arXiv subjects

Jun-Hui Fan

Publications and source records attributed to Jun-Hui Fan.

At least 19 recordsLinked to original sources

arXiv2026

Assessing the Credibility of Gamma-Ray QPO Candidates in 41 TeV-Selected Blazars

We analyze quasi-periodic oscillation (QPO) candidates in the 0.1-100 GeV Fermi-LAT light curves of 41 TeV blazars with a conservative, multi-stage timing analysis combining FFT power spectra, red-noise Monte Carlo simulations, false-discovery-rate control, bootstrap period uncertainties, split-sample cross-validation, Lomb-Scargle and WWZ diagnostics, a detection-only sensitivity test, observingwindow checks, and injection-recovery experiments. A first-pass FFT search flags 16 sources above a raw 95% level and six strong candidates after data-quality and split-sample filtering, none satisfying a fully automated multi-method tier. Source-level significance is quantified with forward simulations that preserve the observed sampling and non-Gaussian flux distribution, treating the red-noise slope as a nuisance parameter and never assuming independence of periodogram powers. At simulation-selected reference slopes, only two of the 41 sources reach a raw source-level p < 0.05,only J1555.7+1111 reaches Benjamini-Hochberg significance, and none survives Benjamini-Yekutieli correction. No source survives the conservative slope envelope. Even J1555.7+1111, which the first-pass search flagged as significant but did not rank among its strong candidates, has a global p-value that rises to 7.5*10^-3 under the least favorable slope (~ 0.31 after the full-sample search), so it is not a robust detection. With substantial period uncertainties, a weak observing window, and limited injection-recovery sensitivity, we establish no robust gamma-ray QPO detection: a sampling-faithful red-noise treatment substantially contracts the candidate set, providing an explicit assessment of QPO credibility.

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arXiv2026

Radio-Gamma-Ray Properties and High-Energy Implications for Fermi Blazars

Radio and $\gamma$-ray emissions in blazars, a subclass of active galactic nuclei (AGNs), provide important insight into their high-energy radiation processes. We studied the relation between radio and $\gamma$-ray emissions using a large sample of 1687 \textit{Fermi} blazars, based on the Radio Fundamental Catalogue and the latest Third Data Release of the Fourth \textit{Fermi} AGN Catalogue. A clear correlation between radio and $\gamma$-ray fluxes for both BL Lacertae objects (BL Lacs) and flat-spectrum radio quasars (FSRQs) suggests a synchrotron self-Compton (SSC) contribution to both subclasses. The ratio of $\gamma$-ray and radio emissions, $\gamma$-ray loudness ($G_{\rm r}$), is further examined with the $\gamma$-ray photon index ($\Gamma_\gamma$) and the synchrotron peak frequency ($\nu_{\rm{peak}}$). An anti-correlation between $G_{\rm r}$ and $\Gamma_\gamma$ is explained by the shift of the spectral energy distribution rather than the Compton cooling effect. We found that $G_{\rm r}$ shows a positive dependence on $\nu_{\rm{peak}}$ for low-synchrotron-peaked BL Lacs (LBLs) and FSRQs, in line with the SSC-contributed scenario, although additional external Compton contributions may account for the substantial scatter observed in LBLs and FSRQs. In contrast, high-synchrotron-peaked BL Lacs (HBLs) reach the plateau of $G_{\rm r}$ between $\log (\nu_{\rm peak}/{\rm Hz}) \simeq15.5-16$, possibly indicating the transition from the Thomson to the Klein--Nishina (KN) regime. Interpreting this feature within a one-zone SSC framework could constrain the magnetic field strength of $-4.14 < \log (B/{\rm G}) < -1.69$ for those HBLs affected by the KN suppression.

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arXiv2026

Gamma-ray bursts reveal the history and faint contributors of cosmic reionization

Star-forming galaxies are generally believed to be the main drivers of cosmic reionization. However, the relative contributions of bright and faint galaxies to this process remain unclear. As the most luminous transient phenomena in the universe, long gamma-ray bursts (LGRBs) provide a unique opportunity to probe star formation occurring in both detectable and undetectable galaxies. In this Letter, we present new estimates of the cosmic star formation rate density (SFRD) at $4<z<10$ using Swift LGRBs detected over the past two decades, by considering LGRBs as unbiased tracers of total star formation at high redshifts. Crucially, we find that the new LGRB-inferred SFRD can naturally explain current measurements of hydrogen reionization without invoking extreme ionizing photon production efficiencies or escape fractions from galaxies. Using these LGRB-inferred SFRD values, we further investigate the faintest magnitude limits of high-redshift galaxies, finding a redshift evolution of the limiting magnitudes from $M_{\mathrm{lim}}\sim-14$ to $-15$ at $z\sim6$ to $M_{\mathrm{lim}}\sim-10$ to $-11$ at $z\sim10$. This result provides one independent piece of evidence for the presence of a large population of faint galaxies at redshifts $z\gtrsim6$, as an important complement to our understanding of the ionizing photon budget in the early universe.

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arXiv2026

Linking {\it Fermi} blazars and radio galaxies through accretion and jet radiation mechanisms

Based on the classical unification, blazars, namely BL Lacertae objects (BL Lacs) and flat-spectrum radio quasars (FSRQs), are believed to correspond with radio galaxies when observed at small jet viewing angles. In this paper, we aim to compile a sample of Fermi blazars and radio galaxies to provide new insights towards a unified accretion and ejection scenario between aligned and misaligned radio-loud active galactic nuclei (AGNs), by considering their optical emission-line classifications (low- and high-excitation radio galaxies, LERGs, HERGs), which are more representative of their accretion states. We adopted statistical analyses of accretion properties and high-energy beaming patterns for both Fermi blazars and radio galaxies to investigate a unified accretion-ejection scenario. In the gamma-ray luminosity-photon index plane, HERGs populate the region of higher luminosities and softer photon indices, akin to FSRQs, whereas LERGs fill lower luminosities with harder photon indices, analogous to BL Lacs. This parallel segregation indicates that LERGs and HERGs represent the misaligned counterparts of BL Lacs and FSRQs, respectively. The unified picture is further supported by the Compton dominance-photon index diagram, where FSRQs and HERGs dominated by external Compton (EC) emissions are distinctly separated from BL Lacs and LERGs governed by synchrotron self-Compton (SSC) emissions. Similarly, the diagram of accretion rate versus gamma-ray photon index reveals two distinct accretion-ejection states: a low-accretion-rate branch (BL Lacs and LERGs) is associated with the SSC model, and a high-accretion-rate branch (FSRQs and HERGs) is linked to the EC model. These results strongly strengthen the idea of a unified accretion and ejection paradigm between blazars and radio galaxies into two distinct states.

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arXiv2025

The Accretion Properties and Jet Mechanisms for the Low-Excitation Radio Galaxies

Radio galaxies (RGs) are a subclass of active galactic nuclei, which are suggested to be the parent populations of blazars. According to the accretion-ejection paragram, RGs can be classified into low-excitation or high-excitation radio galaxies (LERGs or HERGs). In this paper, we compiled a distance-limited ($z<0.15$) sample of 431 LERGs (Fanaroff-Riley, or FR, type 0, I, and II RGs) to discuss their jet formation mechanism with the ADAF (advection-dominated accretion flow) scenario, and compare their accretion properties with Fermi BL Lacertae objects. We explored different jet mechanisms (Blandford-Znajek [BZ] model and a mixture of the BZ and Blandford-Payne, hybrid, model) within the framework of ADAF-type disc around a Kerr black hole for both LERGs and Fermi BL Lacs. Based on standard assumptions on the accretion-ejection coupling in RGs, the maximum kinetic jet and accretion power for FR 0s, FR Is, FR IIs can be, explained by an ADAF with the pure BZ mechanism or hybrid jet mechanism. In addition, for one third of the FR IIs, to account for their higher kinetic jet power than what is simply expected by the hybrid jet mechanism, the magnetic field could play an important role as in the form of magnetization-driven outflows or stronger magnetic structures, as observed in some BL Lacs with high jet powers. Similarities between BL Lacs and LERGs (e.g., accretion-ejection and clustering properties) suggest that high synchrotron peaked BL Lacs could be the beamed counterparts of FR 0s, and a potential general unification between LERGs and BL Lacs populations is discussed. However, a complete sample of BL Lacs is needed to robustly compare the jet and accretion properties with those of LERGs in the future.

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arXiv2024

Ultrahigh-Energy Gamma-ray Emission Associated with Black Hole-Jet Systems

Black holes (BH), one of the most intriguing objects in the universe, can manifest themselves through electromagnetic radiation initiated by the accretion flow. Some stellar-mass BHs drive relativistic jets when accreting matter from their companion stars, forming microquasars. Non-thermal emission from the radio to tera-electronvolt (TeV) gamma-ray band has been observed from microquasars, indicating the acceleration of relativistic particles. Here we report detection of four microquasars (SS 433, V4641 Sgr, GRS 1915+105, MAXI J1820+070) of spectrum extending to the ultrahigh-energy (UHE; photon energy $E>100$ TeV) band and one microquasar (Cygnus X-1) of spectrum approaching 100 TeV, using the Large High Altitude Air Shower Observatory (LHAASO). Notably, the total emission associated with SS 433 cannot be interpreted with a single leptonic component. In the UHE band, its emission is in spatial coincidence with a giant atomic cloud, which is consistent with a hadronic origin. An elongated source is discovered from V4641 Sgr with the spectrum continuing up to 800 TeV. The detection of UHE gamma rays demonstrates that accreting BHs and their environments can operate as extremely efficient accelerators of particles out of 1 peta-electronvolt (PeV), suggesting microquasars to be important contributors to Galactic cosmic rays especially around the `knee' region.

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arXiv2024

Spectral fittings of warm coronal radiation with high seed photon temperature: apparent low-temperature and flat soft excess in AGNs

A warm corona has been widely proposed to explain the soft X-ray excess (SE) above the 2--10 keV power law extrapolation in AGNs. In actual spectral fittings, the warm coronal seed photon temperature ($T_{\rm s}$) is usually assumed to be far away from the soft X-ray, but $kT_{\rm s}$ can reach close to 0.1 keV in standard accretion disc model. In this study, we used Monte Carlo simulations to obtain radiation spectra from a slab-like warm corona and fitted the spectra using the spherical-geometry-based routine \textsc{thcomp} or a thermal component. Our findings reveal that high $T_{\rm s}$ can influence the fitting results. A moderately high $kT_{\rm s}$ (around 0.03 keV) can result in an apparent low-temperature and flat SE, while an extremely high $kT_{\rm s}$ (around 0.07 keV) can even produce an unobserved blackbody-like SE. Our conclusions indicate that, for spectral fittings of the warm coronal radiation (SE in AGNs), $kT_{\rm s}$ should be treated as a free parameter with an upper limit, and an accurate coronal geometry is necessary when $kT_{\rm s}>0.01$ keV.

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arXiv2024

Understanding the phenomenological and intrinsic blazar sequence using a simple scaling model

The blazar sequence, including negative correlations between radiative luminosity $L_{\rm rad}$ and synchrotron peak frequency $\nu$, and between Compton dominance $Y$ and $\nu$, is widely adopted as a phenomenological description of spectral energy distributions (SEDs) of blazars, although its underlying cause is hotly debated. In particular, these correlations turn positive after correcting Doppler boosting effect. In this work, we revisit the phenomenological and intrinsic blazar sequence with three samples, which are historical sample (SEDs are built with historical data), quasi-simultaneous sample (SEDs are built with quasi-simultaneous data) and Doppler factor corrected sample (a sample with available Doppler factors), selected from literature. We find that phenomenological blazar sequence holds in historical sample, but does not exist in quasi-simultaneous sample, and intrinsic correlation between $L_{\rm rad}$ and $\nu$ becomes positive in Doppler factor corrected sample. We also analyze if the blazar sequence still exists in subclasses of blazars, i.e., flat-spectrum radio quasars and BL Lacertae objects, with different values of $Y$. To interpret these correlations, we apply a simple scaling model, in which physical parameters of the dissipation region are connected to the location of the dissipation region. We find that the model generated results are highly sensitive to the chosen ranges and distributions of physical parameters. Therefore, we suggest that even though the simple scaling model can reproduce the blazar sequence under specific conditions that have been fine-tuned, such results may not have universal applicability. Further consideration of a more realistic emission model is expected.

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arXiv2023

The beaming effect for Fermi-LAT-detected FR-I radio galaxies

Our knowledge of Giga-electron volt (GeV) radio galaxies has been revolutionized by the Fermi-LAT Telescope, which provides an excellent opportunity to study the physical properties of GeV radio galaxies. According to the radio power and morphology, radio galaxies can be separated into Fanaroff-Riley Type I radio galaxies (FR-Is) and Type II radio galaxies (FR-IIs). In this paper, we consider the unification of FR-Is and BL Lacertae objects (BL Lacs), and assume FR-Is to be a standard candle to discuss the beaming effect for Fermi-LAT-detected FR-Is. Our main conclusions are as follows: (1) The estimated Doppler factors for 30 Fermi-LAT-detected FR-Is are in a range of $\delta_{\rm{I}}=0.88-7.49$. The average Doppler factor ($<\delta_{\rm{I}}>=2.56\pm0.30$) of the 30 FR-Is is smaller than that ($<\delta_{\rm{BL}}>=10.28\pm2.03$) of the 126 Fermi-LAT-detected BL Lacs, supporting the unification model that FR-Is are regarded as the misaligned BL Lacs with smaller Doppler factors; (2) We propose that different regions of FR-Is in the plot of the $\gamma$-ray luminosity against the photon spectral index $(\log L_{\gamma}-\alpha_{\rm{ph}})$ may indicate the different beaming effects; (3) The average Doppler factor of the 6 TeV FR-Is is similar to that of the 24 non-TeV FR-Is, which implies that the difference between the TeV and GeV emissions is not driven by the beaming effect in the Fermi-LAT-detected FR-I samples.

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arXiv2022

The Classification of Blazars Candidates of Uncertain Types

In this work, the support vector machine (SVM) method is adopted to separate BL Lacertae objects (BL Lacs) and flat spectrum radio quasars (FSRQs) in the plots of photon spectrum index against the photon flux, $\alpha_{\rm ph} \sim {\rm log}\,F$, that of photon spectrum index against the variability index, $\alpha_{\rm ph} \sim {\rm log}\, \textit{V\!I}$, and that of variability index against the photon flux, ${\rm log}\,{V\!I} \sim {\rm log}\,F$. Then we used the dividing lines to tell BL Lacs from FSRQs in the blazars candidates of uncertain types from \textit{Fermi}/LAT catalogue. Our main conclusions are: 1. We separate BL Lacs and FSRQs by $\alpha_{\rm ph} = -0.123\,{\rm log}\,F + 1.170$ in the $\alpha_{\rm ph} \sim {\rm log}\,F$ plot, $\alpha_{\rm ph} = -0.161\,{\rm log}\,{V\!I} + 2.594$ in the $\alpha_{\rm ph} \sim {\rm log}\,{V\!I}$ plot, and ${\rm log}\,{V\!I} = 0.792\,{\rm log}\,F + 9.203$ in the ${\rm log}\,{V\!I} \sim {\rm log}\,F$ plot. 2. We obtained 932 BL Lac candidates and possible BL Lac candidates, and 585 FSRQ candidates and possible FSRQ candidates. 3. Some discussions are given for comparisons with those in literature.

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arXiv2021

Unification of BL Lac objects, FR I and FR II(G) radio galaxies and Doppler factor Estimation for BL Lac Objects

In this work, we collected a sample of BL Lacs, FR I and FR II(G) radio galaxies with available core and extended emissions from published works to discuss the unified schemes and estimate the Doppler factor for BL Lacs. Wilcoxon rank-sum test and Kolmogorov-Smirnov test both suggest that the probabilities for the distribution of the extended luminosity of BL Lacs and that of FR I and FR II(G) radio galaxies to be from the same parent distribution are $p_{\rm{WRS}}=0.779$ and $p_{\rm{K-S}}=0.326$, suggesting they are unified. Based on this unified schemes, we propose to estimate the Doppler factors for BL Lacs. Comparing the Doppler factor estimated by the fitting/regression method with those for the common sources in the literatures, we found a good linear correlation for common sources.

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arXiv2020

Revisiting the Relationship between the Long GRB Rate and Cosmic Star Formation History Based on a Large Swift Sample

The exact relationship between the long gamma-ray burst (LGRB) rate and the cosmic star formation rate (CSFR) is essential for using LGRBs as cosmological probes. In this work, we collect a large sample composed of 371 Swift LGRBs with known redshifts and prompt emission properties. We first compare the rest-frame prompt properties of these bursts in different redshift bins, finding negligible redshift evolution of the luminosity of LGRBs with $L_{\mathrm{iso}}\gtrsim10^{51}\,\mathrm{erg\, s^{-1}}$ between $z\sim1$ and $z\sim4$. Then, by utilizing the CSFR obtained from the large-scale cosmological hydrodynamical simulation, the Illustris simulation, we calculate the cumulative redshift distribution of LGRBs under different metallicity thresholds. After comparing with our sample, we find that the predictions with a moderate threshold between $0.3\,Z_{\odot}\leqslant Z_{\mathrm{th}}\leqslant1.0\,Z_{\odot}$ are consistent with the sample between redshift $0<z<3$, while at higher redshifts between $3<z<5$, all metallicity thresholds fit the data well. When changing to an empirical model based on observations, the predictions show similar results as well. After comparing with the metallicity distribution of the observed LGRB host galaxies between $0<z<1$, we confirm that the production of LGRBs in galaxies with super-solar metallicity is suppressed. Nevertheless, considering that a significant fraction of stars are born in sub-solar metallicity environments at $z\gtrsim3$, we suggest that, as a first approximation, LGRBs can be used as direct tracers of the CSFR in this redshift range.

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arXiv2019

Evaluating the classification of Fermi BCUs from the 4FGL Catalog Using Machine Learning

The recently published fourth Fermi Large Area Telescope source catalog (4FGL) reports 5065 gamma-ray sources in terms of direct observational gamma-ray properties. Among the sources, the largest population is the Active Galactic Nuclei (AGN), which consists of 3137 blazars, 42 radio galaxies, and 28 other AGNs. The blazar sample comprises 694 flat-spectrum radio quasars (FSRQs), 1131 BL Lac-type objects (BL Lacs), and 1312 blazar candidates of an unknown type (BCUs). The classification of blazars is difficult using optical spectroscopy given the limited knowledge with respect to their intrinsic properties, and the limited availability of astronomical observations. To overcome these challenges, machine learning algorithms are being investigated as alternative approaches. Using the 4FGL catalog, a sample of 3137 Fermi blazars with 23 parameters is systematically selected. Three established supervised machine learning algorithms (random forests (RFs), support vector machines (SVMs), artificial neural networks (ANNs)) are employed to general predictive models to classify the BCUs. We analyze the results for all of the different combinations of parameters. Interestingly, a previously reported trend the use of more parameters leading to higher accuracy is not found. Considering the least number of parameters used, combinations of eight, 12 or 10 parameters in the SVM, ANN, or RF generated models achieve the highest accuracy (Accuracy $\simeq$ 91.8\%, or $\simeq$ 92.9\%). Using the combined classification results from the optimal combinations of parameters, 724 BL Lac type candidates and 332 FSRQ type candidates are predicted; however, 256 remain without a clear prediction.

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arXiv2019

The relationship between the radio core-dominance parameter and spectral index in different classes of extragalactic radio sources (III)

Active galactic nuclei (AGNs) can be divided into two major classes, namely radio-loud and radio-quiet AGNs. A small subset of the radio-loud AGNs is called blazars, which are believed to be unified with Fanaroff-Riley type I and type II (FRI&II) radio galaxies. Following our previous work, we present a latest sample of 966 sources with measured radio flux densities of the core and extended components. The sample includes 83 BL Lacs, 473 FSRQs, 101 Seyferts, 245 galaxies, 52 FRIs&IIs and 12 unidentified sources. We then calculate the radio core-dominance parameters and spectral indices and study their relationship. Our analysis shows that the core-dominance parameters and spectral indices are quite different for different types of sources. We also corroborate that the correlation between core-dominance parameter and radio spectral index extends over all the sources in a large sample presented.

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arXiv2019

Radio core dominance of Fermi-LAT selected AGNs

Aims. We present a sample of 4388 AGNs with available radio core-dominance parameters defined as the ratio of the core flux densities to extended ones, namely, R = Score/Sext., which includes 630 Fermi-detected AGNs respect to the catalog of 4FGL, the fourth Fermi Large Area Telescope source catalog, and the rest of them are non-Fermi-detected AGNs. In our sample, 584 blazars are Fermi-detected and 1310 are not, and also consists of other subclasses such as Seyfert, Fanaroff-Riley I/II and normal galaxies. We investigate various different properties between Fermi-detected AGNs and non-Fermi-detected ones by using the core-dominance parameters as the previous study has shown that R is a good indication of beaming effect. Methods. We then calculate the radio spectral indices for whole sample and adopt γ-ray photon indices for Fermi AGNs from 4FGL catalog for discussing their different performances on different subclasses, and obtain the relation between core-dominance parameters and radio spectral indices for both Fermi and non-Fermi sources according to the two components model on radio band, which are consistent with our previous study. Results. We found that the core-dominance parameters and radio spectral indices are quite different for different subclasses of AGNs, not only for Fermi sources but also non-Fermi sources, particularly, R for the former ones is averagely higher than later ones. We also adopt the same relation on core-dominance parameters and γ-ray photon indices for Fermi sources by taking the same assumption with two components model on γ-ray band, and obtain the fitting results indicating that the γ-ray emissions of Fermi blazars are mainly from the core component, which is perhaps associated with the beaming effect. Therefore, Fermi blazars are beamed.

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arXiv2018

The relationship between the radio core-dominance parameter and spectral index in different classes of extragalactic radio sources (II)

Active galactic nuclei (AGNs) can be divided into two major classes, namely radio loud and radio quiet AGNs. A small subset of the radio-loud AGNs is called blazars, which are believed to be unified with Fanaroff & Riley type I/II (FRI/II) radio galaxies. Following our previous work (Fan et al. 2011), we present a sample of 2400 sources with measured radio flux densities of the core and extended components. The sample contains 250 BL Lacs, 520 quasars, 175 Seyferts, 1178 galaxies, 153 Fanaroff & Riley type I and type II galaxies and 104 unidentified sources. We then calculate the radio core-dominance parameters and spectral indices and study their relationship. Our analysis shows that the core-dominance parameters and spectral indices are quite different for different types of sources. We also confirm that the correlation between core-dominance parameter and spectral index exists for a large sample presented in this work.

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arXiv2017

The Ratio of the Core to the Extended Emissions in the Comoving Frame for Blazars

In a two-component jet model, the emissions are the sum of the core and extended emissions: $S^{\rm ob}=S_{\rm core}^{\rm ob}+S_{\rm ext}^{\rm ob}$, with the core emissions, $S_{\rm core}^{\rm ob}= f S_{\rm ext}^{\rm ob}δ^{q}$, being a function of the Doppler factor, $δ$, the extended emission, $S_{\rm ext}^{\rm ob}$, jet type dependent factor, $q$, and the ratio of the core to the extended emissions in the comoving frame, $f$. The $f$ is an unobservable but important parameter. Following our previous work, we collect 65 blazars with available Doppler factor, $δ$, superluminal velocity, $β_{app}$, and core-dominance parameter, $R$, calculate the ratio, $f$, and peform statistical analyses. We find that the ratio, $f$, in BL Lacs is on average larger than that in FSRQs. We suggest that the difference of the ratio $f$ between FSRQs and BL Lacs is one of the possible reasons that cause the difference of other observed properties between them. We also find some significant correlations between $\log f$ and other parameters, including intrinsic (de-beamed) peak frequency, $\log ν_{\rm p}^{\rm in}$, intrinsic polarization, $\log P^{\rm in}$, and core-dominance parameter, $\log R$, for the whole sample. In addition, we show that the ratio, $f$, can be estimated by $R$.

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arXiv2008

Simultaneous multi-wavelength observations of the TeV Blazar Mrk 421 during February - March 2003: X-ray and NIR correlated variability

In the present paper, we have reported the result of simultaneous multi-wavelength observations of the TeV blazar Mrk 421 during February $-$ March 2003. In this period, we have observed Mrk 421 using Pachmarhi Array of Čerenkov Telescopes (PACT) of Tata Institute of Fundamental Research at Pachmarhi, India. Other simultaneous data were taken from the published literature and public data archives. We have analyzed the high quality X-ray (2-20 keV) observations from the NASA Rossi X-Ray Timing Explorer (RXTE). We have seen a possible correlated variability between X-ray and J band (1.25 $μ$) near infrared (NIR) wavelength. This is the first case of X-ray and NIR correlated variability in Mrk 421 or any high energy peaked (HBL) blazar. The correlated variability reported here is indicating a similar origin for NIR and X-ray emission. The emission is not affected much by the environment of the surrounding medium around the central engine of the Mrk 421. The observations are consistent with the shock-in-jet model for the emission of radiations.

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