Disk Instability Model for Quasi-Periodic Eruptions: Investigating Period Dispersion and Peak Temperature

Quasi-periodic eruptions (QPEs) are a class of X-ray repeating burst phenomena discovered in recent years. Many models have been proposed to study this phenomenon, there remains significant debate regarding the physical origin of QPEs. In our previous work, we developed a disk instability model with a large-scale magnetic field and successfully reproduced the light curves and spectral characteristics of several QPE sources. We further investigate the model in this work, aiming to explain two key observational features: the dispersion in eruption periods and the peak temperatures during eruptions. The model reveals critical thresholds ($\dot{M}_{\rm crit}$, $\beta_{1,\rm crit}$) that separate systems into stable regimes with minimal period variations and unstable regimes where periods are highly sensitive to accretion rate and magnetic field parameter, while peak temperatures remain nearly constant across the parameter space. This framework successfully explains both the regular eruptions observed in sources like GSN 069 and the stochastic behavior in sources like eRO-QPE1, and simultaneously accounting for the observed temperature stability during long-term QPEs evolution.