2026ApJ...999..246Z

Using Gaussian process methods, we analyzed the light curves of three extreme solar X-ray flares observed by the RHESSI satellite. Their variability characteristics were then compared with those of HXMT-HE X-ray burst (XRB; in SGR 1935+2154) associated with fast radio burst (FRB) 200428 and blazar γ-ray giant flares to investigate the origins of these extreme flaring events. The variability patterns of the solar X-ray flares follow the stochastically driven damped simple harmonic oscillator model. The derived timescales t_Bsteep_ and t_Bflat_ (corresponding to power spectral density breaks) are in the range of 4-7 and 16-53 s, respectively. The FRB-associated HXMT-HE burst has a Q value near 0.3, matching those of the solar flares that occurred on 2002 July 23 (flare 1) and 2003 November 3 (flare 2). By contrast, blazar γ-ray giant flares show Q > 0.3, similar to the solar flare that occurred on 2014 February 25 (flare 3). We proposed that the critically damped state of the system may be the condition triggering the association between the XRB in SGR 1935+2154 and the FRB. In this scenario, the critical damping Q value of the system is around 0.3, not the theoretical 0.5. The similarity in Q values might imply that the FRB-associated HXMT-HE XRB and solar X-ray flares 1 and 2 share comparable dynamic behavior, while blazar γ-ray flares and solar X-ray flare 3 exhibit another distinct but similar dynamic behavior. Like solar X-ray flares, these extreme flares may all be related to the magnetic reconnection process.