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Gaussian processes method is employed to analyze the light curves of bursts detected by Insight-HXMT, NICER, and GECAM from SGR 1935+2154 between 2020 to 2022. It is found that a stochastically driven damped simple harmonic oscillator (SHO) is necessary to capture the characteristics of the X-ray bursts. Variability timescale of the X-ray bursts, corresponding to the broken frequencies in the SHO power spectral densities (PSDs), are 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 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 X-ray bursts, 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 changing from -4/-2 to 0 in the SHO PSD) is obtained. The results indicate that the FRB-associated HXMT-HE X-ray burst could be produced immediately when the system is responding to the energy disturbance, far before the equilibrium state., Comment: 13 pages,17 figures,1 table

Intrigued by recent high-energy study results for nearby galaxies with gamma-ray emission and in particular NGC~1068 that has been detected as a neutrino-emitting source by the IceCube Neutrino Observatory, we conduct detailed analysis of the $\gamma$-ray data for the galaxies NGC~1068 and NGC~253, obtained with the Large Area Telescope onboard {\it the Fermi Gamma-ray Space Telescope}. By checking for their possible spectral features and then constructing light curves in corresponding energy ranges, we identify spectral-change activity from NGC ~1068 in $\geq$2\,GeV energy range and long-term detection significance changes for NGC~253 in $\geq$5\,GeV energy range. In the former, the emission appears harder in two half-year time periods than that in the otherwise `quiescent' state. In the latter, a $\sim$2-times detection significance decrease after MJD~57023 is clearly revealed by the test-statistic maps we obtain. Considering studies carried out and models proposed for the $\gamma$-ray emissions of the two sources, we discuss the implications of our findings. We suspect that the jet (or outflow) in NGC~1068 might contribute to the \gr\ emission. The nature of the long-term detection significance change for NGC~253 is not clear, but since the part of the GeV emission may be connected to the very-high-energy (VHE) emission from the center of the galaxy, it could be further probed with VHE observations., Comment: 10 pages, 7 figures, 2 tables, revised by incorporating Referee's comments, accepted for publication in ApJ

Blazar jet structure can be indirectly resolved by analyzing the multiwavelength variability. In this work, we analyze the long-term variability of blazars in radio, optical and X-ray energies with the Gaussian process (GP) method. The multiwavelength variability can be successfully characterized by the damped-random walk (DRW) model. The nonthermal optical characteristic timescales of 38 blazars are statistically consistent with the $\gamma$-ray characteristic timescales of 22 blazars. For three individuals (3C 273, PKS 1510-089, and BL Lac), the nonthermal optical, X-ray, and $\gamma$-ray characteristic timescales are also consistent within the measured 95$\%$ errors, but the radio timescale of 3C 273 is too large to be constrained by the decade-long light curve. The synchrotron and inverse-Compton emissions have the same power spectral density, suggesting that the long-term jet variability is irrelevant to the emission mechanism. In the plot of the rest-frame timescale versus black hole mass, the optical-$\gamma$-ray timescales of the jet variability occupy almost the same space with the timescales of accretion disk emission from normal quasars, which may imply that the long-term variabilities of the jet and accretion disk are driven by the same physical process. It is suggested that the nonthermal optical-X-ray and $\gamma$-ray emissions are produced in the same region, while the radio core which can be resolved by very-long-baseline interferometry locates at a far more distant region from the black hole. Our study suggests a new methodology for comparing thermal and nonthermal emissions, which is achieved by using the standard GP method., Comment: Accepted by ApJ; 18 pages

The $\gamma$-ray astronomy in time domain has been by now progressed further as the variabilities of Active Galactic Nuclei (AGNs) on different timescales have been reported a lot. We study the $\gamma$-ray variabilities of 23 jetted AGNs through applying a stochastic process method to the ~12.7 yr long-term light curve (LC) obtained by Fermi-Large Area Telescope (Fermi-LAT). In this method, the stochastically driven damped simple harmonic oscillator (SHO) and the damped random walk (DRW) models are used to model the long-term LCs. Our results show that the long-term variabilities of 23 AGNs can be characterized well by both SHO and DRW models. However, the SHO model is restricted in the over-damped mode and the parameters are poorly constrained. The SHO power spectral densities (PSDs) are same as the typical DRW PSD. In the plot of the rest-frame timescale that corresponds to the broken frequency in the PSD versus black hole mass, the intrinsic $\gamma$-ray characteristic timescales of 23 AGNs occupy almost the same space with the optical variability timescales obtained from the accretion disk emission. This suggests a connection between the jet and the accretion disk. Same as the optical variability of AGN accretion disk, the $\gamma$-ray timescale is also consistent with the thermal timescale caused by the thermal instability in the standard accretion disk of AGN.

The $\gamma$-ray spectral feature of the blazar 1ES 0502+675 is investigated by using Fermi Large Area Telescope (Fermi-LAT) Pass 8 data (between 100 MeV and 300 GeV) covering from 2008 August to 2021 April. A significant ($\sim4\sigma$) hardening at $\sim$ 1 GeV is found in the $\gamma$-ray spectrum during a moderately flaring state (MJD 55050-55350). The photon index below and above the break energy is $\Gamma_1=2.36\pm0.31$ and $\Gamma_2=1.33\pm0.11$, respectively. In the rest of the observations, the $\gamma$-ray spectrum can be described by a power-law form with the photon index of $\approx1.6$. In the frame of a one-zone synchrotron self-Compton (SSC) model, the spectral hardening is interpreted as the transition between the synchrotron component and the SSC component. This could be the result of a slight increase of the break/maximum Lorentz factor of the electrons., Comment: Accepted by MNRAS