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Jiancheng Wang

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Published work

39 published item(s)

preprint2026arXiv

Understanding DNNs in Feature Interaction Models: A Dimensional Collapse Perspective

DNNs have gained widespread adoption in feature interaction recommendation models. However, there has been a longstanding debate on their roles. On one hand, some works claim that DNNs possess the ability to implicitly capture high-order feature interactions. Conversely, recent studies have highlighted the limitations of DNNs in effectively learning dot products, specifically second-order interactions, let alone higher-order interactions. In this paper, we present a novel perspective to understand the effectiveness of DNNs: their impact on the dimensional robustness of the representations. In particular, we conduct extensive experiments involving both parallel DNNs and stacked DNNs. Our evaluation encompasses an overall study of complete DNN on two feature interaction models, alongside a fine-grained ablation analysis of components within DNNs. Experimental results demonstrate that both parallel and stacked DNNs can effectively mitigate the dimensional collapse of embeddings. Furthermore, a gradient-based theoretical analysis, supported by empirical evidence, uncovers the underlying mechanisms of dimensional collapse.

preprint2025arXiv

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.

preprint2022arXiv

A flexible method for estimating luminosity functions via Kernel Density Estimation -- II. Generalization and Python implementation

We propose a generalization of our previous KDE (kernel density estimation) method for estimating luminosity functions (LFs). This new upgrade further extend the application scope of our KDE method, making it a very flexible approach which is suitable to deal with most of bivariate LF calculation problems. From the mathematical point of view, usually the LF calculation can be abstracted as a density estimation problem in the bounded domain of $\{Z_1<z<Z_2,~ L>f_{\mathrm{lim}}(z) \}$. We use the transformation-reflection KDE method ($\hatϕ$) to solve the problem, and introduce an approximate method ($\hatϕ_{\mathrm{1}}$) based on one-dimensional KDE to deal with the small sample size case. In practical applications, the different versions of LF estimators can be flexibly chosen according to the Kolmogorov-Smirnov test criterion. Based on 200 simulated samples, we find that for both cases of dividing or not dividing redshift bins, especially for the latter, our method performs significantly better than the traditional binning method $\hatϕ_{\mathrm{bin}}$. Moreover, with the increase of sample size $n$, our LF estimator converges to the true LF remarkably faster than $\hatϕ_{\mathrm{bin}}$. To implement our method, we have developed a public, open-source Python Toolkit, called \texttt{kdeLF}. With the support of \texttt{kdeLF}, our KDE method is expected to be a competitive alternative to existing nonparametric estimators, due to its high accuracy and excellent stability. \texttt{kdeLF} is available at \url{http://github.com/yuanzunli/kdeLF} with extensive documentation available at \url{http://kdelf.readthedocs.org/en/latest~}.

preprint2022arXiv

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.

preprint2022arXiv

The origin of UV/optical emission in the black hole low-mass X-ray binary Swift J1753.5-0127

The emission from the accreting black holes (BHs) in low-mass X-ray binaries (LMXBs) covers a broad energy band from radio to X-rays. Studying the correlations between emission in different energy bands during outbursts can provide valuable information about the accretion process. We analyse the simultaneous optical, ultraviolet (UV) and X-ray data of the BH-LMXB Swift J1753.5-0127 during its $\sim$ 12-year long outburst with the {\it Neil Gehrels Swift Observatory}. We find that the UV/optical and X-ray emission are strongly correlated during the hard states of the outburst. We fit the relation with a power-law function $F_{UV/optical} \propto F_{X}^β$ and find that the power-law index $β$ increases from $\sim$ 0.24 to $\sim$ 0.33 as the UV/optical wavelength decreases from $\sim$ 5400 Å (V) to $\sim$ 2030 Å (UVW2). We explore the possible reasons for this and suggest that in Swift J1753.5-0127 the UV/optical emission is dominated by a viscously heated accretion disc at large radii. We find that the data that deviate from the correlation correspond to the low-intensity peaks appeared in the X-ray band during the outburst, and suggest that these deviations are driven by the emission from the inner part of the accretion disc.

preprint2021arXiv

Transient phenomena from gas-erupting neutron stars

Starquakes probably occur in rapidly spinning or ultra high field neutron stars. In this article, we argue that highly compressed gas containing electron-positron pairs could evaporate and erupt from inside the neutron star when a crack forms and then heals during a starquake. Under the influence of the existing oscillation modes of the star, the crack may have sufficiently large size and long lifetime. An appropriate amount of gas can erupt into the magnetosphere with relativistic and nearly uniform velocity, producing various transient and bursting phenomena.

preprint2020arXiv

A flexible method for estimating luminosity functions via Kernel Density Estimation

We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding binning of LFs. One challenge in applying KDE to LFs is how to treat the boundary bias problem, since astronomical surveys usually obtain truncated samples predominantly due to the flux-density limits of surveys. We use two solutions, the transformation KDE method ($\hatϕ_{\mathrm{t}}$), and the transformation-reflection KDE method ($\hatϕ_{\mathrm{tr}}$) to reduce the boundary bias. We develop a new likelihood cross-validation criterion for selecting optimal bandwidths, based on which, the posterior probability distribution of bandwidth and transformation parameters for $\hatϕ_{\mathrm{t}}$ and $\hatϕ_{\mathrm{tr}}$ are derived within a Markov chain Monte Carlo (MCMC) sampling procedure. The simulation result shows that $\hatϕ_{\mathrm{t}}$ and $\hatϕ_{\mathrm{tr}}$ perform better than the traditional binned method, especially in the sparse data regime around the flux-limit of a survey or at the bright-end of the LF. To further improve the performance of our KDE methods, we develop the transformation-reflection adaptive KDE approach ($\hatϕ_{\mathrm{tra}}$). Monte Carlo simulations suggest that it has a good stability and reliability in performance, and is around an order of magnitude more accurate than using the binned method. By applying our adaptive KDE method to a quasar sample, we find that it achieves estimates comparable to the rigorous determination by a previous work, while making far fewer assumptions about the LF. The KDE method we develop has the advantages of both parametric and non-parametric methods.

preprint2020arXiv

A self-consistent leptonic-hadronic interpretation of the electromagnetic and neutrino emissions from blazar TXS 0506+056

The potential association between the blazar TXS 0506+056 and the neutrino event IceCube-170922A provides a unique opportunity to study the possible physical connection between the high-energy photons and neutrinos. We explore the correlated electromagnetic and neutrino emissions of blazar TXS 0506+056 by a self-consistent leptonic-hadronic model, taking into account particle stochastic acceleration and all relevant radiative processes self-consistently. The electromagnetic and neutrino spectra of blazar TXS 0506+056 are reproduced by the proton synchrotron and hybrid leptonic-hadronic models based on the proton-photon interactions. It is found that the hybrid leptonic-hadronic model can be used to better explain the observed X-ray and $γ$-ray spectra of blazar TXS 0506+056 than the proton synchrotron model. Moreover, the predicted neutrino spectrum of the hybrid leptonic-hadronic model is closer to the observed one compared to the proton synchrotron model. We suggest that the hybrid leptonic-hadronic model is more favored if the neutrino event IceCube-170922A is associated with the blazar TXS 0506+056.

preprint2020arXiv

Black hole magnetospheres in the Born-Infeld theory

We study the force-free electrodynamics on rotating black holes in the Born-Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realise that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the non-linear theory and the extraction rate gets the maximum in the Maxwell theory.

preprint2020arXiv

Kerr-Newman-AdS Black Hole Surrounded by Perfect Fluid Matter in Rastall Gravity

The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to $T^{μν}_{~~;μ}=λR^{,ν}$. In this work, we derive the Kerr-Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman-Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy ($ω=-2/3$) and the perfect fluid dark matter ($ω=-1/3$). Firstly, the Rastall parameter $κλ$ could be constrained by the weak energy condition and strong energy condition. Secondly, by analyzing the number of roots in the horizon equation, we get the range of the perfect fluid matter intensity $α$, which depends on the black hole mass $M$ and the Rastall parameter $κλ$. Thirdly, we study the influence of the perfect fluid dark matter and dark energy on the ergosphere. We find that the perfect fluid dark matter has significant effects on the ergosphere size, while the dark energy has smaller effects. Finally, we find that the perfect fluid matter does not change the singularity of the black hole. Furthermore, we investigate the rotation velocity in the equatorial plane for the KN-AdS black hole with dark energy and perfect fluid dark matter. We propose that the rotation curve diversity in Low Surface Brightness galaxies could be explained in the framework of the Rastall gravity when both the perfect fluid dark matter halo and the baryon disk are taken into account.

preprint2020arXiv

Searching for Quasi-Periodic Modulations in $γ$-ray Active Galactic Nuclei

We perform a systematic search of quasi-periodic variabilities in $γ$-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 $γ$-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 $γ$-ray light curves with the significance of $>3σ$. The physical implications of our findings are discussed.

preprint2020arXiv

Spectral Diversities of Gamma-ray Bursts in High Energy Bands: Hints from Turbulent Cascade

We statistically examine the gamma-ray burst (GRB) photon indices obtained by the Fermi-GBM and Fermi-LAT observations and compare the LAT GRB photon indices to the GBM GRB photon indices. We apply the jitter radiation to explain the GRB spectral diversities in the high-energy bands. In our model, the jitter radiative spectral index is determined by the spectral index of the turbulence. We classify GRBs into three classes depending on the shape of the GRB high-energy spectrum when we compare the GBM and LAT detections: the GRB spectrum is concave (GRBs turn out to be softer and are labeled as S-GRBs), the GRB spectrum is convex (GRBs turn out to be harder and are labeled as H-GRBs), and the GRBs have no strong spectral changes (labeled as N-GRBs). A universal Kolmogorov index 7/3 in the turbulent cascade is consistent with the photon index of the N-GRBs. The S-GRB spectra can be explained by the turbulent cascade due to the kinetic magnetic reconnection with the spectral index range of the turbulence from 8/3 to 3.0. The H-GRB spectra originate from the inverse turbulent cascade with the spectral index range of the turbulence from 2.0 to 3.5 that occurred during the large lengthscale magnetic reconnection. Thus, the GRB radiative spectra are diversified because the turbulent cascade modifies the turbulent energy spectrum. More observational samples are expected in the future to further identify our suggestions.

preprint2020arXiv

Studies of Extragalactic Background Light with TeV BL Lac Objects

Very high energy (VHE; $E \geq$ 100GeV) $γ-$ray from cosmological distances are attenuated by the extragalactic background light (EBL) in the IR to UV band. By contrasting measured versus intrinsic emission, the EBL photon density can be derived. However, neither the intrinsic spectra nor the EBL is separately known~-~except their combined effect. Here we first present a flexible model-dependent optical depth method to study EBL by fitting the emission spectra of TeV BL Lacs objects via a one-zone leptonic synchrotron self-Compton model (SSC). We have little information about electron energy distributions (EEDs) in the jet, which is critically important to build spectral energy distributions (SEDs) in SSC scenario. Based on the current particle acceleration models, we use two types of EEDs, i,e., a power-law log-parabola (PLLP) EED and a broken power-law (BPL) EED to fit the observed spectra. We obtain that the upper limits of EBL density are around about 30 n W m$^{-2}$ sr$^{-1}$, which are similar to the published measurement. Furthermore, we propose an unprecedented method to test radiation mechanisms involved in TeV objects by simply comparing the reduced EBL density with the limit obtained by galaxy counts, and demonstrate that for some BL Lacs, at least, the one-zone SSC model should be reconsidered.

preprint2020arXiv

The eccentricity enhancement effect of intermediate-mass-ratio-inspirals: dark matter and black hole mass

It was found that the dark matter (DM) in the intermediate-mass-ratio-inspiral (IMRI) system has a significant enhancement effect on the orbital eccentricity of the stellar massive compact object, such as a black hole (BH), which may be tested by space-based gravitational wave (GW) detectors including LISA, Taiji and Tianqin in future observations \citep{2019PhRvD.100d3013Y}. In this paper, we will study the enhancement effect of the eccentricity for an IMRI under different DM density profiles and center BH masses. Our results are as follows: $(1)$ in terms of the general DM spike distribution, the enhancement of the eccentricity is basically consistent with the power-law profile, which indicates that it is reasonable to adopt the power-law profile; $(2)$ in the presence of DM spike, the different masses of the center BH will affect the eccentricity, which provides a new way for us to detect the BH's mass; $(3)$ considering the change of the eccentricity in the presence and absence of DM spike, we find that it is possible to distinguish DM models by measuring the eccentricity at the scale of about $10^{5} GM/c^{2}$.

preprint2020arXiv

Thermodynamics and phase transition in rotational Kiselev black hole

In this work, we investigate the thermodynamic properties of rotational Kiselev black holes (KBH). Specifically, we use the first-order approximation of the event horizon (EH) to calculate thermodynamic properties for general equations of state $ω$. These thermodynamic properties include areas, entropies, horizon radii, surface gravities, surface temperatures, Komar energies and irreducible masses at the Cauchy horizon (CH) and EH. We study the products of these thermodynamic quantities, we find that these products are determined by the equation of state $ω$ and strength parameter $α$. In the case of the quintessence matter ($ω=-2/3$), radiation ($ω=1/3$) and dust ($ω=0$), we discuss their properties in detail. We also generalize the Smarr mass formula and Christodoulou-Ruffini mass formula to rotational KBH. Finally we study the phase transition and thermodynamic geometry for rotational KBH with radiation ($ω=1/3$). Through analysis, we find that this phase transition is a second order phase transition. Furthermore, we also obtain the scalar curvature in the thermodynamic geometry framework, indicating that the radiation matter may change the phase transition condition and properties for Kerr black hole.

preprint2019arXiv

Observational Constraints on the Rastall gravity from Rotation Curves of Low Surface Brightness Galaxies

The Rastall gravity is a modification of Einstein's general relativity, in which the energy-momentum conservation is not satisfied and depends on the gradient of the Ricci curvature. It is in dispute whether the Rastall gravity is equivalent to the general relativity (GR). In this work, we constrain the theory using the rotation curves of Low Surface Brightness (LSB) spiral galaxies. Through fitting the rotation curves of LSB galaxies, we obtain the parameter $β$ of the Rastall gravity. The $β$ values of LSB galaxies satisfy Weak Energy Condition (WEC) and Strong Energy Condition(SEC). Combining the $β$ values of type Ia supernovae and gravitational lensing of elliptical galaxies on the Rastall gravity, we conclude that the Rastall gravity is equivalent to the general relativity.

preprint2019arXiv

The force-free dipole magnetosphere in non-linear electrodynamics

Quantum electrodynamics (QED) effects may be included in physical processes of magnetar and pulsar magnetospheres with strong magnetic fields. Involving the quantum corrections, the Maxwell electrodynamics is modified to non-linear electrodynamics. In this work, we study the force-free magnetosphere in non-linear electrodynamics in a general framework. The pulsar equation describing a steady and axisymmetric magnetosphere is derived, which now admits solutions with corrections. We derive the first-order non-linear corrections to the near-zone dipole magnetosphere in some popular non-linear effective theories. The field lines of the corrected dipole tend to converge on the rotational axis so that the fields in the polar region are stronger compared to the pure dipole case.

preprint2016arXiv

A mixture evolution scenario of the AGN radio luminosity function

We propose a mixture evolution scenario to model the evolution of the radio luminosity function (RLF) of steep spectrum AGNs (active galactic nuclei) based on a Bayesian method. In this scenario, the shape of the RLF is determined by both the density and luminosity evolution. Our models indicate that the density evolution is positive until a redshift of $\thicksim 0.9$, at which point it becomes negative, while the luminosity evolution is positive to a higher redshift ($z \thicksim 5$ for model B and $z \thicksim 3.5$ for model C), where it becomes negative. Our mixture evolution model works well, and the modeled RLFs are in good agreement with previous determinations. The mixture evolution scenario can naturally explain the luminosity-dependent evolution of the RLFs.

preprint2016arXiv

Effect of spectral index distribution on estimating the AGN radio luminosity function

In this paper, we scrutinize the effect of spectral index distribution on estimating the AGN (active galactic nucleus) radio luminosity function (RLF) by a Monte Carlo method. We find that the traditional bivariate RLF estimators can cause bias in varying degree. The bias is especially pronounced for the flat-spectrum radio sources whose spectral index distribution is more scattered. We believe that the bias is caused because the $K$-corrections complicate the truncation boundary on the $L-z$ plane of the sample, but the traditional bivariate RLF estimators have difficulty in dealing with this boundary condition properly. We suggest that the spectral index distribution should be incorporated into the RLF analysis process to obtain a robust estimation. This drives the need for a trivariate function of the form $Φ(α,z,L)$ which we show provides an accurate basis for measuring the RLF.

preprint2015arXiv

Force-free magnetosphere on near-horizon geometry of near-extreme Kerr black holes

We study force-free magnetospheres in the Blandford-Znajek process from rapidly rotating black holes by adopting the near-horizon geometry of near-extreme Kerr black holes (near-NHEK). It is shown that the Znajek regularity condition on the horizon can be directly derived from the resulting stream equation. In terms of the condition, we split the full stream equation into two separate equations. Approximate solutions around the rotation axis are derived. They are found to be consistent with previous solutions obtained in the asymptotic region. The solutions indicate energy and angular-momentum extraction from the hole.

preprint2015arXiv

Location of gamma-ray flaring region in quasar 4C +21.35

4C +21.35 is a flat-spectrum-radio-quasar-type blazar, in which the rapid variability of very high energy (VHE, $E_γ\gtrsim 100$\,GeV) emission as short as $\sim$ 10 minutes was observed by MAGIC Cherenkov telescopes, and the VHE spectrum extends up to at least 400\,GeV. In this paper, by using a flat broad-line region (BLR) structure, we study the location and properties of $γ$-ray emitting region of 4C +21.35 under the constraints of multiwavelength data. We fit three quasi-simultaneous spectral energy distributions (SEDs) using homogeneous one-zone leptonic model, in which the flat BLR with the aperture angle of $α=25^{\circ}$ and a spherically symmetric hot dusty torus with the temperature of $T_{\rm sub}=1200$\,K, are assumed. The results show that the jet structure of 4C +21.35 is nearly conical with a half-opening angle of $θ_{\rm j}\simeq 0.29^{\circ}-0.6^{\circ}$. Furthermore, the emitting region is located within the BLR clouds and approaches to outer radius of the BLR during the flaring states, while it is well beyond the dusty torus in quiescent state. The quiescent high-energy emission is dominated by synchrotron self-Compton (SSC) process, the high-energy emission during the flaring periods is dominated by Compton scattering of BLR and dusty torus photons with the value of Compton-dominance parameter is about 30. Moreover, the fit to optical/ultraviolet data provides a further support that the central black hole (BH) mass of 4C +21.35 is $6\times 10^{8}$\,$M_{\odot}$.

preprint2014arXiv

Modeling the spectral-energy-distribution of 3C 454.3 in a "flat" broad-line-region scenario

The broad-line region (BLR) of flat-spectrum radio quasars (FSRQs) could have a "flat" geometrical structure to allow GeV gamma-ray photons escape, to produce the observed gamma-ray flares with short timescales. In this paper, we collect the quasi-simultaneous spectral energy distributions (SEDs) of the FSRQ 3C 454.3 obtained by the multi-wavelength campaigns spanning from 2007 July to 2011 January, and use a model with the "flat" structure BLR, the accretion disc and the dust torus to explain the SEDs of gamma-ray outbursts. We obtain the following results: (i) The jet is almost in equipartition between magnetic and particle energy densities during the outbursts; (ii) When the emitting region locates inside the cavity of the BLR, the covering factor $f_{\rm BLR}$ of the BLR is very small; as the emitting region goes into the BLR structure, $f_{\rm BLR}$ increases. (iii) The aperture angle $α$ describing the BLR structure is about $45^{\circ}$; (iv) The central black hole (BH) mass is about $5\times 10^{8}$\,$M_{\odot}$ rather than $4.4\times 10^{9}$\,$M_{\odot}$.

preprint2014arXiv

The hadronic origin of hard gamma-ray spectrum from blazar 1ES 1101-232

The very hard $γ$-ray spectrum from distant blazars challenges the traditional synchrotron self-Compton (SSC) model, which may indicate that there is the contribution of an additional high-energy component beyond the SSC emission. In this paper, we study the possible origin of the hard $γ$-ray spectrum from distant blazars. We develop a model to explain the hard $γ$-ray spectrum from blazar 1ES 1101-232. In the model, the optical and X-ray radiation would come from the synchrotron radiation of primary electrons and secondary pairs, the GeV emission would be produced by the SSC process, however, the hard $γ$-ray spectrum would originate from the decay of neutral pion produced through proton-photon interactions with the synchrotron radiation photons within the jet. Our model can explain the observed SED of 1ES 1101-232 well, especially the very hard $γ$-ray spectrum. However, our model requires the very large proton power to efficiently produce the $γ$-ray through proton-photon interactions.

preprint2013arXiv

A graphical analysis of the systematic error of classical binned methods in constructing luminosity functions

The classical 1/Va and PC methods of constructing binned luminosity functions (LFs) are revisited and compared by graphical analysis. Using both theoretical analysis and illustration with an example, we show why the two methods give different results for the bins which are crossed by the flux limit curves $L=L_{lim}(z)$. Based on a combined sample simulated by a Monte Carlo method, the estimate $ϕ$ of two methods are compared with the input model LFs. The two methods give identical and ideal estimate for the high luminosity points of each redshift interval. However, for the low luminosity bins of all the redshift intervals both methods give smaller estimate than the input model. We conclude that once the LF is evolving with redshift, the classical binned methods will unlikely give an ideal estimate over the total luminosity range. Page & Carrera (2000) noticed that for objects close to the flux limit $ϕ_{1/V_{a}}$ nearly always to be too small. We believe this is due to the arbitrary choosing of redshift and luminosity intervals. Because $ϕ_{1/V_{a}}$ is more sensitive to how the binning are chosen than $ϕ_{PC}$. We suggest a new binning method, which can improve the LFs produced by the 1/Va method significantly, and also improve the LFs produced by the PC methods. Our simulations show that after adopting this new binning, both the 1/Va and PC methods have comparable results.

preprint2013arXiv

A magnetic reconnection origin for the soft X-ray excess in AGN

We present a new scenario to explain the soft X-ray excess in Active Galactic Nucleus. The magnetic reconnection could happen in a thin layer on the surface of accretion disk. Electrons are accelerated by shock wave and turbulence triggered by magnetic reconnection, then they take place inverse Compton scattering above accretion disk which contributes soft X-rays. Based on standard disk model, we estimate the magnetic field strength and the energy released by magnetic reconnection along accretion disk, and find that the luminosity caused by magnetic reconnection mainly emits in the inner disk which is dominated by radiation pressure. We then apply the model to fit the spectra of AGNs with strong soft X-ray excess.

preprint2013arXiv

A New Result on the Origin of the Extragalactic Gamma-ray Background

In the paper, we continually use the method of image stacking to study the origin of the extragalactic gamma-ray background (EGB) at GeV bands, and find that the Faint Images of the Radio Sky at Twenty centimeters (FIRST) sources undetected by the Large Area Telescope on the Fermi Gamma-ray Space Telescope can contribute about (56{plus minus}6)% of the EGB. Because the FIRST is a flux limited sample of radio sources with incompleteness at the faint limit, we consider that the point-sources, including blazars, non-blazar AGNs,starburst galaxies, could produce a much larger fraction of the EGB.

preprint2013arXiv

On the location of the gamma-ray emission region for 21 flat spectrum radio quasars with quasi-simultaneous observations

We try to infer the location of the GeV emission region for 21 flat spectrum radio quasars (FSRQs) with quasi-simultaneous spectral energy distributions (SEDs), in which the SEDs of 21 FSRQs are reproduced by the one-zone leptonic model including the synchrotron-self Compton (SSC) and external Compton (EC) processes. We suggest that the X-ray emission could be produced by the SSC process and the GeV emission could come from the EC process. The EC emission could originate from the inverse Compton (IC) scattering of photons from the broad line region (BLR) and accretion disk or dust torus by the same electron population, which mainly depend on the location of the $γ$-ray emission region. We propose a method to constrain the location of the GeV emission region based on the spectral shapes. When the GeV emission is located within the BLR, the IC scattering could occur at the Klein-Nishina regime and produce a broken/steep spectrum in the GeV energy band. When the GeV emission is produced outside the BLR, the IC scattering could take place at the Thomson regime and the GeV spectrum would have the same spectral index as the optical-infrared spectrum. We infer that the location of the GeV emission region is inside the BLR for 5 FSRQs and beyond the BLR for 16 FSRQs. Our results show that the ratio of the magnetic field and electron energy density is close to equipartition condition for 21 FSRQs.

preprint2013arXiv

On the minimum mass ratio of W UMa binaries

Using Eggleton's stellar evolution code, we study the minimum mass ratio ($q_{\rm min}$) of W Ursae Majoris (W UMa) binaries that have different primary masses. It is found that the minimum mass ratio of W UMa binaries decreases with increasing mass of the primary if the primary's mass is less than about 1.3$M_{\rm \odot}$, and above this mass the ratio is roughly constant. By comparing the theoretical minimum mass ratio with the observational data, it is found that the existence of low-$q$ systems can be explained by the different structure of the primaries with different masses. This suggests that the dimensionless gyration radius ($k_1^2$) and thus the structure of the primary is very important in determining the minimum mass ratio. In addition, we investigate the mass loss during the merging process of W UMa systems and calculate the rotation velocities of the single stars formed by the merger of W UMa binaries due to tidal instability. It is found that in the case of the conservation of mass and angular momentum, the merged single stars rotate with a equatorial velocity of about $588\sim819$ km s$^{-1}$, which is much larger than their break-up velocities ($v_{\rm b}$). This suggests that the merged stars should extend to a very large radius (3.7$\sim$5.3 times the radii of the primaries) or W UMa systems would lose a large amount of mass (21$\sim$33 per cent of the total mass) during the merging process. If the effect of magnetic braking is considered, the mass loss decreases to be 12$\sim$18 per cent of their total masses. This implies that the significant angular momentum and mass might be lost from W UMa systems in the course of the merging process, and this kind of mass and angular momentum loss might be driven by the release of orbital energy of the secondaries, which is similar to common-envelope evolution.

preprint2013arXiv

Particle Acceleration And Emission Processes In Mrk 421

We investigate the X-ray and $γ$-ray flares of Mrk 421 on 2008 June 6-15 using the synchrotron self- Compton(SSC) model with electron acceleration, in which an evident correlation between the X-ray and $γ$-ray bands appears, while no significant correlation between the optical and X-ray band is observed. We argue that the emission from Mrk 421 may originate from two different components. One is the steady component from the outer region that is mainly attributed to the optical band, in which the electrons are accelerated by first-order Fermi acceleration mechanism. We use a steady electron spectrum to produce the synchrotron self-Compton emission. The other is the variable component from the inner region, in which the electrons are accelerated by the stochastic acceleration process. We use the time-dependent SSC model to produce the emission from the variable component. We suggest that the flares are due to the hardening of the electron spectrum under the process of the stochastic acceleration, which leads to the hardening of the observed spectrum in the X-ray and $γ$-ray bands. Furthermore, we find that the energy densities of electrons and magnetic fields are near equipartition in both jet regions.

preprint2013arXiv

The effect of the broad-line region with geometrical structures on gamma-ray absorption in blazars

The broad-line region (BLR) is an important component of blazars, especially for the flat spectrum radio quasars (FSRQs). The soft photons arising from the BLR will substantially affect the transparency of the gamma-ray photons produced in the relativistic jet. In the paper, we study the effect of the geometrical structure of the BLR on the absorption of gamma-rays. We find that the gamma-ray optical depth strongly depends on the geometrical structure of the BLR. For a "flat" geometry of the BLR, the gamma-ray photons with specified energies could escape transparently even their emission region locates inside the cavity of the BLR.

preprint2013arXiv

YNOGK: A new public code for calculating null geodesics in the Kerr spacetime

Following \cite{dexagol2009} we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass' and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter $p$, which is an integral value along the geodesic. This is a main difference of our code compares with previous similar ones. The advantage of this treatment is that the information about the turning points do not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles or the observer-emitter problem, etc become root finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as \cite{dexagol2009} did, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by \cite{cunnbard1973} have been extended, which allow one readily to handle the situations, in which the emitter or the observer has arbitrary distance and motion state with respect to the central compact object. The validation of the code has been extensively tested by its application to toy problems from the literature. The source FORTRAN code is freely available for download on the web.

preprint2011arXiv

On the Evolution of the Cores of Radio Sources and Their Extended Radio Emission

The work in this paper aims at determining the evolution and possible co-evolution of radio-loud active galactic nuclei (AGNs) and their cores via their radio luminosity functions (i.e., total and core RLF respectively). Using a large combined sample of 1063 radio-loud AGNs selected at low radio frequency, we investigate the radio luminosity function (RLF) at 408 MHz of steep-spectrum radio sources. Our results support a luminosity-dependent evolution. Using core flux density data of the complete sample 3CRR, we investigate the core RLF at 5.0 GHz. Based on the combined sample with incomplete core flux data, we also estimate the core RLF using a modified factor of completeness. Both results are consistent and show that the comoving number density of radio cores displays a persistent decline with redshift, implying a negative density evolution. We find that the core RLF is obviously different from the total RLF at 408 MHz band which is mainly contributed by extended lobes, implying that the cores and extended lobes could not be co-evolving at radio emission.

preprint2010arXiv

A New Method to Study the Origin of the EGB and the First Application on AT20G

In this letter, we introduce a new method of image stacking to directly study the undetected but possible gamma-ray point sources. Applying the method to the Australia Telescope 20 GHz Survey (AT20G) sources which have not been detected by LAT on Fermi, we find that the sources contribute (10.5+/-1.1)% and (4.3+/-0.9)% of the extragalactic gamma-ray background (EGB) and have a very soft spectrum with the photon indexes of 3.09+/-0.23 and 2.61+/-0.26, in the 1-3 and 3-300GeV energy ranges. In the 0.1-1GeV range, they probably contribute more large faction to the EGB, but it is not quite sure. It maybe not appropriate to assume that the undetected sources have the similar property to the detected sources.

preprint2010arXiv

Constraining Extragalactic Background Light From TeV Blazars

Our goal is to research the upper limits on the extragalactic background light (EBL). The upper limits on the extragalactic background light (EBL), using the Fermi and very high energy (VHE) spectra recently observed in TeV blazars, are presented. We use an assumption that the VHE intrinsic photon index cannot be harder than the Fermi index measured by the Fermi-LAT. Totally, these upper limits on the EBL are compatible with ones given by most of EBL models. However, the models of high EBL density are denied by TeV blazars.

preprint2010arXiv

Redshifts of distant blazar limited by Fermi and VHE $γ$-ray observations

Our goal is to limit the redshifts of three blazars PG 1553+113, 3C 66A and PKS 1424+240, through the investigation of their Fermi and VHE (very high energy) $γ$-ray observations. We assume that the intrinsic spectra of PG 1553+113, 3C 66A, and PKS 1424+240 have not any cutoff across the Fermi and VHE $γ$-ray energy ranges. The intrinsic spectra of VHE $γ$-rays are obtained through the extrapolation of Fermi spectra. Comparing the measured and intrinsic VHE spectra due to extragalactic background light (EBL) absorption, we give the redshift upper limits of three blazars assuming a specific EBL model. The redshift upper limits of PG 1553+113, 3C 66A and PKS 1424+240 are 0.78, 0.58, and 1.19 respectively. Near the TeV energy the optical depth of VHE $γ$ photons might be overestimated by Franceschini (2008) EBL model, or the second emission component might be present in the VHE spectra and lead the intrinsic photon index harder than the Fermi ones.

preprint2009arXiv

Implications of Bulk Velocity Structures in AGN Jets

The synchrotron self-Compton (SSC) models and External Compton (EC) models of AGN jets with continually longitudinal and transverse bulk velocity structures are constructed. The observed spectra show complex and interesting patterns in different velocity structures and viewing angles. These models are used to calculate the synchrotron and inverse Compton spectra of two typical BL Lac objects (BLO) (Mrk 421 and 0716+714) and one Flat Spectrum Radio Quasars (FSRQs) (3c 279), and to discuss the implications of jet bulk velocity structures in unification of the BLO and FR I radio galaxies (FRI). By calculating the synchrotron spectra and SSC spectra of BL Lac object jets with continually bulk velocity structures, we find that the spectra are much different from ones in jets with uniform velocity structure under the increase of viewing angles. The unification of BLO and FRI is less constrained by viewing angles and would be imprinted by velocity structures intrinsic to the jet themselves. By considering the jets with bulk velocity structures constrained by apparent speed, we discuss the velocity structures imprinted on the observed spectra for different viewing angles. We find that the spectra are greatly impacted by longitudinal velocity structures, becasue the volume elements are compressed or expanded. Finally, we present the EC spectra of FSRQs and FR II radio galaxies (FRII) and find that they are weakly affected by velocity structures compared to synchrotron and SSC spectra.

preprint2009arXiv

Mechanism of very high energy radiation in BL Lacertae object 3C 66A

Our goal is to understand the nature of blazars and the mechanisms for the generation of high-energy $γ$-rays, through the investigation of the blazar 3C 66A. We model the high energy spectrum of 3C 66A, which has been observed recently with the Fermi-LAT and VERITAS telescope. The spectrum has a hard change from the energy range of 0.2-100 GeV to 200-500 GeV in recent almost contemporaneous observations of two telescopes. The de-absorbed VERITAS spectrum greatly depends on the redshift, which is highly uncertain. If z=0.444 is adopted, we are able to use the SSC model to produce the Fermi-LAT component and the EC model to the VERITAS component. However, if z=0.1, the intrinsic VERITAS spectrum will be softer, there will be a smooth link between the Fermi-LAT and VERITAS spectra which can be explained using a SSC model.

preprint2009arXiv

The new model of fitting the spectral energy distributions of Mkn 421 and Mkn 501

The spectral energy distribution (SED) of TeV blazars has a double-humped shape that is usually interpreted as Synchrotron Self Compton (SSC) model. The one zone SSC model is used broadly but cannot fit the high energy tail of SED very well. It need bulk Lorentz factor which is conflict with the observation. Furthermore one zone SSC model can not explain the entire spectrum. In the paper, we propose a new model that the high energy emission is produced by the accelerated protons in the blob with a small size and high magnetic field, the low energy radiation comes from the electrons in the expanded blob. Because the high and low energy photons are not produced at the same time, the requirement of large Doppler factor from pair production is relaxed. We present the fitting results of the SEDs for Mkn 501 during April 1997 and Mkn 421 during March 2001 respectively.

preprint2000arXiv

Emissive Mechanism on Spectral Variability of Blazars in High Frequencies

The new results of the evolution of the synchrotron peak for Mrk 421 are mostly likely related to the particle acceleration process. In order to account for the above results, we present a model of blazar variability during the flare in which the emission comes from accelerating electrons. A diffusion advection equation of the electron energy distribution is derived to calculate the spectrum and light curve of synchrotron radiation. We present that the observed shifts of the synchrotron peak moving to higher energies during the flare are caused by shock acceleration. The observed relation between changes in the fluxes at specified frequency ranges and shifts of the peak position is fitted to constrain the physical parameters of the dissipation region.