The neutrino-induced upward muon energy spectrum on Earth at the TeV energy range emitted by the point source 3C273 AGN has been calculated using the AGN-emitted neutrino spectrum of Szabo and Protheroe and the result has been

compared with that expected from background neutrinos. The QCD-based model of Berezinsky et al. has been fairly employed to estimate the muon contribution due to the charge current interactions in rock. The diffuse 

neutrino-induced upward muon energy spectrum from AGN sources has also been estimated and compared with the

expected results from the spectra of prompt neutrinos and atmospheric backgrounds. It is found that the upward muon fluxes generated by AGN neutrinos are dominating

the Universe beyond 10 TeV muon energy

Bhattacharyya, D. P.

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IL NUOVO CIMENTO VOL. 21 C, N. 1 Gennaio-Febbraio 1998Derivation of upward muon energy spectra in the TeV range producedby neutrinos from 3C273 AGN and diffuse atmospheric sourcesD. P. BHATTACHARYYA()Department of Theoretical Physics, Indian Association for the Cultivation of ScienceJadavpur, Calcutta 700 032, India(ricevuto il 2 Gennaio 1997; approvato il 18 Marzo 1997)Summary. — The neutrino-induced upward muon energy spectrum on Earth at theTeV energy range emitted by the point source 3C273 AGN has been calculated usingthe AGN-emitted neutrino spectrum of Szabo and Protheroe and the result has beencompared with that expected from background neutrinos. The QCD-based model ofBerezinsky et al. has been fairly employed to estimate the muon contribution due tothe charge current interactions in rock. The diffuse neutrino-induced upward muonenergy spectrum from AGN sources has also been estimated and compared with theexpected results from the spectra of prompt neutrinos and atmospheric backgrounds.It is found that the upward muon fluxes generated by AGN neutrinos are dominatingthe Universe beyond 10 TeV muon energy.PACS 96.40 – Cosmic rays.1. – IntroductionAstrophysics of high-energy muons and neutrinos is dependent on the decay of non-prompt mesons and charm particles. The primary cosmic nuclei interact with the at-mosphere producing pions and kaons which decay to give the muons and neutrinos. Itis assumed that the TeV neutrino-induced upward muons have extragalactic origin andare produced in Active Galactic Nuclei (AGN) like 3C273: The massive black hole in thecenter of the AGN acts as an accelerator and may be considered as a source of the jetsthat may be detected in radio observations. Active galactic nuclei (AGN) are the mostluminous objects in the Universe and have been considered as possible sources of high-energy neutrinos. The luminosities of AGN usually range from 1042 to 1048 ergs/s, whichcorresponds to black-hole masses from 104 to 1010M, where Mis the solar mass, andare energised by accretion onto a black hole. The AGN is assumed as one of the main() E-mail: tpdpb@iacs.ernet.inG Societa` Italiana di Fisica 6566 D. P. BHATTACHARYYApoint sources of super-high-energy neutrinos apart from the atmospheric diffuse neutri-nos coming from X-ray binaries, supernova remnants and also from the extra galacticcosmic-ray backgrounds. The simple model of AGN used for galactic neutrino spectrumcalculation is based on approximate conditions in the AGN central engines in which ac-cretion onto a supermassive black hole takes place. In general, the high-energy neutrinobackground and cosmic-ray proton intensity calculated using such models would be muchless than given in [1] which may be considered as an estimate from AGN central engines,apart from the AGN jets. AGN may also be a source of cosmic rays in the region of theknee. The AGN -rays detected by EGRET [2] experiments have been blazers and the-ray emission from these objects is associated with jets. It may be assumed that theAGN are the sources of energetic cosmic rays with energies up to 1010 GeV. Such parti-cles would interact with matter in the Galaxy or with the intergalactic medium or with thecosmic microwave background. The generated 0 yields information on the upper limitof the emitted neutrino flux from AGN-based models on the observed X-ray and -rayfluxes. It is also assumed that AGN has confined sufficient matter to stop protons beforethey diffuse out of the Galaxy. AGN is considered as a potential source of high-energy-production. They may be influenced by gravitational energy of matter independent ofsupermassive black hole at the AGN center. The AGN is assumed to behave like a spaceion accelerator and beam dumps which also act as an intense source of high-energy neutri-nos. Investigation on atmospheric neutrinos is of pheneomenological importance for thebackground calibration in the under-earth detectors for studying the problems relating tothe exploration of stellar collapse in neutrino astronomy [3]. In a recent survey, Gaisser etal. [4] have discussed different sources of atmospheric, galactic and extra-galactic (AGN)neutrinos.A portion of neutrinos entering the Earth from the nadir direction usually interactswith Earth material generating upward muons which can be detected in undergrounddetectors. The down-going muons produced by neutrinos incident from the zenithal di-rection are mixed with atmospheric backgrounds like meson decay muons. Usually, theneutrinos on Earth have to travel an average distance  1:3 104 km up the diameter ofthe Earth. The neutrino telescopes detect muons produced by neutrinos in the water orice and also in the detector materials. The Cherenkov detectors are shielded by a thicklayer of water or earth that helps the filtering of a substantial portion of atmosphericbackgrounds. The neutrino telescopes underground the South Pole are investigating theinteraction of neutrinos entering the Earth from the northern hemisphere. Recently, Bar-wick et al. [5] have discussed three kinds of underground detectors: some are under con-struction and some are proposed to be constructed to investigate the atmospheric andextra-galactic neutrino-induced interaction phenomena as carried out at the i) AntarcticMuon and Neutrino Detector Array (AMANDA [6]) using sterile ice, ii) Lake BAIKAL [7]detector in Siberia by eliminating background noise signals using photomultiplier tubes,iii) Deep Underwater Muon and Neutrino Detector (DUMAND [8]) located near HawaiiIslands, at a depth of 4:5 km of ocean water, iv) Neutrinos from Supernovae ExperimentOcean Range (NESTOR [9]) with more than 1 km of ocean water, in the deep Mediter-ranean Sea coast.Gamma-rays and neutrinos are produced in beam dumps by primary cosmic accelera-tors colliding with different stellar targets. As a consequence, the neutrinos are producedby the decay of non-prompt mesons like + and   into  and . The accelerated cos-mic rays interact with the Earth atmosphere, the Sun, and Moon, interstellar gas in ourgalaxy and the cosmic photon background in the Universe. The diffuse neutrinos whichare generated in the interactions of galactic cosmic rays with the microwave backgroundDERIVATION OF UPWARD MUON ENERGY SPECTRA IN THE TeV RANGE ETC. 67is of special astrophysical importance. The cosmic rays of energies 1014 eV are assumedto be accelerated by shocks driven into the ISM by supernova explosions. Recently, Zaset al. [10] have pointed out that astrophysical neutrinos reside at the highest energiesand have a flatter energy spectrum coming from extra-terrestrial sources. They are ex-pected to dominate the atmospheric neutrino production. Theoretical calculations of theneutrino production at AGN have been done by Stecker et al. [11] and also by Szabo andProtheroe [12]. Berezinsky and Ginzburg [13] have pointed out that the AGN are themost luminous objects in the Universe and are the major sources of high-energy signals.The simple model [12] of AGN for galactic neutrino spectrum is based on the approximateconditions in the source AGN central engines in which accretion on supermassive blackhole takes place. Usually, the high-energy neutrino background and cosmic-ray protonintensity derived from such models would be much less than that expected from ref. [13].This may be considered as an estimate from AGN central engines as distinct from AGNjets. AGN may also be treated as a source of cosmic rays in the region of knee for energiesup to 1010 GeV. Such particles would interact with the matter confined in the inter-galacticmedium or with the cosmic microwave background. The generated neutral pions give anestimate on the upper limit of the produced neutrino flux from AGN-based model on theobserved X-ray and -ray fluxes. It is also assumed that AGN has sufficient matter tostop protons before they diffuse out of the galaxy. Stanev [14] has suggested that the totalhigh-energy neutrino signals depend on the power of AGN and on the number density.The knowledge of the hadronic interaction cross-sections is essential for the evaluationof the energy transport at AGN and on the shock acceleration models followed by photo-production processes which accounts for the proton energy loss. So, the charged particlesinjected in the Galaxy are termed cosmic rays and some fraction of the photons and neu-trinos escape the galaxy and reach the Earth in the form of directional beams.The recent model of diffuse neutrino fluxes escaping from the production region atAGN tend to predict higher underground muon fluxes than those expected from promptcharm particle decays. The vertical up-coming underground muon signals from promptneutrino fluxes are very close to the diffuse AGN signal. Neutrinos and gamma-rays aremainly generated from + ! +and 0 ! 2 decays and the subsequent mesondecay + ! + e+ e+. Bugaev and Osipova [15] have studied energy spectrum andintensities of extra-galactic neutrino-produced muons duly generated in the interactionsof cosmic rays with relic photons of energies E>1017eV.In the present work we have considered the neutrino spectra available from the pointand diffuse AGN sources in the central region of 3C273 after Szabo and Protheroe [12]and atmospheric neutrino background from Gaisser et al. [4] and Allkofer andBhattacharyya [16]. By adopting the QCD-based weak-interaction model of Berezin-sky et al. [17], the energy spectra of upward neutrino-induced muons from point and dif-fuse AGN sources have been calculated and compared with the atmospheric-backgroundneutrino-induced upward muon energy spectra.2. – Nuclear physics and resultsSzabo and Protheroe [12] have calculated the neutrino production spectra from radio-quiet AGN by spherical accretion shocks normalized to the luminosity at the galactic cen-tral region of 3C273 escaping and derived the neutrino production spectrum from thepoint source, which has been found to follow the formE(dN=dE) = 1:26 10 8(E=GeV) 1(cm2 s) 1 ;(1)68 D. P. BHATTACHARYYAFig. 1. – The energy spectra neutrinos from point source: The atmospheric background neutrinoswithin 1 after Gaisser et al. [4]—AT; neutrinos from the Active Galactic Nuclei (AGN) sourcesafter Szabo and Protheroe [12]—EG.and the diffuse atmospheric source background neutrino spectrum after Gaisser et al. [4]follows the formE(dN=dE = 1:42 10 3(E=GeV) 2:45(cm2 s) 1 :(2)We have compared those neutrino spectra in fig. 1 which shows that the neutrino spectrafrom AGN sources dominate beyond the 10 TeV energy. The diffuse atmospheric neu-trino spectrum from the decay of non-prompt and prompt meson decay after Allkofer andBhattacharyya [16] has been found to follow the formE(dN=dE) = 2:34E 2:7(cm2 s sr) 1 ;(3)for vertical incidence and the prompt neutrino spectrum obeys the relationE(dN=dE) = 5:95 10 6E 1:7(cm2 s sr) 1 :(4)The extra-galactic AGN-emitted diffuse neutrino spectrum [12] follows the formE(dN=dE) = 4:29 10 8E 1:1(cm2 s sr) 1 :(5)DERIVATION OF UPWARD MUON ENERGY SPECTRA IN THE TeV RANGE ETC. 69Fig. 2. – Energy spectra of isotropic neutrinos: Atmospheric diffuse neutrino spectra at zenithangles 0—AT; prompt neutrino spectrum obtained from the decay of charm mesons [16]—PR. The neutrino spectrum available from the AGN diffuse source 3C273 after Szabo andProthero [12]—EG.The diffuse neutrino spectra from different sources have been compared in fig. 2 andit is found that the background atmospheric neutrinos are decreasing in the high-energyregion. The diffuse extragalactic neutrino spectrum is dominant beyond 50 TeV energy.In fig. 3 we have compared the diffuse AGN neutrino spectrum [12] with the neutrinoflux distribution at the bright phase for the redshifts zf> 10 in the Galaxy [18]. Thebright phase of the galactic evolution enhances the generation of ultra-high-energy par-ticles which occur due to collisions of the primary cosmic rays with the high-density relicphotons and which are created through a chain of meson decay energetic neutrinos. Theatmospheric neutrino spectra derived from non-prompt and prompt particle decay afterAllkofer and Bhattacharyya [16] have also been presented in the same figure. By usingthe BCG [17] method and treating the Earth as a target, the deep underground or under-water TeV upward neutrino fluxN+(> E) producing the muon fluxN(> E) reachingthe detector may be calculated using the relationN(> E) = N+(> E)[0NA=bT][Y ( ;E) + Y+( ;E)] ;(6)70 D. P. BHATTACHARYYAFig. 3. – Spectra of diffuse neutrinos from AGN [12] has been compared with the bright phase neu-trino spectrum (for large redshifts zf= 30) after Berezinsky and Ozernoy [18]. The neutrino spec-tra expected from the non-prompt and prompt meson decay after Allkofer and Bhattacharyya [16]have been displayed in the same figure.where we took 0= 1:11 10 34(mW=81GeV)2cm2;mW= 81GeV, NA= 6:024 1023; =  = 0:5;  = 1; 1:1 for Extra Galactic AGN neutrinos and 1.7, 2.7 for atmosphericprompt and non-prompt neutrino spectra, respectively; bTis the muon energy loss pa-rameter in earth material which is a sum of the muon energy loss coefficients for pairproduction, bremsstrahlung and nuclear interactions, viz. bP, bBand bN, and in the TeVenergy region one can safely assume that the relative energy losses are independent ofthe muon energy E, viz.1E(dE=dt) = bT;(7)where t is the thickness of the absorbing medium. We have chosen those numerical valuesfrom the QED-based estimates of Bezrukov and Bugaev [19]. The generation integralmuon moments Y+(;E) and Y (;E) have been computed for   and + mesons atdifferent TeV energies for + N !  + X and + N ! ++ X reactions usingthe formulation of Berezinsky and Gazizov [20]. In this affair the charge current cross-sections have been considered from the QCD quark distribution. These moments areadoptable for the estimation of the probability of interaction of cosmic neutrinos with theEarth producing an upward muon which has enough energy to reach the undergrounddetector. The derived vertical integral equilibrium spectrum of upward muons on Earthproduced by AGN neutrinos from 3C273 is shown in fig. 4 along with the derived back-ground neutrino-induced upward muon spectrum.DERIVATION OF UPWARD MUON ENERGY SPECTRA IN THE TeV RANGE ETC. 71Fig. 4. – The derived upward muon energy spectra produced by AGN neutrinos from point source:Muon spectrum generated by AGN source neutrinos [12]—EG; muon spectrum derived from at-mospheric neutrino background sources [4]—AT.We have used our earlier estimate on local atmospheric vertical muon neutrino spec-trum arising from the decay of pions and kaons [16] which follows the formNatm+(> E) = 0:8667E 2:7(cm2 s sr) 1 :(8)Using the source spectrum (5) and formula (6), the vertical non-prompt meson decay at-mospheric diffuse neutrino-induced integral muon spectrum has been calculated and theresult is displayed in fig. 5. The derived spectrum of muons by diffuse neutrinos from3C273 AGN source is found flatter than that obtained from the background neutrino-induced muon spectrum and beyond 10 TeV the diffuse AGN neutrino-induced muonspectrum is dominanting. The plot also exhibits the steeper spectrum of upward dif-fuse neutrino-induced muons arising from the neutrinos produced from the decay of non-prompt mesons. The calculated vertical muon flux above 2 TeV has been found to be4:67  10 16(cm2s sr) 1 which is lower than the upper-limit value 8  10 15(cm2s sr) 1obtained from the Frejus experiment [21]. The underground detectors can detect themuon flux produced by the galactic VHE neutrinos moving through the Earth in the di-rection of the upper hemisphere and the background muon flux is mainly arising from the72 D. P. BHATTACHARYYAFig. 5. – Integral energy spectra of upward muons initiated by diffuse atmospheric non-prompt,prompt and extragalactic AGN neutrinos: Spectra of muons initiated by the fluxes of atmosphericneutrinos [16] at zenith angles 0 represented by the curve—AT. The muon spectrum calculatedfrom the prompt neutrinos—PR(00). Muon spectrum estimated from the isotropic neutrinos emit-ted from the 3C273 region of the Galaxy [12]—EG.atmospheric neutrinos. The effective target area of the underground muon detectors isusually large and the high-energy muons are produced mostly outside the detectors. Forthe detection of galactic neutrinos a higher threshold muon energy is required to separateneutrinos from the background ones. The direct AGN neutrino contribution is dominantfor neutrino energies E 105 GeV.3. – ConclusionThe BCG model can be fairly used for the estimation of AGN neutrino-induced upwardmuon spectra near the Earth. It is found that the AGN neutrino-induced muon spectrumexhibits a flatter spectral index when compared to the background neutrino-induced muonspectrum results. The present analysis reveals the fact that AGN neutrino-induced muonfluxes exceed the background atmospheric neutrino-induced muon fluxes beyond 10 TeVenergy. The derived muon flux above 2 TeV is found lower when compared to the mea-sured upper limit result obtained from Frejus experiment.  The author expresses his sincere thanks to Prof. M. BALDO CEOLIN, INFN, Uni-versity of Padua, for presenting him the book she edited on the neutrino astronomy. Theauthor is grateful to Profs. F. HELZEN and T. K. GAISSER for sending their preprints.DERIVATION OF UPWARD MUON ENERGY SPECTRA IN THE TeV RANGE ETC. 73REFERENCES[1] SZABO A. P. and PROTHEROE R. P., Astropart. Phys., 2 (1994) 375.[2] FICHTEL C. E. et al., Astrophys. J. Suppl., 94 (1994) 551; KERRICK A. et al., Astrophys. J.452 (1995) 588; QUINN J. et al., EGRET experiment, Proc. 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Derivation of upward muon energy spectra in the TeV range produced by neutrinos from 3C273 AGN and diffuse atmospheric sources

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Derivation of upward muon energy spectra in the TeV range produced by neutrinos from 3C273 AGN and diffuse atmospheric sources

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