Cong Zhou, Zhen Pan, Ning Jiang

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 disk around a supermassive black hole (SMBH) in galactic nuclei. Previous studies have shown that the SMO trajectory can be reconstructed from QPE timing data, consequently the SMBH mass can be robustly measured from tracing a single SMO. In this Letter, 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 multi-target X-ray telescope, Chasing All Transients Constellation Hunters (CATCH). As a result, we find the QPE timing method is of great potential in precise measurement of SMBH masses (and spins), especially in the lower mass end ($\lesssim 10^7 M_\odot$) where QPEs prevail and relevant dynamical timescales are reasonably short to be measured.