The universal "heartbeat" oscillations in black hole systems accross the mass-scale

The hyperluminous X-ray source (HLX-1, the peak X-ray luminosity $\sim 10^{42}\rm erg\ s^{-1}$) near the spiral galaxy ESO 243-49 is possibly the best candidate for intermediate mass black hole (IMBH), which underwent recurrent outbursts with a period of $\sim 400$ days. The physical reason for this quasi-periodic variability is still unclear. We explore the possibility of radiation-pressure instability in accretion disk by modeling the light curve of HLX-1, and find that it can roughly reproduce the duration, period and amplitude of the recurrent outbursts HLX-1 with an IMBH of ~10^5Msun. Our result provides a possible mechanism to explain the recurrent outbursts in HLX-1. We further find a universal correlation between the outburst duration and the bolometric luminosity for the BH sources with a very broad mass range (e.g., X-ray binaries, XRBs, HLX-1 and active galactic nuclei, AGNs), which is roughly consistent with the prediction of radiation-pressure instability of the accretion disk. These results imply that "heartbeat" oscillations triggered by radiation-pressure instability may appears in different-scale BH systems.