Matter effects on neutrino oscillations in both, a supernova and the Earth,
change the observed supernova neutrino spectra. We calculate the expected
number of supernova neutrino interactions for ICARUS, SK and SNO detectors as a
function of the distance which they traveled in the Earth. Calculations are
performed for supernova type II at 10kpc from the Earth, using standard
supernova neutrino fluxes described by thermal Fermi--Dirac distributions and
the PREM I Earth matter density profile.Comment: Postscript file: 7 pages, 2 figures; tar-compressed file: tex source
  code, eps figures. To appear in Acta. Phys. Pol. B. Talk given at the XXVIII
  Mazurian Lakes School of Physics, Krzyze, Poland, August 31 - September 7,
  200

Bekman, B.

Holeczek, J.

Kisiel, J.

Acta Physica Polonica B

English

arXiv

Matter effects on neutrino oscillations in both, a supernova and the
Earth, change the observed supernova neutrino spectra. We calculate the
expected number of supernova neutrino interactions for ICARUS, SK and
SNO detectors as a function of the distance which they traveled in the
Earth. Calculations are performed for supernova type II at 10 kpc from
the Earth, using standard supernova neutrino fluxes described by thermal
Fermi–Dirac distributions and the PREM I Earth matter density profile

Holeczek, Jacek

Kisiel, Jan

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Detection of supernova neutrinos  Author: B. Bekman, Jacek Holeczek, Jan Kisiel   Citation style: Bekman B., Holeczek Jacek, Kisiel Jan. (2004). Detection of supernova neutrinos. "Acta Physica Polonica. B" (2004, no. 3, s. 1215-1221). Vol. 35 (2004) ACTA PHYSICA POLONICA B No 3DETECTION OF SUPERNOVA NEUTRINOS∗ ∗∗B. Bekman, J. Holeczek and J. KisielInstitute of Physics, University of SilesiaUniwersytecka 4, 40-007 Katowice, Poland(Received February 13, 2004)Matter effects on neutrino oscillations in both, a supernova and theEarth, change the observed supernova neutrino spectra. We calculate theexpected number of supernova neutrino interactions for ICARUS, SK andSNO detectors as a function of the distance which they traveled in theEarth. Calculations are performed for supernova type II at 10 kpc fromthe Earth, using standard supernova neutrino fluxes described by thermalFermi–Dirac distributions and the PREM I Earth matter density profile.PACS numbers: 13.15.+g, 14.60.Pq, 97.60.Bw1. IntroductionIron is the most strongly bound of all elements which means that fusionand fission reactions result in the absorption, rather than the production, ofenergy. The last stage of a massive star life (mass > 10M⊙) is the collapseof its Fe core (the whole core material has already been transformed, viathe chain of nuclear reactions, into Fe). This happens when the mass ofthe Fe core exceeds the Chandrasekhar limit (∼ 1.45M⊙ if one takes equalnumbers of neutrons and protons, [1]) — a supernova (SN) type II birth isa fact. It starts to explode. All flavors of neutrinos are radiated away in theform of two bursts of the duration of milliseconds and seconds. The emittedneutrinos carry almost all (∼99%) of the SN binding energy (∼1053 erg).The only observed, up to now, burst of SN neutrinos came from theSN1987A which had exploded in the Large Magellanic Cloud, at the dis-tance of about 52 kpc away from the Earth. Due to this distinct distance,∗ Presented at the XXVIII Mazurian Lakes School of Physics, Krzyże, Poland,August 31–September 7, 2003.∗∗ This work has been partly supported by the Polish State Committee for ScientificResearch (KBN) under Contracts No. 2 P03B10925 and 160/E-340/SPB/ICARUS/P-03/DZ212/2003-2005.(1215)1216 B. Bekman, J. Holeczek, J. Kisielthe reconstruction of only 19 events of the neutrino interactions by theKamiokande [2] and IMB [3] water Cerenkov detectors had been possible.But, it was enough to confirm the main features of the models of SN explo-sion.Neutrinos, on their way from the production point inside the SN highdense Fe core to the terrestrial detector, interact with matter. Non-zeroneutrino masses, together with flavor mixing enhanced by matter effects,result in considerable differences in neutrino fluxes between the productionand the detection points. Systematic studies of the number of SN neutrinointeractions in three detectors, ICARUS [4], SK [5] and SNO [6], as a functionof the distance passed by neutrinos in the Earth is the aim of this work.2. Neutrino fluxes from a supernovaA supernova is a source of fluxes of neutrinos and antineutrinos of allthree flavors (e, µ, τ). The neutrino/antineutrino energy spectra at theproduction point (i.e. inside the SN) of various flavors can be described bythe thermal Fermi–Dirac distributions (all chemical potentials set to zeros,see [7]):F 0α(E,Tα, Lα) =LαT 4αF3E2eE/Tα + 1,where α = νe, νµ, ντ , ν¯e, ν¯µ, ν¯τ . Here, E represents energy of the neutrinos,Lα is the total energy released in various flavors of neutrinos (Lα ≃ EB/6,with EB ≃ 3 × 1053 ergs — binding energy emitted in the core collapse ofthe star), F3 is a normalizing constant given by F3 = 7pi4/120, Tα is thetemperature of the να gas in the neutrino sphere. We assume the followinghierarchy of temperatures: Tνe = 3.5 MeV, Tν¯e = 5 MeV, Tνx,ν¯x = 8 MeV,where νx and ν¯x mean νµ, ντ and ν¯µ, ν¯τ , respectively.Neutrinos produced deep inside supernova, before escaping from the star,interact with the matter of its mantle. Thus, transitions of neutrino speciescan occur. These oscillations of neutrinos in supernova are considered hereaccording to [8]. The conversions take mainly place in two resonance layersin the outer regions of a supernova mantle. There is a high density reso-nance region (H resonance layer) — ρH ≈ 103–104 g/cm3, and low densityresonance region (L resonance layer) — ρL ≈ 10–30 g/cm3. Transitionsin the H resonance layer are governed by atmospheric neutrino oscillationparameters: ∆m231and Θ13, whereas transitions in the L resonance regionare governed by solar neutrino oscillation parameters: ∆m221and Θ12. Thetransition probabilities (between two neutrino mass eigenstates) in the reso-nance layers are called the flip probabilities — PH, PL for neutrinos and P¯H,P¯L for antineutrinos.Detection of Supernova Neutrinos 1217The final total neutrino/antineutrino mass eigenstates fluxes on a super-nova surface (Fi, Fi¯, i = 1, 2, 3) are given by the following sets of equations(F 0α , F0α¯ are the initial total production fluxes defined above, respectively, e— νe, e¯ — ν¯e, x — νµ or ντ , x¯ — ν¯µ or ν¯τ ).For Direct (normal) mass hierarchy (m1 < m2 ≪ m3):F1 = PHPLF0e + (1− PHPL)F0x ,F2 = (PH − PHPL)F0e + (1− PH + PHPL)F0x ,F3 = (1− PH)F0e + PHF0x ,F1¯ = (1− P¯L)F0e¯ + P¯LF0x¯ ,F2¯ = P¯LF0e¯ + (1− P¯L)F0x¯ ,F3¯ = F0x¯ .For Inverted mass hierarchy (m3 ≪ m1 < m2):F1 = PLF0e + (1− PL)F0x ,F2 = (1− PL)F0e + PLF0x ,F3 = F0x ,F1¯ = (P¯H − P¯HP¯L)F0e¯ + (1− P¯H + P¯HP¯L)F0x¯ ,F2¯ = P¯HP¯LF0e¯ + (1− P¯HP¯L)F0x¯ ,F3¯ = (1− P¯H)F0e¯ + P¯HF0x¯ .A complete discussion of how to calculate flip probabilities can be foundin [8]. For the purpose of this paper we will only state here that, in case oneconsiders the LMA (Large Mixing Angle) neutrino oscillations parameters:PL = P¯L = 0 and, in the so called Large Θ13 case (sin2Θ13 > 3× 10−4, theso called region I in [8]): PH = P¯H = 0, while in the so called Small Θ13case (sin2 Θ13 < 2 × 10−6, the so called region III in [8]): PH = P¯H = 1 (itis interesting to notice here that, in this case, the resulting fluxes are equalfor both, Direct and Inverted, mass hierarchies).The finite spread of the neutrino wave packets, together with the smallvalue of their coherence length and the large distance from supernova to theEarth, imply that neutrinos arrive to the surface of the Earth as fluxes ofincoherent mass eigenstates.1218 B. Bekman, J. Holeczek, J. KisielThus, the above equations describe also (except for a simple geometri-cal factor related to the distance between a supernova and the Earth) theneutrino/antineutrino mass eigenstates fluxes at the surface of the Earth(because there is no matter on the way between a supernova and the Earth,there can be no additional transitions between neutrino mass eigenstates).3. Earth matter effectIn order to calculate oscillation probabilities we used the standard de-scription of neutrino regeneration effect in the Earth [9]. The numericalcalculations were made with use of the CERN library function DEQBS. Weapplied the realistic Earth matter density profile PREM I [10,11].The following LMA I (Large Mixing Angle) neutrino oscillation param-eters were used (note the two values of the sin2 Θ13):∆m221 = 7.1 × 10−5 eV2 ,∆m232 = 2.5 × 10−3 eV2 ,sin2 2Θ12 = 0.84 ,sin2 2Θ23 = 1.0 ,sin2 Θ13 = 0.02 Large Θ13 ,sin2 Θ13 = 10−7 Small Θ13 ,δ = 0 Dirac′s phase .In addition we also considered two cases of mass hierarchies, the Di-rect (normal, m1 < m2 ≪ m3) and the Inverted (m3 ≪ m1 < m2) ones(however, because the energies of SN neutrinos are relatively small and theDirac’s phase δ is set to zero, there are almost no differences in results ofthe regeneration in the Earth between these two hierarchies).4. Detection of supernova neutrinosWe consider three detectors: ICARUS [4], SK [5] and SNO [6]. Thepositions of these detectors on the Earth are shown in Fig. 1. These detectorshave the following feature: in most of the time, when a possible neutrinosignal arrives to the Earth, at least one detector is shielded by the Earth(assuming a supernova exploded in the center of our Galaxy), and thereforewe will see the regeneration effect in the Earth. All possible processes whichcontribute to the total number of neutrino interaction in each detector aretaken into account. The cross sections for these processes which we use comefrom [12] and [13].Detection of Supernova Neutrinos 1219Fig. 1. An example of a possible relative position of ICARUS, SK and SNO detec-tors and a supernova which exploded in the center of our Galaxy.5. Results and discussionThe expected total numbers of supernova neutrino interactions NSN,integrated over neutrino energy in the range 0.1 MeV–100 MeV (the wholesupernova neutrino energy spectrum), for all possible neutrino processesin ICARUS T600 (an “industrial” ICARUS module filled with 600 tons ofliquid argon), SK (32 ktons of light water) and SNO (1 kton of heavy water,1.7 ktons of light water) detectors are calculated (neutrino oscillations insupernova and the regeneration effect in the Earth have been taken intoaccount). It is assumed that a supernova explosion occurred in the center ofour Galaxy, that is 10kpc away from the Earth. The results are presentedin Fig. 2 as a function of the distance which neutrinos traveled in the Earth,for four possible combinations of the mass hierarchy and the Θ13 value.The main neutrino interactions with detector materials which contributeto the NSN are the following (the minimum and maximum contributions ofa particular process, taken for the four considered cases altogether, into thetotal number of interactions are also given):ICARUS νe+40Ar → 40K∗ + e− ∼ (87÷ 93)%SK ν¯e + p → n+ e+∼ (76÷ 80)%νe +O → F+ e−∼ (6÷ 10)%SNO ν¯e + p → n+ e+∼ (31÷ 37)%νe + d → p+ p+ e−∼ (12÷ 16)%νµ,τ + d → νµ,τ + p+ n ∼ (10÷ 12)%ν¯µ,τ + d → ν¯µ,τ + p+ n ∼ (8÷ 12)%1220 B. Bekman, J. Holeczek, J. KisielL [km]0 2000 4000 6000 8000 10000 12000140150160170180190200ICARUS T600DLILDS, ISL [km]0 2000 4000 6000 8000 10000 1200011500120001250013000135001400014500SKILDLDS, ISL [km]0 2000 4000 6000 8000 10000 12000145015001550160016501700SNOILDLDS, ISFig. 2. The expected number of supernova neutrino interactions in ICARUS T600(600 tons of liquid argon), SK (32 ktons of light water) and SNO (1 kton of heavywater, 1.7 ktons of light water) detectors as a function of the distance, L, neutri-nos traveled in the Earth, for different combinations of mass hierarchy and Θ13(DL — Direct mass hierarchy and Large Θ13, IL — Inverted mass hierarchy andLarge Θ13, DS — Direct mass hierarchy and Small Θ13, IS — Inverted masshierarchy and Small Θ13). For details see the description in the text.Detection of Supernova Neutrinos 1221It can be seen that, while νe interactions dominate in the ICARUS de-tector, ν¯e interactions dominate in the SK and SNO detectors. Taking intoaccount that, in case of Large Θ13, neutrino oscillations in supernova makethe νe spectrum harder (hot) for the Direct mass hierarchy and the ν¯e spec-trum harder (hot) for the Inverted mass hierarchy (and that all relevantcross sections increase with energy), one gets the corresponding behavior ofNSN in Fig. 2 (compare the DL versus the IL curves).Two conclusions are straightforward: the distance traveled by neutrinosin the Earth has only little influence on the value of NSN and, in case ofSmall Θ13, the value of NSN does not depend on the mass hierarchy at all.Finally, the NSN from all three detectors should allow us to draw conclusionsabout the value of the Θ13 and, in case the Θ13 is sufficiently large, it shouldalso be possible to say which mass hierarchy is in force.Last, but not least, it should be noted that, in case of the ICARUSdetector, for the purpose of this paper we performed calculations for thecurrently existing ICARUS T600 (600 tons of liquid argon) module. Thefinal total mass of the ICARUS detector (which will be installed in theunderground LNGS Laboratory in Gran Sasso/Italy, see [4]) will be of theorder of 3000 tons of liquid argon. That means that the expected totalnumber of supernova neutrino interactions NSN will be five times largerthan the one presented in this paper.REFERENCES[1] H.A. Bethe, Nucl. Phys. A606, 95 (1996).[2] K.S. Hirata et al., Phys. Rev. Lett. 58, 1490 (1987).[3] R.M. Bionta et al., Phys. Rev. Lett. 58, 1494 (1987).[4] ICARUS Collab., Nucl. Instrum. Methods Phys. Res. A508, 287 (2003).[5] The Super-Kamiokande Collab., accepted for publication in Nucl. Instrum.Methods Phys. Res. A,http://www-sk.icrr.u-tokyo.ac.jp/doc/sk/pub/sknimpaper.pdf[6] The SNO Collab., Nucl. Instrum Methods Phys. Res. A449, 172 (2000).[7] C. Lunardini, A.Yu. Smirnov, Nucl. Phys. B616, 307 (2000).[8] A.S. Dighe, A.Yu. Smirnov, Phys. Rev. D62, 033007 (2000).[9] B. Bekman, J. Gluza, J. Holeczek, J. Syska, M. Zrałek, Phys. Rev. D66,093004 (2002).[10] I. Mocioiu, R. Shrock, Phys. Rev. D62, 053017 (2000).[11] A.M. Dziewonski, D.L. Anderson, Phys. Earth Planet. Inter. 25, 297 (1981).[12] K. Langanke, G. Martinez-Pinedo, private communication.[13] J. Heise (SNO collaboration), PhD Thesis,http://www.sno.phy.queensu.ca/sno/papers/Heise_thesis_2s_colour.pdf

Detection of Supernova Neutrinos

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