Ultra-high Energy Cosmic Rays and Neutrinos from Gamma-Ray Bursts,Hypernovae and Galactic Shocks�

P. Meszaros

Center for Particle and Gravitational Astrophysics, Dept. of Astronomy & Astrophysics, Dept. of Physics, 525 Davey Laboratory,Pennsylvania State University, University Park, PA 16802, U.S.A.

Abstract

I review gamma-ray burst models (GRBs) and observations, and discuss the possible production of ultra-high energy cosmic rays and neutrinos in both the standard internal shock models and the newer generation ofphotospheric and hadronic GRB models, in the light of current constraints imposed by IceCube, Auger and TAobservations. I then discuss models that have been proposed to explain the recent astrophysical PeV neutrinoobservations, including star-forming and star-burst galaxies, hypernovae and galaxy accretion and merger shocks.

Keywords: Cosmic rays, Neutrinos,

1. Introduction

The origin of the cosmic rays above the knee (E >∼1015 eV) and up to the range of ultra-high energycosmic rays (UHECRs, 1018 eV <∼ E <∼ 1021 eV)remains a mystery. Attempts at correlating the ar-rival directions of UHECRs with known AGNs haveso far yielded no convincing results [1, 2, 3]. Partlyfor this reason, other high energy sources, which aredistributed among, or connected with, more com-mon galaxies, have been the subject of much interest.These include gamma-ray bursts (GRBs), hypernovae(HNe) and galactic shocks, the latter being due ei-ther to accretion onto galaxies (or clusters) or galaxymergers.

An important clue for the presumed sources ofUHECR would be the detection of ultra-high en-ergy neutrinos (UHENUs) resulting from either pho-tohadronic (pγ) or hadronuclear (pp, pn) interactions

�Based on a talk given at the Origin of Cosmic Rays: Beyondthe Standard Model conference in San Vito di Cadore, Dolomites,Italy, 16-22 March 2014. This is not a comprehensive review ofthe topics in the title; it is weighted towards work in which I havebeen more personally involved.

of the UHECR within the host source environmentand/or during propagation towards the observer. Thevalue of this is of course that neutrinos travel essen-tially unabsorbed along straight lines (or geodesics)to the observer, thus pointing back at the source. Suchinteractions leading to neutrinos, arising via chargedpions, also result in a comparable number of neu-tral pions leading to high energy gamma-rays, whichare however more prone to subsequent degradationvia γγ cascades against low energy ambient or inter-galactic photons.

The prospect of tagging UHECRs via their sec-ondary neutrinos has recently become extremely in-teresting because of the announcement by IceCube[4] of the discovery of an isotropic neutrino back-ground (INB) at PeV and sub-PeV energies, whichso far cannot be associated with any known sources,but whose spectrum is clearly well above the atmo-spheric neutrino background, and is almost certainlyastrophysical in origin.

Available online at www.sciencedirect.com

Nuclear Physics B (Proc. Suppl.) 256–257 (2014) 241–251

0920-5632/© 2014 Elsevier B.V. All rights reserved.

www.elsevier.com/locate/npbps

http://dx.doi.org/10.1016/j.nuclphysbps.2014.10.028

2. Gamma-Ray Bursts

There are at least two types of GRBs [5], thelong GRBs (LGRBs), whose γ-ray light curve lasts2 s <∼ tγ <∼ few× 103 s, and the short GRBs (SGRBs),whose light curve lasts tγ <∼ 2 s. The spectra of bothpeak in the MeV range, with power law extensionsbelow and above the peak of (photon number) slopesα ∼ −1 and β ∼ −2, the peak energy Epk of theSGRBs being generally harder (few MeV) than thoseof the LGRBs (<∼ MeV) [6]. This broken powerlaw spectral shape, known as a Band spectrum, is ac-companied in some cases by a lower energy (tens ofkeV) and less prominent black-body hump, and/or bya second, higher energy power law component, in thesub-GeV to GeV range, whose photon number slopeis appreciably harder then the super-MeV β slope,e.g. [7, 8] (Fig. 1).

Figure 1: Spectra of GRB090926A observed by the Fermi LAT andGBM instrument, showing the time evolution over four differentsuccesive time bins, the first two of which show a standard (pre-Fermi) broken power law (Band) shape, while the last two showalso a second, harder spectral component [9]..

The MeV light curves exhibit short timescale vari-ability down to ms, extensively charted along with theMeV spectra by the CGRO BATSE, the Swift BATand more recently by the Fermi GBM instruments,while the GeV light curves and spectra have in thelast several years been charted by the Fermi LAT in-strument, e.g. [7]. An extremely interesting propertyshown by most of the LAT-detected bursts is that thelight curves at GeV energies start with a time lag ofseveral seconds for LGRBs, and fractions of a secondfor SGRB, relative to the start of the lightcurves atMeV energies, as seen in Fig. 2.

The GeV emission amounts to about 10% and30-50% of the total energy budget of LGRBs and

Figure 2: Light curves of GRB080916C with the GBM (top twocurves) and LAT (bottom three curves) [10], showing the GeV-MeV relative time lag.

SGRBs respectively, and is detected in roughly 10%of the LGRBs, and in a somewhat larger percentageof SGRBs, although the GeV detection is ubiquitousin the brighter bursts and the non-detections may bedue to being below the LAT sensitivity threshold [11].

The huge energies involved in GRB led to the viewthat it involves a fireball of electrons, photons andbaryons which expands relativistically [12, 13, 14,15, 16, 17], produced by a cataclysmic stellar event.The observational and theoretical work over the pasttwenty years has resulted in a generally acceptedview of LGRBs as originating from the core collapseof massive (>∼ 25M�) stars [18, 19, 20], whose cen-tral remnant quickly evolves to a few solar mass blackhole (BH), which for a fast enough rotating core re-sults in a brief accretion episode powering a jet whichbreaks through the collapsing stellar envelope. Thisview is observationally well supported, the LGRBsarising in star-forming regions, sometimes showingalso the ejected stellar envelope as a broad-line Icsupernova, a “hypernova”, whose kinetic energy is>∼ 1052 erg, an order of magnitude higher than thatof an ordinary SN Ic or garden variety supernova.

For SGRBs, the leading paradigm is that they arisefrom the merger of a compact double neutron star(NS-NS) or neutron star-black hole (NS-BH) binary[13, 16, 17], resulting also in an eventual centralBH and a briefer accretion-fed episode resulting in

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a jet. Observationally this is supported by the lackof an observable supernova, and by the fact that theyare observed both in star-forming and in old pop-ulation galaxies, often off-set from the optical im-age, as expected if in the merger the remnant hasbeen kicked off and had time to move appreciably.While the SGRB origin is less firmly establishedthan that of LGRBs, compact mergers are nonethe-less widely considered the most likely explanation,which are also of great importance as a guaranteedsource of gravitational waves (GWs), being the ob-ject of scrutiny by LIGO, VIRGO and other GW de-tectors.

The MeV radiation providing the detector triggeras well as the slightly delayed GeV radiation arejointly called the prompt emission of the GRB. Ina fraction of bursts, a prompt optical flash is alsodetected by ground-based robotic telescopes [21] orby rapidly slewing multi-wavelength GRB missionssuch as Swift [22]. The most widely accepted viewof the GRB emission is that it is produced by shocksin the relativistic outflows, the simplest example ofwhich are the external shocks where the outflow is de-celerated in the external interstellar medium or in thestellar wind of its progenitor [23, 24]. In such shocksmagnetic field can be amplified, and electrons canbe Fermi accelerated into a relativistic power law en-ergy distribution, leading to broken power law spec-tra peaking initially in the MeV range. Both a for-ward and reverse shock are expected to be present,the latter producing synchrotron radiation in the op-tical range, while inverse Compton (IC) radiation inthe shocks also produces a GeV component [25]. Thefast time variability of the MeV light curves is how-ever better explained through what is called the stan-dard internal shock model [26], which are expected tooccur in the optically thin region outside the scatter-ing photosphere of the outflow, but inside the radiusof the external shocks. The radii of the photosphere,the internal shocks and the external shocks are, re-spectively,

rph � (LσT /4πmpc3η3) ∼ 4 × 1012Lγ,52η−32.5 cm

ris � Γ2ctv ∼ 3 × 1013η22.5tv,−2 cm

res � (3E0/4πnextmpc2η2)1/3

∼ 2 × 1017(E53/n0)1/2η2/32 cm, (1)

where E, L, η ∼ Γ, next, tv are the burst total en-ergy, luminosity, initial dimensionless entropy, coast-ing bulk Lorentz factor, external density and intrin-sic variability timescale, e.g. [27, 28]. If the promptemission is due to an internal shock, the external

shock can naturally result, via inverse Compton, ina delayed GeV component [29].

The above simple picture of internal and externalshocks served well in the CGRO, HETE and Beppo-SAX satellite eras extending into the first half of the2000 decade, including the discovery of X-ray andoptical afterglows as well as the prompt optical emis-sion, which were predicted by the models. It also ac-commodated fairly well the observed fact that the jetis collimated and when the Lorentz factor drops be-low the inverse of the opening angle the light curvessteepen in a predictable manner.

It was however realized that simple internal shocksradiating via electron synchrotron had low radiativeefficiency, and many bursts showed low energy αslopes incompatible with synchrotron [30, 31]. At-tempts at resolving this included different radiationmechanisms, e.g. [32], which addresses the spec-trum, or invoking a larger role for the scattering pho-tosphere [33, 34, 35], which addresses both the spec-trum and efficiency issues. It is worth stressing thatthe need for such ”non standard” internal shocks orphotospheres is important (a fact not widely recog-nized) when considering IceCube neutrino fluxes ex-pected from GRBs.

The Swift satellite launched in 2004 had gamma-ray, X-ray and optical detectors, which revealed newfeatures of the GRB afterglows, including an initialsteep decay followed by a flatter decay portion of theX-ray afterglow, interspersed by X-ray spikes, finallyblending into the previously known standard powerlaw decay behavior. These features could be repre-sented through the high latitude emission [36], a con-tinued or multi-Lorentz factor outflow, and continuedinternal shocks, e.g. [37, 38].

The Fermi satellite, launched in late 2008 and sen-sitive between 1 keV <∼ E <∼ 300 GeV, extended theMeV studies and opened wide the detailed study ofbursts in the GeV band, which can last for >∼ 103 s andwhose spectra extend in some cases up to ∼ 100 GeVin the source frame. The observed GeV-MeV pho-ton delays from bursts at redshifts z ∼ 2 − 4 led toan interesting constraint on quantum gravity theories,excluding the first order term in E/EPlanck of the usualeffective field theory series expansion formulations[39]. This limit is only reinforced by the presence ofadditional astrophysical mechanisms for such delays.

In general, the GeV emission of all but the first fewtime bins is well represented by a forward shock syn-chrotron radiation [40, 41]. This holds also for thebrightest GeV bursts ever discovered, GRB130427A.

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However, the first few time bins of the GeV emission[42] may need to be ascribed to the prompt emission,which is also responsible for the MeV emission - forwhich, as mentioned, a self-consistent analysis mustconsider models going beyond the standard simple in-ternal shock, c.f. below.

In leptonic models, the prompt MeV emission (andthe GeV-MeV delay) can be, and needs to be, ex-plained while avoiding the internal shock spectraland efficiency inconsistencies. This has been done inthe framework of both leptonic and hadronic models.Among leptonic ones, for instance, the MeV radia-tion can arise at smaller radii, e.g. in the photosphereor a cocoon, and upscattering by internal or externalshocks further out produce the delayed GeV radiation[43, 44]. Alternatively, GeV photons may be createdleptonically by pair cascades initiated by MeV pho-ton backscattering [45]. Among hadronic models ofthe prompt emission, one type of models considersdissipative photospheres as responsible for the MeVphotons [34, 35], while the GeV photons are due topp, pn collisions following from neutron-proton de-coupling further out, the GeV γγ optical thinness oc-curring in any case at radii >∼ 1015 cm, leading to theGeV-MeV delay [46, 47]. Another type of alterna-tive to standard internal shocks are the hadronic mod-ified internal shocks, e.g. [48]. In one such model[49], accelerated hadrons lead to pγ secondaries re-sulting in a slower heating than simple shocks, and re-accelerated secondaries lead to a self-consistent pho-ton spectrum of the correct shape and high radiativeefficiency, as well as providing a natural GeV delay.

3. GRB UHE Neutrinos and Cosmic Rays

The pioneering works of [50, 51] have served asthe basis for most of the thinking on UHE cosmicray acceleration and VHE neutrino production inGRBs. These first-generation models, as one maycall them, were based on a simplified “standard” in-ternal shock (IS) model, where the bulk Lorentz fac-tor Γ ≡ η and the variability timescale tv enteringequ. (1) are either assumed of inferred from γ-rayobservations, the photon spectrum is assumed to bea standard Band function and pγ interactions occurvia the Δ-resonance. More detailed calculations ofa diffuse neutrino flux, still based on this simple ISmodel but using specific electromagnetically (hence-forth: EM) observed bursts serving to calibrate theneutrino to photon (or relativistic proton to electron,Lν/Lγ ∼ Lp/Le) luminosity ratio were made by [52].

Figure 3: A comparison of the standard IS Waxman-Bahcall andits Guetta et al [52] type implementation using the Δ-resonanceapproximation at the photon spectral peak for 215 EM observedGRBs, compared to the IceCube upper limits calculated for thismodel spectral shape (see [53]).

The first IceCube data on GRBs using 40 stringsand then 56 strings as the array completion pro-gressed were presented in [54, 55, 53]. The resultsusing 215 EM-detected GRBs with νμ fluxes normal-ized to the γ-ray fluxes indicated that the diffuse neu-trino upper limits were a factor ∼ 5 below this ISmodel predictions (Fig. 3), unless the proton to elec-tron ratio was much less than Lp/Le ∼ 10. Boththis and a model independent analysis using a bro-ken power law photon spectrum with variable breakenergy and Δ-resonance interaction indicated an in-consistency between the νμ upper limits and a signifi-cant contribution of GRB to the UHE cosmic ray fluxobserved by Auger and HiRes. This was a very im-portant first cut in constraining models with IceCube.

Subsequent investigations pointed out that the ISmodel fluxes used for this comparison were overesti-mated [57, 56]. More careful consideration of the pγinteraction in this model beyond the Δ-resonance, in-cluding multi-pion and Kaon channels with the entiretarget photon spectrum yielded substantially lowerpredicted fluxes in the TeV-PeV energy range con-sidered [56], indicating that >∼ 5 years of observationwith the full 86 string array may be needed to rule outthe simple IS model (Fig. 4).

The internal shock radius ris depends on both thebulk Lorentz factor η and the time variability of theoutflow tv, see eq.(1). Both factors also influencethe comoving magnetic field in the shock, the photonspectral peak and the photon luminosity, thus affect-ing the neutrino spectral flux, see Fig. (5).

Another simplification affecting the results is that

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Figure 4: The detailed numerical calculation of the IC model ex-pected νμ+ νμ fluxes compared to recent and future IceCube limits.Shaded zones represent the astrophysical uncertainties [56].

the internal shocks in the above were assumed tohave a constant radius, whereas they advance andexpand with the flow. Calculating numerically suchtime-dependent IS models which accelerate CRs, in-cluding the full range of pγ interactions and the ob-served γ-ray luminosity function and variability dis-tributions, the current IceCube 40+59 strings νμ up-per limits are in fact compatible with GRBs contribut-ing a significant fraction of the ∼ 1020 eV UHECRflux [59] (Fig. 6), but the IceCube PeV neutrino flux.

More importantly, the use of the standard inter-nal shock model, which is favored by observers forits simplicity and ease of computation, needs to bereconsidered. This model has been known for thepast decade to have problems explaining the low en-ergy γ-ray spectral slopes and the radiative efficiency(§2, [28]), and alternatives free of the γ-ray incon-sistencies have been investigated, e.g. photosphericmodels and modified internal shock models. Theneutrino emission of baryonic photosphere models[60, 61] and modified IS models [49] differs quali-tatively from that of the standard IS models.

In the case of photospheric models, it is worthstressing that the spectrum is likely to deviate froma blackbody; a non-thermal of broken power lawcan be produced by dissipative effects, such as sub-photospheric scattering [35], inelastic nuclear colli-sions [47], photospheric shocks or magnetic dissipa-tion [46], etc. The spectrum and luminosity normal-ization also depend on whether the dynamics of the

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Figure 5: Diffuse νμ + νμ neutrino spectral flux for an all-sky GRBrate of 700/yr using two different statistical methods (thick linesand thin lines). Shown are three internal shock models (dot-dashedlines) for tvar = 1, 10, 100 ms (black, dark gray, light gray), a mag-netic photospheric model (red dashed) and a baryonic photosphericmodel (blue dotted). (Note:The online version has color figures).All models are computed for different luminosities (in each model,Lγ = 1053, 1052, 1051 erg/s (top,middle,bottom). Also shown is theIceCube collaboration’s representation of the diffuse flux from astandard Waxman-Bahcall internal shock model, and the IC 40+59observational upper limit (see Fig.3 of [53] for description). Thegray zone labeled ATM is the atmospheric neutrino spectrum. Inthis figure, the Lorentz factor is taken to be η = 300. For a higherLorentz factor, e.g. η = 1000, the fluxes all go down (larger radii,lower fields and comoving photon target densities) and the spectralpeaks are shifted to higher energies. From [58].

expansion is dominated by baryonic inertia, in whichcase the bulk Lorentz factor initially accelerates asΓ(r) = (r/r0) until it reaches the saturation valueΓ � η at the coasting radius rsat = r0η; the photo-spheric radius rph occurs generally beyond the satu-ration radius and is given by the first line of eq.(1).

Alternatively the dynamics might be dominated bymagnetic stresses. In this case the photospheric ra-dius depends on the value of the magnetization indexμ, where Γ(r) = (r/r0)μ and μ = 1/3 for extrememagnetic domination, e.g. [46, 58]. For such mag-netic cases, the photospheric radius is generally in theaccelerating phase Γ ∝ rμ, and is given by

rph = r0η1/μT (ηT /η)1/(1+2μ) (2)

where r0 is the launch radius (∼ 107 cm) and ηT =

(LσT /4πmpc3r0)μ/(1+3μ). Fits to determine the degreeof magnetic domination have been done using FermiGBM and LAT data [62, 63], indicating that a de-gree of magnetic domination does exist, which differsbetween bursts. A related point is that if magneticstresses are significant in a GRB jet, this reduces the

P. Mészáros / Nuclear Physics B (Proc. Suppl.) 256–257 (2014) 241–251 245

Figure 6: The CR (black) and neutrino (red, νμ,νμ after oscilla-tion) diffuse intensities for a time-dependent internal shock GRBmodel assuming neutron conversion [59], compared to the ob-served UHECR intensity (circles). The gray thick line is the neu-trino upper-limits based on the model-independent analysis in [53].

comoving photon density in the jet, allowing heavynuclei in the jet to survive photo-dissociation [64], apoint of interest in view of the Auger [65] data point-ing towards a heavy composition of UHECR at highenergies.

The diffuse neutrino flux from both baryonic andextreme magnetic photospheric models has beencomputed (see Fig. 5, [58]), where the extreme mag-netic photospheric model is shown as red dashed linesand the baryonic photospheric model as blue dot-ted lines. They appear compliant with the IceCube40+59 string upper limits, which however were cal-culated for a canonical Band spectral shapes, and amore spectral-specific comparison is necessary. Thishas been done for baryonic photospheres [66], seeFig. 7. As the observations accumulate, these con-straints are getting tighter, at least for the simple ISand the simple baryonic photosphere models.

Concerning the IceCube non-detection of the EMbrightest burst ever observed, GRB 130427A, a de-tailed calculation [67] shows that for this particularburst, except for the extreme magnetic photospheremodel, the standard IS model, the baryonic photo-sphere model and a model-independent analysis arecompatible with its non-detection.

Figure 7: Fireball (more accurately: standard IS) and simplifiedbaryonic photosphere model diffuse neutrino fluxes versus IC40through IC86 string IceCube limits [66].

4. Hypernovae, SFGs/SBGs, Galactic/Cluster

Shocks, AGNs as UHECR/UHENU Sources

Hypernovae (henceforth HNe) are Type Ic corecollapse supernovae with unusually broad lines, de-noting a much higher ejecta velocity component thanin usual SNeIc. This indicates a component of theejecta reaching up to semi-relativistic velocities, withΓβ ∼ 1, and a corresponding inferred ejecta kineticenergy Ekin ∼ 1052.5 erg, one order of magnitudehigher than that of normal SNeIc and normal SNe ingeneral [68, 69]. Their rate may be 1%-5% of the nor-mal SNIc rate, i.e. as much as 500 times as frequentas GRBs [70]. While core collapse (collapsar) typelong GRBs appear to be accompanied by HNe, themajority of HNe appear not to have a detected GRB,e.g. [71]. The semi-relativistic velocity componentmay be due to an accretion powered jet forming in thecore collapse, as in GRBs, which only for longer ac-cretion episodes is able to break through the collaps-ing envelopes, while for shorter accretion episodes itis unable to break out. In both cases the jet acceleratesthe envelope along the jet axis more forcefully (jet-driven supernova), causing an anisotropic expansion,e.g. [72], whereas in the majority of core collapses aslow core rotation or short accretion times lead to nojet or only weak jets and a “normal” quasi-sphericalSNeIc [73].

The dominant fraction of GRB-less HNe, if in-deed due to a non-emerging (choked) jet, would beeffectively a failed GRB, which could be detected

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via a neutrino signal produced in the choked, non-exiting jet, or a neutrino precursor in those collapseswhere the jet did emerge to produce a successful GRB[74, 75, 76]. Searches with IceCube have so far notfound them, e.g. [77, 78].

An interesting aspect of HNe is that the higher bulkLorentz factor of the ejecta leads to estimates of themaximum UHECR energy accelerated which, unlikefor normal SNe, is now in the GZK range,

εmax � ZeBRβ = 4 × 1018Z eV (3)

especially if heavy nuclei (e.g. Fe, Z = 26) areaccelerated [79, 80, 81]. The photon field is di-lute enough so that the heavy nuclei avoid photo-dissociation [81, 64]. The HNe kinetic energy andoccurrence rate is sufficient then to explain the ob-served UHECR diffuse flux at GZK energies, withoutappearing to violate the IceCube upper limits. TheHNe, as other core collapse SNe and long GRBs, oc-cur in early type galaxies, with a larger rate in star-forming galaxies (SFGs) and even larger rate in star-burst galaxies (SBGs).

Magnetars, another type of high energy source ex-pected from some core collapse supernovae in SFGsand SBGs, are a sub-class of fast-rotating neutronstars with an ultra-strong magnetic field, which havebeen considered as possible sources of UHECR andUHENU [82, 83, 84, 85, 86].

SFGs make up >∼ 10% of all galaxies, while SBGsmake up >∼ 1 − 3%. AGNs make up ∼ 1% of allgalaxies, most AGNs being radio-quiet, i.e. withoutan obvious jet, while radio-loud AGNs (with a promi-nent jet) represent ∼ 0.1% of all galaxies. Radio-loudAGNs have long been considered possible UHECRand UHENU sources, e.g. [87, 88]. However, thelack of an angular correlation between Auger or TAUHECR events and AGNs [1, 3] may be suggestingthat more common galaxies, e.g. SFGs or SBGs, maybe hosting the UHECR sources, which could be HNe,GRBs or magnetars, all of which appear capable ofaccelerating UHECRs at a rate sufficient to give theobserved diffuse UHECR flux.

Another possibility is that UHECR are acceleratedin shocks near the core of radio-quiet AGNs, wherethey would produce UHENUs [89, 90, 91], or alter-natively UHECR could be accelerated in stand-offshocks caused by the infall of intergalactic gas ontoclusters of galaxies [92, 93, 94]. Galactic mergershocks (GMSs) also appear capable of acceleratingUHECR, with a similar energy input rate into theIGM [95]; see below.

5. The PeV Neutrino Background

In 2013 the IceCube collaboration announced thediscovery of the first PeV and sub-PeV neutrinoswhich, to a high confidence level, are of astrophysi-cal origin [96, 4]. The majority of these are cascades,whose angular resolution is 15 − 30o, ascribed toνe, νe, while a minority are Cherenkov tracks with anangular resolution ∼ 1o due to νμ, νμ. Their spectrumstands out above that of the diffuse atmospheric spec-trum by at least 4.1σ, with a best fit spectrum ∝ E−2.2.There is no statistically significant evidence for a con-centration either towards the galactic center or thegalactic plane, being compatible with an isotropicdistribution. No credible correlation has been so farestablished with any well-defined extragalactic ob-jects, such as AGNs, but the working assumption ofan extragalactic origin is widely accepted.

A flux of PeV neutrinos from starburst galaxies ata level close to that observed level was predicted by[97]. The actual accelerators could be hypernovae;the maximum energy of protons, from eq.(3), is suf-ficient for the pp production of PeV neutrinos [98],and statistically, O(1) of the observed events couldbe due to a hypernova (or at most a few) located inthe bulge of the Milky Way. However, the bulk ofthe observed events must come from an isotropic dis-tribution, and hypernovae in ultra-luminous infraredgalaxies (ULIRGs) or SFGs/SBGs could be responsi-ble [99, 100].

Figure 8: The INB flux (right) and IGB flux (left) allowed by ppscenarios [101] for a proton slope p = −2 (thick dashed) and p =−2.18 (thick dashed). The shaded rectangle is the Icecube PeV data[4], while the data points on the left are the Fermi [102] isotropicgamma background data.

P. Mészáros / Nuclear Physics B (Proc. Suppl.) 256–257 (2014) 241–251 247

More generally [101], one can ask whetherhadronuclear (pp) interactions may be responsiblefor this isotropic neutrino background (INB) at PeVenergies, without violating the constraints imposedby the isotropic gamma-ray background (IGB) [102]measured by Fermi. As shown by [101], this requiresthe accelerated protons to reach at least ∼ 100PeVand to have an energy distribution ∝ E−p with an in-dex no steeper than −2.2 <∼ p <∼ 2.0 (Fig. 8). Animportant point is that most events are cascades, in-volving electron flavor neutrinos, and the νe, e crosssection is resonant at CM energies comparable to theW meson mass (Glashow resonance), at around 6.3PeV in the lab frame. Since events are not seen atthis energy, but they would be expected if the pro-ton (and neutrino) slopes where ∼ −2,−2.2, one con-cludes that the proton distribution steepens or cuts offat energies >∼ 100 PeV. Such a cutoffmay be expectedin scenarios where the acceleration occurs in galaxycluster shocks or in SFG/SBGs, where this energymay correspond to that where the escape diffusiontime out of the acceleration region becomes less thanthe injection time or the pp time [101]. Broadly sim-ilar conclusions are reached by [99, 100, 103, 104].

Suggestively, [104] find a weak correlation be-tween five known SFGs (M82, NGC253, NGC4945,SMC and IRAS18293) and the very wide, 15 − 30o

error boxes of some cascade events, but not correla-tion so far with any track events; they estimate that10 years may be needed with IceCube to find trackcorrelations with SFGs at >∼ 99% confidence level.

Another type of large scale shocks in galaxies arethe galaxy merger shocks (GMSs), which occur ev-ery time two galaxies merge. Every galaxy merged atleast once during the last Hubble time, and probablymore then once; in fact mergers are the way galax-ies grow over cosmological time. Such galaxy merg-ers were considered in the PeV neutrino backgroundcontext by [95]. They estimate that individual majormergers involving galaxies with M∗ >∼ 1011M� havean average kinetic energy of Egms ∼ 1058.5 erg, oc-curring at a rate R ∼ 10−4Mpc−3Gyr−1, with a rel-ative shock velocity vs ∼ 107.7 cm s−1. For a CRacceleration fraction ηcr ∼ 10−1 the UHECR en-ergy injection rate into the Universe is Qcr,gms ∼3×1044 ergMpc−3yr−1 (which is also the observation-ally inferred rate UHECR energy injection rate), witha maximum CR energy of εcr,max ∼ 1018.5Z eV. Thepp interactions in the shocks and in the host galaxieslead to PeV neutrinos and <∼ 100 GeV γ-rays (Fig. 9).

Individual GMSs from major mergers at z ∼ 1

Figure 9: The INB flux from massive major GMSs, which is indi-cated by the shaded region. The striped regions show the possibleextensions due to GMSs in minor mergers, or due to a more ef-fective CR acceleration. The solid and dashed lines represent theINB and the atmospheric background flux observed by IceCube,respectively [95].

would yield in IceCube on average ∼ 10−2 muonevents/year, or an isotropic neutrino background(INB) of ∼ 20 − 30% of the IceCube observedPeV-sub-PeV flux. Minor mergers, whose rate ismore uncertain, might contribute up to 70-100% ofthe INB (Fig. 9). The γ-ray flux from individ-ual GMS expected is ∼ 10−13 erg cm−2 s−1, possi-bly detectable by the future CTA, while the cor-responding isotropic gamma background (IGB) is∼ 10−8 GeV cm−2 s−1sr−1, about 20-30% of the ob-served Fermi IGB, or a somewhat larger percentagedue to minor mergers [95].

6. Conclusion, Prospects

In conclusion, the sources of UHECR and the ob-served extragalactic UHENU are still unknown. ForUHECR, an exotic physics explanation is almost cer-tainly ruled out, mainly because any such mecha-nisms would produce a high energy photon compo-nent in UHECR which can be observationally ruledout, e.g. [105]. Anisotropy studies from Auger,which initially suggested a correlation with AGNs[106] have more recently, together with TelescopeArray observations, yielded no significant correla-tion with any specific types of galaxies [1, 2, 3].This might favor some of the more common types of

P. Mészáros / Nuclear Physics B (Proc. Suppl.) 256–257 (2014) 241–251248

galaxies, such as possibly radio-quiet AGNs, or alter-natively stellar type events such as GRBs, hypernovaeor magnetars, as discussed in §§2,3,4.

The indications for a heavy UHECR composi-tion at higher energies [65, 107, 108] would ap-pear to disfavor AGN jets, where the compositionis closer to solar, and favor evolved stellar sources,such as GRBs, hypernovae and magnetars, where aheavy composition is more natural, if the nuclei canavoid photo-dissociation (§4). These sources wouldalso reside in more common galaxies, avoiding theanisotropy constraints.

The PeV and sub-PeV neutrinos discovered byIceCube [96, 4] are an exciting development in thequest for finding the neutrino smoking gun pointingat UHECR sources, even if not at the highest ener-gies. Standard IS GRBs appear to be ruled out as thesources for this observed diffuse neutrino flux, giventhe upper limits for GRBs from IceCube [55, 53].Note however that these limits were obtained for sim-plified internal shock models, and more careful com-parison needs to be made to more realistic models(see §2). Nonetheless, the normal high luminosity,electromagnetically detected GRBs, even if able tocontribute to the GZK end of the UHECR distribution[59], appear inefficient as PeV neutrino sources. Itis possible that low luminosity GRBs (in the electro-magnetic channel) could yield appreciable PeV neu-trinos [109], and also choked GRBs [76] would beelectromagnetically non-detected but might providesignificant PeV neutrino fluxes. The fluxes, however,remain uncertain.

More attractive candidates for the PeV neutrinosare the star-forming and starburst galaxies, hostingan increased rate of hypernovae, or accretion shocksonto galaxies or clusters, or else galaxy mergers,all of which are capable of accelerating CRs up to∼ 100 PeV and produce PeV neutrinos via pp inter-actions is discussed in §4.

It is also remarkable that the PeV neutrino flux isessentially at the Waxman-Bahcall (WB) bound level[51, 111] for UHECR near the GZK range, whichis also comparable to the GeV range CR flux [110],Fig. 10. This suggests the intriguing prospect thatthe same sources may be responsible for the entireGeV-100 EeV energy range, a possibility whose test-ing would require much further work.

We can look forward to much further progresswith continued observations from IceCube, Auger,TA and their upgrades, as well as HAWC, CTAand ground-based Cherenkov arrays and other instru-

Figure 10: Constraints on the energy production rate density ofCRs in the local universe (per logarithmic particle energy). Theproduction of CRs with ε ∼ 10101011 eV (shaded area) is basedon the production in our galaxy and in starbursts galaxies, assum-ing it follows the star formation rate. The lower bound on CRswith ε ∼ 10151017 eV is obtained from the PeV neutrino flux de-tected by Icecube, assumed to be extragalactic. The productionof Ultra-high-energy CRs with ε ∼ 1019 − 1020 eV (solid line) isbased on the observed flux of these CRs, assuming they are mainlyprotons and taking into account the interactions with the Cosmic-Microwave-Background (CMB). From [110].

ments. UHECR composition and UHECR/UHENUclustering will provide important clues, as well asGeV and TeV photon observations to provide muchneeded additional constraints, especially if UHENUsource localization is achieved..

This work was partially supported by NASA NNX13AH50G. I am grateful to the organizers of the Ori-gin of Cosmic Rays conference for their kind hospi-tality and for stimulating discussions, also held withK. Kashiyama, P. Baerwald, S, Gao and N. Senno.

References

[1] The Pierre AUGER Collaboration et al., AstroparticlePhysics 34, 314 (2010).

[2] Pierre Auger Collaboration et al., Astrophys.J.Lett. 762,L13 (2013).

[3] T. Abu-Zayyad and the Telescope Array collaboration,ArXiv e-prints (2013).

[4] IceCube Collaboration, Science 342, (2013).[5] C. Kouveliotou et al., Astrophys.J.Lett. 413, L101 (1993).[6] G. J. Fishman and C. A. Meegan,

Annu.Rev.Astron.Astrophys. 33, 415 (1995).[7] N. Gehrels and P. Meszaros, Science 337, 932 (2012).[8] P. Meszaros and N. Gehrels, Research in Astronomy and

Astrophysics 12, 1139 (2012).[9] M. Ackermann and the Fermi collaboration, Astro-

phys.J. 729, 114 (2011).

P. Mészáros / Nuclear Physics B (Proc. Suppl.) 256–257 (2014) 241–251 249

[10] A. Abdo and the Fermi Collaboration, Science 323, 1688(2009).

[11] V. Pelassa, in American Institute of Physics Conference Se-ries, Vol. 1358 of American Institute of Physics ConferenceSeries, edited by J. E. McEnery, J. L. Racusin, & N. Gehrels(PUBLISHER, ADDRESS, 2011), pp. 41–46.

[12] G. Cavallo and M. J. Rees, M.N.R.A.S. 183, 359 (1978).[13] B. Paczynski, Astrophys.J.Lett. 308, L43 (1986).[14] J. Goodman, Astrophys.J.Lett. 308, L47 (1986).[15] A. Shemi and T. Piran, Astrophys.J.Lett. 365, L55 (1990).[16] R. Narayan, B. Paczynski, and T. Piran, Astro-

phys.J.Lett. 395, L83 (1992).[17] P. Meszaros and M. J. Rees, Astrophys.J. 397, 570 (1992).[18] S. E. Woosley, Astrophys.J. 405, 273 (1993).[19] B. Paczynski, in Gamma-Ray Bursts, 4th Hunstville Sympo-

sium, Vol. 428 of American Institute of Physics ConferenceSeries, edited by C. A. Meegan, R. D. Preece, and T. M.Koshut (PUBLISHER, ADDRESS, 1998), pp. 783–787.

[20] S. E. Woosley and A. Heger, Astrophys.J. 752, 32 (2012).[21] C. Akerlof et al., Nature 398, 400 (1999).[22] N. Gehrels, E. Ramirez-Ruiz, and D. B. Fox,

Annu.Rev.Astron.Astrophys. 47, 567 (2009).[23] M. J. Rees and P. Meszaros, M.N.R.A.S 258, 41P (1992).[24] P. Meszaros and M. J. Rees, Astrophys.J. 405, 278 (1993).[25] P. Meszaros and M. J. Rees, Astrophys.J.Lett. 418, L59+

(1993).[26] M. J. Rees and P. Meszaros, Astrophys.J.Lett. 430, L93

(1994).[27] B. Zhang and P. Meszaros, International Journal of Modern

Physics A 19, 2385 (2004).[28] P. Meszaros, Rept. Prog. Phys. 69, 2259 (2006).[29] P. Meszaros and M. J. Rees, M.N.R.A.S. 269, L41+ (1994).[30] R. D. Preece et al., Astrophys.J.Lett. 506, L23 (1998).[31] G. Ghisellini and A. Celotti, Astron.Astrophys.Supp. 138,

527 (1999).[32] M. V. Medvedev, Astrophys.J. 540, 704 (2000).[33] P. Meszaros and M. J. Rees, Astrophys.J. 530, 292 (2000).[34] M. J. Rees and P. Meszaros, Astrophys.J. 628, 847 (2005).[35] A. Pe’er, P. Meszaros, and M. J. Rees, Astrophys.J. 642, 995

(2006).[36] P. Kumar and A. Panaitescu, Astrophys.J.Lett. 541, L51

(2000).[37] B. Zhang et al., Astrophys.J. 642, 354 (2006).[38] J. A. Nousek et al., Astrophys.J. 642, 389 (2006).[39] A. A. Abdo and the Fermi Collaboration, Nature 462, 331

(2009).[40] G. Ghisellini, G. Ghirlanda, L. Nava, and A. Celotti,

M.N.R.A.S. 403, 926 (2010).[41] P. Kumar and R. Barniol Duran, M.N.R.A.S. 409, 226

(2010).[42] H.-N. He et al., Astrophys.J. 733, 22 (2011).[43] K. Toma, X.-F. Wu, and P. Meszaros, Astrophys.J. 707,

1404 (2009).[44] K. Toma, X.-F. Wu, and P. Meszaros, M.N.R.A.S. 415, 1663

(2011).[45] I. Vurm, R. Hascoet, and A. M. Beloborodov, ArXiv e-

prints (2014).[46] P. Meszaros and M. J. Rees, Astrophys.J.Lett. 733, L40+

(2011).[47] A. M. Beloborodov, M.N.R.A.S. 407, 1033 (2010).[48] S. Razzaque, C. D. Dermer, and J. D. Finke, ArXiv e-prints

(2009).[49] K. Murase, K. Asano, T. Terasawa, and P. Meszaros, Astro-

phys.J. 746, 164 (2012).

[50] E. Waxman, Physical Review Letters 75, 386 (1995).[51] E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292

(1997).[52] D. Guetta et al., Astroparticle Physics 20, 429 (2004).[53] R. Abbasi et al., Nature 484, 351 (2012).[54] M. Ahlers, M. C. Gonzalez-Garcia, and F. Halzen, As-

troparticle Physics 35, 87 (2011).[55] R. Abbasi et al., Physical Review Letters 106, 141101

(2011).[56] S. Hummer, P. Baerwald, and W. Winter, Physical Review

Letters 108, 231101 (2012).[57] Z. Li, Phys.Rev.D 85, 027301 (2012).[58] S. Gao, K. Asano, and P. Meszaros, Jour. Cosmology and

Astro-Particle Phys. 11, 58 (2012).[59] K. Asano and P. Meszaros, ArXiv e-prints (2014).[60] K. Murase, Phys.Rev.D 78, 101302 (2008).[61] X.-Y. Wang and Z.-G. Dai, Astrophys.J.Lett. 691, L67

(2009).[62] P. Veres, B.-B. Zhang, and P. Meszaros, Astrophys.J. 764,

94 (2013).[63] J. M. Burgess et al., Astrophys.J.Lett. 784, L43 (2014).[64] S. Horiuchi, K. Murase, K. Ioka, and P. Meszaros, Astro-

phys.J. 753, 69 (2012).[65] Pierre Auger Collaboration, Jour. Cosmology and Astro-

Particle Phys. 6, 22 (2011).[66] IceCube Collaboration et al., ArXiv e-prints p48, (2013).[67] S. Gao, K. Kashiyama, and P. Meszaros, Astro-

phys.J.Lett. 772, L4 (2013).[68] S. E. Woosley and J. S. Bloom,

Annu.Rev.Astron.Astrophys. 44, 507 (2006).[69] K. Nomoto, M. Tanaka, N. Tominaga, and K. Maeda,

New Ast.Rev. 54, 191 (2010).[70] D. Guetta and M. Della Valle, Astrophys.J.Lett. 657, L73

(2007).[71] A. M. Soderberg et al., Nature 463, 513 (2010).[72] S. Campana et al., Nature 442, 1008 (2006).[73] D. Lazzati, B. J. Morsony, C. H. Blackwell, and M. C.

Begelman, Astrophys.J. 750, 68 (2012).[74] P. Meszaros and E. Waxman, Physical Review Letters 87,

171102 (2001).[75] S. Horiuchi and S. Ando, Phys.Rev.D 77, 063007 (2008).[76] K. Murase and K. Ioka, Physical Review Letters 111,

121102 (2013).[77] I. Taboada, in American Institute of Physics Conference Se-

ries, Vol. 1358 of American Institute of Physics Confer-ence Series, edited by J. E. McEnery, J. L. Racusin, and N.Gehrels (PUBLISHER, ADDRESS, 2011), pp. 365–370.

[78] J. Daughhetee, in APS April Meeting Abstracts (PUB-LISHER, ADDRESS, 2012), p. C7008.

[79] X.-Y. Wang, S. Razzaque, P. Meszaros, and Z.-G. Dai,Phys.Rev.D. in press (astro-ph/0705.0041) 705, (2007).

[80] R. Budnik, B. Katz, A. MacFadyen, and E. Waxman, Astro-phys.J. 673, 928 (2008).

[81] X.-Y. Wang, S. Razzaque, and P. Meszaros, Astro-phys.J. 677, 432 (2008).

[82] J. Arons, Astrophys.J. 589, 871 (2003).[83] B. Zhang et al., Astrophys.J. 595, 346 (2003).[84] G. Ghisellini et al., M.N.R.A.S. 390, L88 (2008).[85] K. Murase, P. Meszaros, and B. Zhang, Phys.Rev.D 79,

103001 (2009).[86] K. Kotera, Phys.Rev.D 84, 023002 (2011).[87] J. P. Rachen, T. Stanev, and P. L. Biermann, Astron. Astro-

phys. 273, 377 (1993).[88] V. Berezinsky, A. Z. Gazizov, and S. I. Grigorieva, ArXiv

P. Mészáros / Nuclear Physics B (Proc. Suppl.) 256–257 (2014) 241–251250

Astrophysics e-prints (2002).[89] F. W. Stecker, C. Done, M. H. Salamon, and P. Sommers,

Physical Review Letters 66, 2697 (1991).[90] J. Alvarez-Muniz and P. Meszaros, Phys.Rev.D 70, 123001

(2004).[91] A. Pe’er, K. Murase, and P. Meszaros, Phys.Rev.D 80,

123018 (2009).[92] U. Keshet et al., Astrophys.J. 585, 128 (2003).[93] S. Inoue, F. A. Aharonian, and N. Sugiyama, Astro-

phys.J.Lett. 628, L9 (2005).[94] K. Murase, S. Inoue, and S. Nagataki, Astro-

phys.J.Lett. 689, L105 (2008).[95] K. Kashiyama and P. Meszaros, Astrophys.J.Lett. 790, L14

(2014).[96] M. G. Aartsen et al., Physical Review Letters 111, 021103

(2013).[97] A. Loeb and E. Waxman, Jour. Cosmology and Astro-

Particle Phys. 5, 3 (2006).[98] D. B. Fox, K. Kashiyama, and P. Meszaros, Astro-

phys.J. 774, 74 (2013).[99] H.-N. He et al., Phys.Rev.D 87, 063011 (2013).

[100] R.-Y. Liu et al., Phys.Rev.D 89, 083004 (2014).[101] K. Murase, M. Ahlers, and B. C. Lacki, Phys.Rev.D 88,

121301 (2013).[102] A. A. Abdo and Fermi LAT Collaboration, Physical Review

Letters 104, 101101 (2010).[103] X.-C. Chang and X.-Y. Wang, ArXiv e-prints (2014).[104] L. A. Anchordoqui et al., ArXiv e-prints (2014).[105] The Pierre AUGER Collaboration and V. Scherini, Nuclear

Physics B Proceedings Supplements 212, 115 (2011).[106] The Pierre Auger Collaboration, Science 318, 938 (2007).[107] The Pierre Auger Collaboration et al., ArXiv e-prints

(2013).[108] K.-H. Kampert, Brazilian Journal of Physics 43, 375

(2013).[109] R.-Y. Liu and X.-Y. Wang, Astrophys.J. 766, 73 (2013).[110] B. Katz, E. Waxman, T. Thompson, and A. Loeb, ArXiv

e-prints (2013).[111] J. Bahcall and E. Waxman, Phys.Rev.D 64, 023002 (2001).

P. Mészáros / Nuclear Physics B (Proc. Suppl.) 256–257 (2014) 241–251 251