Radio galaxies are intensively discussed as the sources of cosmic rays
observed above about 3 EeV, called ultra-high-energy cosmic rays (UHECRs).
Here, the key issues from a recent investigation are summed up, where the
individual characteristics of radio galaxies, as well as the impact by the
extragalactic magnetic-field structures up to a distance of 120 Mpc has been
taken into account. It is shown that the average contribution of radio galaxies
taken over a very large volume cannot explain the observed features of UHECRs
measured at Earth. However, we obtain excellent agreement with the spectrum,
composition, and arrival-direction distribution of UHECRs measured by the
Pierre Auger Observatory, if we assume that most UHECRs observed arise from
only two sources: The ultra-luminous radio galaxy Cygnus A, providing a mostly
light composition of nuclear species dominating up to about 60 EeV, and the
nearest radio galaxy Centaurus A, providing a heavy composition dominating
above 60 EeV. Here we have to assume that extragalactic magnetic fields out to
250 Mpc, which we did not include in the simulation, are able to isotropize the
UHECR events at about 8 EeV arriving from Cygnus A

Eichmann, Björn

EPJ Web of Conferences

English

arXiv

A detailed investigation of radio galaxies has recently stressed these sources as the possible origin of the cosmic rays observed above 3 EeV. Here, the relevance of this model at energies below 3 EeV is investigated. It is shown that the average contribution of radio galaxies can accurately explain the observed CR flux between the second knee and the ankle in the case of a strong source evolution. However, the model cannot provide the increasing heaviness and variance at energies ≲ 1 EeV of the observed chemical composition. In addition, it is exposed that the resulting variance of the chemical composition at Earth shows also at higher energies a clear disagreement with the observations, indicating that the compositional contributions by Centaurus A and Cygnus A need to be less different

Eichmann Björn

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High-Energy Cosmic Rays from Radio GalaxiesBjörn Eichmann1,∗1Ruhr Astroparticle and Plasma Physics Center (RAPP Center), Ruhr-Universität Bochum, Institut für Theoretische Physik IV/ Plasma-Astroteilchenphysik, 44780 Bochum, GermanyAbstract. A detailed investigation of radio galaxies has recently stressed these sources as the possible originof the cosmic rays observed above 3 EeV. Here, the relevance of this model at energies below 3 EeV is inves-tigated. It is shown that the average contribution of radio galaxies can accurately explain the observed CR fluxbetween the second knee and the ankle in the case of a strong source evolution. However, the model cannotprovide the increasing heaviness and variance at energies . 1 EeV of the observed chemical composition. Inaddition, it is exposed that the resulting variance of the chemical composition at Earth shows also at higher en-ergies a clear disagreement with the observations, indicating that the compositional contributions by CentaurusA and Cygnus A need to be less different.1 IntroductionThe origin of the High-Energy Cosmic Rays (HECRs)is still one of the great enigmas of modern astrophysics.From observatories like the Pierre Auger Observatory(Auger) and the Telescope Array (TA) experiment atthe highest energies as well as KASCADE, KASCADE-Grande and a few other detectors at lower energies, thereare basically three main observational characteristics, thatdescribe our current knowledge of the HECRs:(1.) The energy spectrum, which changes at about0.4 EeV — the so-called second knee — to a steeperpower-law distribution with a spectral index ofabout 3.3 and flattens above about 3 EeV — the so-called ankle — to a spectral index of 2.6 and a sharpflux suppression above about 1019.5 eV [1–3].(2.) The chemical composition, that shows a decreaseof the fraction of heavier elements between about1017 eV and 1018.3 eV as well as an increase at ener-gies > 1018.3 eV [4–7].(3.) The large-scale arrival direction distribution, that isusually expressed in terms of the multipoles of theirspherical harmonics. Here, Auger recently reporteda 5σ detection of a dipole with an amplitude of≈ 6.5% at energies > 8 EeV, while higher-ordermultipoles as well as the multipoles at lower ener-gies are still consistent with isotropy [8].A likely source candidate of those extremely energetic par-ticles are radio galaxies due to their powerful accelerationsites within the jets, as already noted by Hillas in 1984[9]. A recent study by Eichmann et al. [10] — here-after referred to as E+18 — investigated in great detail∗e-mail: eiche@tp4.rub.dethe contribution of CRs above 3 EeV, called ultra-high-energy cosmic rays (UHECRs), by radio galaxies. Thismodel comprises three components: (a) a 3D structure ofradio galaxies and EGMF within a radius of 120 Mpc; (b)a continuous source function (CSF) derived from a lumi-nosity function of radio galaxies for the contributions frombeyond 120 Mpc; (c) a contribution of the powerful radiogalaxy Cygnus A, which is near the magnetic horizon andis expected to deliver the dominant contribution to UHE-CRs due to its extreme radio power and brightness. Allsimulations have been carried out with CRPropa3 [11],including deflections inside the Galaxy according to themagnetic field model of Jansson & Farrar [12]. So, E+18draw some solid conclusions on the UHECR contributionby radio galaxies:(i) The average contribution of all radio galaxies cannotexplain both spectrum and composition of UHECR.(ii) The spectrum and composition of UHECR can beexplained by the two brightest radio galaxies in thesky: Cygnus A and Centaurus A. Here, CygnusA needs to provide a solar-like composition, whileCentaurus A needs to have a heavy composition,with an iron fraction comparable to protons at agiven cosmic-ray energy. Further, both sources needa cosmic ray load significantly above the average ofthe bulk of radio galaxies.(iii) Also the anisotropy constraints at energies > 8 EeVare satisfied, if the UHECRs from Cygnus A are sig-nificantly deflected by the EGMF.In this paper, the model of E+18 is used to check addi-tional aspects of the observational data that have not beentaken into account so far. First, the Sect. 2 summarizes thephysics of the E+18 model. Subsequently, in Sect. 3 the© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 210, 04001 (2019) https://doi.org/10.1051/epjconf/201921004001UHECR 2018best-fit models of E+18 is applied in order to discuss theCR contribution by the CSF below the ankle as well as thevariance of the mean logarithm of the mass number.2 The E+18 modelAs shown in great detail in E+18, the established corre-lation between the jet power Qjet and the extended radioluminosity P151 at 151 MHz from Willott et al. [13] givesfor the minimal energy condition [14] a good estimate ofthe cosmic ray luminosityQcr '47Qjet = 1.3 × 1042 gcr(L1.1L∗)6/7 ergs, (1)and the maximal rigidityR̂(Qcr) = gacc√Qcr/c . (2)Here, the typical spectral behavior of Pν ∝ ν−0.6 is usedto obtain the luminosity L1.1 = 1.1 GHz P1.1 at 1.1 GHz inunits of erg/s, and L∗ ≈ 4.9 × 1040 erg/s denotes a charac-teristic luminosity according to Mauch and Sadler [15]. Indoing so, we suppose that the total power in CRs is signif-icantly higher than in relativistic electrons. From the un-certain efficiency of converting jet internal energy into ob-servable radio luminosity, as well as the uncertain detailsof the acceleration process one obtains the dimensionlesscoefficients1 . gcr . 50 and 0.01 . gacc . 0.5 . (3)Introducing different nuclei species i with charge num-ber Zi and an abundance fi, the total cosmic ray power percharge number yieldsQcr,i ≡ Qcr(Zi) = fi Zi Qcr/Z̄ . (4)Here, a simple abundance relation fi = fZqi has beensuggested, where f denotes solar abundances, so that theheaviness of the initial composition can be increased by asingle parameter q. Since q > 2 already leads to a domi-nant contribution at Earth by CR nuclei that left the sourceas an iron nucleus, it is suggested to keep the initial ironabundance below 2%, hence, 0 ≤ q ≤ 2.Apart from the individual treatment of the sourcesfrom the catalog of van Velzen et al. [16], the sources be-yond a distance of 120 Mpc from Earth, except for CygnusA, are treated by a CSF in a 1D simulation. Here, only theimpact of cosmic photon targets is taken into account dueto the lack of a known EGMF. So, the local CSF, Ψi,0(R),is derived asΨi,0(R) ≡dNcr(Zi)dVdR dt=∫ Q̂crQ̌crS i(R, R̂(Qcr), fi) dNRGdV dQcrdQcr ,(5)using the local radio luminosity function, dNRG/(dV dQcr),by Mauch and Sadler [15] and the CR spectrum,S i(R, R̂(Qcr), fi), of element species i with an abundancefi, emitted by a source with total cosmic ray power percharge number, Qcr,i, up to a maximal rigidity R̂(Qcr).The limits of integration are the smallest, Q̌cr, respectivelylargest, Q̂cr, CR powers that need to be considered. Tosolve the integral analytically, as shown in E+18, a sharpcutoff of the individual source spectra at R̂(Qcr) is sup-posed. The function Ψi,0(R) is the local continuous sourcefunction as it is derived from a radio luminosity functiondetermined in the local universe (z < 0.3). To extend it tolarger redshifts, the approximationΨi(R, z) ≈ Ψi,0(R) (1 + z)m−1 , (6)is used with a source evolution index m ∈ [3, 5]. The ana-lytical solution of the CSF (6) shows a spectral break at acritical rigidity R∗ = gacc√gcr Q∗/c ≈ 2×1018 gacc√gcr V.Thus, the spectral behavior of the CSF yields Ψi(R <R∗, z) ∝ R−a, where a denotes the spectral index of theindividual sources, and at high rigiditiesΨi(R > R∗, z) ∝R−3 , for a ≤ 2,R−1−a , for a > 2. (7)As already stressed in E+18, this spectral behavior im-pedes an explanation of the CR data above the ankle bythe CSF.3 New ProspectsIn order to investigate the observational data below the an-kle, the simulations of E+18 are performed again includ-ing energies down to 0.1 EeV. Further, the large compo-sitional gap between oxygen and iron is filled by addingsilicon to the initial composition of the sources. However,there is no significant impact of silicon on the previouslyobtained results.3.1 CR Flux above the second kneeBased on the best-fit scenario from E+18 the impact of theCSF below the ankle is investigated using individual pa-rameter values for Centaurus A and Cygnus A and con-sidering the hadronic interaction model of EPOS-LHC.First the influence of the source evolution parameter is an-alyzed, yielding an accurate explanation of the CR fluxabove the second knee by the E+18 model in the case of asource evolution index m ∼ 5. The Fig. 1 shows that onlya large value of m provides a spectral contribution by theCSF that is steep enough to describe the observed dip ofthe flux at the ankle. Otherwise, Centaurus A and CygnusA need an initial spectral index a  1.8 contravening thefirst-order Fermi acceleration theory, and as a consequencetheir baryonic load needs to become significantly smaller.The parameter values from a simple trial and error fit-ting to the data are given in table 1 and the correspondingCR fluxes are displayed by the red lines in the right Fig. 1.Note, that this result gives rather a proof of principle thanthe most likely parameter configuration. In addition, it isshown that the average distribution of radio galaxies canprovide the same — or even a higher — baryonic load asCentaurus A or Cygnus A in the case of a small accel-eration efficiency compared to Centaurus A. Further, the2EPJ Web of Conferences 210, 04001 (2019) https://doi.org/10.1051/epjconf/201921004001UHECR 2018Table 1. Best-fit parameters using solar abundances for all sources except for Centaurus A.m a ḡcr gCenAcr gCygAcr ḡacc gCenAacc gCygAacc qCenA5 1.8 18 25 27 0.09 0.18 0.08 2Upper index of the parameter indicates the corresponding source (Centaurus A or Cygnus A),bar on top of the parameter corresponds to all other sourcescritical rigidity R∗ significantly decrease with decreasingḡacc leading to a steeper spectral behavior around the ankleas seen in the left Fig. 1. Thus, more detailed parameterstudies are needed to give accurate constraints on the CRphysics of the CSF.17.5 18.0 18.5 19.0 19.5 20.0log(E [eV])1036103710381039 [eV^2/(km^2 yr sr)]Auger data gcr = 10.0 & gacc = 0.16 gcr = 20.0 & gacc = 0.16 gcr = 50.0 & gacc = 0.0217.5 18.0 18.5 19.0 19.5 20.0log(E [eV])1036103710381039 [eV^2/(km^2 yr sr)]Auger data m = 3.0 m = 4.0 m = 5.0Figure 1. Contribution of the CSF (dashed line) on the totalflux (solid line). The left figure shows three different parameterconfigurations in the case of a source evolution index m = 3.The right figure displays three different source evolution indexes,while the other parameters are chosen according to table 1. Theobservational data is taken from Auger [7].3.2 Chemical CompositionThe previously derived fit parameters yield also an excel-lent agreement with the 〈ln A〉 data at energies > 1018.2 eV,as shown in the left Fig. 2. However, the CSF cannot ac-count for the increase of 〈ln A〉 at energies < 1018.2 eV.Here, another source contribution with a rather heavy com-position is needed, as also indicated by the variance of ln Athat is discussed in the following.18.0 18.5 19.0 19.5 20.0 20.5 21.0log(E [eV])0.51.01.52.02.53.0<lnA>Auger (with EPOS­LHC)total18.0 18.5 19.0 19.5 20.0 20.5 21.0log(E [eV])01234Var(lnA) Auger (with EPOS­LHC)totalFigure 2. 〈ln A〉 (left figure) and Var(ln A) (right figure) based onthe fit parameters of table 1. The observational data is taken fromAuger [17].So far, the E+18 model has not been tested with re-spect to the resulting variance of ln A. There are goodreasons, as the observationally derived Var(ln A) valuesneed to be treated with some caution, since there are mul-tiple presumptions needed to obtain this observable. Espe-cially an appropriate parametrization of the Xmax distribu-tion is needed, which is usually done by generalized Gum-bel functions [18]. And note that the hadronic interactionmodel QGSJetII-04 yields negative Var(ln A) values [6],hence, either the QGSJetII-04 model, or the resulting vari-ance analysis needs to be defective.Keeping this in mind, however, it is clearly shown inthe right Fig. 2, that the model cannot explain the ob-served trend of the Var(ln A) values. Basically, the mix-ing of the strongly differing compositions of Centaurus Aand Cygnus A causes too much variance of the chemicalcomposition at Earth. Further, an additional source con-tribution with a rather heavy initial abundance is needed3EPJ Web of Conferences 210, 04001 (2019) https://doi.org/10.1051/epjconf/201921004001UHECR 2018in order to explain the increase in the variance as well asin the mean of the logarithm of the mass number at ener-gies < 1018.2 eV. Obviously, a solar-like CSF can not dothis job. In total, the compositional data by Auger suggesta heavy CR contribution that cuts-off around 1 EeV and arather pure chemical composition around 10 EeV. Both isnot provided by the E+18 model so far.4 ConclusionThe inclusion of observational data and simulations belowthe ankle demonstrates that the CSF for a source evolutionindex m ∼ 5 provides an accurate description of the CRflux data between about the second knee and the ankle,whereas Cygnus A and Centaurus A appropriately takeover at higher energies. Also the 〈ln A〉 data at energies> 1018.2 eV is matched perfectly by the model. However,the comparison of the resulting variance of ln A with ob-servational data shows a clear disagreement and exposesthe need for less variance between the initial abundancesof Centaurus A and Cygnus A. Up to a certain level, thishuge difference is a consequence of the simplified abun-dance relation, which predominantly yields either a pro-ton or an iron dominated outflow, and can hardly accountfor the dominance of the CNO group. Further, the cur-rent upper limits of other high energy messenger particleslike cosmogenic neutrinos show that a strong source evo-lution, m & 6 and a proton fraction fp & 0.27 can be ex-cluded [19]. Thus, the suggested fit scenario is most likelyclose to these upper limits. So, more detailed investiga-tions are needed that on the one hand, include a genericgalactic CR contribution and on the other hand, accountfor the constraints by the diffuse neutrino and extragalac-tic gamma-ray background data, as well as the large-scalearrival direction distribution of the CRs.In total, the E+18 model also provides a promising CRcontribution below the ankle, but the chemical composi-tion clearly indicates the need for an additional heavy CRsource at energies . 1 EeV — most likely of galactic ori-gin.References[1] D.R. Bergman, J.W. Belz, Journal of Physics G: Nu-clear and Particle Physics 34, R359 (2007)[2] R.U. Abbasi et al. (HiRes), Phys. Rev. Lett. 100,101101 (2008), astro-ph/0703099[3] J. Abraham et al. (Pierre Auger), Phys. Lett. B 685,239 (2010), 1002.1975[4] J. Abraham et al. (Pierre Auger), Phys. Rev. Lett.104, 091101 (2010), 1002.0699[5] K.H. Kampert, M. Unger, Astroparticle Physics 35,660 (2012), 1201.0018[6] A. Aab et al. (Pierre Auger), Phys. Rev. D90, 122006(2014), 1409.5083[7] M. Unger for the Pierre Auger Collaboration (PierreAuger), PoS ICRC2017, 1102 (2017), 1710.09478[8] A. Aab et al. (Pierre Auger), Science 357, 1266(2017), 1709.07321[9] A.M. Hillas, Ann. Rev. Astron. Astrophys. 22, 425(1984)[10] B. Eichmann, J. Rachen, L. Merten, A. van Vliet,J.B. Tjus, Journal of Cosmology and AstroparticlePhysics 2018, 036 (2018)[11] R. Alves Batista et al., JCAP 1605, 038 (2016),1603.07142[12] R. Jansson, G.R. Farrar, Astrophys. J.757, 14 (2012),1204.3662[13] C.J. Willott, S. Rawlings, K.M. Blundell, M. Lacy,Mon. Not. Roy. Astron. Soc.309, 1017 (1999),astro-ph/9905388[14] A.G. Pacholczyk, Radio Astrophysics. NonthermalProcesses in Galactic and Extragalactic Sources(W. H. Freeman & Co Ltd, San Francisco, 1970)[15] T. Mauch, E.M. Sadler, Mon. Not. Roy. Astron.Soc.375, 931 (2007), astro-ph/0612018[16] S. van Velzen, H. Falcke, P. Schellart, N. Niersten-höfer, K.H. Kampert, Astron. Astrophys.544, A18(2012), 1206.0031[17] A. Aab et al. (Pierre Auger), Phys. Rev. D 90, 122005(2014)[18] M.D. Domenico, M. Settimo, S. Riggi, E. Bertin,Journal of Cosmology and Astroparticle Physics2013, 050 (2013)[19] A. van Vliet, R. Alves Batista, J.R. Hörand el, arXive-prints arXiv:1901.01899 (2019), 1901.018994EPJ Web of Conferences 210, 04001 (2019) https://doi.org/10.1051/epjconf/201921004001UHECR 2018

High-Energy Cosmic Rays from Radio Galaxies

Björn Eichmann

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Summing up Ultra-High-Energy Cosmic Rays from Radio Galaxies

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