A Unified Timescale Relation for Quasi-Periodic Eruptions and Repeated Nuclear Transients

Abstract: Quasi-periodic eruptions (QPEs) and recurrent nuclear transients (RNTs) exhibit recurrent high-amplitude flares from galactic nuclei, yet their characteristic timescales remain poorly understood. In this work, we compile a sample of these systems and investigate empirical scaling relations between flare timescales and black hole masses. We find that the recurrence timescale exhibits a positive but highly scattered dependence on black hole mass in the combined QPE and RNT sample, approximately following $$t_{\rm rec}\propto M_{\rm BH}<sup>{1.19<sup>{+0.52}_{-0.47}}$$ with an intrinsic scatter of 0.95 dex. Remarkably, we uncover a tight nearly linear relation between recurrence time and flare timescale for QPEs and RNTs, described by $t_{\rm rec}\propto t_{\rm rise}<sup>{1.00\pm0.07}$ with an intrinsic scatter of 0.29 dex. This relation extends across timescales from hours for QPEs to months and years for nuclear transients. We further find that QPEs and RNTs approximately follow a common empirical relation between recurrence time and flare rise time, although the physical origin of this relation remains uncertain. Our findings reveal a common phenomenological timescale link across RNTs, providing a practical framework for characterizing their temporal behavior.