What IceCube data tell us about neutrino emission from star-forming galaxies (so far)
Luis A. Anchordoqui, Thomas C. Paul, Luiz H. M. da Silva, Diego F. Torres, Brian J. Vlcek
WWhat IceCube data tell us about neutrino emission from star-forming galaxies (so far)
Luis A. Anchordoqui,
1, 2
Thomas C. Paul,
2, 3
Luiz H. M. da Silva, Diego F. Torres,
4, 5 and Brian J. Vlcek Department of Physics and Astronomy, Lehman College at CUNY, Bronx NY 10468, USA Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA Department of Physics, Northeastern University, Boston, MA 02115, USA Institute of Space Sciences (IEEC-CSIC), Campus UAB, Torre C5, 2a planta, 08193 Barcelona, Spain Instituci´o Catalana de Recerca i Estudis Avanc¸ats (ICREA), Spain (Dated: June 2014)Very recently, the IceCube Collaboration reported a flux of neutrinos in the energy range 50 TeV (cid:46) E ν (cid:46) . σ level. This fluxis in remarkable agreement with the expected di ff use flux of neutrinos from starburst galaxies, andthe 3 highest energy events have uncertainty contours encompassing some of such systems. Theseevents, all of which have well-measured energies above 1 PeV, exhibit shower topologies, for whichthe angular resolution is about 15 ◦ . Due to this angular uncertainty and the a posteriori nature of cutsused in our study it is not possible to assign a robust statistical significance to this association. Usingmuon tracks, which have angular resolution < ◦ , we compute the number of observations requiredto make a statistically significant statement, and show that in a few years of operation the upgradedIceCube detector should be able to confirm or refute this hypothesis. We also note that double bangtopology rates constitute a possible discriminator among various astrophysical sources. PACS numbers: 98.70.Sa, 95.85.Ry, 96.50.sb
In 2012, the IceCube Collaboration famously an-nounced an observation of two ∼ . σ excess for the combined 28 events compared to ex-pectations from neutrino and muon backgrounds gen-erated in Earth’s atmosphere [3]. Very recently, theseresults have been updated [4]. At the time of writing,37 events have been reported in three years of IceCubedata taking (988 days between 2010 – 2013). The dataare consistent with expectations for equal fluxes of allthree neutrino flavors and with isotropic arrival direc-tions. Moreover, the next to highest energy event hasequatorial coordinates ( α = . ◦ , δ = − . ◦ ) and there-fore cannot originate from the Galactic plane. Assuminga power law spectrum ∝ E − ν , the three year data setis consistent with an astrophysical flux at the level of3 × − E − ν GeV − cm − s − sr − , and rejects a purely at-mospheric explanation at 5 . σ [4]. Herein we considerthe issue of what the data reported so far may suggest re-garding the possibility that the extraterrestrial neutrinosoriginate in star-forming regions [5].Both the neutrino energy spectrum and directionalmeasurements provide clues about which astrophysi-cal sources may be responsible for extraterrestrial neu-trinos. We will begin with a discussion of characteris-tics of the energy spectrum as it pertains to potentialsource candidates, and then move on to the issue of di-rectional correlations with astrophysical objects. First,however, we should remind the reader that the threeneutrino species ν e , ν µ and ν τ induce di ff erent charac-teristic signal morphologies when they interact in ice producing the Cherenkov light detected by the IceCubeoptical modules. The charged current (CC) interactionof ν e produces an electromagnetic shower which rangesout quickly. Such a shower produces a rather symmetricsignal, and hence exhibits a poor angular resolution ofabout 15 ◦ − ◦ [3]. On the other hand, a fully or mostlycontained shower event allows one to infer a relativelyprecise measurement of the ν e energy, with a resolutionof ∆ (log E ν ) ≈ .
26 [6]. The situation is reversed for ν µ events. In this case, CC interaction in the ice gener-ates a muon which travels relatively unhindered leavingbehind a track. Tracks point nearly in the direction ofthe original ν µ and thus provide good angular resolu-tion of about 0 . ◦ , while the “electromagnetic equivalentenergy” deposited represents only a lower bound of thetrue ν µ energy. The true energy may be up to a factor 10larger than the observed electromagnetic equivalent en-ergy. Finally, ν τ CC interactions may, depending on theneutrino energy, produce “double bang” events [7], withone shower produced by the initial ν τ collision in the ice,and the second shower resulting from most subsequent τ decays. Separation of the two bangs is feasible for ν τ energies above about 3 PeV, while at lower energies theshowers tend to overlap one another [8].With these points in mind, we now move to the cur-rent state of the neutrino energy measurements. Onestriking feature of the IceCube spectrum is that, assum-ing an unbroken E − γν , γ = ff or aspectral break evident around 2 PeV. Notably, there is noincrease in observation rate near 6 . γ =
2. Ithas been shown elsewhere that an unbroken power law a r X i v : . [ a s t r o - ph . H E ] J un spectrum with γ = . p γ interactions,the center-of-momentum energy of the interaction mustbe su ffi cient to excite a ∆ + resonance, the ∆ + (1232) hav-ing the largest cross-section. The threshold proton en-ergy for neutrino production on a thermal photon back-ground of average energy E γ is E th = m π ( m p + m π / / E γ , (1)where m π and m p are the masses of the pion and proton,respectively. Since the proton energy must be about 16times higher than the daughter neutrino energies, Eq. (1)implies photons with energies in the range ∼ ∼ PeV neutrinos. Gamma-ray bursts (GRBs)may be the only astrophysical objects capable of gener-ating a photon background of the required energy forthis scenario [11]. Furthermore, production of neutrinosin the 100 TeV range requires photon energies about anorder of magnitude higher. In contrast, if neutrinos areproduced via interaction in gas near the acceleration site,the energy threshold requirement is lifted, as pp interac-tions generate pions over a broad range of energies.Extending previous multifrequency studies of in-dividual galaxies [13], Loeb and Waxman (LW) [14]showed in 2006 that starburst galaxies constitute a com-pelling source for e ffi cient neutrino production up to ∼ . ∼ γ = . ± .
10 which accurately fits the Ice-Cube data, and indeed predicts an observation rate for E ν of 10 . ± . for a 1 km detector, in line with the rate sub-sequently observed by IceCube. Neutrino productionfrom π ± decays must be accompanied by a correspond-ing flux of gamma rays from decays of π ’s producedin the pp interactions, providing a robust cross-checkof the pion production rate and corresponding neutrinospectrum. A spectrum steeper than γ ∼ . γ = . ff or suppression mustbe at play. All in all, the starburst source hypothesistogether with a steepening of the spectrum to at least γ = .
75 above 3 PeV fits well to the IceCube data andsatisfies the constraints from gamma ray observations,as shown in Fig. 1.We now discuss how double bang topologies mayserve as a discriminator among possible astrophysical
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Ø Ø Ø Ø Ø ØØ Ø Ø Ø Ø Ø - - - - - - - - E n @ GeV D E n d N n ê d E n @ G e V c m - s - s r - D ÊÊ cosmic neutrinos H IceCube @ DL ‡ atmospheric neutrino background H IceCube @ DL Ï gamma rays H Fermi @ DL Ï L W f l ux @ D Fermi shock flux
FIG. 1. Neutrino and gamma ray spectra compared totwo neutrino spectral indices. The squares show the back-ground from atmospheric ν µ events as observed by Ice-Cube40 [16]. The circles and arrows show the recently re-ported IceCube flux (points with solid error bars do not in-clude prompt background while those with dash error barsdo) [4]. The The diamonds are gamma ray flux measure-ments from Fermi [17]. The two dashed lines correspond to E ν d N ν / d E ν = − E − . GeV cm − s − sr − and E ν d N ν / d E ν = × − GeV cm − s − sr − , with the spectrum steepening aboveabout 2 PeV to γ = .
75 and γ = .
0, respectively. For these twoneutrino fluxes, the associated predictions for the gamma rayfluxes after propagation are displayed as the upper and lowerbounds of the shaded region [15] . Note that the spectral index γ = .
15 at injection agrees well with both the Fermi-LAT andIceCube measurements. sources powered by highly relativistic winds. Extrater-restrial neutrino production proceeds via the decay chain π + → µ + ν µ (and the conjugate process) . (2) (cid:31) e + ¯ ν µ ν e This decay chain may be complete in the sense thatboth decays indicated in Eq. (2) occur without signifi-cant change in the µ energy, or it may be incomplete,in which case the µ su ff ers possibly catastrophic energyloss before decay. For the case of a complete decay chain,each neutrino carries on average about 1 / µ radiates away energy before it de-cays, the ν µ from the first decay will still carry on average1 / π ± energy, while the other two neutrinos willemerge with less than the nominal 1 / ν µ in the chain can be produced above 3 PeV, whereas¯ ν e may not reach beyond 2 PeV, and in particular maynot be able to reach the energy required to interact at theGlashow resonance.We now discuss the muon energy loss quantitativelyby exploiting the observation of gamma rays accom-panying the neutrino flux. In the case of muons withenergies in excess of 1 PeV, energy losses are domi-nated by synchrotron radiation. The synchrotron losstime is determined by the energy density of the mag-netic field in the wind rest frame. Defining τ µ, syn as thecharacteristic muon cooling time via synchrotron radia-tion and τ µ, decay as the muon decay time, it is necessarythat τ µ, syn < τ µ, decay in order for the decay chain to becomplete. τ µ, syn ∼ τ µ, decay determines a critical energy E syn µ at which energy losses begin to a ff ect the decaychain. For the characteristic parameters of a GRB wind,the maximum energy at which all neutrinos in the decaychain have on average 1 / E syn ν ≈ E syn µ ∼ Γ . ∆ t − L / PeV , (3)where Γ = . Γ . is the wind Lorentz factor, L = L erg / s is the kinetic energy luminosity of the wind,and ∆ t = ∆ t − s is the observed variability time scaleof the gamma-ray signal [18]. Equation 3 is also valid forneutrinos produced in blazars. In this case, ∆ t ∼ s, Γ ∼
10, and L ∼ erg / s, yielding E syn ν ∼ ffi cient to influence the decaychain in such a way as to a ff ect the flavor ratios at PeVenergies, whereas for blazar and starbursts the decaychain is only a ff ected for muon energies (cid:29)
10 PeV. Notethat for GRBs, ∆ t − ∼ p γ interactions produce fewer ¯ ν e than pp ineractions [19].Indeed, most of the ¯ ν e flux originates via oscillations of ¯ ν µ produced via µ + decay. For production of E ν (cid:38) ν µ in the chain of Eq. (2) is more energetic thanthe ¯ ν µ . This may suggest that the softening of the spec-tral index takes place at di ff erent energies for neutrinoand antineutrino fluxes. If this were the case, at pro-duction the high energy end of the GRB flux would bedominated by ν µ produced via π + decay. As describedpreviously, however, IceCube can measure only lowerbounds for the muon energies. As it turns out, IceCubehas recently recorded a ν µ with a minimum energy of 0.5PeV [20], but which may have an energy as much as 10times higher. If this is indeed the case, it could indicatea high energy muon from the first decay of Eq. (2). Wecan also speculate on more potentially convincing ob-servations which may emerge in the future. Assumingmaximal ν µ − ν τ mixing, observation of a high energy ν µ may imply eventual observation of a high energy ν τ ,which above about 3 PeV would exhibit the distinctivedouble bang topology discussed above. Note that somefine tuning of the model presented here may be requiredfor such events to manifest. In particular, the µ ± coolingtime of Eq. (3) must be smaller than the µ ± decay timein order to prevent the ¯ ν e from reaching the Glashowresonance (thus far not observed). Further, the π ± cool-ing time must exceed its lifetime in order to produce a ν τ ¯ ¯ ¯¯ ¯ ¯ ¯¯ ¯ ¯¯ ¯¯ ¯ ¯¯¯ ¯¯ ¯¯ ¯¯¯¯ ¯¯ ¯¯¯ ¯ ¯¯ ¯¯¯¯¯¯ ¯¯¯¯ ¯¯ ¯¯¯¯ ¯¯¯ ¯ ¯¯¯ ¯ ¯¯¯ ¯¯ ¯¯¯¯ ¯¯ ÏÏ Ï ÏÏÏÏÏ
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FIG. 2. Comparison of IceCube event locations [4] with star-forming galaxies [22] and the ultrahigh energy cosmic ray hot-spot reported by the TA Collaboration [27] in a Mollweide pro-jection. The 27 shower events (circles) and 8 track events (dia-monds) reported by the IceCube Collaboration. The 3 highestenergy events are labeled 1, 2, 3, from high to low, respectively.The red stars indicate the 64 star-forming galaxies beyond theLocal Group. The 4 yellow stars indicate galaxies in the lo-cal group. NGC 253 and M82, our two closest starbursts, arelabeled. The shaded band delimits the Galactic plane. Thesquare in the upper right marks the center of the TA hot-spot,with the surrounding dashed line indicating its 20 ◦ extent. above ∼ ff ects.As such, this study is not meant to make a concrete pre-diction, but rather to point out that if such double bangtopologies are observed in the future while the Glashowresonance is not, it would provide a valuable piece tothe puzzle of extraterrestrial neutrino origins, favoringthe GRB hypothesis over the blazar or starburst ones,each of which would require implausible fine-tuning tobe consistent with observation.Now, since starburst galaxies are plausible source can-didates, consistent with the neutrino energetics observedso far, the next obvious step is to check whether there areany correlations with the positions of starburst galax-ies and the observed neutrino arrival directions. Beforeproceeding we note that hypernovae, which may well beresponsible for sub-PeV to PeV neutrino emissions [21],are present in starburst galaxies as well as other starforming regions, though the rate of occurrence is higherin starburst galaxies. To test the hypothesis that starforming regions correlate with the IceCube events, wehave employed the list of star-forming regions compiledby the Fermi-LAT Collaboration [22], which includes 64of the 65 sources of the HCN survey [23] as well as thelocal galaxies (SMC, LMC, M31, and M33). The HCNsurvey is, to date, the most complete study of galaxieswith dense molecular gas content. It includes nearlyall the IR-bright galaxies in the northern sky ( δ ≥ − ◦ )with strong CO emission, as well as additional galaxiestaken from other surveys. Objects within the Galacticlatitudes | b | < ◦ are not included in the survey due todi ff use emission from the Galactic plane.A comparison among all of the IceCube events and thestar-forming galaxy survey is shown in Fig. 2. Not sur-prisingly given the size of the localization error, thereare a few coincidences, among them the two nearbystarbursts M82 and NGC 253 (observed in gamma-rays [24, 25] which are considered to be possible ul-trahigh energy cosmic ray emitters [26]). The highestenergy event correlates with NGC 4945, the second high-est with the SMC, and the third highest correlates withIRAS 18293-3413. However, none of the track topologiescorrelates with an object in the survey.To estimate the number of ν µ required to make a statis-tically significant statement, we have run 10 simulationswith 68 sources and computed the fraction correlating bychance with 1 ◦ circular regions of the sky. Of these, 90%of the simulations show 0 correlations. If future obser-vations contain 5 or more ν µ events which correlate withthe 68 sources in the survey, an association by chancewill be excluded at more than 99% CL [28].For ν µ events, the equivalent electromagnetic energyrepresents only a lower bound on the true neutrino en-ergy. Consequently, escaping the background regionrequires setting a cut on the electromagnetic equivalentenergy (cid:39) . E ν = ∼ configuration. Next gener-ation IceCube, which could increase the instrumentedvolume by up to an order of magnitude (but with largerstring spacing), will therefore be greatly beneficial forthis study, as well as other correlation analyses.We conclude with one additional observation. It wasrecently noted [29] that the ultrahigh energy cosmicray hot-spot reported by the TA Collaboration [27]correlates with 2 of the 28 events initially reportedby the IceCube Collaboration [3], with a statisticalsignificance of around 2 σ . In the newer IceCube data(the 37 event sample [4]) there is one additional showerevent which correlates with the TA hot-spot, as shownin Fig 2. The hot-spot also contains an abundance ofstar-forming regions and is near M82.This work was supported in part by the US NSF grantsCAREER PHY-1053663 (LAA) and PHY-1205854 (TCP),the NASA grant NNX13AH52G (LAA, TCP), the UWMPhysics 2014 Summer Research Award (LHMdaS), thegrant AYA2012-39303 (DFT), and the UWM RGI (BJV). [1] M. G. Aartsen et al. [IceCube Collaboration], Phys. Rev.Lett. , 021103 (2013) [arXiv:1304.5356]. Note, however,that a cosmogenic origin of these events is highly unlikely,M. G. Aartsen et al. [IceCube Collaboration], Phys. Rev. D , 112008 (2013) [arXiv:1310.5477].[2] S. Schonert, T. K. Gaisser, E. Resconi and O. Schulz, Phys.Rev. D , 043009 (2009) [arXiv:0812.4308]; T. K. Gaisser,K. Jero, A. Karle and J. van Santen, arXiv:1405.0525.[3] M. G. Aartsen et al. 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