Search for Supernova Relic Neutrinos at Super-Kamiokande

arXiv:hep-ex/0209028 v2 22 Oct 2002

The Super-Kamiokande Collaboration
M. Malek17 , M. Morii27 , S. Fukuda1 , Y. Fukuda1 , M. Ishitsuka1 , Y. Itow1 , T. Kajita1 , J. Kameda1 , K. Kaneyuki1 ,K. Kobayashi1,17, Y. Koshio1, M. Miura1 , S. Moriyama1, M. Nakahata1 , S. Nakayama1, T. Namba1 , A. Okada1 ,T. Ooyabu1 , C. Saji1 , N. Sakurai1 , M. Shiozawa1, Y. Suzuki1 , H. Takeuchi1 , Y. Takeuchi1 , Y. Totsuka1 ,S. Yamada1 , S. Desai2 , M. Earl2 , E. Kearns2, M.D. Messier2 , J.L. Stone2 , L.R. Sulak2 , C.W. Walter2 ,M. Goldhaber3 , T. Barszczak4, D. Casper4 , W. Gajewski4 , W.R. Kropp4 , S. Mine4 , D.W. Liu4 , M.B. Smy4 ,H.W. Sobel4 , M.R. Vagins4 , A. Gago5 , K.S. Ganezer5 , W.E. Keig5 , R.W. Ellsworth6 , S. Tasaka7 , A. Kibayashi8,
J.G. Learned8 , S. Matsuno8 , D. Takemori8, Y. Hayato9, T. Ishii9 , T. Kobayashi9, T. Maruyama9, K. Nakamura9,
Y. Obayashi9 , Y. Oyama9, M. Sakuda9 , M. Yoshida9 , M. Kohama10, T. Iwashita10 , A.T. Suzuki10 ,A. Ichikawa11,9, T. Inagaki11, I. Kato11 , T. Nakaya11, K. Nishikawa11 , T.J. Haines12,4 , S. Dazeley13 ,S. Hatakeyama13, R. Svoboda13 , E. Blaufuss14 , J.A. Goodman14 , G. Guillian14,8 , G.W. Sullivan14 , D. Turcan14 ,K. Scholberg15 , A. Habig16 , M. Ackermann17 , J. Hill17,5 , C.K. Jung17 , K. Martens17 , C. Mauger17 ,C. McGrew17 , E. Sharkey17, B. Viren17,3 , C. Yanagisawa17, T. Toshito18 , C. Mitsuda19 , K. Miyano19 ,T. Shibata19 , Y. Kajiyama20, Y. Nagashima20 , K. Nitta20 , M. Takita20 , H.I. Kim21 , S.B. Kim21 , J. Yoo21 ,H. Okazawa22, T. Ishizuka23 , M. Etoh24 , Y. Gando24 , T. Hasegawa24, K. Inoue24 , K. Ishihara24, J. Shirai24 ,A. Suzuki24 , M. Koshiba25 , Y. Hatakeyama26, Y. Ichikawa26 , M. Koike26, K. Nishijima26 , H. Ishino27 ,R. Nishimura27 , Y. Watanabe27 , D. Kielczewska28,4,∗, H.G. Berns29 , S.C. Boyd29 , A.L. Stachyra29 , R.J. Wilkes29
1 Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan
2 Department of Physics, Boston University, Boston, MA 02215, USA
Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA
4 Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA
5 Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USA
6 Department of Physics, George Mason University, Fairfax, VA 22030, USA
7 Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
8 Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA
9 Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
10 Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
11 Department of Physics, Kyoto University, Kyoto 606-8502, Japan
12 Physics Division, P-23, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
13 Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA
14 Department of Physics, University of Maryland, College Park, MD 20742, USA
15 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
16 Department of Physics, University of Minnesota, Duluth, MN 55812-2496, USA
17 Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794-3800, USA
18 Department of Physics, Nagoya University, Nagoya, Aichi 464-8602, Japan
19 Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japan
20 Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
21 Department of Physics, Seoul National University, Seoul 151-742, Korea
22 International and Cultural Studies, Shizuoka Seika College, Yaizu, Shizuoka, 425-8611, Japan
23 Department of Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japan
24 Research Center for Neutrino Science, Tohoku University, Sendai, Miyagi 980-8578, Japan
25 The University of Tokyo, Tokyo 113-0033, Japan
26 Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
27 Department of Physics, Tokyo Institute for Technology, Meguro, Tokyo 152-8551, Japan
28 Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
29 Department of Physics, University of Washington, Seattle, WA 98195-1560, USA
3

A search for the relic neutrinos from all past core-collapse supernovae was conducted using 1496
days of data from the Super-Kamiokande detector. This analysis looked for electron-type antineutrinos that had produced a positron with an energy greater than 18 MeV. In the absence of asignal, 90% C.L. upper limits on the total flux were set for several theoretical models; these limits
ranged from 20 to 130 ν̄e cm−2 s−1 . Additionally, an upper bound of 1.2 ν̄e cm−2 s−1 was set forthe supernova relic neutrino flux in the energy region Eν > 19.3 MeV.
PACS numbers: 95.85.Ry,97.60.Bw,14.60.Lm,96.40.Tv

During a core-collapse supernova, approximately 1053

ergs of energy are released, about 99% of which are in the2form of neutrinos. To date, the only time that a burstof such neutrinos has been detected was in the case of
SN1987A [1, 2]. However, it is generally believed thatcore-collapse supernovae have occurred throughout theuniverse since the formation of stars. Thus, there should
exist a diffuse background of neutrinos originating fromall the supernovae that have ever occurred. Detectionof these supernova relic neutrinos (SRN) would offer insight about the history of star formation and supernovae
explosions in the universe.
All types of neutrinos and anti-neutrinos are emitted
from a core-collapse supernova, but not all are equallydetectable. The ν̄e is most likely to be detected by SuperKamiokande (SK). It interacts primarily through inverse
β decay (ν̄e p → n e+ , Ee = Eν - 1.3 MeV) with across section that is two orders of magnitude greater thanthat of neutrino-electron elastic scattering. All further
discussion herein of the SRN refers only to the ν̄e .
Several methods have been used to model the SRN flux
and spectrum [3, 4, 5, 6, 7, 8], with flux predictions ranging from 2 – 54 cm−2 s−1 . In this paper, SK search results are compared to SRN predictions based on a galaxy
evolution model [4], a cosmic gas infall model [5], cosmic
chemical evolution studies [6], and observations of heavy
metal abundances [7]. A model that assumes a constantsupernova rate [4] was also considered; this model wasused to set the previous SRN flux limit at KamiokandeII [9].
It has been shown that neutrinos undergo flavor oscillation [10, 11, 12]. Therefore, an SRN spectrum that
includes the effects of neutrino mixing was also considered [8]. All six species of neutrinos are emitted duringa core-collapse supernova. However, the ν̄µ and the ν̄τdecouple from the neutrinosphere earlier than the ν̄e , resulting in a higher temperature for these flavors; thus,
neutrino mixing would harden the ν̄e energy spectrum.
The cross section for inverse β decay increases as thesquare of the ν̄e energy, so oscillation would enhance the
SRN signal. In this paper, only a large mixing angle
MSW solution (LMA) was used to distort the SRN spectrum – the LMA solution is also favored by the available
solar neutrino data [13, 14].
This paper presents the results of a search for SRNs
in the Super-Kamiokande detector. SK is a water
Cherenkov detector, with a fiducial mass of 22.5 kton,
located in the Kamioka Mine in Gifu, Japan. Descriptions of the detector can be found elsewhere [15]. The
data reported here were collected between May 31, 1996,
and July 15, 2001, yielding a total SRN search livetime of
1496 days. Backgrounds to the SRN signal are solar neutrinos, atmospheric neutrinos, and muon-induced spallation products. Background reduction takes place in thefollowing steps: spallation cut, sub-event cut, Cherenkov
angle cut, and solar direction cut.
Spallation is the most serious background, and theability to remove it determines the lower threshold of
the SRN search. Spallation products are also relevant tosolar neutrino studies, and so a likelihood function had

been developed that uses information about the muonspreceding the possible spallation event [11]. To permit a
low analysis threshold for the SRN search, a tighter spallation cut was implemented: in addition to the likelihood
function cut, all events that occur less than 0.15 seconds
after a cosmic ray muon are rejected. The spallation cut
is applied to all events reconstructed with E < 34 MeV,
and introduces a deadtime of 36%. No discernible spallation events with energies above 18 MeV remain in thedata after this cut is applied and so 18 MeV was set as
the lower analysis threshold.
The sub-event cut removes muons with kinetic energy(T) in the range of 50 – 140 MeV. Cosmic ray muons,
which have much higher energies, originate outside of SK
and are removed because they produce a veto signal in
the SK outer detector (OD). However, atmospheric νµcan produce muons within the inner detector (ID) via
charged current quasi-elastic scattering (νµ N → µ N 0 );such muons will not have been tagged by the OD, butwill be visible in the ID. Muons with low energies willstop in SK and produce a decay electron; often the muonand decay electron are found in the same event. When
this happens, the decay electron is referred to as a “subevent.” After the vertex of each event was found and theflight time of the Cherenkov photons was subtracted, theevent’s 1.3 µs time window was searched; if more than one
timing peak was present, then the event was removed.
The sub-event cut was tested on simulated muons in therelevant energy range, and it was shown to remove 34%of the muon background.
The remaining muons are removed by the Cherenkov
angle cut. This cut exploits the mass difference between the muon and the positron, which results in adifference in their Cherenkov angles θC . Positrons with
E > 18 MeV have θC ≈ 42 degrees. Muons with
T < 140 MeV have θC < 34 degrees; thus, all particles
with θC < 37 degrees were removed from the data. The
efficiency of this selection criterion for retaining signal is98%, as determined by applying it to simulated positron
events. Using simulated muon events, it was shown that
applying the Cherenkov angle cut and the sub-event cut
together results in the rejection of 96% of the muon background. Furthermore, it was found that the full reduction
removes > 99% of the muons. The Cherenkov angle cut
was also used to remove events with θC > 50 degrees; thiseliminated events without clear Cherenkov rings, such as
multiple γ rays emitted during a nuclear de-excitation,from the data sample.
Finally, a cut on the direction of the event is made toremove contamination from solar neutrinos. Events with
E < 34 MeV were removed if the reconstructed event
direction was within thirty degrees of the vector fromthe Sun to the Earth at the time of the event.
By simulating positrons created from SRN, it was
found that the efficiency of the full data reduction is
47±0.4% for E ≤ 34 MeV, and 79±0.5% for E > 34 MeV.
Figure 1 plots the energy spectrum after each cut.
After applying the selection criteria, two irreducible

3

10

2

Events / 1496 day / 22.5 kton / 4 MeV

10Before spallation cut
After spallation cut
After sub-event cut
After Cherenkov cut
After solar direction cut

10

Events / year / 22.5 kton / 4 MeV

3

14
12
10
8
6

5

1

3

1

4

4

2

2

10

-1

6

20

30

40

50

60

70

80

0

20

30

40

50

60

FIG. 1: Energy spectrum at each reduction step. In the final
data set, the spallation cut and solar direction cut are only
applied in the first four bins. The numbered lines represent
the corresponding theoretical predictions from Table I.

backgrounds remain. The first is atmospheric νe andν̄e events. The second comes from atmospheric νµ thatinteract to form a muon with T < 50 MeV. The energy of these muons is below the threshold for emitting
Cherenkov photons, so they are said to be invisible. Decay electrons from visible muons can be eliminated; however, when an invisible muon decays there is no way totag the resulting electron as a background event.
The energy spectra of these backgrounds have shapesthat are very different from each other and from the SRN
signal shape. In the region where SRN events are expected (18 – 34 MeV), the dominant background is decay electrons from invisible muons, which have energies
that are distributed according to the Michel spectrum.
However, at higher energies, atmospheric νe events distort the Michel spectrum. To evaluate the distortion, it isnecessary to extend the upper analysis threshold to energies where only atmospheric νe events are present. Decay
electrons have a maximum energy of 53 MeV, but may
be detected up to ∼ 65 MeV due to the energy resolutionof SK. Beyond 65 MeV, only atmospheric νe are found,so the upper analysis threshold was set above 65 MeV
and the data were analyzed with a three parameter fit.
To determine the final shape of the backgrounds,
100 years of simulated events were generated per background. The initial shape of the decay electrons wasdetermined by the Michel spectrum; the initial shape of
the atmospheric νe events was obtained from previous
works [16, 17]. The background simulations were subjected to the full reduction, and the shape of the resulting
spectra were used to fit the data; each of the SRN mod-70

80

Energy (MeV)

Energy (MeV)

FIG. 2: Energy spectrum of SRN candidates. The dotted anddash-dot histograms are the fitted backgrounds from invisible
muons and atmospheric νe . The solid histogram is the sum ofthese two backgrounds. The dashed line shows the sum of thetotal background and the 90% upper limit of the SRN signal.

els was treated similarly. For the fitting, the data weredivided into sixteen energy bins, each 4 MeV wide (seeFigure 2), and the following χ2 function was minimized
with respect to α, β, and γ.
χ2 =

16
X
[(α · Al ) + (β · Bl ) + (γ · Cl ) − Nl ]2
l=122+ σsysσstat(1)

In this equation, the sum l is over all energy bins andNl is the number of events in the lth bin. Al , Bl , and Cl
represent, respectively, the fractions of the SRN, Michel,and atmospheric νe spectra that are in the lth bin. α, β,and γ are the fitting parameters for the number of SRN
events, decay electrons, and atmospheric νe events.
The total number of events in the data sample is small,so the statistical error σstat is the dominant term in the
denominator. The systematic error σsys considers theeffects that uncertainties in the spectrum shapes haveon the SRN result. Such uncertainties originate fromthe reduction, the SK energy resolution, the theoreticalatmospheric νe spectrum, and other sources. For all bins,
σsys ≈ 6%, which is always much smaller than σstat .
The efficiency-corrected event rate spectrum of SRN
candidates and the results of the fit are shown in Figure 2.
The best fits to γ and β are indicated, respectively, by
the dot-dashed and dotted lines. The solid line is thesum of these lines and represents the total background.
For all six models, the best fit to α was zero and theminimum χ2 value was 8.1 for 13 degrees of freedom. A
90% C.L. limit on α was set for each model; the dashed4
TABLE I: The SRN search results are presented for six theoretical models. The first column describes the method used to
calculate the SRN flux. The second column shows the efficiency-corrected limit on the SRN event rate at SK. The third column
is the flux limit set by SK, which can be compared with the theoretical predictions that are shown in the fourth column. The
fifth column shows the flux predictions above a threshold of Eν > 19.3 MeV . Note that the heavy metal abundance calculation
only sets a theoretical upper bound on the SRN flux [7].
Theoretical model

Event rate limit
SRN flux limit
Predicted flux
Predicted flux
(90% C.L.)(90% C.L.)(Eν > 19.3 MeV)
Galaxy evolution [4]< 3.2 events/year < 130 ν̄e cm−2 s−1 44 ν̄e cm−2 s−1 0.41 ν̄e cm−2 s−1
Cosmic gas infall [5]< 2.8 events/year < 32 ν̄e cm−2 s−1 5.4 ν̄e cm−2 s−1 0.20 ν̄e cm−2 s−1
Cosmic chemical evolution [6] < 3.3 events/year < 25 ν̄e cm−2 s−1 8.3 ν̄e cm−2 s−1 0.39 ν̄e cm−2 s−1
Heavy metal abundance [7] < 3.0 events/year < 29 ν̄e cm−2 s−1 < 54 ν̄e cm−2 s−1 < 2.2 ν̄e cm−2 s−1
Constant supernova rate [4] < 3.4 events/year < 20 ν̄e cm−2 s−1 52 ν̄e cm−2 s−1
3.1 ν̄e cm−2 s−1
−2 −1
−2 −1
Large mixing angle osc. [8] < 3.5 events/year < 31 ν̄e cm s
11 ν̄e cm s
0.43 ν̄e cm−2 s−1line represents the sum of the background and the upperbound on α for the galaxy evolution model. This line
shows the type of distortion in the Michel spectrum thatwould be indicative of an SRN signal.
Figure 2 shows that the expected backgrounds fit thedata well. In this analysis, no flux normalization was chosen for the background rates; only the shapes were used.
This is because there are large uncertainties (∼ 30%) in
the atmospheric neutrino fluxes at these very low energies. As a consistency check, the fit results for the number of background events were compared to the predictions, which were determined by applying the reduction
cuts to 100 years of simulated background events andnormalizing for livetime. For 1496 days of data, the expected number of atmospheric νe events is 75 ± 23, whichis consistent with the best fit result of 88 ± 12 events.
To determine the expected number of decay electrons
from invisible muons, neutrino oscillation must be considered [10]; given the low energy of the atmospheric νµthat produce invisible muons, it is assumed that half ofthe νµ have oscillated into ντ . With this assumption, thepredicted number of decay electron events is 145 ± 43,
which is consistent with the best fit result of 174 ± 16
events.
The limit on α can be used to derive a 90% C.L. limiton the SRN flux from each model. The number of SRN
events is related to the total flux F by the following equation:
F =Np × τ

αf(Eν )σ(Eν )(Eν )dEν
19.3 MeVR∞(2)

In this equation, Np is the number of free protons in SK(1.5 × 1033 ), τ is the detector livetime (1496 days), (E)is the signal detection efficiency, σ(E) is the cross section
for the inverse β decay (9.52 × 10−44 Ee pe ), and f (E) isthe normalized SRN spectrum shape. The integral spansthe energy range of the neutrinos that produce positrons
in the observed region.

Using the above values, the 90% C.L. SRN flux limit
was calculated for each model. The results are in thethird column of Table I, and can be compared withthe predictions, which are in the fourth column. For
the galaxy evolution model [4], the cosmic gas infall
model [5], and the cosmic chemical evolution model [6],the SK limits are larger than the predictions by a factorof three to six. In these models, the dominant contribution to the SRN flux comes from supernovae in the early
universe, so the neutrino energy is red-shifted below the
18 MeV threshold. The heavy metal abundance modelprimarily considers supernovae at red-shifts z < 1, so SK
is sensitive to more of the SRN flux. For this model,
the flux limit is smaller than the calculated total flux [7].
However, this prediction is only a theoretical upper limit,
so these results can constrain this model but they cannot
eliminate it. The LMA model [8] has a harder energy
spectrum, and so SK is sensitive to a larger fraction of
the SRN flux. The increased sensitivity is offset by thefact that this hardened spectrum also results in a larger
limit for α; thus, the SK flux limit is still nearly a factorof three larger than the prediction.
The total SRN flux predicted by the constant model
scales with the rate of core-collapse supernovae, and so
the SRN flux limit can be used to set a 90% C.L. upper limit on the constant supernova rate. The SRN flux
prediction quoted in this paper is based on a reasonablesupernova rate of 1.6 × 103 SN year−1 Mpc−3 . The observed SRN flux limit (20 ν̄e cm−2 s−1 ) corresponds toa supernova rate limit of 6.2 × 102 SN year−1 Mpc−3 .
Thus, the constant model can be ruled out, as the limiton the supernova rate is too low to be consistent with theobserved abundance of oxygen [4, 18], which is synthesized within the massive stars that become supernovae.
At Kamiokande-II, a flux limit of 780 ν̄e cm−2 s−1 was set
with the assumption of a constant supernova model [9];the SK limit is 39 times more stringent.
The SRN limits vary greatly, based on the shape ofthe theoretical SRN spectrum at energies that are be-5
low SK’s SRN analysis threshold. To remove this strongmodel dependence, a limit was set for Eν > 19.3 MeV. In
this region, all six models have similar energy spectrum
shapes, and so an experimental limit that is insensitive
to the choice of model can be obtained as follows:R∞f (Eν )dEνMeV
R∞
Fins = F × 19.3
f (Eν )dEν0(3)Flux limits in this energy region were the same forall models considered: 1.2 ν̄e cm−2 s−1 . Previously, thebest limit on the SRN flux in this region was set using
357 days of data at Kamiokande-II [19]. This limit was
226 ν̄e cm−2 s−1 ; the current SK limit is two orders ofmagnitude lower.
In summary, a search was conducted at Super-[∗] Supported by Polish KBN grant 5P03B06531[1] K.S. Hirata et al., Phys. Rev. D 38, 448 (1988); K.S. Hirata et al., Phys. Rev. Lett. 58, 1490 (1987).
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Kamiokande to detect the diffuse signal of ν̄e from all
previous core-collapse supernovae. No appreciable signal
was detected in 1496 days of SK data. Using various
models, 90% C.L. limits were set on the total SRN flux.
A limit of 1.2 ν̄e cm−2 s−1 was set for the SRN flux
above a threshold of Eν > 19.3 MeV. These results are
more than an order of magnitude better than previous
limits; some theories regarding the supernova rate in theuniverse can be constrained or rejected by these limits.
The authors gratefully acknowledge the cooperation of
the Kamioka Mining and Smelting Company. The SuperKamiokande detector was built and operated with funds
provided by the Japanese Ministry of Education, Culture,
Sports, Science, and Technology; the U.S. Department ofEnergy; and the U.S. National Science Foundation.

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