Electron-beam interaction with emission-line clouds in blazars
Christoph Wendel, Josefa Becerra González, David Paneque, Karl Mannheim
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Accepted for publication in Astronomy and Astrophysics on 07.12.2020. Article comprises 15 pages including the appendices and six figures. Edition with corrected typos and clean grammar
Context: An electron-positron beam escaping from the magnetospheric vacuum gap of an accreting black hole interacts with recombination-line photons from surrounding gas clouds. Inverse-Compton scattering and subsequent pair production initiate unsaturated electromagnetic cascades exhibiting a characteristic spectral energy distribution. Aims: By modelling the interactions of beam electrons (positrons) with hydrogen and helium recombination-line photons, we seek to describe the spectral signature of beam-driven cascades in the broad emission-line region of blazar jets. Methods: Employing coupled kinetic equations for electrons (positrons) and photons including an escape term, we numerically obtain their steady-state distributions, and the escaping photon spectrum. Results: We find that cascade emission resulting from beam interactions can produce a narrow spectral feature at TeV energies. Indications of such an intermittent feature, which defies an explanation in the standard shock-in-jet scenario, have been found at $\approx\,4\,σ$ confidence level at an energy of $\approx$ 3 TeV in the spectrum of the blazar Mrk 501. Conclusions: The energetic requirements for explaining the intermittent 3 TeV bump with the beam-interaction model are plausible: Gap discharges that lead to multi-TeV beam electrons (positrons) carrying $\approx$ 0.1 % of the Blandford-Znajek luminosity, which interact with recombination-line photons from gas clouds that reprocess $\approx$ 1 % of the similar accretion luminosity are required.
The innermost parts of powerful jets in active galactic nuclei are surrounded by dense, high-velocity clouds from the broad-line region, which may penetrate into the jet and lead to the formation of a strong shock. Such jet-cloud interactions are expected to have measurable effects on the $γ$-ray emission from blazars. We characterise the dynamics of a typical cloud-jet interaction scenario, and the evolution of its radiative output in the 0.1-30~GeV energy range, to assess to what extent these interactions can contribute to the $γ$-ray emission in blazars. We use semi-analytical descriptions …
Pair beams produced by very high-energy radiation from TeV blazars emit gamma rays in the GeV band by inverse-Compton scattering of soft photons. The observed GeV-band signal is smaller than that expected from the full electromagnetic cascade. This means that the pair beams must be affected by other physical processes reducing their energy flux. One possible loss mechanism involves beam-plasma instabilities that we consider in the present work. For realistic parameters the pair beams can not be simulated by modern computers. Instead, we use a simple analytical model to find a range of the beam…
This work revisits the electrostatic instability for blazar-induced pair beams propagating through IGM with the methods of linear analysis and PIC simulations. We study the impact of the realistic distribution function of pairs resulting from interaction of high-energy gamma-rays with the extragalactic background light. We present analytical and numerical calculations of the linear growth rate of the instability for arbitrary orientation of wave vectors. Our results explicitly demonstrate that the finite angular spread of the beam dramatically affects the growth rate of the waves, leading to f…
A neutrino outburst between September 2014 and March 2015 was discovered from the blazar TXS 0506+056 by an investigation of $9.5$ years of IceCube data, while the blazar was in a quiescent state during the outburst with a gamma-ray flux only about one-fifth of the neutrino flux. In this work, we give a possible interpretation of the abnormal feature by proposing that the neutrino outburst originates from the interaction between a relativistic jet and a dense gas cloud formed via the tidally disrupted envelope of a red giant being blown apart by the impact of the jet. Gamma-ray photons and ele…
We study the $\rmγ$-ray luminosity and beaming effect for Fermi blazars. Our results are as follows. (i) There are significant correlations between $\rmγ$-ray luminosity and radio core luminosity, and between $\rmγ$-ray luminosity and $\rm{R_{v}}$, which suggests that the $\rmγ$-ray emissions have strong beaming effect. (ii) Using the $\rm{L_{ext}/M_{abs}}$ as an indicator of environment effects, we find that there have no significant correlation between $\rmγ$-ray luminosity and $\rm{L_{ext}/M_{abs}}$ for all sources when remove the effect of redshift. FSRQs considered alone also do not show …
A two-component model of radio emission has been used to explain some radio observational properties of Active Galactic Nuclei (AGNs) and, in particular, of blazars. In this work, we extend the two-component idea to the $γ$-ray emission and assume that the total $γ$-ray output of blazars consists of relativistically beamed and unbeamed components. The basic idea leverages the correlation between the radio core-dominance parameter and the $γ$-ray beaming factor. To do so, we evaluate this correlation for a large sample of 584 blazars taken from the fourth source catalog of the Fermi Large Area …
The fate of relativistic pair beams produced in the intergalactic medium by very high energy emission from blazars remains controversial in the literature. The possible role of resonance beam plasma instability has been studied both analytically and numerically but no consensus has been reached. In this paper, we thoroughly analyze the development of this type of instability. This analysis takes into account that a highly relativistic beam loses energy only due to interactions with the plasma waves propagating within the opening angle of the beam (we call them parallel waves), whereas excitati…
We present results of a variability study in the optical band of 44 newly identified blazar candidates behind the Magellanic Clouds. Our sample contains 27 flat spectrum radio quasars (FSRQs) and 17 BL Lacertae objects (BL Lacs). However, only nine of them are considered as secure blazar candidates, while the classification of the remaining 35 objects is still uncertain. All studied blazar candidates possess infrequently sampled optical light curves (LCs) in I filter provided by the Optical Gravitational Lensing Experiment group. The LCs were analysed with the Lomb-Scargle periodogram, the Hur…
Long-lasting, very bright multiwavelength flares of blazar jets are a curious phenomenon. The interaction of a large gas cloud with the jet of a blazar may serve as a reservoir of particles entrained by the jet. The size and density structure of the cloud then determine the duration and strength of the particle injection into the jet and the subsequent radiative outburst of the blazar. In this presentation, a comprehensive parameter study is provided showing the rich possibilities that this model offers. Additionally, we use this model to explain the 4-months long, symmetrical flare of the fla…
Following the detection of a $\sim$300 TeV neutrino potentially associated with the flaring blazar TXS 0506+056, an excess of neutrinos around its position in 2014-2015 was revealed by IceCube. However, its contemporaneous quiescence in $γ$-rays is challenging to interpret consistently. Meanwhile, the blazar PKS 0502+049, positioned within the neutrino localization uncertainties, was seen to be flaring in $γ$-rays. We show that dense, line-emitting gas clouds that interact with its jet and induce cosmic ray acceleration and hadronuclear interaction can plausibly explain the 2014-2015 neutrino …
Flaring activity in blazars can last for vastly different time-scales, and may be the result of density enhancements in the jet flow that result from the intrusion of an interstellar cloud into the jet. We investigate the lightcurves expected from the ablation of gas clouds by the blazar jet under various cloud and jet configurations. We derive the semi-analytical formulae describing the ablation process of a hydrostatic cloud, and perform parameter scans of artificial set-ups over both cloud and jet parameter spaces. We then use parameters obtained from measurements of various cloud types to …
We revisit the effect of non-linear Landau (NL) damping on the electrostatic instability of blazar-induced pair beams, using a realistic pair-beam distribution. We employ a simplified 2D model in ${\bf k}$-space to study the evolution of the electric-field spectrum and to calculate the relaxation time of the beam. We demonstrate that the 2D model is an adequate representation of the 3D physics. We find that non-linear Landau damping, once it operates efficiently, transports essentially the entire wave energy to small wavenumbers where wave driving is weak or absent. The relaxation time also st…
We report the identification of blazar candidates behind the Magellanic Clouds. The objects were selected from the Magellanic Quasars Survey (MQS), which targeted the entire Large Magellanic Cloud (LMC) and 70\% of the Small Magellanic Cloud (SMC). Among the 758 MQS quasars and 898 of unidentified (featureless spectra) objects, we identified a sample of 44 blazar candidates, including 27 flat spectrum radio quasars and 17 BL Lacertae objects, respectively. All the blazar candidates from our sample were identified with respect to their radio, optical, and mid-infrared properties. The newly sele…
Recent detection of the neutrino event, IceCube-170922A by IceCube observatory from the Blazar TXS 0506+056 in the state of enhanced gamma ray emission indicates for acceleration of cosmic rays in the blazar jet. The non-detection of the broadline emission in the optical spectrum of TXS 0506+056 and other BL Lac objects suggests that external photons emissions are weak and hence photo-meson (p-gamma) interaction may not be a favored mechanism for high energy neutrino production. The lack of broadline signatures also creates doubt about the presence of a high density cloud in the vicinity of th…
The interaction of TeV photons from blazars with the extragalactic background light produces a relativistic beam of electron-positron pairs streaming through the intergalactic medium (IGM). The fate of the beam energy is uncertain. By means of two- and three-dimensional particle-in-cell simulations, we study the non-linear evolution of dilute ultra-relativistic pair beams propagating through the IGM. We explore a wide range of beam Lorentz factors gamma_b>>1 and beam-to-plasma density ratios alpha<<1, so that our results can be extrapolated to the extreme parameters of blazar-induced beams (ga…
The stability properties of a low density ultra relativistic pair beam produced in the intergalactic medium by multi-TeV gamma-ray photons from blazars are analyzed. The problem is relevant for probes of magnetic field in cosmic voids through gamma-ray observations. In addition, dissipation of such beams could affect considerably the thermal history of the intergalactic medium and structure formation. We use a Monte Carlo method to quantify the properties of the blazar induced electromagnetic shower, in particular the bulk Lorentz factor and the angular spread of the pair beam generated by the…
Hadron beams are invoked to explain the peculiar properties of a subclass of BL Lac objects, the so-called extreme BL Lacs (EHBLs). This scenario predicts a quite distinctive feature for the high-energy gamma-ray spectrum of these sources, namely a hard energy tail extending up to $\sim100$ TeV. It has been proposed that the detection of this tail can offer an unambiguous way to distinguish between the hadron beam scenario and the standard one, which instead assumes gamma-ray emission from the jet strongly depleted at the highest energies ($E>30$ TeV) because of the interaction with the optica…
Beaming effect is important for the observational properties of blazars. In this work, we collect 91 $Fermi$ blazars with available radio Doppler factors. $γ$-ray Doppler factors are estimated and compared with radio Doppler factors for some sources. The intrinsic (de-beamed) $γ$-ray flux density ($f^{\rm in}_γ$), intrinsic $γ$-ray luminosity ($L^{\rm in}_γ$), and intrinsic synchrotron peak frequency ($ν_{\rm p}^{\rm in}$) are calculated. Then we study the correlations between $f^{\rm in}_γ$ and redshift and find that they follow the theoretical relation: $\log f = -2.0 \log z + {\rm const}$. …
Fermi has been instrumental in constraining the luminosity function and redshift evolution of gamma-ray bright blazars. This includes limits upon the spectrum and anisotropy of the extragalactic gamma-ray background (EGRB), redshift distribution of nearby Fermi active galactic nuclei (AGN), and the construction of a log(N)-log(S) relation. Based upon these, it has been argued that the evolution of the gamma-ray bright blazar population must be much less dramatic than that of other AGN. However, critical to such claims is the assumption that inverse Compton cascades reprocess emission above a T…
The GeV-range spectra of blazars are shaped not only by non-thermal emission processes internal to the relativistic jet but also by external pair-production absorption on the thermal emission of the accretion disc and the broad-line region (BLR). For the first time, we compute here the pair-production opacities in the GeV range produced by a realistic BLR accounting for the radial stratification and radiation anisotropy. Using photoionization modelling with the CLOUDY code, we calculate a series of BLR models of different sizes, geometries, cloud densities, column densities and metallicities. …
We study the production of VHE emission in blazars as a superposition of a steady component from a baryonic jet and a time- dependent contribution from an inner e-e+ beam launched by the black hole. Both primary relativistic electrons and protons are injected in the jet, and the particle distributions along it are found by solving a one-dimensional transport equation that accounts for convection and cooling. The short-timescale variability of the emission is explained by local pair injections in turbulent regions of the inner beam. For illustration, we apply the model to the case of PKS 2155-3…
Recent detection of the neutrino events IceCube-170922A, 13 muon-neutrino events observed in 2014-2015 and IceCube-141209A by IceCube observatory from the Blazars, namely TXS 0506+056, PKS 0502+049/TXS 0506+056 and GB6 J1040+0617 respectively in the state of enhanced gamma-ray emission, indicates the acceleration of cosmic rays in the blazar jets. The photo-meson ($pγ$) interaction cannot explain the IceCube observations of 13 neutrino events. The non-detection of broadline emission in the optical spectra of the IceCube blazars, however, question the hadronuclear (pp) interaction interpretatio…
Relativistic effects dominate the emission of blazar jets complicating our understanding of their intrinsic properties. Although many methods have been proposed to account for them, the variability Doppler factor method has been shown to describe the blazar populations best. We use a Bayesian hierarchical code called {\it Magnetron} to model the light curves of 1029 sources observed by the Owens Valley Radio Observatory's 40-m telescope as a series of flares with an exponential rise and decay, and estimate their variability brightness temperature. Our analysis allows us to place the most strin…
Recent multi-wavelength work led by the Boston University blazar group (e.g., Marscher et al. 2010) strongly suggests that a fraction of the blazar flares seen by the Fermi Large Area Telescope (LAT) take place a few to several pc away from the central engine. However, at such distances from the central engine, there is no adequate external photon field to provide the seed photons required for producing the observed GeV emission under leptonic inverse Compton (IC) models. A possible solution is a spine-sheath geometry for the emitting region (MacDonald et al. 2015, but see Nalewajko et al. 201…
The IceCube collaboration reported a $\sim 3.5σ$ excess of $13\pm5$ neutrino events in the direction of the blazar TXS 0506+56 during a $\sim$6 month period in 2014-2015, as well as the ($\sim3σ$) detection of a high-energy muon neutrino during an electromagnetic flare in 2017. We explore the possibility that the 2014-2015 neutrino excess and the 2017 multi-messenger flare are both explained in a common physical framework that relies on the emergence of a relativistic neutral beam in the blazar jet due to interactions of accelerated cosmic rays (CRs) with photons. We demonstrate that the neutr…
The Extragalactic Background Light (EBL) is the integrated light from all the stars that have ever formed, and spans the IR-UV range. The interaction of very-high-energy (VHE: E>100 GeV) gamma-rays, emitted by sources located at cosmological distances, with the intervening EBL results in electron-positron pair production that leads to energy-dependent attenuation of the observed VHE flux. This introduces a fundamental ambiguity in the interpretation of the measured VHE blazar spectra: neither the intrinsic spectra, nor the EBL, are separately known - only their combination is. In this paper we…
Blazars are classically divided into the BL Lac (BLL) and Flat-Spectrum Radio Quasar (FSRQ) subclasses, corresponding to radiatively inefficient and efficient accretion regimes, respectively, largely based on the equivalent width (EW) of their optical broad emission lines (BEL). However, EW-based classification criteria are not physically motivated, and a few blazars have previously 'transitioned' from one subclass to the other. We present the first systematic search for these transition blazars in a sample of 602 unique pairs of repeat spectra of 354 blazars in SDSS, finding six clear cases. …
Active galactic nuclei come in many varieties. A minority of them are radio-loud, and exhibit two opposite prominent plasma jets extending from the proximity of the supermassive black hole up to megaparsec distances. When one of the relativistic jets is oriented closely to the line of sight, its emission is Doppler beamed and these objects show extreme variability properties at all wavelengths. These are called "blazars". The unpredictable blazar variability, occurring on a continuous range of time-scales, from minutes to years, is most effectively investigated in a multi-wavelength context. G…
High frequency peaked high redshift blazars, are extreme in the sense that their spectrum is particularly hard and peaks at TeV energies. Standard leptonic scenarios require peculiar source parameters and/or a special setup in order to account for these observations. Electromagnetic cascades seeded by ultra-high energy cosmic rays (UHECR) in the intergalactic medium have also been invoked, assuming a very low intergalactic magnetic field (IGMF). Here we study the synchrotron emission of UHECR secondaries produced in blazars located in magnetised environments, and show that it can provide an al…
We expand our previous studies of the parsec-scale structure of TeV blazars by presenting first-epoch images from VLBA monitoring of ten newer TeV HBLs. All ten sources were successfully detected and imaged, and all showed a one-sided core-jet structure. Many display a morphology common to TeV HBLs: a short, collimated jet followed by a transition to low surface brightness extended emission with a much broader opening angle. The newly detected TeV HBLs tend to be fainter in the radio; the median core flux density was 22 mJy, and the median brightness temperature was 8x10^9 K. The brightness te…
We extend our approach of modeling spectral energy distribution (SED) and lightcurves of blazars to include external Compton (EC) emission due to inverse Compton scattering of an external anisotropic target radiation field. We describe the time-dependent impact of such seed photon fields on the evolution of multifrequency emission and spectral variability of blazars using a multi-zone time-dependent leptonic jet model, with radiation feedback, in the internal shock model scenario. We calculate accurate EC-scattered high-energy spectra produced by relativistic electrons throughout the Thomson a…
Long-term gamma-ray variability of a non-blazar Active Galactic Nucleus (AGN) PKS 0521-36 is investigated by using Fermi-LAT pass 8 data covering from 2008 August to 2021 March. The results show that the histogram of the gamma-ray fluxes follows a log-normal distribution. Interestingly, in the analysis of about 5.8-year (from MJD 56317 to 58447) LAT data between two outbursts (occurring during 2012 October and 2019 May respectively), a quasi-periodic oscillation (QPO) with a period of about 1.1 years (about 5 sigma of significance) is found in the Lomb-Scargle Periodogram (LSP), the Weighted W…
Relativistic jets from blazars are known to be sources of very-high-energy gamma rays (VHEGRs). During their propagation in the intergalactic space, VHEGRs interact with pervasive cosmological photon fields such as the extragalactic background light (EBL) and the cosmic microwave background (CMB), producing electron-positron pairs. These pairs can upscatter CMB/EBL photons to high energies via inverse Compton scattering, thereby continuing the cascade process. This is often used to set limits on intergalactic magnetic fields (IGMFs). However, the picture may change if plasma instabilities, ari…
We study the broad emission line blazars detected in the gamma-ray band by the Large Area Telescope onboard the Fermi satellite and with the optical spectrum studied by Shaw et al. (2012, 2013). The observed broad line strength provides a measure of the ionizing luminosity of the accretion disk, while the gamma-luminosity is a proxy for the bolometric non-thermal beamed jet emission. The resulting sample, composed by 217 blazars, is the best suited to study the connection between accretion and jet properties. We compare the broad emission line properties of these blazars with those of radio-qu…
Collecting experimental insight into the relativistic particle populations and emission mechanisms at work within TeV-emitting blazar jets, which are spatially unresolvable in most bands and have strong beaming factors, is a daunting task. New observational information has the potential to lead to major strides in understanding the acceleration site parameters. Detection of molecular carbon monoxide (CO) in TeV emitting blazars, however, implies the existence of intrinsic gas, a connection often found in photo-dissociated region models and numerical simulations. The existence of intrinsic gas …
We compare Particle-in-Cell simulation results of relativistic electron-ion shear flows with different bulk Lorentz factors, and discuss their implications for spine-sheath models of blazar versus gamma-ray burst (GRB) jets. Specifically, we find that most properties of the shear boundary layer scale with the bulk Lorentz factor: the lower the Lorentz factor, the thinner the boundary layer, and the weaker the self-generated fields. Similarly, the energized electron spectrum peaks at an energy near the ion drift energy, which increases with bulk Lorentz factor, and the beaming of the accelerate…
We present a fully analytical, time-dependent leptonic one-zone model that describes a simplified radiation process of multiple interacting ultrarelativistic electron populations, accounting for the flaring of GeV blazars. In this model, several mono-energetic, ultrarelativistic electron populations are successively and instantaneously injected into the emission region, i.e., a magnetized plasmoid propagating along the blazar jet, and subjected to linear, time-independent synchrotron radiative losses, which are caused by a constant magnetic field, and nonlinear, time-dependent synchrotron self…
Our recently reported lack of Intra-Night Optical Variability (INOV) among Broad-Absorption-Line (BAL) quasars exhibiting some blazar-like radio properties, either questions polar ejection of BAL clouds, and/or hints at a physical state of the relativistic jet modified due to interaction with the thermal BAL wind on the innermost sub-parsec scale. As a robust check on this unexpected finding for the BAL_blazar candidates, we report here the INOV study of a new and much more rigorously defined comparison sample consisting of 9 normal (non-BAL) blazars, matched in both magnitude and redshift to …
The LAT instrument, onboard the Fermi satellite, in its first three months of operation detected more than 100 blazars at more than the 10 sigma level. This is already a great improvement with respect to its predecessor, the instrument EGRET onboard the Compton Gamma Ray Observatory. Observationally, the new detections follow and confirm the so-called blazar sequence, relating the bolometric observed non-thermal luminosity to the overall shape of the spectal energy distribution. We have studied the general physical properties of all these bright Fermi blazars, and found that their jets are mat…
Attenuation of the TeV gamma-ray flux from distant blazars through pair production with extragalactic background light leads to the development of electromagnetic cascades and subsequent, lower energy, GeV secondary gamma-ray emission. Due to the deflection of VHE cascade electrons by extragalactic magnetic fields (EGMF), the spectral shape of this arriving cascade gamma-ray emission is dependent on the strength of the EGMF. Thus, the spectral shape of the GeV-TeV emission from blazars has the potential to probe the EGMF strength along the line of sight to the object. We investigate constraint…
TeV emission from blazars can be used to probe the intergalactic magnetic fields and measure their intensity, coherence length, and helicity. Intergalactic magnetic fields deflect the electron-positron pairs produced by very-high-energy gamma-rays from blazars, resulting in broadened beams of cascade gamma-rays developing along the projected direction of the blazar jet. We present an analysis that uses for the first time the jet orientation of 12 high-synchrotron-peaked (HSP) BL~Lac-type blazars from VLBA radio observations to search for signatures of pair haloes in the Fermi-LAT data. Our sea…
Blazars may accelerate protons and/or nuclei as well as electrons. The hadronic component of accelerated particles in blazars may constitute the bulk of their high-energy budget; nevertheless, this component is elusive due to a high value of the energy threshold of proton interaction with photon fields inside the source. However, broad line regions (BLRs) of some flat spectrum radio quasars (FSRQs) may contain a sufficient amount of matter to render primary protons "visible" in $γ$ rays via hadronuclear interactions. In the present paper we study the persistent $γ$-ray emission of the FSRQ PKS…
We use the third catalog of blazars detected by Fermi/LAT (3LAC) and gamma-ray Narrow-line Seyfert 1 Galaxies (gamma-NLSy1s) to study the blazar sequence and relationship between them. Our results are as follows: (i) There is a weak anti-correlation between synchrotron peak frequency and peak luminosity for both Fermi blazars and gamma-NLSy1s, which supports the blazar sequence. However, after Doppler correction, the inverse correlation disappeared, which suggests that anti-correlation between synchrotron peak frequency and peak luminosity is affected by the beaming effect. (ii) There is a sig…
Recently the IceCube collaboration detected very high energy (VHE) neutrinos and associated them with the blazar \txs{}, raising a possible association of VHE neutrinos with this and other individual blazars. Very Long Baseline Interferometry (VLBI) is so far the only technique enabling the imaging of the innermost jet at milli-arcsec resolution (parsec scale), where the high energy emission possibly originates from. Here, we report on the radio properties of the parsec scale jet in \txs{} derived from the analysis of multi-epoch multi-frequency archive VLBI data. The half opening angle of the…
Very-high-energy (VHE) BL Lac spectra extending above $10 \, \rm TeV$ provide a unique opportunity for testing physics beyond the standard model of elementary particle and alternative blazar emission models. We consider the hadron beam, the photon to axion-like particle (ALP) conversion, and the Lorentz invariance violation (LIV) scenarios by analyzing their consequences and induced modifications to BL Lac spectra. In particular, we consider how different processes can provide similar spectral features (e.g. hard tails) and we discuss the ways they can be disentangled. We use HEGRA data of a h…
The extragalactic gamma-ray sky at TeV energies is dominated by blazars, a subclass of accreting super-massive black holes with powerful relativistic outflows directed at us. Only constituting a small fraction of the total power output of black holes, blazars were thought to have a minor impact on the universe at best. As we argue here, the opposite is true and the gamma-ray emission from TeV blazars can be thermalized via beam-plasma instabilities on cosmological scales with order unity efficiency, resulting in a potentially dramatic heating of the low-density intergalactic medium. Here, we r…
High-energy emission from blazars is produced by electrons which are either accelerated directly (the assumption of leptonic models of blazar activity) or produced in interactions of accelerated protons with matter and radiation fields (the assumption of hadronic models). The hadronic models predict that gamma-ray emission is accompanied by neutrino emission with comparable energy flux but with a different spectrum. We derive constraints on the hadronic models of activity of blazars imposed by non-detection of neutrino flux from a population of gamma-ray emitting blazars. We stack the gamma-ra…
