arXiv subjects

Dahai Yan

Publications and source records attributed to Dahai Yan.

At least 19 recordsLinked to original sources

arXiv2026

Nonstationary Stochastic Timing Signatures in the Prompt Gamma-Ray Light Curve of GRB 170817A

We investigate time-dependent stochastic structure in the weak prompt gamma-ray emission of GRB 170817A using change-point and deep-kernel Gaussian-process (GP) models. The analysis is based on the 10-300 keV Fermi/GBM light curve with 0.10 s time resolution. Two change-point configurations identify similar covariance transitions at 0.269 and 0.237 s after the gravitational-wave merger, with 10-90% transition widths of 0.441 and 0.393 s, respectively. At the representative gate-defined boundary of t_tr = 0.27 s, all four fixed-split assignments yield positive evidence gains over the full-exposure stationary Matern-3/2 reference. The largest gain is Delta ln Z_split = 5.72 +/- 0.16 for the Matern-3/2 to Matern-3/2 assignment, while the gate-matched damped random walk (DRW) to Matern-3/2 assignment gives Delta ln Z_split = 5.50 +/- 0.16. The fixed-split comparison therefore supports segment-specific covariance evolution without requiring a change of covariance family. The deep-kernel models recover localized time-deformation features peaking at 1.65 and 1.75 s after the merger for DRW and Matern-3/2 base kernels, respectively. Their offsets from the adopted gamma-ray onset at 1.74 s are -0.09 and +0.01 s, both within the 0.10 s sampling resolution. The full-band timing features remain stable when the bin width is changed from 0.10 to 0.12 s, whereas energy subdivision produces larger shifts in gate locations than in warp peaks. Residual diagnostics show that the models reproduce the dominant temporal structure, although localized residual dependence remains. We interpret the gate-defined covariance transition and the localized time-deformation feature as model-dependent phenomenological timing diagnostics. Further simulation calibration and count-level modelling are needed to assess the statistical robustness and physical origin of the recovered nonstationary structure.

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arXiv2026

Jet Power, Bulk Lorentz Factor, Black Hole Spin, and Magnetic Field of Accretion Disk in Jetted Active Galactic Nuclei: A Large Gamma-Ray Emission Sample

We present a catalog of physical parameters for powerful jet-accretion disk-black hole systems in one of the largest samples of gamma-ray emitting jetted active galactic nuclei (AGNs), including jet kinetic and radiative powers, jet radiative efficiencies, bulk Lorentz factors, black hole spins, accretion-disk magnetic fields and Compton dominance. Comparing jet kinetic power estimators for blazars, values derived from spectral energy distribution (SED) fitting tend to exceed those estimated via cavity power and other scaling relations. For radiatively efficient AGNs, most sources are inferred to possess high spins; for radiatively inefficient AGNs, many potentially have high spins, though some may differ. This indicates that black hole spin does not effectively distinguish radiatively efficient from inefficient jetted AGNs. Our results suggest accretion-disk magnetic field strength as a key discriminator, proposing a tentative dividing value of $\approx 10^{3.9}$ Gauss between radiatively efficient and inefficient populations. Jet power and bulk Lorentz factor exhibit significant correlations with black hole mass in radiatively efficient AGNs, while weak-to-moderate correlations are observed in radiatively inefficient AGNs within narrow accretion-rate bins. Our analysis reveals that jet power correlates with both disk luminosity and magnetic field strength. Furthermore, correlations linking Eddington ratio and Compton dominance with jet properties are consistent with the jet-accretion connection. Finally, jet radiative power and bulk Lorentz factor show a potential dependence on black hole spin. These results are consistent with the scenario in which jets are powered and accelerated by energy extraction from rapidly spinning black holes via accretion-disk magnetic fields.

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arXiv2026

Gaussian-process evidence for a stochastic-variability transition in the recovering corona of 1ES 1927+654

We investigate the stochastic X-ray variability of the changing-look active galactic nucleus 1ES 1927+654 during its 2018--2024 evolution, focusing on the recovery of the X-ray corona after its 2018 collapse. Using XMM-Newton EPIC-pn light curves in the 0.3--2.0 keV and 2.0--10.0 keV bands, we model the variability with Gaussian process (GP) covariance components including Mat\'ern-3/2, damped-random-walk (DRW), stochastically driven damped simple-harmonic-oscillator (SHO), and white-noise terms. Bayesian model comparison reveals an X-ray stochastic-variability transition during the changing-look recovery phase. In the 2019 May 5 observation, the preferred covariance changes from a Mat\'ern-3/2-like state to a DRW-like state within a single continuous exposure. A phenomenological gated-kernel estimate localizes this transition sharply in the hard band at $t_c\simeq23.5~{\rm ks}$, while the soft band shows the same qualitative change over a broader interval. This transition occurs after the X-ray corona had reappeared but before the later pronounced hardening and brightening of the coronal emission, suggesting an early timing-domain signature of disk--corona reconfiguration. Phenomenologically, the dominant variability evolves from a smoother, finite-memory correlated process to a rougher, shorter-memory red-noise process. In the later 2022--2024 observations, SHO-like components associated with the known millihertz QPO show increasing characteristic frequency and quality factor, indicating a faster and more coherent oscillatory component during the QPO-plus-jet phase. GP-based time-domain inference therefore provides a sensitive probe of stochastic-variability changes in recovering AGN coronae.

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arXiv2026

Gaussian Process Inference of Stochastic Magneto-Active Dynamics and Viscosity in Swift J1727.8-1613

Linking X-ray variability to the underlying magnetohydrodynamic (MHD) dynamics of black hole X-ray binaries remains challenging. We systematically investigate the stochastic and oscillatory variability of the black hole X-ray binary candidate Swift J1727.8$-$1613 during its 2023 outburst using Gaussian process (GP) regression applied to Insight-HXMT multi-band light curves. The variability is modeled with a physically motivated composite kernel comprising one stochastically driven damped simple harmonic oscillator (SHO) and two damped random walk (DRW) components. The SHO term robustly recovers quasi-periodic oscillations (QPOs) with frequencies $\nu_0 \sim 0.07$--$5$ Hz, consistent with the fundamental Alfv\'en mode of a contracting magnetically confined disk--coronal cavity. The quality factor rises from $Q \sim 3$ to $Q \sim 10$, suggesting increasing coherence of the magnetic cavity. We also find an anti-correlation between QPO frequency and the short DRW damping timescale, supporting our proposed stochastic magneto-active dynamics scenario. Associating the short and long DRW timescales with the local turbulent turnover and thermal adjustment timescales, respectively, we infer an effective viscosity parameter of $\alpha \approx 0.1$, supporting a strongly magnetized accretion flow. Strikingly, near the onset of relativistic jet ejection around MJD 60206, both relaxation timescales collapse toward the 0.1 s sampling limit, suggesting a rapid reorganization of the disk internal energy balance immediately before jet launching. Our results establish GP inference as a powerful route to connecting X-ray timing observables with the dynamical state of black hole accretion flows.

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arXiv2025

Gaussian process analysis of type-B quasiperiodic oscillations in the black hole X-ray binary MAXI J1348-630

We analyzed Insight-HXMT data of the black hole X-ray binary MAXI J1348-630 during the type-B QPO phase of its 2019 outburst. Using the Gaussian process method, we applied an additive composite kernel model consisting of an SHO, a DRW, and an additional white noise (AWN) to data from three energy bands: LE (1-10 keV), ME (10-30 keV), and HE (30-150 keV). We find that for the DRW component, correlations on the timescale of $\tau_{\rm DRW}\sim10$ s are absent in the LE band, while they persist in the ME and HE bands over the full duration of the light curves. This energy-dependent behavior may reflect thermal instabilities, with the shorter correlation timescale in the disk compared to the corona. Alternatively, it may reflect variable Comptonizations of seed photons from different disk regions. Inner-disk photons are scattered by a small inner corona, producing soft X-rays. Outer-disk photons interact with an extended, jet-like corona, resulting in harder emission. The QPO is captured by an SHO component with a stable period of $\sim 0.2$ s and a high quality factor of $\sim 10$. The absence of significant evolution with energy or time of the SHO component suggests a connection between the accretion disk and the corona, which may be built by coherent oscillations of disk-corona driven by magnetorotational instability. The AWN components are present in all the three-band data and dominate over the DRW and SHO components. We interpret the AWN as another fast DRW with its $\tau_{\rm DRW} < 0.01$ s. It may trace high-frequency fluctuations that occur in both the inner region of the accretion disk and the corona. Overall, our work reveals a timescale hierarchy in the coupled disk-corona scenario: fast DRW < SHO < disk DRW < corona DRW.

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arXiv2025

Gaussian Process Modeling Coronal X-ray Variability of Active Galactic Nuclei

The corona is an integral component of active galactic nuclei (AGNs) which can produce the X-ray emission. However, many of its physical properties and the mechanisms powering this emission remain a mystery. In this work, we study the coronal X-ray variabilities of 13 AGNs by Gaussian Process. 2-10 keV light curves of 13 AGNs can be successfully described by the damped-random walk (DRW) model. The extracted coronal X-ray timescales range from 3 to 50 days. In the plot of variability timescale versus black hole mass, the coronal X-ray timescales of four sources occupy almost the same region as the optical timescales of the accretion disk, with the latter matching the predicted thermal instability timescale of the disk. In contrast, the X-ray timescales of the remaining sources exhibit a systematic offset toward lower values. We propose that the coronal X-ray variability may be driven by internal processes within the corona itself (such as thermal conduction). On the other hand, it may also be triggered by local thermal instabilities occurring in different regions (close to the central black hole) of the accretion disk, which propagate to the corona via disk-corona coupling.

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arXiv2025

Patterns of X-ray and $\gamma$-ray Flares: from Blazar to Maganetar and Sun

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 $\gamma$-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 (SHO) model. The derived timescales $t_{\rm B\underline{} steep}$ and $t_{\rm B\underline{~} flat}$ (corresponding to PSD breaks) are in the range of 4-7 s and 16-53 s, respectively. The FRB-associated HXMT-HE burst has a $Q$ value near 0.3, matching those of the solar flares occurred on 23 July 2002 (flare 1) and 3 November 2003 (flare 2). By contrast, blazar $\gamma$-ray giant flares show $Q >$ 0.3, similar to the solar flare occurred on 25 February 2014 (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 $\&$ 2 share comparable dynamic behavior, while blazar $\gamma$-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.

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arXiv2025

A characteristic optical variability time scale in jetted active galactic nuclei: a large gamma-ray emission sample

The variability mechanisms from jetted AGNs are still under debate. Here the damped random walk (DRW) model, implemented through Gaussian Processe (GPs), is used to fit the $ZTF$ long-term optical light curves of 1684 $\gamma$-ray emission jetted AGNs. This analysis yields one of the largest samples with characteristic optical variability timescales for jetted AGNs. A single DRW model from GPs can fit the optical light curve of most jetted AGNs well/potentially well, while there are still some jetted AGNs whose light curve can not be fitted well by a single DRW model. After the jet power, proxied by gamma-ray luminosity, is introduced as a new parameter, new relationships among intrinsic variability time scales, black hole mass and jet power are discovered for efficient accretion AGNs ($\tau^{\rm in} \propto M_{\rm BH}^{0.29^{+0.06}_{-0.06}}P_{\rm jet}^{-0.3^{+0.03}_{-0.03}}$ with scatter of approximately 0.09~dex) and for inefficient accretion AGNs ($\tau^{\rm in} \propto M_{\rm BH}^{0.06^{+0.07}_{-0.07}}P_{\rm jet}^{0.37^{+0.11}_{-0.11}}$ with scatter of approximately 0.14~dex), respectively. Our results support that the optical variability of jetted AGNs with efficient accretion may originate within the standard accretion disk at UV emitting radii similar to non-jetted AGNs, and is directly related to the acceleration of shock in the jet and then enhanced through the beaming effect in beamed AGNs. For the jetted AGNs with inefficient accretion, the intrinsic timescale is consistent with the escape timescale of electrons.

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arXiv2025

Pattern and Origin for the Extreme $\gamma$-ray Flares of 3C 454.3 and 3C 279: An Astrophysical Critical Damper?

We apply a Gaussian process method to the extreme $\gamma$-ray flares of 3C 454.3 and 3C 279 to discover the variable patterns and then to investigate the physical origins of the giant flares. The kernels of stochastically driven damped simple harmonic oscillator (SHO), the damped random-walk (DRW), and Mat$\acute{\rm e}$rn-3/2 are respectively used to describe the adaptive-binning $\gamma$-ray light curves of the two flares. Our findings show that both the extreme $\gamma$-ray flares of 3C 454.3 and 3C 279 clearly prefer the SHO kernel in the over-damped mode and the Mat$\acute{\rm e}$rn-3/2 kernel over the DRW kernel. The resulted SHO and Mat$\acute{\rm e}$rn-3/2 power spectral densities (PSDs) are the same for each object, with the index changing from -4 at high frequencies to 0 at low frequencies. The patterns of the two flares are both approaching the critical damping mode with the quality factor Q $\approx$ 0.4 (i.e., the damping ratio $\eta \approx$ 1.25), but with slightly different damping timescales. The characteristic timescale (corresponding to the broken frequency in the PSD) for 3C 454.3 is 2-3 days and 3-5 days for 3C 279. The variable patterns found here suggest that once the system responds to the energy injection disturbance, the release of the energy in the system is finished abruptly. The obtained timescale provides a constraint on the size of energy dissipation region for each source.

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arXiv2025

Detection of the cosmological evolution of the Doppler factor for blazars jets

The Doppler factor ($\delta$) is a fundamental quality for the relativistic jets from active galactic nuclei (AGNs). It is also fundamental to assessing the number of the entire population of the jetted AGN at high redshift ($z$), and therefore is important for tracing the growth of supermassive black holes (SMBHs) across cosmic time. Here we present the identification of the positive cosmic evolution of the Doppler factor in {\it Fermi}-detected bright $\gamma-$ray blazars. The redshift dependence of the Doppler factor, $\delta\propto(1+z)^{0.8}$, is measured from the observed characteristic energies in the gamma-ray spectra of 141 blazars. Moreover, the analysis of the characteristic timescales derived from modeling the long-term optical light curves of 89 blazars with Gaussian process regression gives $\delta\propto(1+z)^{1.1}$, but with a larger scatter. \textbf{Note that each index is derived from the entire sample, representing an average evolution. Interestingly, the index itself also appears to evolve, with low-luminosity sources showing stronger evolution, as indicated by a larger index.} This detection straightly suggests that relativistic jets from AGNs are much more common at high redshifts than what is previously estimated.

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arXiv2025

Evidence for Magneto-gravitational Processes in Supermassive Black Hole Binary PG 1553+113

PG1553+113 has drawn significant attention for its quasi-periodic oscillation (QPO) in gamma-ray variability, though the origin of its variability remains uncertain. In this study, we propose a physical mechanism to explain the observed gamma-ray variability within the framework of a supermassive black hole binary (SMBHB) system, supported by a newly identified component hidden in the light curve. A detailed analysis for its about 16-year light curve obtained from Fermi-LAT observations is performed by Gaussian process (GP). As anticipated, the QPO of 2.1 years is effectively captured by the stochastically-driven damped simple harmonic oscillator (SHO) kernel within the under-damped regime, and the overall stochastic nature of the variability is described by the damped random walk (DRW) kernel albeit with an unconstrained damping timescale. Additionally, our results reveal a previously unrecognized component in active galactic nuclei variability, characterized by the Mat\'ern-3/2 kernel, which is typically associated with systems undergoing abrupt energy release. These findings can be consistently interpreted within the SMBHB framework. The QPO of about 2.1 years is likely attributed to the orbital motion in a SMBHB system. The Mat\'ern-3/2 component is interpreted as resulting from magnetic reconnection events triggered by gravitational perturbations of the magnetic field within the jet, occurring as one black hole approaches the other. Meanwhile, in this case, the damping timescale of the common DRW kernel remains unconstrained due to the influence of new perturbations within the system.

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arXiv2024

Insights from the Gaussian Processes Method for the FRB-associated X-ray Burst of SGR 1935+2154

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.

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arXiv2023

Dissecting the gamma-ray emissions of the nearby galaxies NGC 1068 and NGC 253

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 $γ$-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 $γ$-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.

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arXiv2023

Gaussian Process Modeling Blazar Multiwavelength Variability: Indirectly Resolving Jet Structure

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 $γ$-ray characteristic timescales of 22 blazars. For three individuals (3C 273, PKS 1510-089, and BL Lac), the nonthermal optical, X-ray, and $γ$-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-$γ$-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 $γ$-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.

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arXiv2022

Characterizing the $γ$-Ray Variability of Active Galactic Nuclei with Stochastic Process Method

The $γ$-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 $γ$-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 $γ$-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 $γ$-ray timescale is also consistent with the thermal timescale caused by the thermal instability in the standard accretion disk of AGN.

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arXiv2022

Detection of Gamma-Rays from the Protostellar Jet in the HH 80-81 System

Considering that the existence of relativistic particles in the protostellar jet has been confirmed by the detection of linearly polarized radio emission from the HH 80-81 jet, we search for gamma-rays from the HH 80-81 system using ten-year {\it Fermi}-LAT observations. A significant point-like $γ$-ray excess is found in the direction of the HH 80-81 system with Test-Statistic (TS) value $>$100, which is likely produced in the HH 80-81 jet. The $γ$-ray spectrum extends only to 1 GeV with a photon index of 3.5. No significant variability is found in the gamma-ray emission. It is discussed that the properties of HH 80-81 jet suffice for producing the observed $γ$-rays.

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arXiv2022

The Large High Altitude Air Shower Observatory (LHAASO) Science Book (2021 Edition)

Since the science white paper of the Large High Altitude Air Shower Observatory (LHAASO) published on arXiv in 2019 [e-Print: 1905.02773 (astro-ph.HE)], LHAASO has completed the transition from a project to an operational gamma-ray astronomical observatory LHAASO is a new generation multi-component facility located in Daocheng, Sichuan province of China, at an altitude of 4410 meters. It aims at measuring with unprecedented sensitivity the spectrum, composition, and anisotropy of cosmic rays in the energy range between 10$^{12}$ and 10$^{18}$~eV, and acting simultaneously as a wide aperture (one stereoradiant) continuously operating gamma-ray telescope in the energy range between 10$^{11}$ and $10^{15}$~eV with the designed sensitivity of 1.3\% of the Crab Unit (CU) above 100 TeV. LHAASO's capability of measuring simultaneously different shower components (electrons, muons, and Cherenkov/fluorescence light), will allow it to investigate the origin, acceleration, and propagation of CR through measurement of the energy spectrum, elemental composition, and anisotropy with unprecedented resolution. The remarkable sensitivity of LHAASO will play a key role in CR physics and gamma-ray astronomy for a general and comprehensive exploration of the high energy universe and will allow important studies of fundamental physics (such as indirect dark matter search, Lorentz invariance violation, quantum gravity) and solar and heliospheric physics. The LHAASO Collaboration organized an editorial working group and finished all editorial work of this science book, to summarize the instrumental features and outline the prospects of scientific researches with the LHAASO experiment.

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arXiv2022

A spectral hardening in the Fermi-LAT Data of 1ES 0502+675

The $γ$-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 ($\sim4σ$) hardening at $\sim$ 1 GeV is found in the $γ$-ray spectrum during a moderately flaring state (MJD 55050-55350). The photon index below and above the break energy is $Γ_1=2.36\pm0.31$ and $Γ_2=1.33\pm0.11$, respectively. In the rest of the observations, the $γ$-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.

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