PHYSICAL REVIEW D, VOLUME 65, 103003

Ultrahigh energy cosmic rays from neutrino emitting acceleration sources?

Oleg E. Kalashev,1 Vadim A. Kuzmin,1 Dmitry V. Semikoz,2 and Gunter Sigl31Institute for Nuclear Research of the Academy of Sciences of Russia, Moscow, 117312, Russia

2Max-Planck-Institut fu¨r Physik (Werner-Heisenberg-Institut), Fo¨hringer Ring 6, 80805 Mu¨nchen, Germany3Institut d’Astrophysique de Paris, C.N.R.S., 98 bis boulevard Arago, F-75014 Paris, France

~Received 4 February 2002; published 9 May 2002!

We demonstrate by numerical flux calculations that neutrino beams producing the observed highest energycosmic rays by weak interactions with the relic neutrino background require a nonuniform distribution ofsources. Such sources have to accelerate protons at least up to 1023 eV, have to be opaque to their primaryprotons, and should emit the secondary photons unavoidably produced together with the neutrinos only in thesub-MeV region to avoid conflict with the diffuseg-ray background measured by the EGRET experiment.Even if such a source class exists, the resulting large uncertainties in the parameters involved in this scenariocurrently do not allow us to extract any meaningful information on absolute neutrino masses.

DOI: 10.1103/PhysRevD.65.103003 PACS number~s!: 98.70.Sa, 95.85.Ry, 98.70.Vc, 98.80.2k

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I. INTRODUCTION

In acceleration scenarios ultrahigh energy cosmic r~UHECRs! with energies above 1018 eV are assumed to bprotons accelerated in powerful astrophysical sources. Ding their propagation, for energies above*50 EeV ~1 EeV51018 eV! they lose energy by pion production and paproduction ~protons only! on the cosmic microwave background~CMB!. For sources further away than a few dozMpc this would predict a break in the cosmic ray flux knowas the Greisen-Zatsepin-Kuzmin~GZK! cutoff @1#, around50 EeV. This break has not been observed by experimsuch as Fly’s Eye@2#, Haverah Park@3#, Yakutsk@4# and theAkemo Giant Air Shower Array~AGASA! @5#, which insteadshow an extension beyond the expected GZK cutoff aevents above 100 EeV. However, the new experiment Hi@6# currently seems to see a cutoff in the monocular data@7#.Taking into account that all old experiments except perhAGASA do not have sufficient statistics in the highest eneregion to settle the question, the existence of a possibleoff remains unclear at the moment. The apparent absenca cutoff especially in the AGASA data has in recent yetriggered many theoretical explanations ranging from cventional acceleration in astrophysical sources to modelsvoking new physics, such as the top-down scenarioswhich energetic particles are produced in the decay of msive relics from the early Universe@8#. This enigma has alsofostered the development of large new detectors of ultrahenergy cosmic rays which will increase very significantly tstatistics at the highest energies@9#.

In bottom-up scenarios of UHECR origin, in which protons are accelerated in powerful astrophysical objects suchot spots of radio galaxies and active galactic nuclei@10#,one would expect to see the source in the direction ofarrival of UHECRs, but above the GZK cutoff in general nsuitable candidates have been found within the typicalergy loss distance of a few tens of Mpc for the known eltromagnetically or strongly interacting particles@11,12#.Even assuming significant deflection by large scale extralactic magnetic fields requires at least several sources@13#whose locations have not been identified yet.

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Moreover, recent observations of small scale clusteringthe AGASA experiment@14# suggest that sources of UHECare pointlike @15,16#. This fact together with the lack onearby sources favors the possibility of sources much furaway than 100 Mpc, at redshifts of order unity. An additionmotivation for this possibility comes from recently reportepossible correlations of the arrival directions of observUHECR above.50 EeV with certain classes of sourcesuch as compact radio galaxies@17# or BL Lacertae objects@18#. In the latter case it is still possible that the sourceslocated at moderate distancesz.0.1. In this case photonwith extremely high energiesE.1023 eV can propagateseveral hundred Mpc~constantly losing energy! and can cre-ate secondary photons inside the GZK volume@19#. How-ever, this model requires both extreme energies of primphotons and extremely small extra galactic magnetic fie~EGMFs! B&10212 G. Moreover, if a correlation with anysource at a redshiftz.0.2 is found, this model will be ruledout.

If sources of the highest energy cosmic rays are indeecosmological distancesz;1, the only known mechanism noinvolving new physics except for neutrino masses assuneutrinos as messenger particles: Charged particles accated in such sources give rise to a secondary neutrino bwhich can propagate essentially unattenuated. If this neutbeam is sufficiently strong it can produce the observUHECRs within 100 Mpc by electroweak~EW! interactionswith the relic neutrino background@20#. Specifically, if therelic neutrinos have a massmn , Z bosons, whose decaproducts can contribute to the UHECR flux, can be renantly produced by ultrahigh energy~UHE! neutrinos of en-ergy En.MZ

2/(2mn).4.231021 eV (eV/mn).However, this ‘‘Z-burst’’ mechanism is severely con

strained by at least two types of observational data: Fithere are upper limits on the UHE neutrino flux, based onnonobservation of horizontal air showers by the old FlEye experiment@21# or by the AGASA experiment@22# andfrom the nonobservation of radio pulses that would be emted from the showers initiated by the UHE neutrinos onmoons rim@23#. Second, even if the sources exclusively emneutrinos, the EW interactions also produce photons

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KALASHEV, KUZMIN, SEMIKOZ, AND SIGL PHYSICAL REVIEW D 65 103003

electrons which initiate an electromagnetic~EM! cascadewhich transfers the injected energy down to below the pproduction threshold for photons on the CMB@8#. The cas-cade thus gives rise to a diffuse photon flux in the GeV rawhich is constrained by the flux observed by the EnergGamma Ray Experiment Telescope~EGRET! on board theComptong-ray observatory@24#. Reproducing the observeUHECR flux by theZ-burst mechanism under these two costraints has been shown to in general require local relic ntrino overdensities in order to increase the local UHECflux. These overdensities turn out to be much higher thvalues 2–3 which would be expected from the overdensitthe local supercluster@25#.

In order to avoid this difficulty one can suppose that tZ-burst mechanism is responsible only for part of tUHECR flux @26#. In this case, one can reduce both primaneutrino and secondary photon fluxes and obey all exislimits. However, the price for this is to explain only a partthe UHECR events by theZ-burst mechanism and the necesity for a second source mechanism for UHECRs.

Furthermore, Ref.@26# claims that already the presedata provides possible evidence for the relic neutrino baground and starts to constrain the absolute neutrino mapossibility that has recently been discussed in principleRef. @32#. This claim is based on tuning many unknown prameters such as the value of the EGMF, the universal rabackground~URB! which governs pair production of UHEgrays, and the neutrino source distribution. Also, Ref.@26# didnot take into account propagation of UHE photons, insteassuming that all photons are down-scattered into the Gregion. In addition, simply due to the much larger statisticslower energies, the quality of the fits performed in Ref.@26#is dominated by the low-energy background component.nally, Ref. @26# assumed that the sources do not emit anygrays, although theg-ray energy fluence produced by pioproduction of accelerated nuclei should be comparable toproduced neutrino fluence, as will be discussed in Sec. I

In the present paper we show that for all neutrino masin the range 0.07 eV<mn<1 eV one can find parameterthat fit the UHECR observations with comparable qualWe therefore conclude that, at least at the current statknowledge, it is impossible to extract evidence for the reneutrino background or even best fit values for absolute ntrino masses from UHECR data.

We do not consider in the present paper neutrino intetion channels with multipleW6 and/orZ0 production. Thesechannels could be important in case of neutrino masm*3 eV @27#, which however are strongly disfavored bconsiderations on large scale structure formation@28#.

We also do not discuss here the scenario with large checal potential of the relic neutrinosx i5m/T;3 –4 @29#. Suchchemical potentials are disfavored by the combined analof neutrino oscillation data, CMB radiation~CMBR!, and bigbang nucleosynthesis, which suggestx i,0.1 @30#.

By detailed numerical flux calculations we show thatnonuniform source distribution allows theZ-burst mecha-nism to explain the UHECR flux without substantial reneutrino overdensities. However, this only works if tsources exclusively emit neutrinos. Heavy particles w

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massm;1014–1016 eV, decaying mostly into neutrinos@31#constitute a nonacceleration scenario for such sourcescase of astrophysical sources, favored by apparent cortions of observed arrival directions with sources at large dtances@18#, because isospin symmetry requires the enefluence of neutrinos andg rays produced by hadronicharged primary interactions in the source are comparathis will require the photons to be down-scattered belowGeV range within the source.

All the results presented in this paper, except neutrfluxes, are qualitatively applicable to the model of Ref.@31#.The neutrino fluxes in this model will be peaked at highenergies and only secondary neutrinos fromZ burst will ap-pear in the region interesting for Auger and Euso.

II. NEUTRINO SOURCE

We assume in this section that a pure neutrino soumodel can somehow be constructed and start with this cIn the next section we relax this condition and include othprimary particles in consideration.

Our simulations are based on two independent codeshave extensively been compared down to the level of invidual interactions. Both of them are implicit transport codthat evolve the spectra of nucleons,g rays, electrons, electron, muon, and tau neutrinos, and their antiparticles alostraight lines. Arbitrary injection spectra and redshift distbutions can be specified for the sources and all relevstrong, electromagnetic, and weak interactions have bimplemented. For details see Refs.@33,34#. Specifically rel-evant for neutrino interactions in the current problem aboth thes-channel production ofZ bosons and thet-channelproduction ofW bosons. The decay products of theZ bosonwere taken from simulations with the@35# Monte Carlo eventgenerator using the tuned parameter set of the OPAL Claboration @36#. The main ambiguities in propagation concern the unknown rms magnetic field strengthB which caninfluence the predictedg-ray spectra via synchrotron coolinof the electrons in the EM cascade, and the strength ofURB which influences pair production by UHEg rays@37#.Photon interactions in the GeV to TeV range are dominaby infrared and optical universal photon backgrounds~IR/O!,for which we took the results of Ref.@38#. The resultingphoton flux in GeV range is not sensitive to details of tIR/O backgrounds.

Predictions for the nucleon fluxes agree within tenspercents whereas photon fluxes agree only within a fa.2 between the two codes. The latter mostly reflectsambiguities in photon propagation mentioned above, butno influence on the conclusions of this paper.

For the present investigation we parametrize the neutinjection spectra per comoving volume in the following wa

fn~E,z!5 f ~11z!mE2qnQ~Emaxn 2E!,

zmin<z<zmax, ~1!

wheref is the normalization that has to be fitted to the daThe free parameters are the spectral indexqn , the maximal

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ULTRAHIGH ENERGY COSMIC RAYS FROM NEUTRINO . . . PHYSICAL REVIEW D65 103003

neutrino energyEmaxn , the minimal and maximal redshift

zmin , zmax, and the redshift evolution indexm. We assumefor simplicity that all six neutrino species~three flavorsincluding antiparticles! are completely mixed as suggestby experiments@39# and thus have equal fluxes given bEq. ~1!. Finally we chose the Hubble parameterH0570 km s21 Mpc21 and a cosmological constantVL

50.7, as favored today.For a given set of values for all these parameters we

the neutrino flux amplitudef in Eq. ~1! obeying all experi-mental bounds on photon and neutrino fluxes and explainthe UHECR flux at highest energies above some valueEminby the secondary UHE protons and photons by a maximlikelihood fit. The fit quality is characterized by ax2 value.Note that there are many different kinds of extragalacsources which can contribute to the observed UHECRwith energies below the GZK cutoffEGZK.431019 eV.Thus, one should takeEmin&EGZK if one wants to explain allUHECR data above the cutoff by theZ-burst model.

Figure 1 illustrates how unrealistically high local neutrinbackground overdensity could be avoided by assumsources that are more abundant at low redshifts. In this figwe show primary neutrino and secondary proton and phofluxes for the casemn50.5 eV. The following values havebeen assumed for the parameters of Eq.~1!: spectral indexqn51, maximal neutrino energyEmax

n 5231022 eV, andminimal and maximal redshiftszmin50 andzmax53. Threecases, corresponding to the redshift evolution indexm523, 0, and 3 are plotted as solid, dashed, and dotted lirespectively. A typical value,B51029 G, is assumed for theEGMF as well as the minimal strength consistent with oservations for the poorly known URB@37#. The latter resultsin optimistic predictions for the UHEg-ray flux. The neu-

FIG. 1. Fluxes of neutrinos,g rays, and nucleons predicted bthe Z-burst mechanism formn50.5 eV, assuming sources exclusively emitting neutrinos with fluxes equal for all flavors. We shothree cases of the source evolution parameter,m523, 0, and 3 bysolid, dashed, and dotted lines, respectively. Values assumed foother parameters areB51029 G, minimal URB strength,zmin

50, zmax53, Emaxn 5231022 eV, andqn51. For each case the neu

trino flux amplitude f is obtained from minimizingx2 for Emin

52.531019 eV. Also shown are experimental upper limits ong-rayand neutrino fluxes~see text and Ref.@8# for more details!.

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trino flux amplitude was fitted as described above forEmin

52.531019 eV. Thus we require that theZ-burst model con-tributes to 9 bins of nonvanishing flux in the AGASA datFor all three cases in Fig. 1 we obtainedx2(9).4.

As one can see from Fig. 1, the value of the source elution parameterm mainly affects photons with GeV energies. The valuem53 which was chosen in previous wor@25# is similar to evolution of active galaxies. The secondaphoton flux for such a source distribution is in conflict withe diffuse GeV photon background observed by the EGRexperiment. The uniform source distribution,m50, is al-ready in agreement with the EGRET flux, while negativalues of the flux,m523, lead to GeV photon fluxes welbelow it. The latter case corresponds to sources whichmore abundant now than at high redshifts. For example,Lacertae objects for which correlations with UHECRs wefound in Ref.@18# are distributed in such a way. Note that thchoice of unknown EGMF strengthB and the URB flux af-fect only the UHE flux of photons and is not important in thEGRET region which is only sensitive to the total injectEM energy.

Figure 2 shows results for varying neutrino masses wthe unknown parametersB, radio background strength, awell as f, qn , Emax

n , zmin , zmax, and m chosen such as toproduce fits to the UHECR data of comparable quality. Wpresent in Fig. 2 two extreme cases of smallmn50.1 eV andhigh mn51 eV neutrino masses. Because parameter spahuge, we fix some parameters to given values (zmin50,zmax53, and minimal URB strength! and vary only the evo-lution parameterm, the EGMF strengthB, and the maximumenergyEmax

n for every given neutrino mass. Again, we detemine the neutrino flux amplitudef from minimizing x2. Formn50.1 eV we getx2(6)51.6, while formn51 eV we havex2(9)52.6, i.e., the fit qualities are comparable. For all itermediate masses we also find similar fit qualities. Fromwe conclude that no preferred values for the neutrino masmn can be extracted. Instead, for every neutrino mass thexists a large parameter region in which theZ-burst modelwith pure neutrino sources may work.

In Fig. 2~a! we show the case of small neutrino masmn50.1 eV, with m523, B55310211 G, and Emax

n

51023 eV. For small neutrino masses the resonance energlarge and thus secondary photons and protons are prodat higher energies, apart from the photons producedt-channel leptons. Due to electromagnetic cascades mothe EM energy ends up in the GeV region and thusEGRET flux gives the most stringent bound. In particular,mn,0.1 eV, the parameter space for theZ-burst modelshrinks, and even am523 distribution of sources is noconsistent with the data. However, there is no pronouncutoff for photons in this case~due to thea,1 power law,see details in Ref.@19#!. This allows us to explain somefraction of the UHECR events by photons. Finally, the rquired neutrino flux is higher for small neutrino masswhich makes the GLUE experiment bound on the UHE ntrino flux @23# a crucial constraint for theZ-burst model.

In Fig. 2~b! we present the case of large neutrino mamn51 eV, with m50, B510212 G, andEmax

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KALASHEV, KUZMIN, SEMIKOZ, AND SIGL PHYSICAL REVIEW D 65 103003

this case the required flux of neutrinos is somewhat smaThe available parameter space for theZ-burst mechanism islarge and the EGRET bound on the GeV photon flux canmet even for a uniform distribution of sources.

III. PHOTON AND NEUTRINO SOURCE

It is well known that sources capable of acceleratUHECRs produceg rays up to at leastEmax

g ;100 TeV@40#.Since in acceleration scenarios bothg rays and neutrinos arproduced as secondaries, the powerf g;1 radiated ing raysrelative to neutrinos has to be of order unity. For theg-rayinjection spectrum this implies

fg~E,z!56 f f g~11z!mg~qn ,Emax

n !

g~qg ,Emaxg !

3E2qgQ~Emaxg 2E!,

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FIG. 2. Dependence of flux predictions in theZ-burst model onneutrino mass.~a! Small neutrino massmn50.1 eV, withm523,B55310211 G, andEmax

n 51023 eV. ~b! Large neutrino massmn

51 eV, with m50, B510212 G, andEmaxn 51022 eV. See also Fig.

1 for explanations.

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Here, qg is the g-ray spectral index, andg(q,Emax)[*Emin

EmaxdE E12q, where we have introduced some small lo

energy cutoffEmin for convergence.In this section we consider the more realistic case wh

the sources also emitg rays with a power comparable to themitted neutrino power,f g51, up toEmax

g 5100 TeV in Eq.~2!. For all other parameters we chose values that minimthe tension with the observational upper limits on the UHneutrino flux and the diffuse GeVg-ray flux. Figure 3 showsthat in this case theZ-burst scenario cannot be made constent with observations. A possible solution to this problemto down-scatter most of the EM energy into the sub-Mrange within the source. Only in this case can the EGRbound be satisfied. This would require a very strong phofield up to*keV within the source.

Even the scenario in Fig. 3 is still optimistic becauseassumes that the source is completely opaque to the primnucleons. While this may be achieved easier than contment of g rays, for example, by magnetic fields, it is clefrom Fig. 3 that even if only a small fraction of the primarnucleons leave the source, the nucleon flux between.1018

eV and.1019 eV would be much higher than observed,agreement with the conclusions of Ref.@41#. This problemcould be avoided if the protons are deflected strongly enoso that they could not reach the Earth. However, this pobility also appears unrealistic as has been discussed in@42#. This problem can only be solved if the protons atrapped in the source.

Finally we note that theZ-burst mechanism also poseextreme requirements on the acceleration mechanism isince the primary protons have to be accelerated to enerEmax

p ;10Emaxn *431022 eV (eV/mn). In contrast, known

mechanisms are usually limited toEmaxp &1022 eV @43#.

Thus theZ-burst model imposes the following requirements onto the sources: They should emit energy onlyneutrinos and in sub-MeVg rays, and should also trap moof the primary protons.

FIG. 3. Same as Fig. 1 (mn50.5 eV! for sources emitting equapower in neutrinos andg rays, f g51 in Eq. ~2!. The other param-eters are chosen asm50, qg52, andEmax

g 5100 TeV.

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ULTRAHIGH ENERGY COSMIC RAYS FROM NEUTRINO . . . PHYSICAL REVIEW D65 103003

IV. CONCLUSIONS

The Z-burst mechanism where the highest energy cosrays are produced by neutrino beams interacting withrelic neutrino background only works with sources excsively emitting neutrinos in the ultrahigh energy regime.order to avoid conflict with the known diffuse backgrounof g rays, these sources should emit photons only insub-MeV region. In addition, they should trap primary prtons in order to avoid an excessive nucleon flux fromsource, and should be able to accelerate these protonsEmax

p *1023 eV (eV/mn). None of the astrophysical accelertion models existing in the literature seem to meet thisquirement.

Under the assumption that such an extreme source cnevertheless exists we have shown that theZ-burst mecha-nism can work without unrealistically high local relic netrino overdensities if the neutrino sources are typically mabundant at present than in the past. Especially neutmassesmn&0.5 eV require a nonuniform source distributio}(11z)m with negative evolution factor,m,0, as is thecase with BL Lacertae objects.

The contribution to the UHECR flux from such a speclative extragalactic neutrino source class due to theZ-burst

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mechanism would exhibit a GZK cutoff for nucleons anwould be dominated byg rays at higher energies. Furthemore, the required UHE neutrino fluxes are close to existupper limits and should be easily detectable by future expments such as Auger@44#, Euso@45#, RICE @46#, or by otherradio detection techniques@47#.

The space of parameters characterizing neutrino souand their evolution is highly degenerate when fluxes are fithe observed UHECR fluxes. Since evidence of relic neunos and extraction of absolute neutrino masses requiresservative assumptions about these unknown parametersconclude that the current state of knowledge does not alus to extract any meaningful information on neutrino masfrom UHECR data.

ACKNOWLEDGMENTS

We would like to thank Zoltan Fodor, Sandor Katz, Adreas Ringwald, Andrey Neronov, Igor Tkachev and ToWeiler for detailed discussions on this subject. We are graful to Otmar Biebel for providing us withZ-decay data andto Joel Primack and James Bullock for making availableus their results for the infrared-optical background in eletronic form.

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