Energetics of the ultrahigh-energy cosmic rays (UHECRs) generated in the universe is crucial for pinning down their candidate sources. Using the recent Auger data on UHECR spectra, we calculate the UHECR energy generation rate density for different species of nuclei at the injection, considering intermediate and heavy nuclei as well as protons, through scanning over source parameters on the spectral index, maximum energy and redshift evolution. We find the resulting UHECR energy generation rate density to be $\approx(0.2-2)\times$10$^{44}$~erg~Mpc$^{-3}$~yr$^{-1}$ at $10^{19.5}$~eV with a nontrivial dependence on the spectral index. Nuclei other than protons and irons favor hard spectral indices at the injection, and the required value of energy budget is smaller for intermediate nuclei. Given significant uncertainties in hadronic interaction models and astrophysical models for the Galactic-extragalactic transition, our results can be regarded as conservative. The composition data on $X_{\rm max}$ give additional constraints, but the results are consistent within the model uncertainties.
Combined recent data from cosmic-ray detectors and gamma-ray detectors have produced some surprising insights regarding the sources of ultrahigh-energy cosmic rays (UHECRs), magnetic fields inside and outside the Milky Way, and the universal photon backgrounds. The energy-dependent composition of UHECRs implies a non-negligible contribution of sources located in the Milky Way, such as past gamma-ray bursts that took place in our Galaxy. Extended halos of distant sources seen in the Fermi data imply that intergalactic magnetic fields have average strengths of the order of a femtogauss. Such rel…
In this work we study how the turbulent component of the Galactic magnetic field (GMF) affects the propagation of ultrahigh energy heavy nuclei. We investigate first how the images of individual sources and of the supergalactic plane depend on the properties of the turbulent GMF. Then we present a quantitative study of the impact of the turbulent field on (de-) magnification of source fluxes, due to magnetic lensing effects. We also show that it is impossible to explain the Pierre Auger data assuming that all ultrahigh energy nuclei are coming from Cen A, even in the most favorable case of a s…
We investigate the production of magnetic flux from rotating black holes in active galactic nuclei (AGNs) and compare it with the upper limit of ultrahigh energy cosmic ray (UHECR) luminosities, calculated from observed integral flux of GeV-TeV gamma rays for nine UHECR AGN sources. We find that, for the expected range of black hole rotations (0.44<a<0.80), the corresponding bounds of theoretical magnetic luminosities from AGNs coincides with the calculated UHECR luminosity. We argue that such result possibly can contribute to constrain AGN magnetic and dynamic properties as phenomenological t…
It is crucial to identify the ultrahigh-energy cosmic-ray (UHECR) sources and probe their unknown properties. Recent results from the Pierre Auger Observatory favor a heavy nuclear composition for the UHECRs. Under the requirement that heavy nuclei survive in these sources, using gamma-ray bursts as an example, we predict a diagnostic gamma-ray signal, unique to nuclei - the emission of de-excitation gamma rays following photodisintegration. These gamma rays, boosted from MeV to TeV-PeV energies, may be detectable by gamma-ray telescopes such as VERITAS, HESS, and MAGIC, and especially the nex…
Observations are consistent with a significant fraction of heavy nuclei in the cosmic ray flux above a few times 10^19 eV. Such nuclei can be deflected considerably in the Galactic magnetic field, with important implications for the search of their sources. We perform detailed simulations of heavy nuclei propagation within recent Galactic magnetic field models. While such models are not yet sufficiently constrained to predict deflection maps in detail, we find general features of the distribution of (de-) magnified flux from sources. Since in most theoretical models sources of heavy nuclei are…
We perform Monte Carlo simulations of transrelativistic shear acceleration dedicated to a jet-cocoon system of active galactic nuclei. A certain fraction of galactic cosmic rays in a halo is entrained, and sufficiently high-energy particles can be injected to the reacceleration process and further accelerated up to 100 EeV. We show that the shear reacceleration mechanism leads to a hard spectrum of escaping cosmic rays, $dL_E/dE\propto E^{-1}-E^0$, distinct from a conventional $E^{-2}$ spectrum. The supersolar abundance of ultrahigh-energy nuclei is achieved due to injections at TeV-PeV energi…
Sombrero Galaxy as an Accelerator of Ultrahigh Energy Cosmic Ray Nuclei
Lehman College, City University of New York（纽约市立大学莱曼学院）；Graduate Center, City University of New York（纽约市立大学研究生中心）；American Museum of Natural History（美国自然历史博物馆）
Motivated by Pierre Auger Observatory results favoring a heavy nuclear composition for ultrahigh-energy (UHE) cosmic rays, we investigate implications for the cumulative neutrino background. The requirement that nuclei not be photodisintegrated constrains their interactions in sources, therefore limiting neutrino production via photomeson interactions. Assuming a $dN_{\rm CR}/dE_{\rm CR} \propto E_{\rm CR}^{-2}$ injection spectrum and photodisintegration via the giant dipole resonance, the background flux of neutrinos is lower than $E_ν^2 Φ_ν\sim {10}^{-9} {\rm GeV} {\rm cm}^{-2} {\rm s}^{-1} …
The energy spectrum, composition and arrival directions of ultrahigh energy cosmic rays (UHECRs) with energy above the cosmic ray ankle, measured by the Pierre Auger Observatory, are inconsistent if their origin is assumed to be extragalactic. Their observed properties, however, are those expected from UHECRs accelerated by the highly relativistic jets emitted in Galactic gamma ray bursts, most of which are beamed away from Earth. If this alternative interpretation is correct, the observed break in the energy spectrum of UHECRs around 50 EeV is not the Greisen-Zatsepin-Kuzmin cutoff but the en…
Transrelativistic supernovae (SNe), which are likely driven by central engines via jets or winds, have been among candidate sources of ultrahigh-energy cosmic rays (UHECRs). We investigate acceleration and survival of UHECR nuclei in the external reverse shock scenario. With composition models used in Zhang et al. (2018), we calculate spectra of escaping cosmic rays and secondary neutrinos. If their local rate is $\sim1$% of the core-collapse supernova rate, the observed UHECR spectrum and composition can be explained with the total cosmic-ray energy ${\mathcal E}_{\rm cr}\sim10^{51}$ erg. The…
The acceleration of ultrahigh energy nuclei in fast spinning newborn pulsars can explain the observed spectrum of ultrahigh energy cosmic rays and the trend towards heavier nuclei for energies above $10^{19}\,$eV as reported by the Auger Observatory. Pulsar acceleration implies a hard injection spectrum ($\sim E^{-1}$) due to pulsar spin down and a maximum energy $E_{\rm max} \sim Z \, 10^{19}$ eV due to the limit on the spin rate of neutron stars. We have previously shown that the escape through the young supernova remnant softens the spectrum, decreases slightly the maximum energy, and gener…
We study the survival of ultrahigh energy nuclei injected in clusters of galaxies, as well as their secondary neutrino and photon emissions, using a complete numerical propagation method and a realistic modeling of the magnetic, baryonic and photonic backgrounds. It is found that the survival of heavy nuclei highly depends on the injection position and on the profile of the magnetic field. Taking into account the limited lifetime of the central source could also lead in some cases to the detection of a cosmic ray afterglow, temporally decorrelated from neutrino and gamma ray emissions. We calc…
Young, fast-rotating neutron stars are promising candidate sources for the production of ultrahigh energy cosmic rays (UHECRs). The interest in this model has recently been boosted by the latest chemical composition measurements of cosmic rays, that seem to show the presence of a heavy nuclear component at the highest energies. Neutrons stars, with their metal-rich surfaces, are potentially interesting sources of such nuclei, but some open issues remain: 1) is it possible to extract these nuclei from the star's surface? 2) Do the nuclei survive the severe conditions present in the magnetospher…
The flux of ultrahigh energy cosmic rays reaching the Earth is affected by the interactions with the cosmic radiation backgrounds as well as with the magnetic fields that are present along their trajectories. We combine the SimProp cosmic ray propagation code with a routine that allows to account for the average effects of a turbulent magnetic field on the direction of propagation of the particles. We compute in this way the modification of the spectrum which is due to the magnetic horizon effect, both for primary nuclei as well as for the secondary nuclei resulting from the photo-disintegrati…
We re-examine the possibility of ultrahigh energy cosmic rays being accelerated in nearby dormant quasars. We particularize our study to heavy nuclei to accommodate the spectrum and nuclear composition recently reported by the Pierre Auger Collaboration. Particle acceleration is driven by the Blandford-Znajek mechanism, which wires the dormant spinning black holes as Faraday unipolar dynamos. We demonstrate that energy losses are dominated by photonuclear interactions on the ambient photon fields. We argue that the local dark fossils of the past quasar activity can be classified on the basis o…
In this work, we present detailed simulations for propagation of ultra-high energy (UHE) heavy nuclei, with E > 60 EeV, within recent Galactic Magnetic Field (GMF) models. We investigate the impacts of the regular and turbulent components of the GMF. We show that with UHE heavy nuclei, there is no one-to-one correspondence between the arrival directions of cosmic rays (CR) measured at Earth and the direction of their extragalactic sources. Sources can have several distorted images on the sky. We compute images of galaxy clusters and of the supergalactic plane in recent GMF models and show the …
We propose a new method to search for heavy nuclei sources, on top of background, in the Ultra-High Energy Cosmic Ray data. We apply this method to the 69 events recently published by the Pierre Auger Collaboration and find a tail of events for which it reconstructs the source at a few degrees from the Virgo galaxy cluster. The reconstructed source is located at ~ 8.5 degrees from M87. The probability to have such a cluster of events in some random background and reconstruct the source position in any direction of the sky is about 7 x 10^(-3). The probability to reconstruct the source at less …
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）；Virginia Tech（弗吉尼亚理工大学）；The University of Tokyo（东京大学）
Newly-born pulsars offer favorable sites for the injection of heavy nuclei, and for their further acceleration to ultrahigh energies. Once accelerated in the pulsar wind, nuclei have to escape from the surrounding supernova envelope. We examine this escape analytically and numerically, and discuss the pulsar source scenario in light of the latest ultrahigh energy cosmic ray (UHECR) data. Our calculations show that, at early times, when protons can be accelerated to energies E>10^20 eV, the young supernova shell tends to prevent their escape. In contrast, because of their higher charge, iron-pe…
The luminosity densities of high-energy cosmic radiations are studied to find connections among the various components, including high-energy neutrinos measured with IceCube and gamma rays with the Fermi satellite. Matching the cosmic-ray energy generation rate density in a GeV-TeV range estimated for Milky Way with the ultrahigh-energy component requires a power-law index of the spectrum, $s_{\rm cr}\approx2.1-2.2$, somewhat harder than $s_{\rm cr}\approx2.3-2.4$ for the local index derived from the AMS-02 experiment. The soft GeV-TeV cosmic-ray spectrum extrapolated to higher energies can be…
Recent results from the Pierre Auger Collaboration have shown that the composition of ultrahigh-energy cosmic rays (UHECRs) becomes gradually heavier with increasing energy. Although gamma-ray bursts (GRBs) have been promising sources of UHECRs, it is still unclear whether they can account for the Auger results because of their unknown nuclear composition of ejected UHECRs. In this work, we revisit the possibility that low-luminosity GRBs (LL GRBs) act as the sources of UHECR nuclei, and give new predictions based on the intrajet nuclear composition models considering progenitor dependencies. …
We study possible correlations between ultrahigh energy cosmic rays (UHECRs), observed by Auger, AGASA and Yakutsk, and nearby active galactic nuclei (AGNs) and $Fermi$ sources. We consider the deflection effects by a Galactic magnetic field (GMF) model constrained by the most updated measurements. We found that the average deflection angles of UHECRs by the Galactic magnetic fields are less than $4^\circ$. A correlation between the Auger cosmic-ray events and nearby AGNs with a significance level of $\sim 4σ$ was found for the Auger UHECR data sets with or without deflection correction. No co…
We propose an innovative test of Lorentz symmetry by observing pairs of simultaneous parallel extensive air showers produced by the fragments of ultrahigh-energy cosmic ray nuclei which disintegrated in collisions with solar photons. We show that the search for a cross-correlation of showers in arrival time and direction becomes background free for an angular scale < 3^\circ and a time window {\cal O}(10 s). We also show that if the solar photo-disintegration probability of helium is {\cal O} (10^{-5.5}) then the hunt for spatiotemporal coincident showers could be within range of existing cosm…
The baryonic mass composition of ultrahigh energy ($\gtrsim 10^{18}$ eV) cosmic rays (UHECRs) at injection accompanied by their interactions on universal photon backgrounds during propagation directly governs the UHECR flux on the Earth. Secondary neutrinos and photons produced in these interactions serve as crucial astrophysical messengers of UHECR sources. A modeling of the latest data obtained by the Pierre Auger Observatory (PAO) suggests a mixed element composition of UHECRs with the sub-ankle spectrum being explained by a different class of sources than the super-ankle region ($> 10^{18.…
Data of Pierre Auger Observatory show a proton-dominated chemical composition of ultrahigh-energy cosmic rays spectrum at (1 - 3) EeV and a steadily heavier composition with energy increasing. In order to explain this feature we assume that (1 - 3) EeV protons are extragalactic and derive their maximum acceleration energy, E_p^{max} \simeq 4 EeV, compatible with both the spectrum and the composition. We also assume the rigidity-dependent acceleration mechanism of heavier nuclei, E_A^{max} = Z x E_p^{max}. The proposed model has rather disappointing consequences: i) no pion photo-production on …
Astrophysical sources of nuclei are expected to produce a broad spectrum of isotopes, many of which are unstable. An unstable nucleus can beta-decay outside the source into a single-electron ion. Heavy one-electron ions, thus formed, can be excited in their interactions with cosmic microwave background photons, in which case they relax to the ground state with the emission of a gamma ray. Repetitive cycles of excitation and gamma-ray emission can produce an observable feature in the gamma-ray spectrum with a maximum around 8 GeV (for iron). We find that the observed spectrum of Centaurus A is …
The photo-disintegration of cosmic ray nuclei by starlight leads to the production of secondary antineutrinos. We have assumed that the flux of the ultrahigh energy cosmic ray nuclei near the Galactic plane region is the same as that observed near the earth and calculated the antineutrino flux produced from their photo-disintegration. The IceCube detector has measured the neutrino/antineutrino flux in the TeV-PeV energy range. Our calculated secondary antineutrino flux in the energy range of 10-100 TeV is found to be much less compared to the flux detected by the IceCube collaboration. The upp…
We fit the ultrahigh-energy cosmic-ray (UHECR, $E\gtrsim0.1$ EeV) spectrum and composition data from the Pierre Auger Observatory at energies $E\gtrsim5\cdot10^{18}$ eV, i.e., beyond the ankle using two populations of astrophysical sources. One population, accelerating dominantly protons ($^1$H), extends up to the highest observed energies with maximum energy close to the GZK cutoff and injection spectral index near the Fermi acceleration model; while another population accelerates light-to-heavy nuclei ($^4$He, $^{14}$N, $^{28}$Si, $^{56}$Fe) with a relatively low rigidity cutoff and hard inj…
Ultrahigh energy cosmic rays are the most energetic of any subatomic particles ever observed in nature. The quest for their mysterious origin is currently a major scientific challenge. Here we explore the possibility that these particles originate from nearby starburst galaxies, a scenario that matches the recent observation by the Telescope Array experiment of a cosmic-ray hotspot above 57~EeV not far from the direction of the starburst galaxy M82. Specifically, we study the stochastic propagation in space of ultrahigh energy cosmic rays through the state-of-the-art simulation framework CRPro…
The sharp change in slope of the ultrahigh-energy cosmic ray spectrum around 10^{9.6} GeV (the ankle), combined with evidence of a light but extragalactic component near and below the ankle which evolves to intermediate/heavy composition above, has proved exceedingly challenging to understand theoretically. Recently, we introduced a very general model in which, for a range of source conditions, photo-disintegration of ultrahigh-energy nuclei in the region surrounding the accelerator naturally accounts for the observed spectrum and composition of the entire extragalactic component, which domina…
Charmed mesons may be produced when a primary cosmic ray or the leading hadron in an air shower collide with an atmospheric nucleon. At energies \ge 10^8 GeV their decay length becomes larger than 10 km, which implies that they tend to interact in the air instead of decaying. We study the collisions of long-lived charmed hadrons in the atmosphere. We show that (Λ_c,D)-proton diffractive processes and partonic collisions of any q^2 where the charm quark is an spectator have lower inelasticity than (p,π)-proton collisions. In particular, we find that a D meson deposits in each interaction just a…
In this paper we review the extragalactic propagation of ultrahigh energy cosmic-rays (UHECR). We present the different energy loss processes of protons and nuclei, and their expected influence on energy evolution of the UHECR spectrum and composition. We discuss the possible implications of the recent composition analyses provided by the Pierre Auger Observatory. The influence of extragalactic magnetic fields and possible departures from the rectilinear case are also mentioned as well as the production of secondary cosmogenic neutrinos and photons and the constraints their observation would i…
In the present paper, it is assumed that there exist two dark matter particles: superheavy dark matter particles (SHDM), whose mass $\sim$ inflaton mass, and light fermion dark matter (DM) particles which are the ultrahigh energy (UHE) products of its decay. The Earth will be taken as a detector to directly search for the UHE DM particles. These upward-going particles, which pass through the Earth and air and interact with nuclei, can be detected by the fluorescence detectors (FD) of the Pierre Auger observatory (Auger), via fluorescent photons due to the development of an EAS. The numbers and…
Tidal disruption events (TDEs) by supermassive or intermediate mass black holes have been suggested as candidate sources of ultrahigh-energy cosmic rays (UHECRs) and high-energy neutrinos. Motivated by the recent measurements from the Pierre Auger Observatory, which indicates a metal-rich cosmic-ray composition at ultrahigh energies, we investigate the fate of UHECR nuclei loaded in TDE jets. First, we consider the production and survival of UHECR nuclei at internal shocks, external forward and reverse shocks, and nonrelativistic winds. Based on the observations of Swift J1644+57, we show that…
The Pierre Auger Collaboration has reported an excess in the number of muons of a few tens of percent over expectations computed using extrapolation of hadronic interaction models tuned to accommodate LHC data. Very recently, we proposed an explanation for the muon excess assuming the formation of a deconfined quark matter (fireball) state in central collisions of ultrarelativistic cosmic rays with air nuclei. At the first stage of its evolution the fireball contains gluons as well as $u$ and $d$ quarks. The very high baryochemical potential inhibits gluons from fragmenting into $u \bar u$ and…
The sources of ultrahigh-energy cosmic rays (UHECRs) have been difficult to catch. It was recently pointed out that while sources of UHECR protons exhibit anisotropy patterns that become denser and compressed with rising energy, nucleus-emitting-sources give rise to a cepa stratis (onion-like) structure with layers that become more distant from the source position with rising energy. The peculiar shape of the hot spots from nucleus-accelerators is steered by the competition between energy loss during propagation and deflection on the Galactic magnetic field (GMF). Here, we run a full-blown sim…
Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences（高能物理研究所，中国科学院粒子天体物理重点实验室）；TIANFU Cosmic Ray Research Center（天府宇宙线研究中心）
Ultrahigh-energy cosmic rays (UHECRs) arrive at Earth from the most energetic astrophysical accelerators in the universe. They collide with atoms in the upper atmosphere with energies about ten times higher than any man-made accelerator, and produce gigantic cascades of secondary particles, called extensive air showers (EAS). Extensive air showers can be detected spreading particle detectors over a large area to record the interactions of secondary particles. The Pierre Auger Observatory has been designed to investigate the origin and nature of UHECRs using the combination of information from …
We use a multimessenger approach to constrain realistic mixed composition models of ultrahigh energy cosmic ray sources using the latest cosmic ray, neutrino, and gamma-ray data. We build on the successful Unger-Farrar-Anchordoqui 2015 (UFA15) model which explains the shape of the spectrum and its complex composition evolution via photodisintegration of accelerated nuclei in the photon field surrounding the source. We explore the constraints which can currently be placed on the redshift evolution of sources and the temperature of the photon field surrounding the sources. We show that a good fi…
The origin of the highest energy cosmic rays is still unknown. The discovery of their sources will reveal the workings of the most energetic astrophysical accelerators in the universe. Current observations show a spectrum consistent with an origin in extragalactic astrophysical sources. Candidate sources range from the birth of compact objects to explosions related to gamma-ray bursts or to events in active galaxies. We discuss the main effects of propagation from cosmologically distant sources including interactions with cosmic background radiation and magnetic fields. We examine possible acc…
The high-energy universe has revealed that energetic particles are ubiquitous in the cosmos and play a vital role in the cultivation of cosmic environments on all scales. Though they play a key role in cultivating the cosmological environment and/or enabling our studies of it, there is still much we do not know about AGNs and GRBs, particularly the avenue in which and through which they supply radiation and energetic particles, namely their jets. This White Paper is the second of a two-part series highlighting the most well-known high-energy cosmic accelerators and contributions that MeV gamma…
The Universe is filled with a diffuse background of MeV gamma-rays and PeV neutrinos, whose origins are unknown. Here, we propose a scenario that can account for both backgrounds simultaneously. Low-luminosity active galactic nuclei have hot accretion flows where thermal electrons naturally emit soft gamma rays via Comptonization of their synchrotron photons. Protons there can be accelerated via turbulence or reconnection, producing high-energy neutrinos via hadronic interactions. We demonstrate that our model can reproduce the gamma-ray and neutrino data. Combined with a contribution by hot c…
The origin of the ultrahigh energy cosmic ray remains being a mystery. However, a considerable progress has been made in the past few years due to the good quality data recorded by current cosmic ray observatories. One of the recent achievements is obtaining firm observational evidence about the extragalactic origin of the most energetic cosmic rays by the Pierre Auger observatory. On the other hand, it is believed that there is a non-null turbulent magnetic field that fills the intergalactic medium. Therefore, the presence of the intergalactic magnetic field can play an important role on the …
The Probe Of Extreme Multi-Messenger Astrophysics (POEMMA) is a potential NASA Astrophysics Probe-class mission designed to observe ultra-high energy cosmic rays (UHECRs) and cosmic neutrinos from space. POEMMA will monitor colossal volumes of the Earth's atmosphere to detect extensive air showers (EASs) produced by extremely energetic cosmic messengers: UHECRs above 20 EeV over the full sky and cosmic neutrinos above 20 PeV. We focus most of this study on the impact of POEMMA for UHECR science by simulating the detector response and mission performance for EAS from UHECRs. We show that POEMMA…
Rapidly-spinning magnetars can potentially form by the accretion induced collapse of a white dwarf or by neutron star mergers if the equation of state of nuclear density matter is such that two low mass neutron stars can sometimes form a massive neutron star rather than a black hole. In either case, the newly born magnetar is an attractive site for producing ultrahigh-energy cosmic rays (particles with individual energies exceeding $10^{18}\,{\rm eV}$; UHECRs). The short-period spin and strong magnetic field are able to accelerate particles up to the appropriate energies, and the composition o…
Measurements of proton and nuclear collisions at the Large Hadron Collider at nucleon-nucleon c.m. energies up to $\sqrt{s_{NN}}=$ 13 TeV, have improved our understanding of hadronic interactions at the highest energies reached in collisions of cosmic rays with nuclei in the earth atmosphere, up to $\sqrt{s_{NN}}\approx 450$ TeV. The Monte Carlo event generators (EPOS, QGSJET, and SIBYLL) commonly used to describe the air showers generated by ultrahigh-energy cosmic rays (UHECR, with $E_{CR}\approx 10^{17}$--$10^{20}$ eV) feature now, after parameter retuning based on LHC Run-I data, more cons…
Exploring the role of accretion shocks in galaxy clusters as sources of ultrahigh-energy cosmic rays
Instituto de Tecnologías en Detección y Astropartículas (ITeDA, CNEA-CONICET-UNSAM)（探测与天体粒子技术研究所）；Centro Atómico Constituyentes（孔斯蒂图延特斯原子中心）；Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA)（天体物理学与空间物理研究所）
The origin and nature of the ultrahigh energy cosmic rays (UHECRs) are still unknown. However, great progress has been achieved in past years due to the observations performed by the Pierre Auger Observatory and Telescope Array. Above $10^{18}$ eV the observed energy spectrum presents two features: a hardening of the slope at about $10^{18.7}$ eV, which is known as the ankle and a suppression at approximately $10^{19.6}$ eV. The composition inferred from the experimental data, interpreted by using the current high energy hadronic interaction models, seems to be light below the ankle, showing a…
Ultrahigh energy protons and nuclei from extragalactic cosmic ray sources initiate intergalactic electromagnetic cascades, resulting in observable fluxes of $γ$-rays in the GeV-TeV energy domain. The total spectrum of such cascade $γ$-rays of hadronic nature is significantly harder than the one usually expected from blazars. The spectra of some sources known as "extreme TeV blazars" could be well-described by this "intergalactic hadronic cascade model" (IHCM). We calculate the shape of the observable point-like spectrum, as well as the observable angular distibution of $γ$-rays, for the first …
