Detection potential for the diffuse supernova neutrino background in the large liquid-scintillator detector LENA

0.52 MB·English

by  M. Wurm

Detection potential for the diffuse supernova neutrino background in the large
liquid-scintillator detector LENA
M. Wurm,1,∗ F. von Feilitzsch,1 M. G¨oger-Neff,1 K. A. Hochmuth,2
T. Marroda´n Undagoitia,1 L. Oberauer,1 and W. Potzel1
1Physik-Department E15, Technische Universit¨at Mu¨nchen, James-Franck-Str., D-85748 Garching, Germany
2Max-Planck-Institut fu¨r Physik, F¨ohringer Ring 6, D-80805 Mu¨nchen, Germany
(Dated: February 5, 2008)
The large-volume liquid-scintillator detector LENA (Low Energy Neutrino Astronomy) will pro-
videhigh-grade background discrimination and enable thedetection of diffuse supernovaneutrinos
(DSN) in an almost background-free energy window from ∼ 10 to 25MeV. Within ten years of
exposure,itwillbepossibletoderivesignificantconstraintsonbothcore-collapsesupernovamodels
and thesupernovarate in thenear universeup to redshifts z<2.
7
0 PACSnumbers: 29.40.Mc,95.55.Vj,95.85.Ry,97.60.Bw
0
2
I. INTRODUCTION detection of 10 DSN events per year in the almost
n
∼
a background-free energy range from about 10 to 25MeV.
J After an observation time of 10 years a spectral anal-
0 Thecosmicbackgroundofneutrinosgeneratedbycore- ysis of the DSN is possible, h∼aving implications on both
1 collapse supernova explosions throughoutthe universe is core-collapsesupernova (SN) models and the SNR up to
known as supernova relic neutrinos (SRN) [1] or more redshifts z 2. If no signalwas detected, the new limits

1 preciselyasdiffusesupernovaneutrinos(DSN)[2]. These aresignifica≃ntlylowerthanallmodelpredictionsandim-
v neutrinos are generally believed to provide a new source prove the limit given by Super-Kamiokande by a factor
5
of information on the core-collapse supernova explosion of 9.
0
3 mechanism and both on the supernova rate (SNR) and Th∼is paper mainly focusses on the observationalwindow
1 on the star formation rate (SFR) up to high redshifts of thatisgivenbytheremainingbackgroundofatmospheric
0 z 5 [1, 3, 4]. and reactor ν¯ that are indistinguishable from the ac-
≃ e
7 However, the detection of DSN is demanding, as both tual DSN signal. In Sections II and III, a description of
0 their integral flux of 102νcm−2s−1 and their energy the planned detector and an overview of the predictions
h/ of Eν <50MeV are lo∼w. In general,all ν and ν¯ flavours on the DSN flux and spectrum are given. In Sect.IV
p are contained in the DSN. However, ν¯e are the most the ν¯e detection channel is discussed. The results of the
- likely to be detected as the inverse beta decay reaction, calculationsonthesite-dependentreactorneutrinoback-
o
r ν¯e+p→e++n,hasthelargestcrosssectionintheDSN’s groundrateanditsspectralshape,consideringespecially
t energyregion[1]. Liquidscintillatordetectors(LSD)pro- the highly energetic part, areshownin Sect.V. The cos-
s
a vide a large number density of free protons, a clear de- mogenic background, mainly 9Li and fast neutrons pro-
v: layed coincidence signal for this detection channel and duced by muons, is shortly discussed in Sect.VI. Using
i high energy resolution at low energies. A large-volume this information, the expected event rates for LENA in-
X LSD is therefore an ideal candidate for DSN detection. side the energy window from 10 to 25MeV are given
ar T1.h2ecmb−es2ts−e1xpfoerrimEν¯eent>al 1li9m.3itMoenVt(h9e0%DSCN.Lfl.)uxhaΦsν¯beee<n fsoprecdtirffaelrdeinstcrDimSNinamtioodneolsfdiniffSeer∼cetn.tVDIIS.NFmurotdheelrsmhoarseb,etehne
achieved by the Super-Kamiokande experiment [4, 5]. investigated by Monte Carlo simulations. Their results
However, this limit is strongly determined by the back- aswellasamethodtofindalowerboundaryfortheSNR
ground events present in a pure water Cherenkov detec- at z < 2 are also described in this section. Conclusions
tor(WCD).Asaliquid-scintillatordetector(LSD)allows are given in Sect.VIII.
far better background discrimination, it opens a nearly
background-free energy window from 10 to 25MeV
∼
for DSN detection. The target masses of KamLAND [6]
II. DETECTOR CONCEPT
and of near-future experiments like BOREXINO [7] and
SNO+ [8] are not sufficient to reach significant statis-
tics [9]. A large-scale detector like LENA (Low Energy The LENA concept foresees a cylindrically shaped de-
Neutrino Astronomy) [10, 11] with about 50kt of liquid tectorofabout100minlengthand30mindiameter(see
scintillator is required. Fig.1). An inner part of 26m diameter contains about
We show in the present paper that LENA allows the 5 104m3 ofliquidscintillator,whereasanoutermantle
×
with a thickness of 2m filled with water is intended as
a Cherenkov muon veto. The fiducial volume is defined
withinaradiusof12mofthe innercylinderandencloses
∗Correspondingauthor,e-mail:[email protected] a volume of 4.4 104m3. About 12000 photomultipli-
×
2
III. THEORETICAL PREDICTIONS
The energy-dependent DSN flux discussed in this
paper was taken from the publications by S. Ando et al.
[1, 20]. In general, theoretical models for the expected
DSN spectrum depend on two sources of input:
Supernova neutrino spectrum. The spectral form
of the DSN flux is strongly dependent on the supernova
FIG. 1: Sketchof theLENA detector (SN) core-collapse model applied. Three different
predictions have been made in [1] with reference to the
SN simulations performed by the Lawrence Livermore
Group (LL) [21], by Thompson, Burrows and Pinto
ers (PMs, 50cm diameter) installed on the inner surface
(TBP) [22] and by Keil, Raffelt and Janka (KRJ) [23].
provide a surface coverage of about 30%. The effective
The observed ν spectra on earth will differ from those
coverage could be further increased by mounting light-
emitted by the proto-neutron star as the ν and ν¯ are
collecting concentrators to the PMs.
affectedbythematterpotentialofthedyingstar[24,25].
At present, a preference exists for a liquid scintillator
As the neutrinos pass from the large matter potential
based on the organicsolvent PXE (C H , ρ=985g/ℓ)
16 18 of the central region to the surrounding potential-free
that was already tested in the BOREXINO prototype,
vacuum, the change in the mixing parameters leads to
the Counting TestFacility (CTF) atthe GranSassoNa- a partial conversion of (ν¯) into (ν¯) and vice versa.
tional Laboratory (LNGS) [12]. Due to the large detec- e µ,τ
In most SN models, the larger mean energy of (ν¯)
tor radius, an attenuation length of 10m at 430nm µ,τ
has to be achieved in order to obtain∼an adequate pho- at production hardens the resulting (ν¯e) spectrum. In
toelectron (pe) yield in the PMs. It has been shown addition, allmodels predict atleast one resonantflavour
that this aim can be reached by purification of the PXE conversion inside the SN envelope due to the mixing
in an Aluminum-column [12, 13]. Furthermore, adding angle θ12 that applies to the neutrino sector only. A
80 weight-percent of Dodecane (C12H26, ρ = 749g/ℓ) to second resonance might occur if the value of θ13 is
the solvent has a positive impact on the transparency larger than 1◦ and therefore enables an adiabatic
∼
of the liquid and increases the number of free protons conversion. Thiswillaffecteithertheν sectorincaseofa
in the scintillator - and therefore the ν¯ event rate - by normalneutrino mass hierarchy,or the ν¯ for an inverted
e
almost 25% [13]. As Dodecane slightly lowers the light hierarchy. In the case of full adiabaticity the resonance
yieldofthescintillator,bothpurePXEandthedescribed will lead to analmost complete conversionof ν¯e ν¯τ as
mixture provide similar photoelectron yields of at least θ13 is limited to values θ13 12.5◦ [24, 25, 26].↔In the
≤
100pe/MeVforaneventinthecenterofthedetector. As following, we will refer to this resonant conversion of ν¯e
primary and secondary wavelengthshifters (fluors) 6g/ℓ and ν¯τ as resonance case. All other combinations of the
PPO and 20mg/ℓ bisMSB will be used [13]. value of θ13 and the mass hierarchyresult in identical ν¯e
Besides detection of the DSN ν¯ , LENA will be an ob- spectra. This situation we call no resonance case.
e
servatory for solar neutrinos [10], geoneutrinos [14], and If the mean energy of the ν¯τ is much larger than that of
the neutrinos emitted by a galactic core-collapse SN the ν¯e as predicted by the LL model, the resonance case
[10, 11, 15, 16]. Moreover, the detector will allow to noticably shifts the spectrum of the ν¯e to higher ener-
investigate the properties of neutrinos via beam experi- gies. However, if one assumes only a small gap between
ments, and to search for proton decay [17, 18]. those energies as in the KRJ model, the effect becomes
At the moment, the preferred detector sites are a mine, negligible. For further explanation see [1, 24, 25].
theCenterofUndergroundPhysicsinPyha¨salmi(CUPP,
Finland) [19], or the underwater plateau in the Mediter- Supernova rate. Additional information is re-
ranean Sea used by the NESTOR Collaboration next to quired on the redshift-dependent supernova rate ρ˙ (z)
SN
Pylos (Greece). Both sites provide an effective shielding (SNR)1. The SNR can either directly be measured
of 4000m.w.e. againstcosmicradiation. We havecho- [27,28]orcanbederivedbycombiningtheobservedstar
∼
senLENAatCUPPasourdefaultscenario,asPyha¨salmi formationrateρ˙∗(z)(SFR)withtheinitialmassfunction
isfarawayfromthemiddle-Europeanreactorsandisable (IMF) of the forming stars [29]. As only massive stars
toprovidetherequiredinfrastructureforalarge-scaleex- with more than 8 solar masses (M⊙) will end in a core-
periment. Inaddition,localrepresentativeshavesignaled collapse SN [1], their rather short lifecycles constitute a
big interest in the project. However, as the background
duetopowerreactorν¯ -fluxismostimportant,locations
e
inFrance,theUS,nexttotheislandsofHawaii,andNew
Zealand have also been investigated for comparison (see 1 In the present paper, SNR isalways referringtothe rateof the
Sect.V). core-collapseSNoftypeIb,candII.
3
FIG.2: Thez-dependentsupernovaratecalculatedaccording
to Ando et al. [1] (solid line) in comparison to the best fit
(dashedline) [29]ofdirect SNRobservations (diamonds)for FIG. 3: DSN model spectra for ν¯e calculated by Ando et al.
z<1 [27, 28]. [20] using core-collapse SN simulations performed by the
Lawrence Livermore group (LL) [21], Thompson, Burrows
andPinto(TBP)[22]andKeil,RaffeltandJanka(KRJ)[23].
Inaddition,anLLres spectrumisshownincaseofaresonant
negligibleaberrationincomparisontocosmictimescales. flavourconversion in the SNenvelope.
Nevertheless, there is an uncertainty in the proportion
of heavy SN-progenitor stars due to the uncertainty in
the mass dependence of the IMF [29, 30] at low masses.
The standard Salpeter IMF (φ(m) m−2.35) returns
the relation ρ˙SN(z) = 0.0122M⊙−1ρ˙∗(∝z) [1], whereas for
modified IMF assumptions the conversion factor varies
from 25% to +8% relative to the Salpeter result [30].
−
Resulting DSN spectra. In the present paper, we
follow the model calculations by Ando [1] in combining
anobservationallyobtainedSFR withthe Salpeter IMF.
We obtain a redshift-dependent SNR
e3.4z
ρ˙ (z)=3.9 10−4f h
SN × SN 70e3.8z+45
pΩ (1+z)3+Ω
m Λ yr−1Mpc−3, (1)
× (1+z)3/2
where h =1 for a Hubble constant of H =70 km .
70 sMpc
Ω = 0.3 and Ω = 0.7 are the cosmological parame-
m Λ
FIG.4: ContributionsofdifferentredshiftregionstotheDSN
ters of the matter and dark energy density, respectively.
energy spectrum [20]. Neutrinos emitted by far away super-
The overall normalization uncertainty in the SNR is pa-
novaeare redshifted by cosmic expansion.
rameterised by f . The resulting values of the SNR
SN
for f = 1 are in reasonable agreement with direct SN
SN
observations for z <0.9 [27, 28, 29], as shown in Fig.2.
In combination with the different SN models men- pansion [20]. For this reason, DSN from high-z regions
tionedaboveoneobtainsthreemodelsfortheDSNspec- willdominatethelow-energeticpartoftheobservedspec-
trum as depicted in Fig.3, assuming f = 1 and the trum. As shown in Fig.4, the flux of neutrinos from
SN
absence of a matter resonance in the ν¯ sector. For the sources at z > 1 is substantially limited to energies
LL model, an additional DSN spectrum LLres is shown E <10MeV.
ν¯e
for the resonance case. As discussed above,the actual flux of DSN could vary
Unlike the neutrinos that are produced by nearby SN widely from the predictions, as apart from the depen-
thespectralportionscorrespondingtoSNexplosionsfur- dence on the used SN model there are uncertainties
ther away will be increasingly redshifted by cosmic ex- due to the assumed value of ρ˙ (z). Direct measure-
SN
4
ments reach no further than redshifts z = 0.9 and suf- For the calculation of the expected event rate in LENA,
fer from light extinction due to interstellar dust [29]. the DSN flux must be convoluted with the energy-
The same is true for observations of star formation re- dependentcrosssection. Therateisthenmultipliedwith
gionsinthe ultraviolet(UV) [31,32, 33]andfarinfrared the number of free protons in the fiducial volume. This
(FIR) [34, 35] band. According to [1], these uncertain- numberis 2.9 1033 forthe caseofascintillatormixture
×
ties in the SFR translate to a factor f between 0.7 of 20% PXE and 80% Dodecane and a fiducial volume
SN
and 4.1 if one assumes a Salpeter IMF. However, com- of 44 103m3.
×
bining the data of these observations with the cosmic We calculated the expected energy resolution in LENA
gamma-ray background and the limits on the DSN flux by using the results of both laboratory measurements of
bySuper-Kamiokande,Strigariet al. havederivedacon- the scintillator properties and Monte Carlo (MC) sim-
cordancemodelofthestarformationrate(CMSFR)with ulations: The proposed scintillator mixture provides a
a favoured value of f 2.5 [36]. New measurements lightyieldof 8 103photonsperMeV,anattenuation
SN
≃ ∼ ×
of the SFR further reduce the parameter space, as dis- length of 10m and a scattering length of 30m for
∼ ∼
cussed by Hopkins and Beacom [30]. While these new the scintillation light (at 430nm) [13]. Assuming a wall
predictions develop differently with redshift especially coverageof30%andaquantumefficiencyof20%forthe
for z > 1, they are well contained inside the limits of PMTs,aphotoelectron(pe)yieldofatleast110pe/MeV
0.7<f <4.1 given by Ando [1]. canbe achievedforaneventinthe centerofthe detector
SN
CurrentUVandFIRastronomyandtheirfutureprojects [17]. The resulting 1σ energy resolution is 0.10/√E (in
might be able to determine both the SNR and the SFR MeV).
with high accuracy [4]. The present uncertainty of the For the three DSN models, we find in the noresonance
SFR is only 30 50% in the redshift region z < 1 case that LL [21] provides the largest event number:
≈ −
[30]. However,astheDSNdetectionisnotsufferingfrom 6.8f (see Eq.(1)) detected ν¯ in 1 year of measure-
SN e
∼
dust extinction, neutrinos could test the validity of the ment time in LENA, followed by the KRJ ( 6.1f )
SN
∼
assumedmodelsforlightextinction. Especiallymeasure- and by the TBP model ( 4.7f ). This variation of
SN
∼
ments in the energy region below 10MeV would provide rates originates from the different spectral forms of the
valuable information on high redshift regions. However, models: As the cross section increases with energy, the
in this energy regime reactorν¯ prove to be an undistin- LL model which predicts the largest flux above 10MeV
e
guishablebackgroundandpartiallyhide the DSN due to also provides the largest event rates. This is especially
the high ν¯ rates, as will be discussed in Sect.V. true for LLres ( 7.7f ). For all models, most of the
e SN
∼
ν¯ eventsareexpectedtobeintheenergyregionbetween
e
6 and 14MeV. However, for these estimates background
events have been neglected.
IV. ν¯e DETECTION CHANNEL
As mentionedbefore,ν¯ arethebestchoiceforthe de-
e V. ν¯e BACKGROUND
tection of the DSN background. The crosssection of the
charged current interaction of a ν¯ with a Hydrogen nu-
e
cleusinthetarget,theinversebetadecayν¯ +p n+e+, A large fraction of the ν¯e events cannot be attributed
e
→ to the DSN because of the background events due to
is substantially larger than that of all other detection
channels, σ = 6.8 10−42cm2 at 10MeV [37]. More- ν¯e generated both by air showers and nuclear power
× plants. Theseareintrinsicallyindistinguishablefromthe
over, the reaction provides a low energy threshold of
ν¯ of the DSN and therefore independent of the type of
1.8MeV (corresponding to the mass difference between e
detector used.
proton and neutron plus positron).
Both decay particles can be detected in a liquid-
scintillator detector, providing a coincidence that can
be used for a very effective background reduction (see
Sect.V): Thepromptsignalduetotheionisingprocesses A. Reactor ν¯e
and annihilation of the positronis followedby the signal
of a 2.2MeV gamma quantum. This is released after a For energies below 10MeV, the man-made back-
∼
delay of 180µswhenthe neutron is capturedby a free ground due to nuclear reactors sets a threshold for
proton in∼the scintillator, n+p d+γ. DSN detection. The ν¯ are generated by the β− decay
e
→
Due to the large mass of the neutron the positron will of neutron-rich fission products of 235U, 238U, 239Pu
carry most of the energy that was deposited by the ν¯ . and 241Pu inside the reactor. As the reactor ν¯ flux is
e e
Ingoodapproximation,thekineticenergyofthepositron quadraticallydecliningwithdistance,atleastthe closest
will be reducedby 1.8MeV comparedto the incoming reactors must be considered for a good estimate of the
∼
neutrino due to the Q-value of the reaction. However, actual flux in the detector.
the annihilation of the positron in the scintillator adds Above the Q-value of 1.8MeV, the spectral shape of
another 2m c2 of energy to the detected signal, leading the reactor neutrinos is best known up to energies of
e
to a total reduction of 0.8MeV. E = 8MeV, both from experimental data and from
∼ ν¯e
5
sites. The Laboratoire Souterrain de Modane (LSM) at
TABLE I: Contributions of the fission products of uranium
Frejus(France)wasincludedasanexampleforamiddle-
andplutoniumtothefissionprocessesandthereforetotheν¯e
Europeandetectorsite. TheUSAmericansitesKimball-
flux emitted by a reactor (averaged over time) [39]. The last
ton, Henderson, and Homestake Mine were used as they
columnshowsthefissionyieldsofthehigh-endpointβ-emitter
94Br [40]. have uttered interest in a LENA-like liquid-scintillator
detector and one of them will most likely be the home
Contribution to 94Br of the Deep Underground Science and Engineering Lab-
Isotope total fission rate fission yield
oratory(DUSEL). HawaiiandNew Zealandwere chosen
235U 0.59 1.66×10−6
as they are far away from the nuclear power plants on
238U 0.04 7.90×10−5
the northernhemisphere and are from this point of view
239Pu 0.285 2.71×10−5
241Pu 0.075 1.05×10−6 optimal detector sites for observing the DSN.
When calculating the ν¯ flux, in a first step the number
e
ofneutrinosemitted per secondR bya nuclearreactor
ν¯e
can be derived:
theoretical calculations that have been using the fission
P
yields and β decay schemes of the isotopes in question. R =N th e=(1.38 0.14)1020P s−1,
ν¯e ν,fissE ± th[GW]
However,as the DSN flux is severalorders of magnitude fiss
(2)
lower than that of the reactor neutrinos, it is necessary
where N 6 [42] and E = 205.3 0.6MeV [43]
to take the high-energetic tail of their spectrum (up to ν,fiss ≃ fiss ±
are the average number of neutrinos and the mean en-
E 13MeV) into accountwhen determining the lower
ν¯e ≈ ergyproducedperfission,respectively,P isthethermal
detection threshold for DSN observation. th
powerofthereactorande=0.75 0.06[44]istheaverage
±
fraction of time that a reactor is running (energy avail-
Reactor Neutrino Spectrum. Especially for ener-
ability factore). The thermalpowerP canbe foundin
gies above 8MeV, the exact spectrum of the reactor ν¯ th
e the online databases of the InternationalAtomic Energy
cannot be measured directly at a reactor because of the
Agency (IAEA) [44].
poor statistics. Instead, the spectrum is deduced from
In a next step, using the coordinates of eachreactorand
fission yields, β endpoint energies and decay schemes
the detector site their distance d can be found. The flux
of the neutron-rich isotopes produced in a reactor.
without oscillations can be calculated dividing R by
The experimental challenge is set by the extremely ν¯e
4πd2.
neutron-rich isotopes with high Q-values and lifetimes
Finally, foreachdistance to a particularpower plantthe
in the range of 10−2 seconds.
effect of oscillations ν¯ ν¯ has to be taken into ac-
Tengblad et al. have indirectly determined the reactor e → µ,τ
count. This was achieved by convoluting the normal-
neutrino spectrum up to an energy of 12MeV by a
ized spectrum F(E) with the energy-dependent oscilla-
measurement of the beta-decay spectra of the relevant
tion probability and weighing it with the expected inte-
fission products of 235U, 238U, 239Pu [38]. These three
gral flux,
elements are, on average, responsible for about 92% of
the fission processes (see TableI) and therefore of the R
neutrino flux generated by the reactor [39]. In contrast Φ(E,d)dE = 4πν¯de2F(E)(1−sin2(2θ12)sin2(πℓ(E)/d))dE,
to 238U, 241Pu contributes only a small portion of the (3)
fission products emitting high energetic neutrinos. For whereℓ(E)istheoscillationlengthandθ thesolarmix-
12
this reason, the spectral contribution of 241Pu can be ing angle. This procedure was repeated for all reactors
neglected to good approximation. and the individual fluxes were summed for different de-
However, there is at least one additional element known tectorlocations. Thenecessarydataconcerningthecoor-
to be produced in fission processes which has an even dinates was taken from the International Nuclear Safety
higher β endpoint energy: 94Br with a Q-value of Center (INSC) [45] and includes all major power plants
13.3MeV [40]. Due to its short lifetime of 70ms and running worldwide in the year 2005. Future changes as
its low fission yields (as shown in TableI) its exact β the launch of the Finnish nuclear plant TVO3 as well as
decay scheme is not known [41]. Thus, in the present the possible shutdown of Swedish plants have not been
paper we have only been able to give an upper limit for taken into account but will not substantially change the
its contribution to the spectrum, using its fission yield, ν¯ fluxes. The integral ν¯ fluxes and the corresponding
e e
Q-value, and the information that it decays in 70% of event rates for LENA are summarized in TableII. The
all cases without emitting an additional neutron [41]. calculated flux (φ = 2.1 106cm−2s−1) in the Kamioka
×
mine(Japan)iscomparabletotheoneactuallymeasured
Site-dependent Reactor Neutrino Flux. Using inKamLANDandisgivenforreference[46]. Inaddition,
the reactorν¯ spectrumjust described,the reactorback- Fig.5 shows the energy spectra of the reactor ν¯ at Fre-
e e
groundfluxandtheeventratesinLENAwerecalculated jus, Pyha¨salmi and Hawaii, i.e. at a high, medium and
atanumber ofdifferentlocations: At presentPyha¨salmi low-flux site.
(Finland) and Pylos (Greece) are the preferred detector For an estimate of the overall uncertainties, we have
6
TABLE III: Dependence of the total atmospheric neutrino
fluxbelow60MeVonthedetectorlocation. Thescalingfactor
satm compares this fluxto theone at theKamioka site.
Site latitude (N) satm
◦
Hawaii 1.5 0.8
◦ ◦ ◦
Kamioka, Pylos, Kimballton 36.5 , 36.6 , 37.4 1
Henderson, Wellington 39.8◦, -41.5◦ 1.25
◦ ◦
Frejus, Homestake 45.1 , 44.3 1.5
◦
Pyh¨asalmi 63.7 2.0
ν¯ is dependent on the geographic (geomagnetic) lati-
e
tude and will therefore depend on the detector site [48].
TheindividualspectracanbecalculatedusingMCmeth-
ods. However, for easier comparison and in accordance
with publications by Ando and Sato we have extrapo-
lated the model spectra calculated by Gaisser et al. [48]
(including the corrections by Barr et al. [49]) to ener-
FIG. 5: Spectra of reactor ν¯e at Frejus, Pyh¨asalmi and gies below 60MeV. We have estimated the atmospheric
Hawaii. Shaded regions correspond to experimental and ν¯ spectraforhighgeomagneticlatitudesas,forinstance,
e
modeluncertainties. Above12MeV,weaddedanupperlimit forPyha¨salmiusingthe3DsimulationsbyLiuetal. [50].
for the spectral contribution of 94Br neutrinos. For compari- Astheenergyspectrumoftheatmosphericν¯ onlymildly
e
son,theDSNspectrumaccordingtotheKRJmodel[23]with
dependsonlocation[48],weleftthespectrumunchanged
fSN =1 (see Eq.(1)) is shown. and have only taken into account the dependence of the
total flux on the detector site. TableIII shows our re-
sults. The total flux of atmospheric ν¯ at a particular
e
TABLE II: Reactor ν¯e fluxes and event rates for LENA at site can be related to the flux at the Kamioka site by a
various detector locations. Uncertainties of both fluxes and scaling factor satm.
event rates are ∼14%. In water Cherenkov detectors, atmospheric ν and ν¯
µ µ
provideanadditionalbackgroundsourcebycreating”in-
reactor ν¯e flux reactor ν¯e events
DetectorLocation (cm−2s−1) (0.5Mtyrs) visible muons” [51] with energies below the Cherenkov
Kamioka (J) 2.1×106 2.5×105 threshold. However, such muons do not pose a back-
Frejus (F) 1.6×106 2.0×105 groundinaliquid-scintillatordetectorduetoitsdifferent
Kimballton (US) 6.4×105 7.3×104 detection mechanism.
Pyh¨asalmi (FIN) 1.9×105 2.1×104
Pylos (GR) 9.2×104 11.5×103
Homestake (US) 7.5×104 8.6×103 VI. COSMOGENIC BACKGROUND
Henderson (US) 7.4×104 8.4×103
Hawaii (US) 10.9×103 12.4×102
Wellington (NZ) 5.4×103 6.2×102 Up to now, the discussion only included background
events due to additional ν¯ sources. However, muons
e
that pass the detector or the surrounding medium (rock
or water) also have to be considered. Most of the spal-
taken into account possible deviations due to the frac- lation products of these muons can be easily discrim-
tion of annual runtime e as well as the temporal vari- inated due to the signature of the inverse beta decay.
ation of the abundancies of Uranium and Thorium iso- Still, radionuclides like the β-n-emitter 9Li [52] or fast
topes ( 5%) [39]. In addition, the most recent values neutrons canmimic this e+ n coincidence. For anesti-
and un∼certainties of the oscillation parameters ∆m2 = mateoftherates,onlyevent−sintheenergywindowfrom
12
8.2+−00..65 × 10−5eV2 and tan2θ12 = 0.40+−00..1007 [47] have 10 to 25MeV have to be considered. All our calcula-
been included in the calculations. In Fig.5, these overall tions were performed for LENA at Pyha¨salmi assuming
uncertainties are indicated as shaded regions. a depth of 3960 m.w.e. and a corresponding muon flux
of (1.1 0.1) 10−4/m2s [53].
± ×
B. Atmospheric ν¯e
A. 9Li In-situ Production
The flux of the atmosphericν¯ is increasingwith their
e
energy and starts to surpass the DSN signal at energies As the β endpoint of 9Li is at 13.6MeV, it will af-
around 25MeV. However, the total flux of atmospheric fect the DSN detection only in the lower energy region
7
of the observational window. For a rough estimate of
TABLE IV: Lower and upperenergy thresholds for DSN ob-
the expectedeventrate,one canadoptthe value derived
servation and predicted signal and background events inside
for KamLAND: 0.6 events in 0.28 kt yrs exposure for
× the energy window for LENA at different locations after 10
E > 9.5MeV [6]. Scaling the mass to 44 kt yrs fiducial
× yearsofmeasuringtimeandfSN =1(seeEq.(1)). Therange
volume in LENA, including a reduction of the integral
in the signal rates is determined by the LL and TBP model
muon flux by a factor of 9 in Pyha¨salmi [54] and con- predictions (noresonance, see Sect.III). The background in-
∼
sidering the dependence of the production rate on the cludes atmospheric and reactor ν¯e events and signals due to
muon energy ( E0.75) [55], the resulting rate is approx- fast neutrons.
∝ µ
imately 20 events per year.
Energy Window DSNS/B
However, as the muon passes through the fiducial vol- Detector Location (MeV) (0.5Mtyrs)
ume, it can be clearly identified and a time as well as a Kamioka (J) 11.1 - 28.1 21-42/11
volume cut can be applied. The 9Li cannot travel far, Frejus (F) 10.8 - 26.4 22-41/12
as its half-life is T1/2 = 0.18s. Therefore, excluding a Kimballton (US) 10.6 - 28.1 23-44/11
cylindrical volume of 2m aroundeach muon’s path for 1 Pyh¨asalmi (FIN) 9.7 - 25.1 24-45/13
second( 5 T )decreasesthebackgroundsufficiently. Pylos (GR) 9.4 - 28.1 27-49/12
1/2
As the fi∼duc×ial volume is hit by a muon about every 5s, Homestake (US) 9.0 - 26.4 28-49/13
one loses about 0.2% of exposure time. Henderson (US) 8.9 - 27.2 28-50/13
∼ Hawaii (US) 8.4 - 29.0 31-54/12
Wellington (NZ) 8.2 - 27.2 31-53/12
B. Fast Neutrons
A. Energy Window
Whereas muon tracks in the inner detector or in the
muon veto can be clearly identified, muons passing the
surroundingrockgenerateabackgroundoffastneutrons. Using the information on the two ν¯e background
Usually, such a neutron will be accompanied by a num- sourcesinaLSD(seeSect.VAandVB),itispossibleto
berofchargedparticlesthatcanbeidentifiedintheveto. define an optimal energy window for DSN observation.
However, there is a certain probability that the neutron As both the atmospheric and the reactor neutrino flux
will pass into the inner detector unnoticed. The neutron are dependent on the selected detector site, an individ-
deposits its remaining kinetic energy in the scintillator ualupperandlowerenergylimitforDSNobservationhas
and thereafter is captured by a proton, mimicking a real to be set for every location. In a spectral analysis it is
ν¯ event. desirable to include as much of the DSN signal as possi-
e
Using the estimates by Kudryavtsev et al. [54] for neu- ble, without increasing the backgroundsignal too much.
tronproductionat4000m.w.e. andassumingameanab- We have chosen the lower (upper) energy thresholds at
sorptionlengthof0.75m[54],oneobtainsarateofabout those energy values where the flux of the KRJ model
105 neutrons per year entering the muon veto. However, (fSN = 1) begins (ends) to dominate in comparison to
if one assumes a more realistic energy spectrum at the the total background flux (see Fig.6 described below).
boundarybetweenrockandcavern[54], simulationsper- The site-dependentdetectionthresholdsarelistedinTa-
formed with Geant4 [56] show that only 7 neutrons bleIV. The best limits can be achieved at Hawaii with
∼
per year will reach the fiducial volume and only 0.5 per a window from about 8.4 to 29.0MeV. At Pyha¨salmi, it
year will generate a signal in the relevant energy region will be from around 9.7 to 25.1MeV.
from 10 to 25MeV. As mentioned before, this number
willbe further decreasedby the detectionofaccompany-
ing shower particles in the muon veto and is therefore a B. Event Rates
conservative value. In the further discussion we assume
the neutron spectrum to be energy independent.
The detection thresholds as well as the event rates
varywiththe locationthatis chosenforLENA.As TBP
providesthe lowesteventratesand LL the highest, their
VII. DETECTION POTENTIAL OF LENA rates are given in TableIV for the different detector
sites. In addition, the number of background events
This Section mainly deals with the dependence of the inside the energy window is shown.
observationalwindowandthesignal-to-backgroundratio At Pyha¨salmi, we have obtained between 24f (TBP)
SN
on the actual detector location. As Pyha¨salmi is one of to45f (LL)eventsin10yearsofmeasurementwithin
SN
the preferredsites, a statisticalanalysishas been carried the energy window (no resonance, see Sect.III). In case
out for this place in order to investigate the sensitivity of LLres, 53f events would be detected. For a value
SN
ofthe detectorregardingtheseparationofdifferentDSN of f = 2.5 [36], one expects therefore 100 events in
SN
∼
model predictions and the possibility to give constraints this time period. The background due to reactor and
on the SNR. The results of such a spectral analysis are atmospheric neutrinos within the same time would give
described in part VIIC. 8 events, and up to 5 events from fast neutrons have
∼
8
TABLEV:Usingthecalculated backgroundlevelsintwoen-
ergy bins, an upper limit on the DSN flux can be achieved.
Values are given for 10 years of measuring and 100% detec-
tion efficiency both for signal and background. For compar-
ison, lowest model predictions (fSN = 0.7 in the SNR) and
thecurrent Super-Kamiokandelimit are also given.
Energy Range (MeV) 10.5-19.3 19.3-25
atmosperic ν¯e events 2.2 3.6 in 10yrs
reactor ν¯e events 0.2 0
fast neutron events 2.7 2.0
total 5.1 5.6 in 10yrs
flux limit (90% C.L.) 0.3 0.13 cm−2s−1
lowest model prediction 1.4 0.16
Super-Kamiokandelimit 1.2
tions for both energy regions. The limits of 0.3cm−2s−1
(0.13cm−2s−1)obtainedbyLENAare20%(80%)ofthe
FIG.6: Eventratesofreactor,atmosphericandDSNν¯e (LL, fluxforfSN =0.7below(above)19MeV.Inaddition,the
KRJ, TBP, see Fig.3) as expected for LENA in Pyh¨asalmi limitfromSuper-Kamiokandeisshown. LENAcouldim-
afterten yearsofmeasurement andfSN =1. Theshaded re- prove the present limit by a factor of 9 within 10 years.
gionrepresentstheuncertaintiesoftheDSNratesduetofSN.
The energy window is chosen such that the flux of the KRJ
model exceeds the background flux. The Super-Kamiokande
C. Spectral Analysis
limit is also indicated.
According to the current DSN model predictions,
LENA will provide a sufficient event rate for probing
tobe added. Takingintoaccountthe overalluncertainty both parameters that enter into the actual DSN spec-
in the supernova rate for z = 0 (factor fSN = 0.7 4.1, trum: the redshift-dependent supernova rate (SNR) and
−
see Eq. (1)) the predicted DSN event range is widened the core-collapse SN ν¯ spectrum.
e
further to 17 220 events. However, the direct upper Limits on SNR. The event numbers in the energy
−
limit on the DSN flux of Super-Kamiokande [5] corre- regime from 10 to 14MeV are quite similar for all DSN
sponds to 185 events in LENA. In any case, a significant models,yieldingbetween1.48f to1.97f eventsper
SN SN
detection signal of the DSN appears to be certain. The year, as can be seen in TableVI. Using the actually de-
spectra of both signal and background events are shown tected event rate in this energy bin, to derive limits on
in Fig.6 for LENA located at Pyha¨salmi. the scaling-factorf in the SNR the SN neutrino spec-
SN
trum does not have to be known. Fig.7 shows LENA’s
It should be emphasized that in Pyha¨salmi about exclusion potential if one assumes f =2.5 to be true.
SN
25% of the registered DSN in the energy window are The depicted curves show the significance level for re-
originating from redshifts z > 1. Their flux is expected jection of other f values dependent on the exposure.
SN
to influence the spectral form at low energies visibly. After 10 years of measurement, f 1.3 could be ex-
SN
≤
cluded at a 2σ level.
Flux limits. Assuming there is no signalofthe DSN, In this way, LENA will be able to independently ver-
we calculatedthe flux limit that LENA wouldbe able to ify the value of f derived from optical observations of
SN
give for two energy regions: One for the most sensitive theSNR,andcross-checkthevalidityoftheapplieddust
regionfrom 10.5 to 19.3MeV where the backgroundlev- corrections. At present, SNR observations reach out to
elsarelowest. Asecondoneintheregimefrom19.3MeV z 0.9 [27, 28, 29]. With the lower energy threshold of
≈
to 25MeV that corresponds to the limit achieved by the 9.7MeVforLENAinPyha¨salmi,therewillbealsoanon-
Super-Kamiokande detector [5]. Assuming a 100% effi- neglegibleamountofDSNeventsdue toSNat1<z <2
ciency for the detection of all ν¯ and other background that can be used to derive limits on the SNR for this
e
events, one can derive the statistical uncertainty corre- redshift region. Combined with assumptions about the
sponding to 90% C.L.. If one assumes the spectral form IMF [30], DSN observation will also be able to provide
of the KRJ model, one can match the number of DSN constraints on the SFR.
events to the uncertainty of the background by scaling Discrimination of DSN models. The progress in
the DSN flux by means of the factor f . The derived opticalobservationsislikelytoprovideasolidprediction
SN
limits on the flux are well below the current model pre- forboththe SFRandSNRuptoz 2. Usingthisinfor-
≈
dictions. TableVshowsbackgroundeventrates,fluxlim- mation,ananalysisoftheDSNeventspectruminLENA
its after 10 years of measuring and lowest model predic- could be used to constrain the parameter range for dif-
9
TABLE VI: Rates for the DSN models used in the MC-
calculations and χ2-tests performed in order to analyse the
potential for model discrimination. Values are given for
50ktyrs of exposure (one year of measuring time in LENA)
at Pyh¨asalmi and fSN =2.5.
Rates(NB1) Rates (NB2)
DSNmodel 9.7-14.5MeV 14.5-25.1MeV
LL (nores.) 4.93 6.20
TBP 3.70 2.65
KRJ 4.88 4.73
LL (res.) 4.50 8.70
background 0.60 0.73
ferent SN models or even to discriminate between them.
For testing LENA’s potential, MC simulations of typi-
cal DSN event spectra have been carried out. In these FIG.7: Potentialtoderiveboundsonthescalefactor fSN in
theSNR.IfoneassumesfSN =2.5accordingtotheCMSFR,
tests, one DSN model and the currently favoured value
the curves shown in the plot depict the significance level at
of f = 2.5 have been assumed to be true, and in ac-
SN which other values of fSN can be rejected after a certain ex-
cordance with these assumptions 104 MC spectra have
posure time.
been simulated. As the event numbers are low, only
two energy bins have been chosen: the first one reach-
ing from 9.7 to 14.5MeV and the second one from 14.5
to 25.1MeV. In TableVI, the expected event numbers
per year for the three DSN models and the background
rates are shown, including the resonance case for the LL
model (see Sect.III). As only two energy bins have been
chosen, the excellent energy resolution of the detector of
better than 3% for E >10MeV and the reactionkine-
ν¯e
matics have almost no effect on the analysis. Both have
therefore been neglected.
Viaaχ2-analysis,anexclusionprobabilitycanbegiven
that a MC spectrum created according to a given model
is wrongly assigned to a different combination of event
numbersandthereforetoanalternativeSNmodel. Fig.8
showsexclusionplotsforeachofthethreemodelsassum-
ing an exposure time of 10 years. 2σ and 1σ exclusion
regionsarelocatedoutsidethedepictedcurves. Forcom-
parison, the predicted event numbers for all models are
shown.
The evaluation shows that the separation potential for
the models LL and TBP is best, as their spectral slopes
differ most. For f =2.5, LENA is able to discriminate
SN FIG. 8: Exclusion plot for the assignment of a simulated
between these two models with a significance of 2.6σ af-
eventspectrum in LENA to a wrong DSN model. A valueof
ter 10 years of exposure. However, a separation at 2σ fSN = 2.5 and 10 years of exposure are assumed. MC spec-
level between spectra with very similar slopes as KRJ tra created according to one of the models are compared to
and LL would require long exposure times of >30 years all possible combinationsof eventnumbersin thetwoenergy
unless f is very close to the upper limit (f 4.1). bins(seeTab.VI). Regionsofmorethan1σ and2σ exclusion
SN SN
≤
For the case of the LL model, the exclusion probability probability for a wrong assignment are located outside the
for the other models is shown in TableVII as a function depicted lines. Predictions assuming the noresonance (dots)
and the resonance case (diamond) are shown. LL and TBP
of the exposure time. Note that an exclusion at >2σ of
model can be discerned at a significance level of more than
a resonant flavour conversion in the SN envelope (corre-
sponding to LLres) would be possible after 15 years of 2.6σ.
measuring.
10
In addition, by an analysis of the flux in the energy re-
TABLEVII:Exclusionprobabilityforawrongmodelassign-
gion from 10 to 14MeV the SFR for z < 2 could be
ment of a simulated DSN event spectrum in LENA. The LL
constrainedathighsignificancelevels. Thecurrentlower
model(noresonance case) isassumed tobetrue,significance
bound of f = 0.7 [1] could be increased to f = 1.3
levelsoftherejectionofothermodelsareshownasafunction SN SN
of the exposuretime and fSN. at a 2σ level within 10 years of measuring time.
LENAwillthereforenotonly be abletodetectthe DSN;
Parameters Significance of exclusion (σ)
it will also be able to make valuable contributions to
fSN exposure (yrs) TBP KRJ LLres both, core-collapse SN models and the redshift depen-
2.5 5 1.8 1.1 1.5
dent supernova rate.
10 2.6 1.3 1.8
15 3.0 1.5 2.1
20 3.3 1.6 2.4
25 3.7 1.8 2.6
30 >4 1.9 2.9 Acknowledgements
4.1 30 >4 2.3 3.6
We thank G. Raffelt, T. Janka and S. Ando for both
valuable information and helpful suggestions concerning
VIII. CONCLUSIONS supernova physics and diffuse supernova neutrinos. This
workhasbeensupportedbyfundsoftheMaier-Leibnitz-
It has been shown in this paper, that in a large Laboratorium (Garching), of the Deutsche Forschungs-
liquid-scintillator detector (LSD) like LENA diffuse su- gemeinschaft DFG (Sonderforschungsbereich 375), and
pernovaneutrino (DSN) eventscanbe detected in anal- of the Virtual Institute for Dark Matter And Neutrinos
most background-free energy window between 10 and (VIDMAN).
∼
25MeV. High background suppression is achieved due
to the fact that the neutron produced in the detection
reaction - the inverse beta decay - can be detected in a
LSD.Above 10MeVthehigh-energetictailoftheman-
∼
made reactor ν¯ is becoming negligible in comparison to
e
the DSN flux. Above 25MeV the atmospheric ν¯ flux
e
∼
starts to dominate.
IfplacedinPyha¨salmi,thelowerthresholdforLENAwill
be close to 9.7MeV. For this location and for the most
likely value of f = 2.5 (see Eq.(1)) in the supernova
SN
rate (SNR), about 6 to 13 events per year will be con-
tained in the energy window and can be detected. This
would be the first detection of the DSN background. It
shouldalsobenotedthatabout25%ofthedetectedDSN
willbeoriginatingfromared-shiftregion1<z <2. Ifno
signal was detected, a new limit of 0.13cm−2s−1 on the
flux above 19.3MeV could be achieved within 10 years
thatwouldsurpasstheoneoftheSuper-Kamiokandede-
tector by a factor 9. In the lowest background re-
gionbetween10.5an∼d19.3MeVthelimitof0.3cm−2s−1
would be 20% of the lowest current model predictions.
Apartfrommere detection, LENAwill be able to distin-
guishbetweendifferentDSNmodelsandgiveconstraints
on the form of the neutrino spectrum emitted by a core-
collapse supernova. This can be reached via an analysis
of the DSN’s spectral slope. The significance of the re-
sults will be highly dependent on the exposure time and
the supernova rate in the near universe. For a known
SNR with f = 2.5, the discrimination between the
SN
discussed LL and TBP models for the DSN will be pos-
sible at a 2.6σ level after 10 years of measuring time.
Distinguishing between DSN models with more similar
spectral slopes, however, would require higher statistics.