The Astrophysical Journal, 698:L138–L141, 2009 June 20 doi:10.1088/0004-637X/698/2/L138C© 2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

COMPOSITION OF COSMIC RAYS ACCELERATED IN ACTIVE GALACTIC NUCLEI

E. G. Berezhko

Yu. G. Shafer Institute of Cosmophysical Research and Aeronomy, 31 Lenin Ave., 677980 Yakutsk, Russia; berezhko@ikfia.ysn.ruReceived 2009 April 6; accepted 2009 May 20; published 2009 June 1

ABSTRACT

The composition of the overall spectrum of cosmic rays (CRs) is studied under the assumption that ultra highenergy CRs above the energy 1017 eV are produced at the shock created by the expanding cocoons aroundactive galactic nuclei (AGNs). It is shown that the expected CR composition is characterized by two peaksin the energy dependence of the mean CR atomic number 〈A(ε)〉. The first one at the energy ε ≈ 1017 eVcorresponds to the very end of the Galactic CR component, produced in supernova remnants (SNRs). It isfollowed by a sharp decrease of 〈A(ε)〉 within the energy interval from 1017 to 1018 eV. This is a signatureof the transition from Galactic to extragalactic CRs. The second peak, with 〈ln A〉 ≈ 2, at energy ε ≈ 1019

eV, expected at the beginning of the GZK cutoff, is the signature of the CR production by the nonrelativis-tic cocoon shocks. The calculated CR composition is consistent with the existing data. The alternative sce-nario, which suggests reacceleration increasing the energy of CRs produced in SNRs by a factor of 30, is alsoexamined.

Key words: acceleration of particles – cosmic rays – galaxies: active – shock waves – supernova remnants

1. INTRODUCTION

The overall origin of cosmic rays (CRs), in particular at ultrahigh energies, above 1018 eV, is still an unresolved problemin astrophysics (e.g., Nagano & Watson 2000; Stanev 2004;Cronin 2005; Inoue 2008). Understanding this origin requiresthe determination of the astrophysical objects that are the CRsources, and of the appropriate acceleration processes that formthe CR spectrum in these objects. During the last several yearsconsiderable progress has been achieved in this field, bothexperimentally and theoretically. Recently, the sharp steepeningof the CR spectrum above 3 × 1019 eV was established inthe HiRes (Bergman et al. 2007) and Auger (Abraham et al.2008) experiments. It presumably corresponds to the so-calledGreizen–Zatsepin–Kuzmin (GZK) cutoff, caused by energylosses of the CRs in their interactions with the microwavebackground radiation. This is evidence that the highest energypart of the CR spectrum is of extragalactic origin. It was alsorecently demonstrated (Berezhko & Volk 2007) that the CRswith energies up to ε ∼ 1017 eV can be produced in supernovaremnants (SNRs) as a result of diffusive shock acceleration(Krymsky 1977; Bell 1978), and that the observed CR energyspectrum can be well represented by two components: thefirst, dominant up to 1017 eV, consists of CRs produced inGalactic SNRs; the second, dominant at energies above 1018

eV, is of extragalactic origin. The latter component can beproduced at the shock that is formed by the expanding cocoonaround active galactic nuclei (AGNs): above the energy 1018

eV the overall energy spectrum of CRs, produced during theAGN evolution and released into intergalactic space, has anappropriate power-law form, which extends at least up to theenergy εmax ∼ 1020 eV, well above the GZK cutoff (Berezhko2008). This is the “dip scenario” of the overall CR spectrumformation (Berezinsky et al. 2006). Within the alternative “anklescenario,” extragalactic CRs are expected to dominate onlyabove the energy 1019 eV (Berezinsky et al. 2006). It was noted(Berezhko & Volk 2007; Berezhko 2008) that the compositionof CRs at ε > 1017 eV is expected to be very different inthese two scenarios. Therefore, the study of CR compositioncan in principle provide the signature of the acceleration

mechanism, which creates the spectrum of the extragalactic CRcomponent.

Here, we present the calculations of the expected compositionof CRs, accelerated by cocoon shocks, and demonstrate that ithas well pronounced peculiarities, which can be considered as asignature of ultra high energy CR production by nonrelativisticshocks. The calculated composition is compared with thecomposition expected within the alternative scenario and withthe existing data. The alternative scenario, which suggestsreacceleration increasing the energy of CRs produced in SNRsby a factor of 30, is also examined.

2. RESULTS AND DISCUSSION

The composition of CRs is determined if we know not onlytheir all-particle spectrum,

J (ε) =∑

A

JA(ε) (1)

that is the differential intensity J (ε) with respect to particleenergy ε, but also the spectra JA(ε) of all relevant elementswith atomic number A. Since the shock-accelerated CRs comeoriginally from the thermal background plasma, one has toexpect that the flux of each CR element in/near the sourceis proportional to the number density of this element NA inthe background plasma: J s

A(ε) ∝ NA. Therefore, it is useful torepresent the spectrum of each CR element in the form

J sA(ε) = eA(ε)aAJ s

H(ε), (2)

where aA = NA/NH is the abundance of element A relative tothe hydrogen abundance and eA(ε) is an enrichment factor whichdescribes the preferential production of element A relative to theproduction of protons (marked by the subscript H).

Direct measurements of CR fluxes at energies ε < 1014 eVshow that the factor eA > 1 considerably exceeds unity and thatit progressively increases with the increase of A (e.g., Berezhko& Ksenofontov 1999). This means a considerable enrichmentof CRs in heavy elements compared with the interstellarabundance. Note that at these relatively low energies, where

L138

No. 2, 2009 COMPOSITION OF CRs FROM AGNs L139

direct determination of CR particle parameters is possible, thefluxes JA and JH are usually compared at the same energyper nucleon, that is for εA = AεH. Since it is impossible todetermine the mass of individual CR particles at ultra highenergies, the particle energy instead of the energy per nucleonis the most appropriate variable for the analysis of CR spectrumand composition in this case.

The observed CR composition at ε < 1017 eV is wellconsistent with the scenario in which Galactic CR componentis produced by supernova shocks (Berezhko & Volk 2007). Theenrichment of shock-accelerated CRs by heavy elements is dueto a more effective injection and subsequent acceleration ofheavy ions (see Berezhko & Ksenofontov 1999, for the details).

The spectra of ultra high energy CRs produced by nonrela-tivistic cocoon shocks can be represented in the form (Berezhko2008)

J sA(ε) = CAε−γ , (3)

where γ ≈ 2.6 and the values of parameters CA ∝ eANA aredetermined by the background medium’s composition NA andby the enrichment factors eA. Since the injection/accelerationof CRs at cocoon and supernova shocks are expected to be verysimilar, the values of the enrichment factors eA in the formercase can be extracted from the experimentally measured fluxesof the Galactic CR component JA(ε) at some fixed energy, sayε = 1 TeV (see, e.g., Berezhko & Volk 2007), according to theexpression

eA = JA(1 TeV)/JH(1 TeV)(NH/NA)�. (4)

Here, (NA/NH)� is the solar system relative abundance ofelements with atomic number A.

In order to calculate the spectra of extragalactic CRs insidethe Galaxy one needs to take into account the modificationof the CR spectra due to their interaction with the cosmicmicrowave background (CMB) and due to their modulation inthe Galactic wind. This can be done by representing the observedextragalactic CR spectrum in the form

JA(ε) = PlPhJsA(ε), (5)

where factors Pl and Ph describe CR flux modification dueto Galactic wind and CMB, respectively. Since the diffusivemobility of the CRs is inversely proportional to the particlecharge number Z, the first factor can be represented in the form

Pl = exp(−Zεl/ε), (6)

where εl ∼ 1017 eV (Berezhko & Volk 2007). This expressionshows that at a given energy the lighter CR species canmore easily penetrate the inner Galaxy from outside. Due tothis factor the observed extragalactic CR component becomesprogressively heavier with increasing energy.

To describe the effects of CRs interacting with the CMB radi-ation during their propagation from extragalactic sources to theobserver—pion and pair production, CR nuclei photodesinte-gration and adiabatic cooling—we use a simple analytical formof the factor Ph

Ph = exp[−(Aε/εh)2]. (7)

At εh = 1.3 × 1018 eV for the case of helium and iron nucleiit satisfactorily fits the results of detailed calculations whichconsistently describes all these effects (Berezinsky et al. 2006).In the case of protons, instead of the modification factor Ph we

Figure 1. Overall CR intensity as a function of energy (thick solid line),Galactic CR component produced in SNRs (thick dashed line), and extragalacticcomponent produced in the IGM (thick dash-dotted line). The spectra of differentextragalactic components are shown by thin lines. Experimental data obtainedin the ATIC-2 (Panov et al. 2007), JACEE (Asakimori et al. 2003), KASCADE(Antoni et al. 2005), Akeno (Takeda et al. 2003), and HiRes (Bergman et al.2007) experiments are shown as well.

directly use their modified spectrum calculated by Berezinskyet al. (2006).

As is clear from expression (7), the interaction of CR nucleiwith the CMB radiation produces a sharp cutoff in their spectraat the energy, which is proportional to the nuclear mass. Due tothis fact CRs are expected to become progressively heavier atenergies above 1018 eV.

The cocoon shock propagates initially through the interstellarmedium (ISM) of the host galaxy and later through the inter-galactic medium (IGM). The IGM is less abundant in heavyelements than the ISM: the median metallicity of the IGM is(NA/NH) = 0.2(NA/NH)� for all relevant elements heavierthan helium (e.g., Cen & Ostriker 2006). Since the maximal CRenergy produced by the expanding cocoon shock decreases withtime (Berezhko 2008), the local metallicity at the shock frontchanges from the ISM value (NA/NH) ≈ (NA/NH)� at earlyphases, when the shock produces CRs up to εmax ∼ Z × 1020

eV, to the IGM value at late phases, when εmax ∼ Z × 1018

eV. To describe this effect we use a metallicity (NA/NH) =0.2[ε/(Z×1018 eV)]0.35(NA/NH)�. For helium we use the cos-mological value NHe = 0.08NH (e.g., Berezinsky et al. 2006).Using these number densities one can calculate the relative val-ues of the coefficients CA/CH for all elements except protons.The proton coefficient CH depends on a number of physicalfactors such as the IGM hydrogen number density NH and thepower and spatial distribution of nearby AGNs. Its value is de-termined by the fit of the expected all-particle CR flux J (ε)to the existing measurements of the CR intensity at energiesε > 1018 eV.

Secondary protons appearing as a result of photodesintegra-tion of helium nuclei are also included in an approximate way:it is assumed that the secondary protons (whose total numberequals four times the number of helium nuclei in the sourcespectrum with energy above 2 × 1018 eV) have the normal en-ergy distribution around ε0 = 5 × 1017 eV within the intervalΔε = ε0.

In Figure 1, we present the all-particle spectrum whichincludes two components: CRs produced in SNRs (Berezhko& Volk 2007) and extragalactic CRs, which consist of protons(H), helium (He), and three groups of heavier nuclei, producedin AGNs. Note that the dip at energy ε ≈ 1019 eV is stillclearly seen even though it is less pronounced compared with

L140 BEREZHKO Vol. 698

Figure 2. Mean logarithm of the CR nucleus atomic number as a function ofenergy. The solid and dashed lines correspond to the dip and ankle scenarios,respectively. Experimental data obtained in the ATIC-2, JACEE, KASCADE(QGSJET and SYBYLL; Horandel 2005), and HiRes (QGSJET and SYBYLL;Abbasi et al. 2005) experiments are shown.

the case of pure proton composition. The calculated overallCR spectrum is in a satisfactory way consistent with theexperimental data, except in the energy interval 1017 < ε < 1018

eV in the transition region, where, contrary to the experiment,the calculated spectrum has a small dip. Taking into accountthe existing experimental uncertainties at these energies it is notclear whether this discrepancy is a serious problem for the modelor not. Note that the size and the shape of this peculiarity is verysensitive to the details of the galactic CR high-energy cutoff andto the extragalactic low-energy spectrum part. Therefore, it ishard to predict it quantitatively. At the same time the overallspectrum, which is a mixture of two independent components,should have such peculiarity within the transition region. If theactual CR spectrum is indeed so uniform within the energy range1017 < ε < 1018 eV, as it looks according to the Akeno data,then it should be considered as a serious problem for the dipscenario.

The mean logarithm of CR atomic number is representedin Figure 2 as a function of energy. As already qualitativelypredicted (Berezhko 2008), the CR mass energy dependence〈ln A(ε)〉 has two peaks. The first one at the energy ε ≈ 1017

eV corresponds to the very end of the galactic CR component(Berezhko & Volk 2007), whereas the second, at the energyε ≈ 1019 eV, is at the beginning of the GZK cutoff. Note that athigh energies ε > 1015 eV information about CR compositionis obtained from the mean values of the shower maxima Xmax(usually measured in g cm−2), determined by the ground-baseddetectors. Knowing the average depth of the shower maximumfor protons, XH

max, and for iron nuclei, XFemax, from simulations,

the mean logarithmic mass can be estimated from the measuredXmax according to the relation (e.g., Horandel 2005)

〈ln A〉 = (Xmax − XHmax)/(XFe

max − XHmax)〈ln 56〉. (8)

This conversion requires the choice of a particle interactionmodel. Here, we use the values of Xmax, measured in the HiResexperiment (Abbasi et al. 2005), and the QGSJET and SYBYLLmodels to determine 〈ln A〉. It is seen from Figure 2 that theHiRes data are very well consistent with the expected sharpdecrease of 〈ln A〉 within the energy interval 1017–1018 eV. Athigher energies, between 1018 and 1019 eV, the experimentalvalues of 〈ln A(ε)〉 have a quite irregular behavior. Nevertheless,the experiment reveals a trend of progressive increase of the

Figure 3. Same as in Figure 1, but for the ankle scenario. The dashed linerepresents the Galactic component, which includes CRs produced in SNRs andreaccelerated CRs. The dash-dotted line represents the extragalactic component;it corresponds to the source spectrum J s

A ∝ ε−2 (Berezinsky et al. 2006).

mean CR mass so that the expected peak value 〈ln A〉 ≈ 1.7at the energy ε ∼ 1019 eV is consistent with the existingHiRes data. It is also clear from Figure 2, that a more preciseexperimental determination of the CR mass composition forε > 1015 eV is required for a more complete conclusion aboutthe CR origin.

3. ALTERNATIVE SCENARIO

The alternative scenario for the overall CR spectrum isthe “ankle scenario” (Berezinsky et al. 2006). In this case,the extragalactic source spectrum, as compared with the dipscenario, is assumed to be much harder J s

A ∝ ε−2 so thatit becomes dominant above an energy of ε = 1019 eV (e.g.,Berezinsky et al. 2006). Therefore, to fit the observed overallCR spectrum one needs a third component to fill the gapbetween the Galactic CR spectrum, produced by SNRs, andthe hard extragalactic spectrum. It is hard to believe that thisthird CR component could be completely independent of theCR component produced in SNRs, since in such a case oneshould expect some peculiarity in the spectral shape at energyε ≈ 1017 eV, where these two components are expected tomatch. The appropriate solution of this problem is the existenceof some kind of reacceleration process which picks up themost energetic CRs from SNRs and substantially increasestheir energy, resulting in a smooth extension of the first CRcomponent toward the higher energies.

We model the spectra of reaccelerated CRs in the followingway, without specifying the reacceleration mechanism. Forevery element with the nuclear charge number Z, as in the dipscenario, we use the spectrum, which coincides with JA(ε) forε < εZ

max1 and has a form

JA(ε) = JA(εZmax1)(ε/εZ

max1)−γ exp(−ε/εZmax2) (9)

at ε > εZmax1. Here, εZ

max1 is the minimum energy of particlesinvolved in reacceleration, and εZ

max2 is the maximum particleenergy achieved during reacceleration. It is natural to assumethat these energies scale proportional to the rigidity εZ

max =Zε

pmax. Here, the superscript p denotes protons. The quantities

εpmax1, ε

pmax2, and γ are treated as free parameters whose values

are determined as a result of the best fit. CR acceleration by spiraldensity shocks in the Galactic wind (Volk & Zirakashvili 2004),or acceleration in the vicinity of pulsars (Bell 1992; Berezhko1994) could play the role of the reacceleration mechanism.

No. 2, 2009 COMPOSITION OF CRs FROM AGNs L141

We present in Figure 3 the CR spectrum calculated withinthe ankle scenario, with the adopted values ε

pmax1 = 5 × 1015

eV, εpmax2 = 1.5 × 1017 eV, and γ = 3, which provide the best

fit to the observed CR spectrum. Following Berezinsky et al.(2006), we use the extragalactic CR source spectrum in theform J s

A ∝ ε−2 and assume the composition of these CRs with〈A(ε)〉 = 1.

It is seen that at ε > 1017 eV it is well consistent with thedata. However, such a well known peculiarity in CR spectrumas the knee at ε ≈ 3 × 1015 eV is much less pronounced in thetheoretical CR spectrum than in the experiment. This may beconsidered as an indication against the ankle scenario.

As it is seen in Figure 2, the CR composition correspondingto the ankle scenario is considerably heavier at energies 1017ε <1019 eV than in the dip scenario and is inconsistent withthe HiRes measurements. Note that CR composition of thereaccelerated CRs is a direct consequence of the heavy CRcomposition at the energy ε > εZ

max1, where the reaccelerationis assumed to start, and it is not sensitive to the details ofreacceleration process.

Since the expected spectrum of CRs produced in gamma-raybursts (GRBs) has a form J s ∝ ε−γ with γ = 2–2.2 only anklescenario is possible if GRBs are the source of extragalactic CRcomponent (see Berezinsky et al. 2006, and references therein).It means that HiRes CR composition is against GRBs as a sourceof ultra high energy CRs. In addition, as Berezinsky et al. (2006)argued, the energy output of GRBs has a serious problem if theyare considered as the main source of the extragalactic CRs. Notealso that based on the data collected at the Auger experiment,correlation between the arrival directions of CRs with energyabove 6 × 1019 eV and the position of nearby AGNs has beenfound (Abraham et al. 2007) that strongly supports AGNs as aprime candidate for the source of ultra high energy CRs.

4. SUMMARY

The composition of ultra high energy CRs produced bynonrelativistic cocoon shocks around AGNs is characterizedby well pronounced peculiarities which are two peaks in theenergy dependence of the mean CR atomic number 〈A(ε)〉. Thefirst peak at the energy ε ≈ 1017 eV corresponds to the very endof the Galactic CR component, produced in SNRs (Berezhko& Volk 2007), whereas the second, at the energy ε ≈ 1019

eV, is expected at the beginning of the GZK cutoff. The strong

energy dependence of the CR composition within the energyinterval from 1017 to 1018 eV is expected as a signature ofthe transition from heavy Galactic to light extragalactic CRs,whereas the detection of a heavy CR composition at ε ≈ 1019

eV has to be considered as the signature of CR production bythe nonrelativistic cocoon shocks.

The existing measurements of CR composition are consistentwith the dip scenario with a formation of the CR spectrum inSNRs and AGNs and are inconsistent with the ankle scenario,which includes reacceleration of CR produced in SNRs as athird CR component. Additional peculiarity in the overall CRspectrum—the dip in the transition region 1017 < ε < 1018

eV—is expected within the dip scenario. Since it is not seenin the existing data it is a real difficulty for the dip scenario.It is therefore clear that a more precise measurements of CRspectrum and composition at energies above 1017 eV are neededfor a strict determination of CR origin.

I thank H. J. Volk for the helpful discussions. The work wassupported by the Russian Foundation for Basic Research (grants06-02-96008, 07-02-00221).

REFERENCES

Abbasi, R. U., et al. 2005, ApJ, 622, 910Abraham, J., et al. (Pier Auger Collaboration) 2007, Science, 318, 938Abraham, J., et al. 2008, Phys. Rev. Lett., 101, 061101Antoni, T., et al. 2005, Astropart. Phys., 24, 1Asakimori, K., et al. 2003, ApJ, 502, 278Bell, A. R. 1978, MNRAS, 182, 147Bell, A. R. 1992, MNRAS, 257, 493Berezhko, E. G. 1994, Astron. Lett., 20, 75Berezhko, E. G. 2008, ApJ, 684, L69Berezhko, E. G., & Ksenofontov, L. T. 1999, J. Exp. Theor. Phys., 89, 391Berezhko, E. G., & Volk, H. J. 2007, ApJ, 661, L175Berezinsky, V. S., et al. 2006, Phys. Rev. D, 74, 043005Bergman, D. R., et al. 2007, Nucl. Phys. B (Proc. Supl.), 165, 19Cen, R., & Ostriker, J. 2006, ApJ, 650, 560Cronin, J. W. 2005, Nucl. Phys. B (Proc. Supl.), 138, 465Horandel, J. R. 2005, arXiv:astro-ph/0508014Inoue, S. 2008, J. Phys. Conf. Ser., 120, 062001Krymsky, G. F. 1977, Sov. Phys. Dokl., 23, 327Nagano, M., & Watson, A. A. 2000, Rev. Mod. Phys., 72, 689Panov, A. D., et al. 2007, Bull. Russian Acad. Sci., 71, 494Stanev, T. 2004, in High Energy Cosmic Rays, (Chichester: Springer)Takeda, M., et al. 2003, Astropart. Phys., 19, 447Volk, H. J., & Zirakashvili, V. N. 2004, A&A, 417, 807