Inhomogeneous Jet Model Research Articles

Optically thick, nonlocal, inhomogeneous, stationary jet model for high-energy radiation from blazars: Application to Mrk 421

Context. There is an increasing number of observational evidence that very high energy γ-rays in radio-loud activ galactic nuclei are produced in the direct vicinity of a supermassive black hole (SMBH), close to the base of a relativistic jet. In the case of some blazars, the angle between the jet axis and the observer’s line of sight is smaller than the angular extent of the jet. γ-rays that are produced close to SMBH therefore have to propagate in the nonthermal radiation of the extended jet before reaching the observer. This γ-ray emission can be strongly absorbed in the extended jet radiation, producing a second generation of e± pairs that loses energy mainly via the synchrotron process. Aims. We developed a nonlocal, inhomogeneous, stationary jet model in order to describe the multiwavelength emission from blazars. With this advanced model, we investigated the impact of the extended jet radiation on the propagation of γ-rays that are ejected from the direct vicinity of SMBH toward an observer located within the solid angle of the jet. We determined the conditions under which γ-rays are absorbed in the jet radiation and explored the effect of this absorption process on the γ-ray spectra and on the hard X-ray emission observed from some blazars. Methods. We first developed an inhomogeneous, stationary jet model in which the radiation that is produced nonlocally in the jet was taken into account when we calculated the nonthermal emission in the broad energy range. This emission serves as a target on which γ-rays, produced close to SMBH, can be absorbed. As a result, the cascade is initiated within the jet through inverse Compton and synchrotron processes. Results. We show that this advanced inhomogeneous jet model can explain the multiwavelength spectrum of the BL Lac object Mrk 421 in a nonflaring state for reasonable parameters of the jet and the SMBH. Moreover, we argue that synchrotron emission from the secondary e± pairs, which appear as a result of absorption of γ-rays that are produced close to the SMBH within the jet radiation, is consistent with the concave hard X-ray emission observed from Mrk 421.

Numerical analysis of long-term variability of AGN jets through RMHD simulations

ABSTRACT Relativistic AGN (active galactic nucleus) jets exhibit multitime-scale variability and a broad-band non-thermal spectrum extending from radio to gamma-rays. These highly magnetized jets are prone to undergo several magnetohydrodynamic (MHD) instabilities during their propagation in space and could trigger jet radiation and particle acceleration. This work aims to study the implications of relativistic kink mode instability on the observed long-term variability in the context of the twisting in-homogeneous jet model. To achieve this, we investigate the physical configurations preferable for forming kink mode instability by performing high-resolution 3D relativistic MHD simulations of a portion of highly magnetized jets. In particular, we perform simulations of cylindrical plasma column with Lorentz factor ≥5 and study the effects of magnetization values and axial wavenumbers with decreasing pitch on the onset and growth of kink instability. We have confirmed the impact of axial wavenumber on the dynamics of the plasma column including the growth of the instability. In this work, we have further investigated the connection between the dynamics of the plasma column with its time-varying emission features. From our analysis, we find a correlated trend between the growth rate of kink mode instability and the flux variability obtained from the simulated light curve.

Inferring the jet parameters of active galactic nuclei using Bayesian analysis of VLBI data with a non-uniform jet model

ABSTRACTThe physical parameters of the jets of active galactic nuclei observed with Very Long Baseline Interferometry (VLBI) are usually inferred from core-shift measurements or from the flux and size measured at the peak frequency of the synchrotron spectrum. Both methods are preceded by modelling the observed VLBI jet structure with simple Gaussian templates. Here we infer the jet parameters using an inhomogeneous jet model directly, bypassing the modelling of the source structure with a Gaussian template or image deconvolution. We apply Bayesian analysis to multifrequency VLBA observations of radio galaxy NGC 315 and find that its parsec-scale jet is well described by an inhomogeneous conical model. Our results favour an electron–positron jet. We also detect a component as a part of a counter jet. Its position implies the presence of an external absorber with a steep density gradient close (r = 0.1 pc) to the central engine.

Lepto-hadronic model for the broadband emission of Cygnus X-1

Cygnus X-1 is a well observed microquasar. Broadband observations at all wavelengths have been collected over the years. The origin of the MeV tail observed with COMPTEL and INTEGRAL is still under debate and it has mostly been attributed to the corona, although its high degree of polarization suggests it is synchrotron radiation from a jet. The origin of the transient emission above $\sim 100$ GeV is also unclear. We aim to disentangle the origin of the broadband spectral energy distribution (SED) of Cygnus X-1, focusing particularly on the gamma-ray emission, and to gain information on the physical conditions inside the jets. We develop and apply a lepto-hadronic, inhomogeneous jet model to the non-thermal SED of Cygnus X-1. We calculate the contributions to the SED of both protons and electrons accelerated in an extended region of the jet. We also estimate the radiation of charged secondaries produced in hadronic interactions, through several radiative processes. Absorption effects are considered. We produce synthetic maps of the jets at radio wavelengths. We find two sets of model parameters that lead to good fits of the SED. One of the models fits all the observations, including the MeV tail. This model also predicts hadronic gamma-ray emission slightly below the current upper limits. The flux predicted at 8.4 GHz is in agreement with the observations available in the literature, although the synthetic source is more compact than the imaged radio jet. Our results show that the MeV emission in Cygnus X-1 may be jet synchrotron radiation. This depends mainly on the strength of the jet magnetic field and the location of the injection region of the relativistic particles. Our calculations show that there must be energetic electrons in the jets quite far from the black hole.

An Inhomogeneous Jet Model and Its Application in BL Lacertae Objects

In the inhomogeneous conical jet model, the electron number den- sity and magnetic field strength have a power-law distribution with the distance from the jet apex. This model can interpret successfully the flat-spectrum radio radiation from the core regions of active galactic nuclei. But the existing model calculation suits only the situation when the enclosed angle between the moving direction of a jet and the line of sight is very large, hence, we need to build a formula for calculating the radiation of inhomogeneous conical jets with any viewing angles. It is generally believed that the enclosed angle between the di- rection of jet motion and the line of sight is very small in BL Lac objects. With the extended inhomogeneous jet model, we have made fitting on the observed radio spectra of three BL Lac objects, and obtained the physical parameters, such as the electron number density and magnetic field strength in their jets. The result indicates that the nearest distance of the conical jet from the black hole is determined by the transition frequency of the observed radiation spec- trum, and that the nearest distance between the conical jet and the black hole is approximately the Schwarzschild radius for the three BL Lac objects.

Synchrotron and inverse-Compton emission from blazar jets – IV. BL Lac type blazars and the physical basis for the blazar sequence

In this paper, we investigate the properties of a sample of six BL Lacs by fitting their spectra using our inhomogeneous jet model with an accelerating, magnetically dominated, parabolic base, which transitions to a slowly decelerating conical jet with a geometry based on observations of M87. Our model is able to fit very well to the simultaneous multiwavelength spectra of all the BL Lacs including radio observations. We find that the BL Lacs have lower jet powers and bulk Lorentz factors than the sample of Compton-dominant blazars investigated in Paper III, consistent with the blazar sequence. Excitingly, we find a correlation between the radius at which the jet first comes into equipartition and the jet power, in agreement with our prediction from Paper III. We interpret this result as one of two physical scenarios: a universal jet geometry which scales linearly with black hole mass or a dichotomy in Eddington accretion rates between flat-spectrum radio quasars (FSRQs) and BL Lacs. If we assume that the jet geometry of all blazars scales linearly with black hole mass, then we find a plausible range of masses (∼107–1010 M⊙). We find that the quiescent gamma-ray spectrum of Markarian 421 is best fitted by scattering of external cosmic microwave background photons. We are unable to fit the spectrum using synchrotron self-Compton emission due to strong gamma-ray absorption via pair production even using a compact, rapidly decelerating, jet with a very large bulk Lorentz factor (50), as has been suggested recently. This is because the ratio of synchrotron to inverse-Compton emission requires a high density of synchrotron photons to scatter which makes the region opaque to TeV gamma-rays even with large bulk Lorentz factors. Finally, we fit to the spectral energy distributions of the four high power high synchrotron peak frequency BL Lacs recently found by Padovani et al. We find that their high peak frequency emission is caused by high maximum electron energies whilst the rest of their jet properties are typical of relatively high power BL Lacs and consistent with our predictions.

Uncovering the physics behind the blazar sequence using a realistic model for jet emission

Blazar spectra are one of the most important windows into the physical processes occurring along jets. The spectrum, composed from the different emitting regions along the jet, allows us to constrain the physical conditions in the jet. I present my work modelling blazar spectra using an extended inhomogeneous jet model with an accelerating, magnetically dominated, parabolic base transitioning to a slowly decelerating, conical section motivated by observations, simulations and theory. We set the inner geometry of our multizone jet using observations of the jet in M87 which transitions from parabolic to conical at 105 Schwarzschild radii. This model is able to reproduce quiescent blazar spectra very well across all wavelengths (including radio observations) for a sample of 42 BL Lacs and FSRQs.

WHAT GOVERNS THE BULK VELOCITY OF THE JET COMPONENTS IN ACTIVE GALACTIC NUCLEI?

We use a sample of radio-loud active galactic nuclei (AGNs) with measured black hole masses to explore the jet formation mechanisms in these sources. Based on the K\"{o}nigl's inhomogeneous jet model, the jet parameters, such as the bulk motion Lorentz factor, magnetic field strength, and electron density in the jet, can be estimated with the very long-baseline interferometry and X-ray data. We find a significant correlation between black hole mass and the bulk Lorentz factor of the jet components for this sample, while no significant correlation is present between the bulk Lorentz factor and the Eddington ratio. The massive black holes will be spun up through accretion, as the black holes acquire mass and angular momentum simultaneously through accretion. Recent investigation indeed suggested that most supermassive black holes in elliptical galaxies have on average higher spins than the black holes in spiral galaxies, where random, small accretion episodes (e.g., tidally disrupted stars, accretion of molecular clouds) might have played a more important role. If this is true, the correlation between black hole mass and the bulk Lorentz factor of the jet components found in this work implies that the motion velocity of the jet components is probably governed by the black hole spin. No correlation is found between the magnetic field strength at $10R_{\rm S}$ ($R_{\rm S}=2GM/c^2$ is the Schwarzschild radius) in the jets and the bulk Lorentz factor of the jet components for this sample. This is consistent with the black hole spin scenario, i.e., the faster moving jets are magnetically accelerated by the magnetic fields threading the horizon of more rapidly rotating black holes. The results imply that the Blandford-Znajek (BZ) mechanism may dominate over the Blandford-Payne (BP) mechanism for the jet acceleration at least in these radio-loud AGNs.

An inhomogeneous lepto-hadronic model for the radiation of relativistic jets

Conceptually reconstructing the physical conditions in relativistic jets, given the observed electromagnetic spectrum, poses a complex inverse problem. We aim to obtain a better understanding of the mechanisms operating in relativistic jets through the modeling of their broadband electromagnetic spectrum. We develop an inhomogeneous jet model where the injection of relativistic primary and secondary particles takes place in a spatially extended region. We calculate the contribution of all particles species to the jet emissivity due to several processes, and assess the effect of gamma-ray absorption in internal and external photon fields. A number of specific models with different parameters are computed to explore the possibilities of this scenario. We obtain a variety of spectral shapes depending on the model parameters, some of them predicting significant gamma-ray emission. The observed broadband spectrum of the low-mass microquasar XTE J1118+480 can be satisfactorily reproduced by the model. Our results indicate that outbursts similar to those displayed in the past by XTE J1118+480 might be detected with present-day gamma-ray instruments.

The bulk kinetic power of radio jets in active galactic nuclei

Based on the K\"onigl's inhomogeneous jet model, we estimate the jet parameters, such as bulk Lorentz factor $\Gamma$, viewing angle $\theta$ and electron number density $n_{\rm e}$ from radio VLBI and X-ray data for a sample of active galactic nuclei (AGNs) assuming that the X-rays are from the jet rather than the intracluster gas. The bulk kinetic power of jets is then calculated using the derived jet parameters. We find a strong correlation between the total luminosity of broad emission lines and the bulk kinetic power of the jets. This result supports the scenario that the accretion process are tightly linked with the radio jets, though how the disk and jet are coupled is not revealed by present correlation analysis. Moreover, we find a significant correlation between the bulk kinetic power and radio extended luminosity. This implies that the emission from the radio lobes are closely related with the energy flux transported through jets from the central part of AGNs.

An inhomogeneous jet model for the rapid variability of TeV blazars

Abstract We present a new time-dependent inhomogeneous jet model of non-thermal blazar emission, which reproduces the entire spectral energy distribution together with the rapid gamma-ray variability. Ultrarelativistic leptons are injected at the base of a jet and propagate along the jet structure. We assume continuous reacceleration and cooling, producing a relativistic quasi-maxwellian (or ‘pile-up’) particle energy distribution. The synchrotron and synchrotron self-Compton jet emissivity are computed at each altitude. Klein–Nishina effects as well as intrinsic gamma–gamma absorption are included in the computation. Due to the pair production optical depth, considerable particle density enhancement can occur, particularly during flaring states. Time-dependent jet emission can be computed by varying the particle injection, but due to the sensitivity of pair production process, only small variations of the injected density are required during the flares. The stratification of the jet emission, together with a pile-up distribution, allows significantly lower bulk Lorentz factors, compared to one-zone models. Applying this model to the case of PKS 2155-304 and its big TeV flare observed in 2006, we can reproduce simultaneously the average broad-band spectrum of this source as well as the TeV spectra and TeV light curve of the flare with bulk Lorentz factor lower than 15.

A New Approach for Estimating Kinetic Luminosity of Jet in AGNs

The K¨ onigl inhomogeneous jet model can successfully reproduce most observa- tional features of jets in active galactic nuclei (AGN), when suitable physical parameters are adopted. We improve K¨ onigl's calculations on the core emission from the jet with a small viewing angle �0 ∼ � (� is half opening angle of the conical jet). The proper motion of the jet component provides a constraint on the jet kinematics. Based on the inhomogeneous jet model, we use the proper motion data of the jet component to calculate the minimal kinetic luminosity of the jet required to reproduce the core emission measured by the very-long- baseline interferometry (VLBI) for a sample of BL Lac objects. Our results show that the minimal kinetic luminosity is slightly higher than the bolometric luminosity for most sources in the sample, which implies that radiatively inefficient accretion flows (RIAFs) may be in those BL Lac objects, or/and the properties of their broad-line regions (BLRs) are signifi- cantly different from flat-spectrum radio-loud quasars.

Tail emission of prompt gamma-ray burst jets

Tail emission of the prompt gamma-ray burst (GRB) is discussed using a multiple emitting sub-shell (inhomogeneous jet, sub-jets or mini-jets) model, where the whole GRB jet consists of many emitting sub-shells. One may expect that such a jet with angular inhomogeneity should produce spiky tail emission. However, we found that the tail is not spiky but is decaying roughly monotonically. The global decay slope of the tail is not so much affected by the local angular inhomogeneity but affected by the global sub-shell energy distribution. The fact that steepening breaks appeared in some events prefers the structured jets. If the angular size of the emitting sub-shell is around 0.01-0.02 rad, some bumps or fluctuations appear in the tail emission observed frequently in long GRBs. If the parameter differences of sub-shell properties are large, the tail has frequent changes of the temporal slope observed in a few bursts. Therefore, the multiple emitting sub-shell model has the advantage of explaining the small-scale structure in the observed rapid decay phase.

Shallow Decay of Early X-Ray Afterglows from Inhomogeneous Gamma-Ray Burst Jets

Almost all the X-ray afterglows of γ-ray bursts (GRBs) observed by the Swift satellite have a shallow decay phase in their first few thousand seconds. We show that in an inhomogeneous-jet model (multiple-subjet or patchy-shell), the superposition of the afterglows of off-axis subjets (patchy shells) can produce the shallow decay phase. The necessary condition for obtaining the shallow decay phase is that γ-ray-bright subjets (patchy shells) have γ-ray efficiencies higher than previously estimated and that they be surrounded by γ-ray-dim subjets (patchy shells) with low γ-ray efficiency. Our model predicts that events with dim prompt emission will have a conventional afterglow light curve without a shallow decay phase, like GRB 050416A.

Ep‐EisoCorrelation in a Multiple Subjet Model of Gamma‐Ray Bursts

We perform Monte Carlo simulations to study Ep-Eiso correlation in the context of a multiple subjet model (or inhomogeneous jet model) for gamma-ray bursts (GRBs), X-ray--rich GRBs (XRRs), and X-ray flashes (XRFs). For a single subjet, we find that Ep prop. Eiso^0.4 for large viewing angles. For the multiple subjet model in which all the subjets have the same intrinsic properties, off-axis events show Ep prop. Eiso^a with 0.4<a<0.5. If the intrinsic properties of the subjets are distributed so that on-axis emission of each subjet follows a correlation Ep prop. Liso^1/2, we obtain the Amati correlation (Ep prop. Eiso^1/2) over three orders of magnitude in Ep. Although the scatter around the Amati correlation is large in the simulation, the results are consistent with the observed properties of GRBs with known redshifts and the BASTE GRBs with pseudo redshifts derived from the lag-luminosity correlation. We also calculate the event rates, the redshift distributions, and the T90 duration distributions of GRBs, XRRs, and XRFs which can be detected by HETE-2, assuming that the source redshift distribution is in proportion to the cosmic star formation rate. It is found that the event rates of three classes are comparable, that the average redshift of the XRRs is a little larger than those of the GRBs and the XRFs, and that short XRRs arise when a single subjet is viewed off-axis or viewed on-axis with slightly high redshift.

A unified model of short and long gamma-ray bursts, X-ray rich gamma-ray bursts, and X-ray flashes

We propose a possible unified model of short and long gamma-ray bursts (GRBs), X-ray rich GRBs, and X-ray flashes. The jet of a GRB is assumed to consist of multiple sub-jets or sub-shells (i.e., an inhomogeneous jet model). The multiplicity of the sub-jets along a line of sight n s is an important parameter. If n s is large (≫1) the event looks like a long GRB, while if n s = 1, the event looks like a short GRB. Finally, when n s = 0, the event looks like an X-ray flash or an X-ray rich GRB. Furthermore, our model may also explain the bimodal distributions of T 90 duration of BATSE-GRBs.

General properties of X-Ray Riches and X-Ray Flashes in comparison with Gamma-Ray Bursts

The X-Ray Flashes (XRFs) and X-Ray Riches (XRRs) are two subclasses of Gamma-Ray Bursts (GRBs), which have respectively no detection in the gamma-ray energy and very faint gamma to X-ray fluence. To investigate their nature we compiled a sample of 54 events observed by BeppoSAX and HETE-2, available in literature and from the web. To classify XRRs/XRFs for those two experiments, we adopted the same spectral hardness ratio. We studied their prompt emission in the X and γ range and their spectral parameters and compared them with those of GRBs. We find XRRs/XRFs are characterized by a significantly smaller value of Epeak while the spectral slopes α and β are quite similar. We analysed also the optical and X-ray afterglow fluxes and their ratio and compared them with that obtained for GRBs. We find that the distribution of X-ray flux of XRR/XRF afterglow is consistent with that of GRBs, which is incompatible with the off-axis model. For example, in the inhomogeneous jet model it implies that the observer anglefor an XRR/XRF is at most 2◦. It is also not explained by the high Redshift scenario.

A Unified Model of Short and Long Gamma-Ray Bursts, X-Ray-rich Gamma-Ray Bursts, and X-Ray Flashes

Taking into account the recent suggestion that a short gamma-ray burst (GRB) looks like the first 1 s of a long GRB, we propose that the jet of a GRB consists of multiple subjets or subshells (i.e., an inhomogeneous jet model). The multiplicity of the subjets along a line of sight ns is an important parameter. If ns is large (≫1) the event looks like a long GRB, while if ns is small (~1) the event looks like a short GRB. If our line of sight is off-axis to any subjets, the event looks like an X-ray flash or an X-ray-rich GRB. The lognormal distribution of durations of short and long GRBs are also suggested in the same model.

The VLBI core in Radio Loud AGNs

We present statistical results on VLBI cores from large VLBI samples at C, L and S/X bands. Most of the results are consistent with the inhomogeneous jet model. The magnetic field distribution and particle density in the inhomogeneous jet model were estimated. We also found that the flux densities and luminosities of the cores at 5 GHz were correlated with those at optical band in the rest-frame.

VSOP brightness temperature in NRAO 530 exceeds the inverse Compton limit

Abstract We present here space-based VLBI observations with VSOP and a southern hemisphere ground array of the gamma-ray blazar NRAO 530 at 1.6 and 5 GHz. The 5 GHz show a single component with a brightness temperature of ∼ 3 × 10 12 K, significantly in excess of the inverse Compton limit and of the equipartition brightness temperature limit (Readhead 1994). This is strong evidence for relativistic motion in a jet and implies model-dependent Doppler boosting factors in the range 6 to 60. We show that a simple homogeneous sphere probably does not model the emission region accurately. We favor instead an inhomogeneous jet model which requires a Doppler boosting factor of 15.