High Energy Neutrino Emissions from GRBs:

Predictions and Issues

Bing ZhangDepartment of Physics and Astronomy, University of Nevada Las Vegas

E-mail: bzhang@physics.unlv.edu

Abstract. Gamma-ray bursts (GRBs) are believed to be cosmic ray accelerators and highenergy neutrino emitters. Within the framework of the standard GRB fireball model, neutrinosof a wide range of energy are produced from different emission sites. The published predictionsof GRB neutrino emission are reviewed, especially in view of the latest GRB observations withSwift. Issues regarding the uncertainties in those predictions are discussed.

1. IntroductionGamma-ray bursts (GRBs) are short, energetic bursts of gamma-rays that mark the most violent,cataclysmic explosions in the universe. Followed by the broad-band afterglows, these event areobservationally accessible in essentially all electromagnetic wavelengths. Within the standardfireball model of GRBs [1], GRBs are originated from a relativistic ejecta that moves towardsthe Earth. gamma-rays are emitted by the shock-accelerated electrons in the so-called internalshocks, while afterglow photons are emitted by the electrons accelerated from an external forwardshock as the fireball is decelerated by the circumburst medium.

The external shock afterglow model has been successful to interpret much of the broad-bandafterglow data. The latest observations with NASA’s dedicated mission Swift reveal a richphenomenology of GRB afterglows, which requires additional emission components other thanthe external shock to interpret the X-ray (and probably also the optical) afterglows [2,3]. Inany case, one could safely accept that the external shock indeed exists. There is no directproof for the existence of internal shocks, on the other hand. They are introduced to mainlyinterpret the erratic, irregular gamma-ray lightcurves during the burst. Alternative suggestionsto interpret the prompt emission include other energy dissipation mechanisms such as magneticreconnection.

The suggestion that GRBs are high energy neutrino emitters has been rooted in the beliefthat GRB outflows are baryonic in nature (not dominated by a Poynting flux) and that shocksare the sites of energy dissipation. While electrons must have been accelerated to high energiesto radiate and give rise to the observed GRBs, associated ions (mainly protons) must havebeen also accelerated to high energies. The interactions between these high energy protons andsoft photons or other nucleons would give rise to intense emission of high energy neutrinos.Originally, the suggestion that GRBs are neutrino emitters was derived from the argument thatGRBs are likely sources of ultra-high energy cosmic rays (UHECRs) [4]. More generally, GRBscan be important neutrino emitters even if the shocks cannot accelerate particles to the desiredhigh energies of UHECRs, as long as shocks are in operation.

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Nuclear Physics B (Proc. Suppl.) 221 (2011) 324–327

0920-5632/$ – see front matter © 2011 Published by Elsevier B.V.

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doi:10.1016/j.nuclphysbps.2011.09.025

2. GRBs as emitters of neutrinos of different energiesWidely discussed processes for high energy neutrino emission include

• pγ process: pγ → Δ+→ nπ

+→ ne

+νeνμνμ;

• pp process: pp → π±/K

±. . . → μνμ . . . → eνeνμνμ . . .;

• pn process: pn → π±/K

±. . . → μνμ . . . → eνeνμνμ . . .

The dominant pγ process occurs at the Δ-resonance, which has the threshold conditionεpεγ ∼ 0.2 GeV2 in the center of mass frame. In the case of GRBs, this is usually translatedin the observer’s frame to εpεγ ∼ 0.2 GeV2Γ2 if both protons and photons are generated inrelativistic shocks, where Γ is the bulk Lorentz factor. The threshold condition for both pp andpn interactions is that the relative drift energy between these baryons exceed the pion rest mass,i.e., ε

′≥ 140 MeV. Since both p and n have a rest mass close to 1 GeV, the threshold of pp and

pn interaction only demands semi-relativistic relative motions.In a GRB event, there are multiple sites where neutrinos with different energies are generated.

Below is an non-exhaustive list which encompasses most of the processes discussed in theliterature, in a sequence of ascending neutrino energy, which is essentially also in a sequence ofascending distance from the central engine:

• MeV neutrinos: Long GRBs are believed to be originated from stellar collapses, whileshort GRBs are likely related to mergers of compact objects. In both cases, they shouldbe associated with thermal MeV neutrinos. In most models, the central engine involvesa black hole - torus system, and the thermal neutrino annihilation is one of the leadingprocesses for launching the fireball. For long GRBs, MeV neutrino signals are expectedsuch as those in supernovae. However, these thermal neutrinos are extremely difficult todetect from cosmological distances, due to the very low cross section for νN interactions atthese energies.

• multi-GeV neutrinos: GRB fireballs may be neutron-rich. During the fireball accelerationphase, neutrons can decouple from protons when the elastic scattering condition breaksdown. The relative drift between both species results in inelastic pn interactions giving riseto 5-10 GeV neutrinos [5]. A similar process also occurs within sub-photospheric internalshocks, which extends significantly the parameter space for the inelastic neutrino collisioncondition [6]. pp interactions within the internal shocks can also give rise to a 30 GeVneutrino burst, although magnetic fields can inhibit the inter-penetration of charged speciesstreams with different velocities [7];

• multi-TeV neutrinos: Within the collapsar scenario, the relativistic jet launched from thebase of the flow (presumably the black hole and the torus) has to penetrate through thestellar envelope before breaking out and generating the GRB. The internal shocks below theenvelope accelerate protons that interact with thermal photons within the envelope (i.e. pγ

interaction). Regardless of whether the jet finally penetrates through the envelope or getschoked, it will generate strong multi-TeV neutrino signals [8]. The signature is enhancedor even dominated by pn, pp interactions and could be used as a diagnostic about the typeof progenitor stars [9];

• ∼ PeV neutrinos: pγ interactions within the conventional internal shocks which produceprompt gamma-rays typically generate 1014

− 1016 eV neutrinos [10]. For a long-durationGRB with a dense medium (e.g. in the stellar wind environment), the internal shock gamma-rays may overlap the external shock region (both the forward and the reverse shock) andinteract with the protons accelerated in those shocks. These interactions also give rise to∼ PeV range neutrinos [11].

• ∼ EeV neutrinos: pγ interactions within the external reverse shock give rise to even higherenergy neutrinos. For a constant density medium the typical energy is 1017

−1019 eV, while

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for a wind medium, the typical energy is ∼ 3× (1015−1017) eV and extending above it [12].

In the forward shock region, assuming the blast wave can accelerate protons to ultrahighenergies, a neutrino afterglow is expected with the peak energy ∼ 1018 eV [13].

The latest observations by Swift provide two new interesting possibilities of GRB neutrinoemissions.

• Erratic X-ray flares are observed in about half GRBs [14]. The properties of these flaresstrongly suggest that they are of “internal” origin, marking the reactivation of the GRBcentral engine [2,15,16]. If these late internal emissions are also from internal shocks, pγ

interactions would generate high energy neutrinos as well, which peaks at a higher energythan the traditional internal shock component for the GRB prompt emission [17].

• The discovery of the nearby low-luminosity (LL) GRB 060218 suggests a much higher localevent rate of LL-GRBs [18]. Although these X-ray flashes are less energetic individually,the high event rate compensates the energy deficit, making LL-GRBs form an interestingsecond high-energy component in the diffuse neutrino spectrum [19,20].

The flux levels of the above mentioned various neutrino emission components have beencalculated. Neutrinos from individual GRBs can be only detected from nearby, bright events(e.g. GRB 030329 [9]). For the majority of GRBs, what is observationally interesting is thediffuse neutrino background from all GRBs. For sources that are optically thin for pγ and pp

interactions (which are also likely the best candidates of high energy neutrino sources such asGRBs and AGNs), an upper limit of diffuse neutrino background could be placed using theobserved UHECR data [21].

E2

νΦ < E2

νΦWB

ν = 2× 10−8ζz

[E

2pdNp/dEp)z=0

1044 ergs Mpc−3 yr−1

]GeV cm−2 s−1 sr−1

. (1)

A good list of neutrino telescopes are being constructed [22]. In order to reach the WB limitand therefore to place an interesing limit on the diffuse neutrino flux, kilometer-size (giga-ton) detectors are needed. The Antarctic Muon and Neutrino Detector Array (AMANDA) hasbeen in operation since 2000, and has achieved an effective detector mass of ∼ 0.1 Gton. Theextension of AMANDA, Icecube, is planned to reach the ∼ 1 Gton effective detector mass by2008-2009. Other neutrino detectors include ANTARES (Astronomy with a Neutrino Telescopeand Abyss Environment Research), NESTOR (Neutrino Extended Submarine Telescope withOcceanographic Research), RICE, ANITA, KM3Net, etc. Although no neutrino signals fromGRBs have been reported so far, it looks promising that breakthrough will be made in the nextseveral years.

Among the neutrino emission components discussed above, the most promising componentsfrom observational point of view are the ∼ PeV neutrino emission from internal shocks [10](or “overlapping” external shocks [11]) and the multi-TeV emission from slow jets inside thestellar envelopes [8,9]. This is because at lower energies (below TeV) the atmospheric neutrinobackground sharply increases with decreasing energies, and at higher energies (above severalPeV) a much larger effective detector mass is needed.

3. Uncertainties in the neutrino flux predictionsIn view that directly detecting the GRB neutrino background (or posing a stringent upper limit)becomes plausible in the near future, it would be informative to collect various issues regardingthe predicted neutrino fluxes. This would serve to answer the questions such as “what if theneutrino background is not detected at the predicted level?”, etc. This section is dedicated tothis topic.

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The most important issue is the composition of the GRB ejecta. As discussed above, theobservationally most interesting component (∼ PeV component) solely relies on the assumptionthat GRB prompt emission is produced in internal shocks. While this is the most popular modelof prompt emission, there is no robust proof. A list of concerns regarding the internal shockmodel have been raised in the literature.

• Gamma-ray polarization and reverse shock modeling both suggest that the GRB centralengine is likely strongly magnetized [23]. Weak or negligible reverse shock emission frommany GRBs is at least consistent with a Poynting flux dominated flow [24,25].

• Independent arguments have been raised to suggest a prompt emission radius orders ofmagnitude larger than the standard internal shock radius [26.

• At least for X-ray flares, mechanisms involving magnetic fields are needed, and there is aclean argument based on energetics only to suggest that the GRB outflow is launched viamagnetic processes [16].

• The internal shock model predicts much wider distributions of spectral peak energy (Ep)within a same burst and among different bursts, which are inconsistent with the data [27].

• It has been argued recently by several different groups that some empirical relations invokingprompt emission parameters are more naturally interpreted by invoking energy dissipationnear the photosphere of the fireball where internal shocks are no longer necessarily needed[28].

Although none of the above objections can rule out the internal shock model, they do raisethe caution that the ∼ PeV neutrino signals [10] are not guaranteed. Positive detections of thesesignals, on the other hand, would greatly support the internal shock model and would rule outthe Poynting-flux-dominated model of GRBs. The ∼ PeV neutrino signals due to overlappingthe prompt gamma-ray front and the external shock region [11] are more robust if overlappingindeed happen, since it is almost certain that an external forward shock exists. The conditionfor overlapping, on the other hand, is not easy to satisfy in the constant density ISM mediumbut is likely satisfied in a stellar wind medium. Recent Swift observations however suggest thata wind-type medium, if any, is very rare [2,25].

Even if GRBs are baryonic in nature, the predictions of the ∼ PeV neutrino flux is still subjectto uncertainties. Two effects, in particular, affect the predicted neutrino flux level significantly[19]. First, in order to maximize the predicted neutrino flux, usually a p = 2 proton spectrumis assumed. Studies of prompt and afterglow emissions suggest that p is typically steeper than2 for electrons. If protons also have p > 2, the predicted neutrino spectrum no longer has a flatplateau, and the flux would drop at high energies above the peak. Second, usually the neutrinospectrum for a burst with typical parameters is taken to estimate the diffuse neutrino flux [10].In principle, one needs to average over bursts with a wide range of distributions of luminosityand other parameters. Such an analysis [19] suggests that the predicted diffuse backgroundemission sensitively depends on some unknown parameters, especially the bulk Lorentz factorof GRBs. The predicted diffuse neutrino flux level is therefore rather uncertain. On the otherhand, the detection (or tight upper limit) would present severe constraints on the bulk Lorentzfactor distribution of GRBs.

4. ConclusionsThere are good reasons to believe that GRBs are one of the best candidates for high energyneutrino emission. Within the standard GRB fireball framework, neutrinos from MeV to EeV areproduced. The detectability of these signals depend on detectors’ capability, and it is optimisticthat neutrinos in the TeV-PeV range may be detectable in the near future. The predicted fluxlevels in this energy range, on the other hand, suffer important uncertainties of some unknown

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