Insights from the Gaussian Process Method for the Fast Radio Burst–associated X-Ray Burst of SGR 1935+2154

The Gaussian process method is employed to analyze the light curves of bursts detected by Insight-HXMT, Neutron Star Interior Composition Explorer (NICER), and Gravitational Wave High-energy Electromagnetic Counterpart All-sky Monitor from SGR 1935+2154 between 2020 and 2022. It is found that a stochastically driven damped simple harmonic oscillator (SHO) is necessary to capture the characteristics of the X-ray bursts (XRBs). A variability timescale of the XRBs, corresponding to the broken frequencies in the SHO power spectral densities (PSDs), is extracted. In particular, a high broken frequency of 35 Hz where the index of the SHO PSD changes from −4 to −2 is constrained by the HXMT-HE burst associated with fast radio burst (FRB) 200428. It is suggested that the corresponding timescale of 0.03 s could be the retarding timescale of the system driven by some energy release, and the production of the HE photon should be quasi-simultaneous with the response. The other special event is a NICER burst with a retarding timescale of 1/(39 Hz) ≈ 0.02 s. In the normal XRBs, no retarding timescale is constrained; a long relax/equilibrium timescale (corresponding to a broken frequency of 1–10 Hz, where the index of the SHO PSD changes from −4/−2 to 0 in the SHO PSD) is obtained. The results indicate that the FRB-associated HXMT-HE XRB could be produced immediately when the system is responding to the energy disturbance, far before the equilibrium state.