynamical time-scales are reasonably short to be measured.