We study the propagation of ultra-high energy cosmic ray nuclei through the background of cosmic microwave and intergalactic infrared photons, using recent re-estimates for the density of the last ones. We perform a detailed Monte Carlo simulation to follow the disintegration histories of nuclei starting as Fe and reaching the Earth from extragalactic sources. We obtain the maximum energies of the arriving nuclear fragments as well as the mass composition as a function of the distance traveled. Cosmic rays with energies in excess of 2 × 1020 eV cannot originate from Fe nuclei produced in sources beyond 10 Mpc.Facultad de Ciencias Exacta

Epele, Luis Nicolás

Roulet, Esteban

Journal of High Energy Physics

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JHEP10(1998)009Received: August 12, 1998, Accepted: October 8, 1998HYPER VERSIONOn the propagation of the highest energycosmic ray nucleiLuis N. Epele and Esteban RouletDepto. de F́ısica, Universidad Nacional de La PlataCC67, 1900, La Plata, ArgentinaE-mail: roulet@venus.fisica.unlp.edu.arAbstract: We study the propagation of ultra-high energy cosmic ray nuclei throughthe background of cosmic microwave and intergalactic infrared photons, using recentre-estimates for the density of the last ones. We perform a detailed Monte Carlosimulation to follow the disintegration histories of nuclei starting as Fe and reachingthe Earth from extragalactic sources. We obtain the maximum energies of the arrivingnuclear fragments as well as the mass composition as a function of the distance traveled.Cosmic rays with energies in excess of 2 × 1020 eV cannot originate from Fe nucleiproduced in sources beyond 10 Mpc.Keywords: High Energy Cosmic Rays, Electromagnetic Processes and Properties.JHEP10(1998)009Contents1. Introduction 12. The propagation of heavy nuclei 23. Results 41. IntroductionThe cosmic ray (CR) spectrum is known to extend up to energies beyond 1020 eV, withthe highest energy air showers observed having energies of 2–3×1020 eV. The originand nature of these ultra-high energy (UHE) events are one of the pressing unsolvedproblems defying us today. The CR spectrum has the overall shape of a leg, and is wellfitted by power laws, whose index increases (spectrum steepening) for energies abovethe ‘knee’ (E ∼ 3×1015 eV), flattening again above the ‘ankle’ (at E ∼ 5×1018 eV). TheCR composition becomes heavier for increasing energies around the knee, and the CRare probably mostly of galactic origin up to the ankle. Approaching the ankle, the CRcomposition seems to become lighter again, and the increasing rigidity of CRs does notallow anymore their confinement into the Galaxy. Hence, CR fluxes are most probablyof extragalactic origin above the ankle. There have been studies suggesting that thearrival direction of the highest energy events may be indicating that their origin liesin the local supercluster, but they are not conclusive. The small anisotropies observedmay also be compatible with a cosmological origin of the highest energy events.The big difficulty which appears is that CR protons with E >∼ 5 × 1019 eV, i.e.relativistic γ factors >∼ 5 × 1010, are not able to propagate more than ∼ 100 Mpc dueto their energy losses by photopion production off the cosmic microwave background(CMB) photons, giving rise to the well known GZK cutoff [1]. At energies 2× 1020 eVtheir mean free path is already only 30 Mpc. Heavy nuclei with smaller γ factors,but comparable energies, also get attenuated but mainly by photodisintegrations offthe intergalactic infrared (IR) background and off CMB photons, as well as by paircreation losses to a lesser extent [2, 3, 4, 5, 6, 7].A detailed study of the propagation of UHECR Fe nuclei, including all the relevantenergy loss mechanisms, was performed more than twenty years ago by Puget, Steckerand Bredekamp [5]. However, the estimates of the density of IR photons employedthen were about an order of magnitude larger than the new empirically based estimates1JHEP10(1998)009obtained using the measured emissivity of IRAS galaxies [8]. In the light of the lowerIR background densities inferred recently, it was suggested that UHECR nuclei maypropagate much longer distances unattenuated [9], so that the events with energies2–3×1020 eV could have possibly originated as Fe nuclei produced at distances upto 100 Mpc, and hence in particular in the whole local supercluster.1 However, as weshowed in a recent letter [10], at energies larger than 1020 eV it is photodisintegration offCMB photons (and not off IR ones) which dominates the opacity for Fe disintegration.This implies that the maximum energies with which the surviving fragments can reachthe Earth are not significantly changed (for distances below a few hundred Mpc) withthe new estimates of the IR density. In particular, for sources at distances of 100 Mpcthe maximum energies of the surviving fragments do not exceed ∼ 1020 eV, and canarrive to 2× 1020 eV only for distances below 10 Mpc.The aim of the present paper is to re-evaluate in detail the propagation of heavynuclei, following the photodisintegration histories by means of a Monte Carlo whichincludes all relevant processes, much in the spirit of the original Puget et al. paper [5].From this we can establish all the effects resulting from the new estimates of the IRbackground density. In particular, we obtain the final mass composition and energy asa function of the distance to the source, as well as the possible fluctuations in thesequantities which may arise from the particular way in which the photodisintegrationtakes place in each case. We also study the effects of pair creation losses, which turnout to be important in some cases for the determination of the final mass composition.2. The propagation of heavy nucleiAs we said before, CR with energies above the ankle are most probably extragalactic.This means that in their journey they may be attenuated by the interactions with thephoton background. This background consists essentially of the microwave photonsof the 2.7◦K cosmic background radiation and, at larger energies, of the intergalacticbackground of IR photons emitted by galaxies. The background of optical radiationturns out to be of no relevance for UHECR propagation.Although the CMB density is well known, the intergalactic IR one cannot be mea-sured directly and has to be estimated from the observation of the spatial distribution,IR spectra and emissivity of the galaxies which are sources for this IR emission. Thiswas done recently by Malkan and Stecker [8], who obtained a result which is aboutan order of magnitude smaller than previous estimates. We will then adopt for thespectral density of the IR backgrounddnd= 1.1× 10−4eV−2.5cm−3eV−1 (2.1)1It has to be stressed that Fe nuclei are good candidates for UHECRs, due to their high abundancein supernova environments and their large value of Z, which enhances the energy achievable in theacceleration process.2JHEP10(1998)009for photon energies  in the range between 2×10−3 eV and 0.8 eV. This is a factor of 10smaller than the “high infrared (HIR)” density adopted in ref. [5], and is in the upperrange of the recent estimates. In order to quantify the possible effects of an opticalintergalactic background, we just modeled this last with a Planckian distribution withT = 5000◦K and a dilution factor of 1.2× 10−15, as in [5].UHECR nuclei propagating through these photon backgrounds will loose energymainly by two processes:i) photopair production, which has a threshold corresponding to photon energies inthe rest frame of the nucleus of 2mec2 ' 1 MeV. This process was studied in detail byBlumenthal [11], and the main contribution arises from interactions with CMB photons.We used for the energy loss rate the expressions given in ref. [12].ii) photodisintegration losses, for which the rate of emission of i nucleons from anucleus of mass A (with cross section σA,i) is given byRA,i =12γ2Z ∞0d2dndZ 2γ0d00σA,i(0) , (2.2)where γ is the relativistic factor of the nucleus,  the photon energy in the observer’ssystem and 0 its energy in the rest frame of the CR nucleus.The cross sections for photodisintegration σA,i(0) contain essentially two regimes.At 0 < 30 MeV there is the domain of the giant resonance and the disintegrationproceeds mainly by the emission of one or two nucleons. At higher energies, the crosssection is dominated by multi-nucleon emission for heavy nuclei and is approximatelyflat up to 0 ∼ 150 MeV. We fitted the various σA,i with the parameters in Table I andII of ref. [5]. A useful quantity to estimate the energy loss rate by photodisintegrationis given by the effective rateReff,A =dAdt=XiiRA,i . (2.3)Since neglecting pair creation processes one has that photodisintegrations alonelead to E−1dE/dt = A−1dA/dt, the energy loss time for photodisintegration is thenA/Reff,A. The different contributions to this quantity are plotted in fig. 1. We showseparately the contributions to the disintegration from CMB, IR and optical photonsfor Fe nuclei, together with the total one (solid line) and the photopair creation energyloss rate.2It is apparent that the optical background has no relevant effect, that the IR onedominates the photodisintegration processes below 1020 eV and the CMB dominatesabove 1020 eV. The pair creation rate is relevant for Fe energies 4×1019 eV–2×1020 eV(i.e. γ factors ∼ 1–4×109), for which the typical CMB photon energy in the rest frameof the nucleus is above threshold (> 1 MeV) but still well below the peak of the giantresonance (∼ 10–20 MeV). The effect of pair creation losses is to reduce the γ factorof the nucleus, obviously leaving A unchanged.2Looking at this and the following figures, it is important to keep in mind that 1 Mpc= 1.03×1014 s.3JHEP10(1998)0091e+141e+151e+161e+171e+181e+191e+201e+18 1e+19 1e+20 1e+21Energy Loss Time  [s]E [eV]IRCMBPCOPFigure 1: Effective energy loss time for Fe photodisintegration off microwave (CMB), infrared(IR) and optical (OP) photons, as well as the total one (solid line) and the pair creation (PC)energy loss time.3. ResultsUsing the rates just discussed, we performed a Monte Carlo simulation in order to followthe possible disintegration histories of Fe nuclei. In figures 2 and 3 we plot the finalmass (i.e. A) and energy E of the heaviest fragment surviving from the disintegrationprocess. We show in these figures the results of simulations with initial values of therelativistic factor γ0 = 1× 1010, 4× 109 and 1× 109. The curves shown for each valueof γ0 correspond, in fig. 2, to the average value hAi from all the simulations (solid line)and the region (between the two dashed lines) including 95% of the simulations.3 Thisgives a clear idea of the range of values which can result from fluctuations from theaverage behaviour.To further understand the relevance of the different processes and the impact ofthe new determinations of the IR density, we also plot the results for hAi obtained insimulations which do not include pair creation processes (dotted lines) and also theresults we would obtain (dot-dashed line) with an IR density a factor of ten larger (i.e.the HIR density of ref. [5]). Figure 3 is similar but for the final values of the energy.From these figures we can draw the following conclusions:i) For large initial energies (E0 > 2.5× 1020 eV, i.e. γ0 > 5× 109), both the effectsof the IR photons and of pair creation processes are of no relevance along the wholejourney of the nucleus, and the energy losses are essentially due to photodisintegrationoff CMB photons alone.3Only 2.5% of the simulations are below the lower curves and 2.5% are above the upper ones.4JHEP10(1998)00901020304050601e+13 1e+14 1e+15 1e+16 1e+17At [s]1.E94.E91.E10Figure 2: Evolution of the mass number A of the heaviest fragment surviving photodisinte-gration vs. travel time t. The initial γ factors considered are 1× 1010 (1.E10 curve), 4× 109(4.E9 curve) and 1× 109 (1.E9).1e+191e+201e+211e+13 1e+14 1e+15 1e+16 1e+17E [eV]t [s]1.E94.E91.E10Figure 3: Similar as fig. 2 but for the final energy E vs. t.ii) At γ0 < 5×109 the pair creation losses start to be relevant, reducing the value ofγ significantly as the nucleus propagates distances O(100 Mpc). The effect is maximumfor γ0 ' 4×109 but becomes small again for γ0 <∼ 1×109, for which appreciable effectsonly appear for cosmological distances (> 103 Mpc), as can be simply understood fromfig. 1. The effect of neglecting pair creation losses translates into keeping γ = γ0constant during the propagation, and this enhances the photodisintegration rates andthen reduces hAi more rapidly.5JHEP10(1998)00901020304050601e+13 1e+14 1e+15 1e+16 1e+17<A>t [s]2.E101.E108.E96.E94.E92.E91.E9Figure 4: hAi vs. t for more sample values of γ0.iii) Also for γ0 < 5 × 109 the reduction in the IR density adopted has sizeableeffects. In this respect point ii) is relevant, since pair creation losses shift the values ofγ towards a domain where IR photons become increasingly important with respect toCMB ones. With the new values of the IR density the effects of photodisintegrationsbecome small already for γ0 ' 1 × 109 if we consider propagation distances below103 Mpc (i.e. for t < 1017 s).iv) The effects of neglecting pair creation losses are less pronounced in fig. 3. Forinstance, for γ0 = 4×109 the average energies with and without pair creation processesare similar up to t ' 1016 s while the hAi values differ sizeably already for t ' 3×1015 s.This is due to a partial cancellation between the effects of the evolution of γ and of Ain the values of the final energy (E = mpγA), since neglecting pair creation losses doesnot allow γ to decrease but makes instead A to drop faster.4v) The effects of fluctuations due to different photodisintegration histories are notnegligible. They give a spread in A (and E) of the order of 10% (considering the 95%probability range) for hAi ' 40 but relatively larger for smaller hAi, since variations∆A ∼ 10–15 at a given time t can appear between different simulations.In figures 4 and 5 we plot more sample values of hAi and hEi, for values of γ0 =2 × 1010, 1 × 1010 and (8, 6, 4, 2, 1)×109. Looking at fig. 5 it is easy to infer themaximum energies which can be obtained from Fe nuclei injected at any fixed distanced. In particular, for d = 100 Mpc (t = 1016 s) the maximum average energy is Emax '8×1019 eV and originates from γ0 ' 2–4×109. Comparing with fig. 4 we see that thesemaximum energy events would correspond to fragments with masses A(Emax) ' 30–50,i.e. a rather heavy composition.4This in particular shows that the inclusion of pair creation losses does not modify the maximumattainable energies computed in [10].6JHEP10(1998)0091e+191e+201e+211e+13 1e+14 1e+15 1e+16 1e+17E [eV]t [s]2.E101.E108.E96.E94.E92.E91.E9Figure 5: hEi vs. t for several sample values of γ0. The dotted line indicates the upperboundaries of the 95% probability range obtained in the simulations.Fluctuations from the average behaviour can only slightly increase the maximumattainable energies, and this is illustrated with the dashed line, which represents theupper boundary of the 95% CL ranges (i.e. 97.5% of the simulations are below thiscurve) for any initial value of γ0.For source distances d = 10 Mpc, average energies up to Emax ' 2 × 1020 eV canresult, and an interesting pile-up effect is observed since a broad range of initial energies(with γ0 ∼ 4–8× 109) lead to approximately the same final energy (∼ Emax). This canproduce a bump in the spectrum from sources at these distances if indeed the highestenergy events originate from heavy nuclei. Due to the spread in values of γ0 at Emax,we see from a comparison with fig. 4 that there will also be a wide spread in the finalcomposition, with A(Emax) ' 10–45. Events with energies 2–3×1020 eV may appear aslow probability fluctuations from the mean behaviour if d ' 5–8 Mpc, having initiallyγ0 > 1010 and a low mass final composition (A < 10).For smaller source distances (d ∼ few Mpc), events with E ' 3× 1020 eV could beheavier nuclei with smaller initial energies (γ0 > 6× 109).For very large values of γ0 (γ0 > 2× 1010), the heavy nuclei completely disintegratein less than 10 Mpc, and the photopion production (not included here) becomes themain attenuation process for the secondary nucleons, which are then subject to theusual GZK cutoff.In conclusion, the main implication of the lower values of the IR density recentlyestimated is to increase the mean free path of the heavy nuclei with initial γ factorsbelow ∼ 5×109, for which most CMB photons are below the peak of the giant resonancefor photodisintegration. Due to the fragmentation of the nuclei by photodisintegrationand the pair creation energy losses, the final energies of the fragments are typically7JHEP10(1998)009below 2 × 1020 eV for travel distances ∼ 10 Mpc, and below 1020 eV for distances∼ 100 Mpc. The new value of the IR density is then of little help in the attempts tounderstand the highest energy events observed (E ∼ 2–3× 1020 eV), which could nothave originated as heavy nuclei at distances beyond ∼ 10 Mpc. The lack of obviouscandidate sources at closer distances [7] leave the nature and origin of these events stilla mistery.AcknowledgmentsWork partially supported by CONICET, Argentina. We thank Luis Anchordoqui andM. Teresa Dova for discussions.References[1] K. Greisen, Phys. Rev. Lett. 16 (1966) 748;G. T. Zatsepin and V. A. Kuz’min, Sov. Phys. JETP Lett. 4 (1968) 78.[2] F. Stecker, Phys. Rev. 180 (1969) 1264.[3] W. Tkaczyk, J. Wdowczyk and A. W. Wolfendale, J. Phys. A 8 (1975) 1518.[4] V.S. Berezinsky, S. I. Grigorieva and G. T. Zatsepin, Proc. 14th ICRC, Munich 1975,v. 2, p. 771.[5] J. L. Puget, F. W. Stecker and J. H. Bredekamp, Astrophys. J. 205 (1976) 638.[6] L. A. Anchordoqui et al., Phys. Rev. D 57 (1998) 7103 [astro-ph/9708082].[7] J. W. Elbert and P. Sommers, Astrophys. J. 441 (1995) 151.[8] M. A. Malkan and F. W. Stecker, Astrophys. J. 496 (1998) 13.[9] F. W. Stecker, Phys. Rev. Lett. 80 (1998) 1816 [astro-ph/9710353].[10] L. N. Epele and E. Roulet, Phys. Rev. Lett. 81 (1998) 3295 [astro-ph/9806251].[11] G. R. Blumenthal, Phys. Rev. D 1 (1970) 1596.[12] M. J. Chodorowski, A. A. Zdziarski and M. Sikora, Astrophys. J. 400 (1992) 181.8

On the propagation of the highest energy cosmic ray nuclei

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On the propagation of the highest energy cosmic ray nuclei

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