Search

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

Using a time-dependent one-zone leptonic model that incorporates both shock acceleration and stochastic acceleration processes, we investigate the formation of the narrow spectral feature at $\sim3$ TeV of Mrk 501 which was observed during the X-ray and TeV flaring activity in July 2014. It is found that the broadband spectral energy distribution (SED) can be well interpreted as the synchrotron and synchrotron-self-Compton emission from the electron energy distribution (EED) that is composed by a power-law (PL) branch and a pileup branch. The PL branch produces synchrotron photons which are scattered by the electrons of the pileup branch via inverse-Compton scattering and form the narrow spectral feature observed at the TeV energies. The EED is produced by two injection episodes, and the pileup branch in EED is caused by shock acceleration rather than stochastic acceleration., Comment: 9 pages, 6 figures, 1 table, accepted for publication in MNRAS

Long-term gamma-ray variability of a non-blazar Active Galactic Nucleus (AGN) PKS 0521-36 is investigated by using Fermi-LAT pass 8 data covering from 2008 August to 2021 March. The results show that the histogram of the gamma-ray fluxes follows a log-normal distribution. Interestingly, in the analysis of about 5.8-year (from MJD 56317 to 58447) LAT data between two outbursts (occurring during 2012 October and 2019 May respectively), a quasi-periodic oscillation (QPO) with a period of about 1.1 years (about 5 sigma of significance) is found in the Lomb-Scargle Periodogram (LSP), the Weighted Wavelet Z-transform (WWZ) and the REDFIT results. This quasi-periodic signal also appears in the results of Gaussian process modeling the light curve. Therefore, the robustness of the QPO is examined by four different methods. This is the first gamma-ray QPO found in a mildly beamed jet. Our results imply that the gamma-ray outbursts play an important role in the formation of the gamma-ray QPO.

Blazar variability may be driven by stochastic processes. On the other hand, quasi-periodic oscillation (QPO) behaviors are recently reported to be detected in $\it{Fermi}$-LAT data of blazars. However, the significances of these QPO signals given by traditional Fourier-like methods are still questioned. We analyze $\gamma$-ray light curves of the QPO blazars with two Gaussian process methods, CARMA and $\it{celerite}$, to examine the appropriateness of Gaussian processes for characterizing $\gamma$-ray light curves of blazars and the existence of the reported QPOs. We collect a sample of 27 blazars with possible $\gamma$-ray periodicity and generate their $\sim11$ years $\it{Fermi}$-LAT light curves. We apply the Gaussian process models to the $\gamma$-ray light curves, and build their intrinsic power spectral densities (PSDs). The results show that in general the $\gamma$-ray light curves can be characterized by CARMA and $\textit{celerite}$ models, indicating that $\gamma$-ray variabilities of blazars are essentially Gaussian processes. The resulting PSDs are generally the red noise shapes with slopes between $-0.6$ and $-1.7$. Possible evidence for the $\gamma$-ray QPOs in PKS 0537$-$441 and PG 1553$+$113 are found in the Gaussian process modelings., Comment: 21 pages, 9 figures, 3 tables. Accepted for publication in ApJ

We continuously monitored the blazar S5 0716+714 in the optical $g$, $r$ and $i$ bands from Nov. 10, 2017 to Jun. 06, 2019. The total number of observations is 201 nights including 26973 data points. This is a very large quasi-simultaneous multicolor sample for the blazar. The average time spans and time resolutions are 3.4 hours and 2.9 minutes per night, respectively. During the period of observations, the target source in the $r$ band brightens from $14^{\rm m}.16$ to $12^{\rm m}.29$ together with five prominent sub-flares, and then first becomes fainter to $14^{\rm m}.76$ and again brightens to $12^{\rm m}.94$ with seven prominent sub-flares. For the long-term variations, we find a strong flatter when brighter (FWB) trend at a low flux state and then a weak FWB trend at a higher flux state. A weak FWB trend at a low flux state and then a strong FWB trend at a higher flux state are also reported. Most of sub-flares show the strong FWB trends, except for two flares with a weak FWB trend. The particle acceleration and cooling mechanisms together with the superposition of different FWB-slopes from sub-flares are likely to explain the optical color behaviours. A scenario of bent jet is discussed., Comment: 27 pages, 9 figures, 4 tables, accepted for publication in ApJS

We perform a systematic search of quasi-periodic variabilities in $\gamma$-ray active galactic nuclei (AGNs) in the third \emph{Fermi} Large Area Telescope source catalog (3FGL). We employe two techniques, Lomb-Scargle Periodogram (LSP) and Weighted Wavelet Z-transform (WWZ), to obtain power spectra of $\gamma$-ray light curves covering from 2008 August to 2016 December. The results show that besides several objects that have been reported in previous works, an additional source, the FSRQ PKS 0601-70 has a possible quasi-periodic variability of 450 days in its $\gamma$-ray light curves with the significance of $>3\sigma$. The physical implications of our findings are discussed., Comment: 7 pages, 4 figures. Accepted for publication in ApJ

The acceleration of electrons in 3C 279 is investigated through analyzing the injected electron energy distribution (EED) in a time-dependent synchrotron self-Compton + external Compton emission model. In this model, it is assumed that relativistic electrons are continuously injected into the emission region, and the injected EED [$Q_e^\prime(\gamma^\prime)$] follows a single power-law form with low- and high-energy cutoffs $\rm \gamma_{min}'$ and $\rm \gamma_{max}'$, respectively, and the spectral index $n$, i.e, $Q_e^\prime(\gamma^\prime)\propto\gamma^{\prime-n}$. This model is applied to 14 quasi-simultaneous spectral energy distributions (SEDs) of 3C 279. The Markov Chain Monte Carlo fitting technique is performed to obtain the best-fitting parameters and the uncertainties on the parameters. The results show that the injected EED is well constrained in each state. The value of $n$ is in the range of 2.5 to 3.8, which is larger than that expected by the classic non-relativistic shock acceleration. However, the large value of $n$ can be explained by the relativistic oblique shock acceleration. The flaring activity seems to be related to an increased acceleration efficiency, reflected in an increased $\gamma'_{\rm min}$ and electron injection power., Comment: 18 pages, 12 figures, 3 tables, accepted for publication in MNRAS

Using a significantly enlarged \textit{Fermi}-LAT BL Lac objects (BL Lacs) sample, we construct the gamma-ray luminosity function (GLF) of BL Lacs, by the joint use of the space density distribution and source counts distribution. We use three well-studied forms of the GLF, i.e., the forms of pure density evolution (PDE), pure luminosity evolution (PLE) and luminosity-dependent density evolution (LDDE). The Markov Chain Monte Carlo (MCMC) technique is used to constrain model parameters. Our results suggest that LDDE model can give the best description for the BL Lac GLF. And the model shows that the BL Lacs with a harder GeV spectrum and a less luminosity evolve as strongly as FSRQs, and the evolution decreases as increasing luminosity. We also model the average photon spectra of BL Lacs with a double power laws model. Using this modeled spectra, BL Lacs contribute $ \sim 20\%$ of the total extragalactic gamma-ray background (EGB) at $E>100$ MeV, $\sim 100\%$ of the EGB at $E>50$ GeV, and the unresolved BL Lacs contribute $\sim 20 \%$ of the isotropic diffuse gamma-ray background (IGRB) at $E>100$ MeV. A prediction of the TeV EGB spectra are given, which may be tested by the future detectors., Comment: 9 pages, 5 figures, Accepted for publication in MNRAS

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 $\gamma$-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 $\gamma$-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 $\gamma$-rays., Comment: Research in Astronomy and Astrophysics, Volume 22, Issue 2, id.025016

The statistical properties of X-ray flares from two separate locations (nucleus and HST-1) in the M87 jet are investigated to reveal the physical origin of the flares. We analyse the archival \textit{Chandra} data for M87, and identify 14 flares in the nucleus and 9 flares in HST-1. The peak intensity ($I_{\rm{P}}$) and the flaring duration time ($T_{\rm{fl}}$) for each flare are obtained. It is found that the distributions of both $I_{\rm{P}}$ and $T_{\rm{fl}}$ for the nucleus obey a power-law form with a similar index. A similar result is also obtained for HST-1, and no significant inconsistency between the nucleus and HST-1 is found for the indices. Similar to solar X-ray flares, the power-law distributions of the flare event parameters can be well explained by a self-organized criticality (SOC) system, which are triggered by magnetic reconnection. Our results suggest that the flares from nucleus and HST-1 are possibly triggered by magnetic reconnection process. The consistent indices for the distributions of $I_{\rm{P}}$ and $T_{\rm{fl}}$ in the CORE and HST-1 indicate that the dimensions of the energy dissipation of the magnetic reconnection is identical in the two regions. A strong correlation between the flares in the two regions also suggests a similar physical origin for the flares., Comment: 10 pages, 6 figures, accepted for publication in MNRAS

The attenuation produced by extragalactic background light (EBL) in $\gamma$-ray spectra of blazars has been used to constrain the Hubble constant ($H_0$) and matter density ($\Omega_{\rm m}$) of the Universe. We propose to estimate $H_0$ and $\Omega_{\rm m}$ using the well measured $>$10 GeV extragalactic $\gamma$-ray background (EGB). This suggestion is based on the facts that the $>$10 GeV EGB is totally explained by the emissions from blazars, and an EBL-absorption cutoff occurs at $\sim$50 GeV in the EGB spectrum. We fit the $>$10 GeV EGB data with modeled EGB spectrum. This results in $H_0=64.9^{+4.6}_{-4.3}\rm \ km\ s^{-1}\ Mpc^{-1}$ and $\Omega_{\rm m}=0.31^{+0.13}_{-0.14}$. Note that the uncertainties may be underestimated due to the limit of our realization for EBL model. $H_0$ and $\Omega_{\rm m}$ are degenerate in our method. Independent determination of $\Omega_{\rm m}$ by other methods would improve the constraint on $H_0$., Comment: Accepted by ApJ

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., Comment: This document is a collaborative effort, 185 pages, 110 figures

A relativistic electron-positron pair beam can be produced in the interaction of TeV photons from a blazar with the extragalactic background light (EBL). The relativistic $e^{\pm}$ pairs would loss energy through inverse-Compton scattering (ICS) photons of cosmic microwave background (CMB) or plasma instabilities. The dominant energy-loss process is under debate. Based on the assumption that the dominant energy-loss process is ICS, the resulted cascade GeV radiation is usually used to constrain the intergalactic magnetic field (IGMF). Here, we include the energy-loss due to plasma oblique instability in the calculation of cascade gamma-ray flux, and investigate the impact of the plasma instability on the constraint of IGMF. The up-to-date GeV data and archival TeV data of the blazar 1ES 0229+200 are used. The results indicate that even if the oblique instability cooling is dominating over ICS cooling, the cascade flux could be still used to constrain the IGMF. It is found that with the ratio between the cooling rates of the oblique instability and the ICS varying from 0.1, 1 to 10, the lower limit of the IGMF putted by the cascade flux and the gamma-ray data changes from $8\times10^{-18}\ $G, $5\times10^{-18}\ $G to $10^{-18}\ $G. If the ratio between the two cooling rates is 30, the estimate of IGMF based on the cascade flux is invalid., Comment: Accepted by ApJ

The energy dissipation mechanism in blazar jet is unknown. Blazar's flares could provide insights on this problem. Here we report statistical results of XMM-Newton X-ray flares of Mrk 421. We analyze all public XMM-Newton X-ray observations for Mrk 421, and construct the light curves. Through fitting light curves, we obtain the parameters of flare-profiles, such as peak flux ($F_{\rm p}$) and flaring time duration ($T_{\rm fl}$). It is found that both the distributions of $F_{\rm p}$ and $T_{\rm fl}$ obey a power-law form, with the same index of $\alpha_{\rm F}=\alpha_{\rm T}\approx1$. The statistical properties are consistent with the predictions by a self-organized criticality (SOC) system with energy dissipation in one-dimensional space. This is similar to solar flare, but with different space dimensions of the energy dissipation domain. This suggests that X-ray flaers of Mrk 421 are possibly driven by a magnetic reconnection mechanism. Moreover, in the analysis, we find that variability on timescale of $\sim1000\ $s frequently appears. Such rapid variability indicates a magnetic field of $\geq 2.1\delta_{\rm D}^{-1/3}$ G ($\delta_{\rm D}$ is the Doppler factor) in emission region., Comment: Accepted by ApJ

The mechanism for producing gamma-ray quasi-periodic oscillation (QPO) in blazar is unknown. One possibility is the geometric model, in which without the need for intrinsic quasi-periodic variation, the relativistic Doppler factor changes periodically, resulting in observed gamma-ray QPO. We propose a method to test this geometric model. We analyze the {\it Fermi}-LAT data of PG 1553+113 spanning from 2008 August until 2018 February. According to 29 four-month average spectral energy distributions (SEDs) in the energy range of 0.1-300 GeV, we split the {\it Fermi}-LAT energy range into three bands: 0.1-1 GeV, 1-10 GeV, and 10-300 GeV. The spectrum in each energy range can be successfully fitted by a power-law. The light curves and photon indices in the three energy ranges are obtained. Then, light curves in three narrow energy ranges, i.e., 0.2-0.5 GeV, 2-5 GeV and 20- 40 GeV, are constructed, and the relative variability amplitudes in the three narrow energy ranges are calculated. A discrete-correlation analysis is performed for the light curves. Our results indicate that (i) the light curves in the different energy ranges follow the same pattern showed in the light curve above 0.1 GeV; (ii) the three groups of photon indices in the energy ranges of 0.1-1 GeV, 1-10 GeV, and 10-300 GeV keep nearly constant; (iii) the ratio between relative variability amplitudes in different narrow energy ranges are equal (within their errors) to the prediction by the Doppler effect. Our results support the scenario of the relativistic boost producing the gamma-ray QPO for PG 1553+113., Comment: Accepted by ApJ

The production site of gamma-rays in blazar jet is an unresolved problem. We present a method to locate gamma-ray emission region in the framework of one-zone emission model. From measurements of core-shift effect, the relation between the magnetic field strengths ($B'$) in the radio cores of jet and the distances ($R$) of these radio cores from central supermassive black hole (SMBH) can be inferred. Therefore once the magnetic field strength in gamma-ray emission region ($B'_{\rm diss}$) is obtained, one can use the relation of $B'$-$R$ to derive the distance ($R_{\rm diss}$) of gamma-ray emission region from SMBH. Here we evaluate the lower limit of $B'_{\rm diss}$ by using the criteria that the optical variability timescale $t_{\rm var}$ should be longer or equal to the synchrotron radiation cooling timescale of the electrons that emit optical photons. We test the method with the observations of PSK 1510-089 and BL Lacertae, and derive $R_{\rm diss}<0.15\delta_{\rm D}^{1/3}(1+A)^{2/3}\ $pc for PSK 1510-089 with $t_{\rm var}\sim$ a few hours, and $R_{\rm diss}<0.003\delta_{\rm D}^{1/3}(1+A)^{2/3}\ $pc for BL Lacertae with $t_{\rm var}\sim$ a few minutes. Here $\delta_{\rm D} $ is the Doppler factor and $A$ is the Compton dominance (i.e., the ratio of the Compton to the synchrotron peak luminosities)., Comment: 5 pages, 0 figures, accepted by ApJ

We model simultaneous or quasi-simultaneous multi-band spectral energy distributions (SEDs) for a sample of 25 blazars that have radio core-shift measurements, where a one-zone leptonic model and Markov chain Monte Carlo technique are adopted. In the SED fitting for 23 low-synchrotron-peaked (LSP) blazars, the seed photons from broad line region (BLR) and molecular torus are considered respectively in the external Compton process. We find that the SED fitting with the seed photons from the torus are better than those utilizing BLR photons, which suggests that the $\gamma$-ray emitting region may be located outside the BLR. Assuming the magnetic field strength in the $\gamma$-ray emitting region as constrained from the SED fitting follows the magnetic field distribution as derived from the radio core-shift measurements (i.e., $B(R)\simeq B_{\rm 1 pc}(R/\rm 1pc)^{-1}$, $R$ is the distance from the central engine and $B_{\rm 1 pc}$ is the magnetic field strength at 1 pc), we further calculate the location of the $\gamma$-ray emitting region, $R_{\gamma}$, for these blazars. We find that $R_{\gamma}\sim2\times10^{4}R_{\rm S}\simeq10 R_{\rm BLR}$ ($R_{\rm S}$ is the Schwarzschild radius and $R_{\rm BLR}$ is the BLR size), where $R_{\rm BLR}$ is estimated from the broad line luminosities using the empirical correlations obtained using the reverberation mapping methods., Comment: 20 pages, 10 Figures, ApJ, in press

We present a model-dependent method to estimate the redshifts of three TeV BL Lac objects (BL Lacs) through fltting their (quasi-) simultaneous multi-waveband spectral energy distributions (SEDs) by one-zone leptonic synchrotron self-Compton (SSC) model. Considering the impact of electron energy distributions (EEDs) on the results, we use three types of EEDs, such as the power-law EED with exponential cut-ofi (PLC), the log-parabola (PLLP) and the broken power-law (BPL) EEDs, to flt the SEDs. We also use a parameter fi to describe the uncertainties of the extragalactic background light (EBL) models, as in (Abdo et al. 2010b). We then use Markov Chain Monte Carlo (MCMC) method to explore multi-dimensional parameter space and obtain the uncertainties of the model parameters based on the observational data. We apply our method to obtain the redshifts of three TeV BL Lac objects in the marginalized 68% confldence, and flnd that the PLC EED does not flt the SEDs. For 3C66A, the redshift is 0.14 - 0.31 and 0.16 - 0.32 in the BPL and PLLP EEDs; for PKS1424+240, the redshift is 0.55 - 0.68 and 0.55 - 0.67 in the BPL and PLLP EEDs; for PG1553+113, the redshift is 0.22 - 0.48 and 0.22 - 0.39 in the BPL and PLLP EEDs. We also estimate the redshift of PKS1424+240 in the high stage to be 0.46 - 0.67 in the PLLP EED, roughly consistent with that in the low stage., Comment: 11 pages, 2 figures

We search for $\gamma$-ray and optical periodic modulations in a distant flat spectrum radio quasar (FSRQ) PKS 0426-380 (the redshift $z=1.1$). Using two techniques (i.e., the maximum likelihood optimization and the exposure-weighted aperture photometry), we obtain $\gamma$-ray light curves from \emph{Fermi}-LAT Pass 8 data covering from 2008 August to 2016 December. We then analyze the light curves with the Lomb-Scargle Periodogram (LSP) and the Weighted Wavelet Z-transform (WWZ). A $\gamma$-ray quasi-periodicity with a period of 3.35 $\pm$ 0.68 years is found at the significance-level of $\simeq3.6\ \sigma$. The optical-UV flux covering from 2005 August to 2013 April provided by ASI SCIENCE DATA CENTER is also analyzed, but no significant quasi-periodicity is found. It should be pointed out that the result of the optical-UV data could be tentative because of the incomplete of the data. Further long-term multiwavelength monitoring of this FSRQ is needed to confirm its quasi-periodicity., Comment: 6 pages, 7 figures; accepted for publication in ApJ

We examine the gamma-ray quasi-periodic variability of PKS 2155-304 with the latest publicly available \emph{Fermi}-LAT Pass 8 data which covers the years from 2008 August to 2016 October. We produce the light curves in two ways, i.e., the exposure-weighted aperture photometry and the maximum likelihood optimization. The light curves are then analyzed by using Lomb-Scargle Periodogram (LSP) and Weighted Wavelet Z-transform (WWZ); and the results reveal a significant quasi-periodicity with a period of $1.74\pm0.13$ years and a significance of $\sim$ 4.9 $\sigma$. The constraint of multifrequencies quasi-periodic variabilities on blazar emission model is discussed., Comment: 7 pages, 5 figures; Accepted by ApJ

We test one-zone synchrotron self-Compton (SSC) models with high-quality multiwavelength spectral energy distribution (SED) data of Mrk 421. We use Markov chain Monte Carlo (MCMC) technique to fit twelve day-scale SEDs of Mrk 421 with one-zone SSC models. Three types of electron energy distribution (EED), a log-parabola (LP) EED, a power-law log-parabola (PLLP) EED and a broken power-law (BPL) EED, are assumed in fits. We find that the one-zone SSC model with the PLLP EED provides successful fits to all the twelve SEDs. However, the one-zone SSC model with the LP and BPL EEDs fail to provide acceptable fits to the highest energy X-ray data or GeV data in several states. We therefore conclude that the one-zone SSC model works well in explaining the SEDs of Mrk 421, and the PLLP EED is preferred over the LP and BPL EEDs for Mrk 421 during the flare in March 2010. We derive magnetic field $B'\sim0.01$\ G, Doppler factor $\delta_{\rm D}\sim$30--50, and the curvature parameter of EED $r\sim1$--$10$ in the model with the PLLP EED. The evolutions of model parameters are explored. The physical implications of our results are discussed., Comment: Accepted by MNRAS. We find that the PLLP EED is preferred over the LP and BPL EEDs for Mrk 421 during the flare in March 2010

In external Compton scenario, we investigate the formation of the very hard electron spectrum in the fast-cooling regime, using a time-dependent emission model. It is shown that a very hard electron distribution $N'_{\rm e}(\gp)\propto\gp^{-p}$ with the spectral index $p\sim1.3$ is formed below the minimum energy of injection electron when inverse Compton scattering takes place in the Klein-Nishina regime, i.e., inverse Compton scattering of relativistic electrons on broad-line region radiation in flat spectrum radio quasars. This produces a very hard gamma-ray spectrum, and can reasonably explain the very hard \emph{Fermi}-LAT spectrum of the flat spectrum radio quasar 3C 279 during the extreme gamma-ray flare in 2013 December., Comment: Accepted by MNRAS

We study the dynamic changes of electron energy distribution (EED) through systematically analysing the quasi-simultaneous spectral energy distributions (SEDs) of the flat spectrum radio quasar 3C 279 in different states. With Markov chain Monte Carlo (MCMC) technique we model fourteen SEDs of 3C 279 using a leptonic model with a three-parameter log-parabola electron energy distribution (EED). The 14 SEDs can be satisfactorily fitted with the one-zone leptonic model. The observed $\gamma$ rays in 13 states are attributed to Compton scattering of external infrared photons from a surrounding dusty torus. The curved $\gamma$-ray spectrum observed during 2-8 April 2014 is well explained by the external Compton of dust radiation. It is found that there is a clear positive correlation between the curvature parameter $b$ of the EED and the electron peak energy $\gamma'_{\rm pk}$. No clear correlation between $b$ and the synchrotron peak frequency $\nu_{\rm s}$ is found, due to the varied product of Doppler factor and fluid magnetic field from state to state. We interpret the correlation of $b-\gamma'_{\rm pk}$ in a stochastic acceleration scenario. This positive correlation is in agreement with the prediction in the stage when the balance between acceleration and radiative cooling of the electrons is nearly established in the case of the turbulence spectral index $q=2$., Comment: Accepted by MNRAS

Precise spectra of 3C 279 in the 0.5-70 keV range, obtained during two epochs of \emph{Swift} and \emph{NuSTAR} observations, are analyzed using a near-equipartition model. We apply a one-zone leptonic model with a three-parameter log-parabola electron energy distribution (EED) to fit the \emph{Swift} and \emph{NuSTAR} X-ray data, as well as simultaneous optical and \emph{Fermi}-LAT $\gamma$-ray data. The Markov Chain Monte Carlo (MCMC) technique is used to search the high-dimensional parameter space and evaluate the uncertainties on model parameters. We show that the two spectra can be successfully fit in near-equipartition conditions, defined by the ratio of the energy density of relativistic electrons to magnetic field $\zeta_{\rm e}$ being close to unity. In both spectra, the observed X-rays are dominated by synchrotron-self Compton photons, and the observed $\gamma$ rays are dominated by Compton scattering of external infrared photons from a surrounding dusty torus. Model parameters are well constrained. From the low state to the high state, both the curvature of the log-parabola width parameter and the synchrotron peak frequency significantly increase. The derived magnetic fields in the two states are nearly identical ($\sim1$\ G), but the Doppler factor in the high state is larger than that in the low state ($\sim$28 versus $\sim$18). We derive that the gamma-ray emission site takes place outside the broad-line region, at $\gtrsim$ 0.1 pc from the black hole, but within the dusty torus. Implications for 3C 279 as a source of high-energy cosmic-rays are discussed., Comment: accepted by MNRAS

Fermi-LAT analyses show that the gamma-ray photon spectral indices Gamma_gamma of a large sample of blazars correlate with the vFv peak synchrotron frequency v_s according to the relation Gamma_gamma = d - k log v_s. The same function, with different constants d and k, also describes the relationship between Gamma_gamma and peak Compton frequency v_C. This behavior is derived analytically using an equipartition blazar model with a log-parabola description of the electron energy distribution (EED). In the Thomson regime, k = k_EC = 3b/4 for external Compton processes and k = k_SSC = 9b/16 for synchrotron self-Compton (SSC) processes, where b is the log-parabola width parameter of the EED. The BL Lac object Mrk 501 is fit with a synchrotron/SSC model given by the log-parabola EED, and is best fit away from equipartition. Corrections are made to the spectral-index diagrams for a low-energy power-law EED and departures from equipartition, as constrained by absolute jet power. Analytic expressions are compared with numerical values derived from self-Compton and external Compton scattered gamma-ray spectra from Ly alpha broad-line region and IR target photons. The Gamma_gamma vs. v_s behavior in the model depends strongly on b, with progressively and predictably weaker dependences on gamma-ray detection range, variability time, and isotropic gamma-ray luminosity. Implications for blazar unification and blazars as ultra-high energy cosmic-ray sources are presented. Arguments by Ghisellini et al. (2014) that the jet power exceeds the accretion luminosity depend on the doubtful assumption that we are viewing at the Doppler angle., Comment: 13 pages, 9 figures, accepted to ApJ; includes corrections in response to referee report, including consideration of a model with a low-energy power law

We propose a scenario for self-consistent interpretation of GeV - TeV spectrum of a distant blazar PKS 1424+240. In this scenario, ultra-high energy (UHE) protons are assumed to exist in the blazar jet and produce gamma rays through synchrotron emission emitted by relativistic protons and pair cascades (resulted from $p\gamma$ interaction); meanwhile, some of these UHE protons may escape from the jet and are injected into intergalactic space. Therefore, we assume that UHE cosmic rays (CR) originate from relativistic protons in the jet and use energy-independent escape timescale to obtain UHECR injection spectrum. Both contributions of gamma rays injected by the source and secondary gamma rays produced in interactions of UHECRs emitted by the blazar with photon background during their propagation through intergalactic space are calculated. Our results show that this scenario is able to reproduce the GeV-TeV spectrum of PKS 1424+240 self-consistently in a broad range of redshifts $0.6

We investigate the formation of TeV spectrum of a distant blazar PKS 1424+240 residing at a redshift $z\geq0.6$ in two scenarios in the frame of a lepto-hadronic jet model taking both the uncertainties of the extragalactic background light (EBL) and its redshift into account. In the first scenario, TeV emission is attributed to the synchrotron emission of pair cascades resulting from $p\gamma$ interaction; in the second scenario, TeV emission is attributed to the proton-synchrotron emission, and an internal absorption due to interaction with the photons around the jet is included. The results show that in the first scenario the 68\% upper limit of its redshift within which this scenario can explain the VERITAS TeV spectrum in 2009 well is $\sim0.75$; in the second scenario, this upper limit of the redshift becomes $\sim1.03$. However, the second scenario can be excluded because it requires an unreasonable photon field around the jet with a luminosity of $\sim10^{43}\rm \ erg\ s^{-1}$. In conclusion, the jet model can explain its TeV spectrum with a low EBL density if $0.6