Xing Zh., Zhou Sh. Neutrinos in Particle Physics, Astronomy and Cosmology
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256 7 Neutrinos
f
rom
S
upernovae
F
ermi-Dirac distribution
f
unctions with temperatures at the neutrino spheres.
Since muon and tau neutrinos only under
g
o the neutral-current interactions
,
t
h
e correspon
d
ing neutrino sp
h
eres are
l
ocate
d
muc
hd
eeper in t
h
ecoret
h
a
n
that o
f
electron neutrinos.
S
o one obtains the inequality o
f
neutrino avera
g
e
energ
i
es
E
ν
e
<
E
ν
x
(
for ν
x
=
ν
μ
,
ν
μ
,
ν
τ
,
ν
τ
)
. It is worth mentioning tha
t
the interaction rate of electron antineutrinos
(
ν
e
+
p
→
e
+
+
n
)
is smalle
r
than that of electron neutrinos
(
ν
e
+
n
→
e
−
+
p
)
because of the neutron-rich
c
ore. There
f
ore, the avera
g
eener
g
yo
f
ν
e
should be lar
g
er than that o
f
ν
e
but
s
maller than that of other kinds of neutrinos
;
i.e.
,
E
ν
e
<
E
ν
e
<
E
ν
x
.
Their typical values are obtained from a numerical simulation
(
Raffelt, 1996
):
E
ν
=
⎧
⎨
⎧⎧
⎩
⎨⎨
10
∼
12
M
e
V
ν
e
,
14
∼
18 MeV
ν
e
,
18
∼
2
4
M
e
V
ν
x
,
(
7.11
)
where
ν
x
d
enotes
ν
μ
,
τ
a
n
d
ν
μ
,τ
. Fig. 7.1 shows that the luminosities of thre
e
d
i
ff
erent neutrino
fl
avors are approximately equilibrated, so the neutrino
n
umber
fl
uxes should satis
fy
F
ν
FF
e
>F
ν
F
F
e
>F
ν
F
F
x
,where
E
ν
e
<
E
ν
e
<
E
ν
x
h
as been taken into account. The detailed flavor-dependent fluxes and energy
s
pectra can only be achieved by doing specific numerical simulations
(
Raffelt
,
2
001
;
Kei
l
e
tal
.
,
2003
).
T
o estimate t
h
e tota
l
neutrino energy, we ca
l
cu
l
ate t
h
e gravitationa
l
en
-
er
g
y released
f
rom the collapse o
f
an iron core with mas
s
M
c
∼
1
.
4
M
a
n
d
radius R
c
∼
1
0
3
k
m into the neutron star with the same mass but a muc
h
s
m
alle
rr
ad
i
us
R
N
S
∼
1
0 km. The gravitational binding energy of the neutron
s
tar turns out to be
(
Raffelt, 1996
)
E
b
=
3
G
N
M
2
c
5
R
N
S
≈
3
×
1
0
53
M
c
1
.
4
M
2
1
0km
R
NS
er
g
.
(
7.12
)
A
ssuming the energy equilibration among all kinds of neutrinos, we can then
o
b
tain t
h
e tota
l
neutrino ener
gy
E
ν
=
E
b
/
6
≈
5
×
10
52
er
gf
or each neutrin
o
or ant
i
neutr
i
no s
p
ec
i
es.
7
.2 Lessons from the Supernova 1987A
On 24 February 1987, Ian Shelton and Oscar Duhalde at the Las Campana
s
Observatory in Chile saw a new star in the Large Magellanic Cloud
(
Shel
-
t
on
e
tal., 1987
)
. They actually discovered the first supernova since 1604
,
a
nd it was visible even by the naked eye. This observation was confirmed b
y
s
ome ot
h
er astronomers at s
l
i
gh
t
l
y
l
ater times. More important
l
y, t
h
eneutri
-
n
os emitted from the SN 1987
A
were detected. In this section we shall firs
t
s
ummarize the experimental detection of supernova neutrinos and show tha
t
7
.2 Lessons from the Supernova 1987A 257
t
h
eo
b
servations are essentia
lly
compati
bl
ewit
h
t
h
eoretica
l
pre
d
ictions. T
h
e
n
the lessons that we have learnt from the SN 1987
A
observations, in
p
articular
s
ome constraints on the intrinsic properties of neutrinos, will be discussed
.
We shall briefly comment on the relic neutrinos from old supernovae
(
i.e., the
d
iffuse supernova neutrino background
)
and the future experiments aimin
g
to o
b
serve supernova neutrinos
.
7.2.1 Discoveries o
f
the Neutrino Burst
N
eutrinos emitted from the SN 1987
A
explosion were independentl
y
discov
-
ered by two laboratories, Kamiokande-II in Japan
(
Hirat
a
et a
l.
,
1987, 1988
)
a
nd Irvine-Michigan-Brookhaven
(
IMB
)
in Ohio, USA
(
Biont
a
et al
.
,
198
7
;
Bratto
n
et al.
,
1988
)
. The Kamiokande experiment was intended to detec
t
proton
d
ecays, an
d
it was upgra
d
e
d
in 1985 to Kamio
k
an
d
e-II so as to o
b-
se
r
ve sola
r
8
B
neutrinos. T
h
e IMB experiment was ori
g
ina
ll
y
d
esi
g
ne
d
t
o
d
etect proton deca
y
s, too. Both of them utilized water Cherenkov detec
-
tors. As discussed above, neutrinos of all flavors are emitted from a super
-
n
ova explosion. The dominant si
g
nals come
f
rom the char
g
ed-current process
ν
e
+
p
→
n
+
e
+
o
f electron antineutrinos. In comparison, the charged-curren
t
pr
ocess
ν
e
+
16
O
→
e
−
+
16
F
o
f
e
l
ect
r
o
nn
eut
rin
os a
n
dt
h
ee
l
ast
i
c
n
eut
rin
o
-
e
l
ectron scatterin
g
ν
α
+
e
−
→
ν
α
+
e
−
co
n
t
ri
bute at a subdo
min
a
n
t level.
T
he Kamiokande-II detector’s energy threshold fo
r
ν
e
i
sabout8MeV
.
It recorded the first supernova neutrino event at 7 : 35 : 35 UT
(
Universa
l
Time
)
on 23 February 1987. In total 12 neutrino events were observed, an
d
the signals lasted about 12 seconds. The probability for these events to b
e
c
aused by statistical
fl
uctuations or cosmic muon back
g
rounds was
f
ound t
o
be extremely small
(
Hirat
a
et al.
, 1987
)
. The output o
f
ν
e
w
ithanavera
ge
energy around 15 MeV is 8
×
1
0
52
e
rg, well consistent with the theoretical
pre
d
ictio
n
E
ν
=
E
b
/
6
≈
5
×
10
52
e
r
g
. The neutrino si
g
nals were
fi
rst re
g
is
-
tered b
y
the IMB detector at 7 : 35 : 4
1
.
37 UT on the same da
y
,andthe
y
l
asted about 6 seconds. With a high energy threshold of 20 MeV, the IM
B
experiment totally recorded 8 neutrino events
(
Bionta
et al
., 1987
)
.
T
he re
g
istration time and ener
g
ies of supernova neutrino events in th
e
K
amio
k
an
d
e-II an
d
IMB experiments are summarize
d
in Ta
bl
es 7.1 an
d
7.2
.
T
h
e
y
are compati
bl
ewit
h
t
h
estan
d
ar
dd
e
l
a
y
e
d
-exp
l
osion scenario. First,
the duration of neutrino signals was measured to be several seconds, jus
t
a
s expected for the neutrino-cooling time of neutron stars. Second, the tota
l
ener
g
y taken away by neutrinos
f
rom the supernova is essentially equal to th
e
gravitational binding energy given in Eq.
(
7.12
)
. So 99% of the gravitational
binding energy stores in the form of neutrinos, 1
%
is used for the explosion,
a
nd onl
y0
.
0
1% is emitted in the form of
p
hotons
.
T
able 7.1 shows that there were 9 neutrino events within 2 seconds
,
bu
t
t
h
e
l
ast 3 events arrive
d
a
b
out 7 secon
d
s
l
ater. However, t
h
eIMB
d
etec
-
tor recorded two neutrino events durin
g
this time interval. This discrepancy
s
eems to be a statistical accident, which was observed with an a
pp
reciabl
e
258 7 Neutrinos
f
rom
S
upernovae
Table 7.1 The measured properties of twelve neutrino events in the Kamiokande-
II experiment
(
Hirata
et al
., 1987. With permission from the
A
merican Ph
y
sical
Society
)
. Note that the energy and angular distributions refer to the recoil electrons
or positrons. The registration time for the first supernova neutrino event is 7 : 35 :
35 UT
E
vent number Time
(
seconds
)
Energy
(
MeV
)
Angle
(
degrees
)
1020
.
0
±
2
.
918
±
18
20
.
1
07
1
3
.
5
±
3
.
215
±
2
7
30
.
303
7
.
5
±
2
.
0 108
±
32
4
0
.
324 9
.
2
±
2
.
7
70
±
3
0
50.507 1
2
.
8 ±
2
.
9
135 ±
2
3
60
.
686 6
.
3
±
1
.
768
±
77
71
.
54
1
35
.
4
±
8
.
032
±
16
81
.
7
28 2
1
.
0
±
4
.
230
±
18
9
1
.
915 1
9
.
8
±
3
.
2
38
±
22
1
0
9
.219 8
.
6
±
2.
7
122 ±
30
11 10
.4
33
1
3
.
0
±
2
.
6
4
9
±
26
12 12
.
4
39 8
.
9
±
1
.
991
±
39
Table 7.2 The measured properties of eight neutrino events in the IMB experiment
(
Biont
a
et al
., 1987. With permission from the American Physical Society
)
.Not
e
that the registration time of neutrino events is given in the Universal Time
(
UT
)
,
the uncertainties of the ener
g
yandan
g
ular distributions are
±
15
%
an
d
±
15
◦
,
respectivel
y
E
vent number Time
(
UT
)
Energy
(
MeV
)
Angle
(
degrees
)
1
7
:
35
:
41
.
37 38 74
27:35:
41
.
79 37 5
2
37:35:4
2
.
02 40 5
6
47
:
35
:4
2
.
5
2
35 63
57
:
35
:4
2
.
9
42
9
4
0
67
:
35
:
44
.
06 37 52
7
7 : 35 :
46
.
38 20 39
87:35:4
6
.
9
624 10
2
f
requency in numerical simulations
(
Bahcall et al.
,
1988
)
. Two other experi-
m
ents, Baksan
(
Alexeye
v
et a
l.
, 1988
)
and Mont Blanc
(
Aglietta et a
l.
,
1987
),
reporte
d
t
h
e supernova neutrino si
g
na
l
stoo.T
h
eBa
k
san scinti
ll
ation te
l
e
-
s
co
p
e in the North Caucasus observed 5 neutrino events within
9
.1 seconds a
t
7
.2 Lessons from the Supernova 1987A 259
7
:
36
:1
1
.
8
UT on 23 Februar
y
1987, but it recorded the
fi
rst event 25 second
s
l
ater than the IMB detector did. The Baksan Collaboration later found that
the registration time of the first neutrino event should be 7 : 36 : 11
.
8
+2
−
54
U
T
,
essentia
lly
compati
bl
ewit
h
t
h
at reporte
dby
t
h
eKamio
k
an
d
e-II an
d
IMB ex
-
periments
(
Suzuki, 2008
)
. The Mont Blanc Neutrino Observatory reported
the neutrino burst of 5 pulses at 2 : 52 : 36 UT on 23 February 1987, about
4
.
5h
ours ear
l
ier t
h
an t
h
eKamio
k
an
d
e-II
d
etector
d
i
d
.T
h
is resu
l
t
h
as
b
ee
n
c
ontroversial, and it should have nothing to do with the SN 1987A
(
de Rujula
,
1
987; Arnett
et al.
,
1989
)
.
B
ecause of the poor statistics
(
i.e., totally 20 events obtained from th
e
K
amiokande-II and IMB experiments
)
, it is impossible to determine the en
-
er
g
y spectra o
f
supernova neutrinos. Future hi
g
h-statistics observations o
f
the
n
eutrino burst
f
rom a
g
alactic supernova will de
fi
nitely help us understand
the ex
p
losion mechanism and
p
robe the intrinsic
p
ro
p
erties of neutrinos
.
7.2.2
C
onstraints on Neutrino Propertie
s
A
measurement of the neutrino burst from the SN 1987A provides a strong
s
upport
f
or the standard picture o
f
core-collapse supernovae.
O
ne ma
y
extrac
t
u
seful information on the intrinsic
p
ro
p
erties of massive neutrinos, such a
s
their lifetimes, masses and magnetic moments
(
Bethe, 1990
)
.
(
1
)
N
eutrino li
f
etime
s
.
The SN 1987
A
is situated in the Lar
g
eMa
g
ellani
c
Cloud
,
whose distance from the Earth i
s
D
=50
±
5kpc=
(
16
0
±
1
6
)
×
10
3
ly
(
Andreani
et al
.
,
1987
)
. If the number of supernova neutrinos or antineutrinos
i
s assumed not to be si
g
ni
fi
cantly reduced by neutrino decays, the laboratory
n
eutrino lifetime
τ
should be much longer than the propagation time
(
i.e.
,
τ>D
/
c
≈
5
×
10
12
s)
. Note that relativistic neutrinos with
E
ν
m
ν
t
r
avel
a
lmost at the speed of li
g
ht. This is always the case for supernova neutrinos
wit
h
an average energ
y
E
ν
∼
1
0 MeV. More accurate
l
y, t
h
eneutrinove
l
ocity
v
ν
is
g
iven
b
y
β
ν
≡
v
ν
/c
≈
1
−
m
2
ν
/
(2
E
2
ν
)
. Hence the neutrino lifetim
e
τ
0
τ
τ
in
the rest frame should satisf
y
τ
0
ττ
=
τ
1
−
β
2
ν
>
5
×
10
5
s
m
ν
1
eV
10 M
e
V
E
ν
,
(
7.13
)
which essentiall
y
rules out neutrino deca
y
s as a possible solution to the sola
r
n
eutrino problem
(
Bethe, 1990
).
(
2
)
Neutrino masses
.Nowt
h
at neutrinos are massive, t
h
eir arriva
l
time
s
m
ust be different from the arrival time of massless neutrinos. For a distanc
e
of 50 kpc, the time dela
y
Δ
t
o
f a massive neutrino is determined b
y
Δ
t
=
D
c
−
D
v
ν
≈
2
.
5
s
m
ν
10 eV
2
1
0M
e
V
E
ν
2
.
(
7.14
)
To co
n
st
r
a
i
n
m
ν
,onemayar
g
ue tha
t
Δ
t
s
h
ou
l
d
n
ot e
x
ceed t
h
edu
r
at
i
o
n
of
n
eutrino signals observed in the Kamiokande-II and IMB experiments. Takin
g
260 7 Neutrinos
f
rom
S
upernovae
Δ
t
<
1
0
s
f
o
r
E
ν
=10MeV,
f
or example, we obtai
n
m
ν
<
20 eV. However,
the emission of su
p
ernova neutrinos is distributed in time.
A
more reasonabl
e
s
tatistica
l
treatment yie
ld
s
m
ν
<
1
6eV
(
Spergel and Bahcall, 1988
)
.
(
3
)
Neutrino ma
g
netic moments
.
Theexistenceo
f
ma
g
netic moments ma
y
i
nduce the spin flip of neutrinos in the supernova via some scattering pro-
c
esses
(
e.g., the neutrino-electron scattering
)
. After the spin flip, the left
-
ha
n
ded
n
eut
rin
os
ν
L
are converte
d
into t
h
eri
gh
t-
h
an
d
e
d
ones
ν
R
,
w
h
ic
hh
ave
n
o standard weak interactions with matter and can freel
y
escape from th
e
s
upernova. T
h
e rapi
d
energy
l
oss cause
db
yrig
h
t-
h
an
d
e
d
neutrinos wou
ld
s
i
g
ni
fi
cantly reduce the duration o
f
neutrino si
g
nals and thus contradict the
relevant experimental results. Along this line, the neutrino magnetic momen
t
μ
ν
c
an
b
estrict
l
y constraine
d
a
s
μ
ν
<
10
−
12
μ
B
w
i
th
μ
B
b
ein
g
t
h
eBo
h
rma
g-
n
eton
(
Raffelt and Seckel, 1988; Lattimer and Cooperstein, 1988; Barbieri an
d
Mohapatra, 1988
)
. It is worth mentioning that this energy-loss argument ha
s
been widely used to constrain the properties o
f
weakly-interactin
g
particles
,
s
uch as sterile neutrinos and axions
(
Raffelt, 1990, 1996
).
I
n addition
,
the observed neutrino burst from the SN 1987A can also
s
hed li
g
ht on the neutrino mass spectrum and the
fl
avor mixin
g
pattern.
This as
p
ect will be discussed in Section 7.3 and Section 7.4.
7.2.3 The Di
ff
use Supernova Neutrino Back
g
round
A
ver
y
important lesson learnt from the SN 1987
A
is that the core-collaps
e
s
u
p
ernovae emit neutrinos. The flux of neutrinos and antineutrinos emitted
f
rom all the core-collapse supernovae in the causally-reachable Universe is
c
alled the diffuse supernova neutrino background
(
DSNB
)
. The DSNB pro-
vides us with an isotro
p
ic and time-inde
p
endent source of su
p
ernova neutri-
n
os. A measurement of the DSNB will be complementary to that of a
g
alacti
c
s
upernova neutrino burst
(
Ando and Sato, 2004; Beacom, 2010; Lunardini,
2
010
)
. The flavor-dependent flux of the DSNB at the Earth is determined by
the neutrino emission
f
rom a sin
g
le supernova explosion, the cosmic super
-
n
ova rate and neutrino oscillations.
G
iven
R
SN
(
z
)
as the supernova rate per
c
omoving volume at the redshif
t
z
,
one may write
d
own t
h
enum
b
er
d
ensit
y
of supernova neutrinos
(
e.g.
,
ν
e
)
in the energy interval
[
E
ν
,
E
ν
+
d
E
ν
](
And
o
a
nd Sato, 2004
):
d
n
ν
(
E
ν
)
=
R
SN
(
z
)(
1+
z
)
3
d
t
dz
d
z
d
N
ν
NN
(
E
ν
)
d
E
ν
d
E
ν
(
1
+
z
)
−
3
,
(
7.15
)
whe
r
e
E
ν
=
(
1
+
z
)
E
ν
is the neutrino ener
g
y at the redshi
f
t
z
,
w
h
ic
h
is
n
ow measured a
s
E
ν
. The factors
(
1
+
z
)
±
3
i
nEq.
(
7.15
)
take account of the
expansion o
f
the Universe, an
d
d
N
ν
NN
(
E
ν
)
d
E
ν
stands
f
or the number spectrum
of neutrinos from one supernova explosion.
A
ssumin
g
the standar
d
Λ
C
DM
model w
i
th
k
= 0 and neglecting the tiny contribution fro
m
Ω
r
,
we
h
av
e
1
1
S
ee Section 9.1.3 for a detailed discussion.
7
.2 Lessons from the Supernova 1987A 26
1
d
z
d
t
=
−
H
0
HH
(
1
+
z
)
Ω
m
(
1+z
)
3
+
Ω
v
,
(
7.16
)
whe
r
e
H
0
HH
i
sto
d
ay
’
sHu
bbl
e constant
,
Ω
m
≈
0
.
26
an
d
Ω
v
≈
0
.
7
4 measure t
h
e
d
ominant energy budget of today’s Universe. A combination of Eqs.
(
7.15
)
a
nd
(
7.16
)
yields the differential number flux of the DSNB:
d
φ
d
E
ν
≡
c
d
n
ν
d
E
ν
=
c
H
0
HH
z
m
a
x
0
R
S
N
(
z
)
d
N
ν
NN
(
E
ν
)
d
E
ν
·
d
z
Ω
m
(
1
+
z
)
3
+
Ω
v
,
(
7.17
)
w
h
e
r
e
z
max
= 5 denotes the time when the
g
ravitational collapse took plac
e
(
Ando and Sato, 2004
)
. The theoretical predictions for the DSNB flux are
c
omp
l
icate
db
yt
h
e supernova rate
d
ensit
y
R
SN
(
z
)
, which is determined by the
sta
r
fo
rm
at
i
o
nr
ate
R
SF
(
z
)
and the distribution of stellar masse
s
ψ
(
M
)
.Given
the conventional Sal
p
eter functio
n
ψ
(
M
)=
d
n
d
M
∝M
−
2
.
35
f
or
0
.
1
M
M
100
M
,
one finds
(
Beacom, 2010
)
R
S
N
(
z
)
=
R
SF
(
z
)
7
50
8
77
ψ
(
M
)d
M
7
100
0
7
7
.
1
M
ψ
(
M
)d
M
R
SF
(
z
)
142
M
,
(
7.18
)
whe
r
e
M
i
s
g
iven in units o
f
M
.InEq.
(
7.18
)
we have assumed tha
t
the stars with masses between
8
M
a
nd 5
0
M
m
ay
g
ive rise to the core-
c
o
ll
apse supernovae. T
h
emo
d
e
l
pre
d
ictions are consistent wit
h
t
h
eo
b
ser
-
vational data o
f
the star
f
ormation rate, yieldin
g
R
S
F
(
0
)
=
(
0
.
5
∼
2
.
9
)
×
1
0
−
2
M
year
−
1
M
pc
−
3
(
Baldry and Glazebrook, 2003
)
. The rate increases
f
or higher redshifts and the results are quite robust for
0
<z
2
, a regio
n
which is most relevant to the D
S
NB. Finall
y
,wehavetoknowthenumber
s
pectrum of neutrinos from a t
y
pical supernova explosion. Since neither the
i
nitial neutrino spectra nor the neutrino mixin
g
e
ff
ects are well understood,
it
i
sco
n
ve
ni
e
n
ttota
k
et
h
e effect
i
ve
F
e
rmi-Dir
ac fo
r
m
d
N
ν
N
N
d
E
ν
=
E
tot
ν
1
2
0
7
π
4
·
E
2
ν
T
4
·
1
e
E
ν
/T
+1
,
(
7.19
)
w
h
ere
E
t
o
t
ν
d
enotes t
h
e tota
l
neutrino energy, an
d
T
=
E
ν
/
3
.
15
is t
h
e
temperature at t
h
eneutrinosp
h
ere. Bot
h
E
tot
ν
a
n
d
E
ν
ca
n
be dete
rmin
ed
f
rom the SN 1987
A
observations.
S
everal events of the DSNB per year are expected in the Super-Kamiokande
(
SK
)
experiment. However, such events must have been hidden by the de
-
tector backgrounds, which can be substantially reduced by adding gadolin-
i
um to detect neutrons
(
Beacom, 2010
)
. The SK experiment has set a limi
t
φ
(
E
ν
>
1
9
.
3
MeV
)
1
.
2
c
m
−
2
s
−
1
at the 99% confidence level
(
Malek
et
a
l
.
,
2003
)
. Fig. 7.2 shows the predicted DSNB signal at the SK detector with
a
m
ass of
2
2
.
5 kton, to
g
ether with the back
g
rounds
f
rom reactor and atmo-
s
pheric neutrinos
(
Beacom and Vagins, 2004
)
. It is obvious that the discover
y
p
ros
p
ects for the DSNB are excellent in the future
.
262 7 Neutrinos
f
rom
S
upernovae
0
5
10
15
20
25
30
35
40
M
easure
d
E
e
[
MeV
]
1
0
-2
10
-
1
10
0
10
1
10
2
10
3
d
N
/d
E
e
[
(
22.5
k
ton
)
y
r MeV]
-
1
R
eactor
ν
e
Su
p
ernova
ν
e
(
DSNB
)
ν
μ
ν
e
Atmosp
h
er
ic
GA
DZ
OO
K
S!
Fig. 7.2 The predicted energy spectrum of the DSNB at the SK experiment,
where the backgrounds from reactor and atmospheric neutrinos have also been
shown
(
Beacom and Vagins, 2004. With permission from the American Physical
Society
)
7.2.4 Future Supernova Neutrino Experiment
s
We have
g
ot only one lucky chance to observe the neutrino burst
f
rom th
e
s
upuernova explosion
(
i.e., the SN 1987A
)
. A high-statistics neutrino signa
l
f
rom nearby
g
alaxies will shed li
g
ht both on the mechanism o
f
supernov
a
ex
p
losions and on the intrinsic
p
ro
p
erties o
f
neutrinos. Based on the mea
-
s
urements of su
p
ernova neutrino bursts, the observations of the DSNB wil
l
h
elp us understand the cosmic supernova rate and variations o
f
the neutrino
emission
f
rom one supernova to another. Let us brie
fly
summarize a
f
ew ex
-
perimenta
l
met
h
o
d
sw
h
ic
hh
ave
b
een or wi
ll b
euse
d
to o
b
serve supernova
n
eutrinos
(
Scholberg, 2007
).
(
1
)
I
nverse beta deca
ys
. The inverse beta deca
y
ν
e
+
p
→
e
+
+
n
i
scur
-
rent
l
yt
h
e most promising process to
d
etect supernova neutrinos. T
h
e reaso
n
i
s simply that its decay rate is typically two orders o
f
ma
g
nitude lar
g
er tha
n
other interaction rates in any detectors with a lar
g
e amount of protons. In a
water Cherenkov detector
(
e.g., SK and IceCube
)
, the Cherenkov light of the
fi
nal-state positron is measured.
S
ince the Ice
C
ube detector is intended t
o
d
etect high-energy or ultrahigh-energy neutrinos, it is unable to record the
MeV supernova neutrinos on an event-by-event basis. Such low-energy neu
-
trino events can be identi
fi
ed with a coincident increase in sin
g
le count rates
f
rom many phototubes
(
Halze
n
et al
.
,
1994
;
Ahrens
e
tal., 2002
)
. To reduc
e
the back
g
rounds in the
S
K experiment, it has been su
gg
ested to spike th
e
7.3 Matter E
ff
ects on
S
upernova Neutrinos 26
3
water wit
hg
a
d
o
l
inium tric
hl
ori
d
esoastoen
h
ance t
h
e neutron capture rate
(
Beacom and Vagins, 2004
)
. The inverse beta decay of supernova neutrinos
c
an a
l
so
b
eo
b
serve
d
in a scinti
ll
ation
d
etector
,
suc
h
as t
h
eBa
k
san
,
LVD
,
K
amL
A
ND, Borexino and MiniBooNE detectors
.
(
2
)
Char
g
ed-current interactions on nucle
i
.
The electron neutrinos from
c
ore-collapse supernovae
(
e.g., the prompt
ν
e
b
urst
)
are crucial for probing
the dynamics o
f
supernova explosions. They can be detected via the char
g
ed
-
c
urrent react
i
ons
ν
e
+
A
(
Z, N
)
→
A
(
Z
+1
,
N
−
1
)+
e
−
, although their
c
ross sections are usua
ll
ysma
ll
. For examp
l
e,
ν
e
+
16
O
→
16
F
+
e
−
fo
r
a
water
C
herenkov detector
;
ν
e
+
D
→
p
+
p
+
e
−
f
or heav
y
water; an
d
ν
e
+
12
C
→
12
N
+
e
−
f
or a scintillation detector. The proposed liquid-argo
n
d
etectors, such as ICARUS
(
Hargrove
et al
.
,
1996
)
and LANNDD
(
Buen
o
et
al.
,
2003
)
, will make use of the reactio
n
ν
e
+
40
Ar
→
4
0
K
∗
+
e
−
a
n
dobse
r
ve
the
p
hotons from the deexcitation o
f
40
K
∗
. Such ex
p
eriments are ex
p
ected t
o
b
eexc
l
usive
l
y sensitive to supernova e
l
ectron neutrinos.
(
3
)
E
lastic scatterin
g
and neutral-current interaction
s
.In
t
h
esta
n
da
r
d
picture of core-collapse supernovae, neutrinos of all three flavors are emitted
.
F
lavor conversions o
f
supernova neutrinos
f
urther
g
uarantee the presence o
f
m
uon and tau neutrinos. The measurements of different neutrino fluxes ca
n
therefore provide a strong support for the supernova theory and independen
t
evidence
f
or neutrino oscillations. The elastic scatterin
g
ν
α
+
e
−
→
ν
α
+
e
−
(
for
α
=
e, μ, τ
)
in a water Cherenkov detector is less important than the invers
e
beta decay of
ν
e
,
but it can measure the direction of incident neutrinos whic
h
points back to the location o
f
the supernova. For a neutral-current reaction
ν
x
+
A
→
ν
x
+
A
∗
(
fo
r
x
=
μ, τ
)
, it is possible to tag the ejected nucleons o
r
d
eexcitation photons from the excited nucleu
s
A
∗
.
Interesting
l
y, t
h
e
d
etector
s
i
nten
d
e
d
to
d
etect
d
ar
k
matterorso
l
ar neutrinos ma
y
a
l
so
b
e sensitive t
o
s
upernova neutrinos via the coherent neutrino-nucleus scattering.
S
ome current and
f
uture experiments sensitive to supernova neutrinos ar
e
l
isted in Table 7.3, where the neutrino events
f
or a su
p
ernova ex
p
losion at a
d
istance of
8
.
5 kpc are roughly estimated
(
Scholberg, 2010
)
. It is worth men
-
tionin
g
that
g
ravitational waves should be produced
f
rom the core collapses
.
S
o an analysis o
f
the correlation between
g
ravitational waves and neutrino
s
ignals would be very interesting and helpful in the study of supernova physic
s
(
Pagliarol
i
et al
., 2009; Halzen and Raffelt, 2009
)
.
7
.3 Matter E
ff
ects on Su
p
ernova Neutrino
s
The neutrino spectra of three different flavors at the neutrino spheres can b
e
a
pproximatel
y
described b
y
the Fermi-Dirac distributions with di
ff
erent e
ff
ec
-
tive temperatures. When neutrinos freely stream from the neutrino spheres t
o
the supernova sur
f
ace, however, the oscillation e
ff
ects may chan
g
e the spectra.
In this section we shall discuss the ordinar
y
matter e
ff
ects on supernova neu
-
trino oscillations, in particular the Mikheyev-Smirnov-Wolfenstein
(
MSW
)
264 7 Neutrinos
f
rom
S
upernovae
Table 7.3 A summary of current and proposed detectors with sensitivities to super-
nova neutrinos, where the number o
f
events is estimated
f
or a su
p
ernova ex
p
losion
at a distance of 8.
5
kpc
(
Scholberg, 2010. With permission from the Institute o
f
Physics
)
D
etector Type Mass
(
kton
)
Location No. of Events Statu
s
Baksan
C
n
H
2
n
0.33
C
aucasus 50 Runnin
g
S
u
p
er-K
H
2
O
32 Japan 8000 Runnin
g
LVD C
n
H
2
n
1
Italy 300 Runnin
g
KamLAND
C
n
H
2
n
1J
apan 300
R
unnin
g
M
iniBooNE
C
n
H
2
n
0
.7 USA 200 Running
Borexino
C
n
H
2
n
0
.3 Ita
l
y 100 Runnin
g
IceCube Long string 0.4
/
PMT South Pole N
/
A Runnin
g
SNO
+C
n
H
2
n
0
.8 Canada 300 Near Futur
e
H
AL
O
Pb
0
.
07 C
anada
80
Near Future
I
CARUS Ar 0.6 Italy 230 Near Future
N
O
ν
AC
n
H
2
n
1
5 USA 3000
Near Futur
e
L
BNE L
A
r Liquid
A
r
g
on 5 US
A
1900 Futur
e
LBNE WC
H
2
O
300 US
A
78
,
000 Future
MEMPHY
SH
2
O
440 Euro
p
e 120,000 Future
H
yper-
KH
2
O
500 Japan 130,000 Future
L
EN
AC
n
H
2
n
5
0 Europe 15,000 Future
GL
A
CIER
A
r 100 Europe 38,000 Future
resonant conversions
(
Wolfenstein, 1978, 1979; Mikheyev and Smirnov, 1985
)
.
The resonances associated with high
(
|
Δ
m
2
31
|
≈ 2
.
4
×
1
0
−
3
eV
2
)
and lo
w
(
Δ
m
2
21
≈
8
.
0
×
10
−
5
e
V
2
)
neutrino mass-squared differences can take place
i
n the mantle and envelope of a supernova.
A
ccordin
g
ly, the initial flavo
r
d
istribution at the neutrino sphere will be significantly modified, leading to
so
m
eobse
r
vab
l
e effects
.In
add
i
t
i
o
n
to t
h
e
r
eso
n
a
n
tco
n
ve
r
s
i
o
n
s
in
s
i
de t
h
e
s
upernova, the matter e
ff
ects inside the Earth ma
yf
urther reprocess the neu
-
trino spectra. A measurement of the neutrino burst from a future galacti
c
s
upernova exp
l
osion cou
ld h
e
l
ppin
d
own t
h
esma
ll
est neutrino mixin
g
an
gl
e
θ
13
a
nd the neutrino mass hierarchy
(
Dutt
a
e
tal.
,
2000; Di
g
he and Smirnov
,
2
000
)
. On the other hand, the neutrinos just above the neutrino sphere are
s
o
d
ense t
h
at t
h
eco
h
erent neutrino-neutrino scatterin
g
may
d
ominate over
the neutrino interactions with ordinar
y
matter. In this case the collective
n
eutrino flavor conversions can happen, and they may have already changed
the neutrino spectra be
f
ore the ordinar
y
matter e
ff
ects do their work. This
i
ntriguing phenomenon will be discussed in detail in Section 7.4.
7.3 Matter E
ff
ects on
S
upernova Neutrinos 26
5
7.3.1 Neutrino Fluxes and Energy
S
pectr
a
Be
f
ore discussin
g
neutrino oscillations and matter e
ff
ects, one should kno
w
n
eutrino fluxes and energy spectra of different flavors. Note that the neutrino
s
phere is defined for a specific energy, and neutrinos with different energies
a
re actuall
y
emitted
f
rom di
ff
erent neutrino spheres. More accuratel
y
,th
e
c
ross section of the neutrino-nucleon scattering becomes larger for neutrinos
with hi
g
her ener
g
ies, so does the radius o
f
the neutrino sphere.
S
ince th
e
temperature decreases with the increasin
g
radius in a supernova, the neutri
-
n
os with higher energies have lower temperatures. This observation implies
t
h
at t
h
eener
g
y spectrum must
g
et pinc
h
e
d
at t
h
e
h
i
gh
ener
g
yen
d
.T
h
eori
g-
i
nal neutrino
fl
ux
f
rom the supernova core can be e
ff
ectivel
y
described b
y
a
pinched Fermi-Dirac spectrum
(
Raffelt, 1996
)
:
F
0
ν
F
F
α
(
E
ν
α
,T
ν
TT
α
,
η
ν
α
,
L
ν
α
,
d
)
=
L
ν
α
4
π
d
2
·
1
T
4
ν
T
T
α
F
3
FF
(
η
ν
α
)
·
E
2
ν
α
e
(
E
ν
α
/T
ν
T
T
α
−
η
ν
α
)
+1
,
(
7.20
)
whe
r
e
E
ν
α
is the ener
g
yo
f
ν
α
,
T
ν
TT
α
denotes the e
ff
ective temperature at th
e
n
eutrino s
p
here
,
η
ν
α
is the pinching parameter,
L
ν
α
s
tands for the neutrino lu
-
m
inosity, an
d
d
r
epresents t
h
e
d
istance to t
h
e supernova. Note t
h
at
F
3
FF
(
η
ν
α
)
≡
7
∞
0
7
7
x
3
[
e
x
−
η
ν
α
+1
]
−
1
d
x
is a Fermi-Dirac inte
g
ra
l
,an
d
F
3
FF
(
0
)
=7
π
4
/
1
20
h
o
ld
s
.
W
e stress tha
t
η
ν
α
s
hould not be identified with
μ
ν
α
/T
ν
T
T
α
in the thermal
F
ermi-Dirac
d
istri
b
ution, w
h
er
e
μ
ν
α
i
st
h
ec
h
emica
l
potentia
l
. Hence t
h
ere
-
lat
i
o
n
η
ν
α
=
−
η
ν
α
does
n
ot
h
o
l
dfo
rn
eut
rin
os
ν
α
a
n
da
n
t
in
eut
rin
os
ν
α
.In
other words, the distribution in Eq.
(
7.20
)
is not thermal.
Numerical simulations o
f
the neutrino transport in the supernova core
i
ndicate that the average neutrino energies satisfy
E
ν
e
=(
14
∼
2
2
)
MeV,
E
ν
e
=
(
0
.
5
∼
0
.
8
)
E
ν
e
a
n
d
E
ν
x
=
(
1
.
1
∼
1
.
6
)
E
ν
e
,w
h
ere
ν
x
de
n
otes
the non-electron flavors
ν
μ
,
ν
μ
,
ν
τ
an
d
ν
τ
(
Keil et al
.
,
2003
)
. Moreover, one
o
b
tains
0
η
ν
e
3
,
0
η
ν
e
3
an
d0
η
ν
x
2, imp
l
ying t
h
at e
l
ectro
n
n
eutrinos and electron antineutrinos mi
g
ht have stron
g
er pinchin
g
e
ff
ects
.
Given a value o
f
η
ν
α
, the effective tem
p
erature
T
ν
TT
α
for each neutrino flavor
c
an
b
e
d
etermine
db
y
E
ν
α
.T
h
e time-integrate
d
neutrino
l
uminosit
y
L
ν
α
i
s
typically
(1
∼
5)
×
10
52
e
rg, an
d
d
∼
10 kpc holds for a galactic supernova.
The luminosities o
f
di
ff
erent neutrino
fl
avors are expected to be equal withi
n
a
factor of two or so
(
Keil et al., 2003
)
.
Note t
h
at t
h
eneutrino
l
uminosities, temperatures an
d
pinc
h
ing parame-
ters s
h
ou
ld b
etime-
d
epen
d
ent as t
h
e supernova evo
l
ves. Hence t
h
einte
g
rate
d
n
eutrino fluxes may differ from that given by Eq.
(
7.20
)
. The time-dependent
effects
(
e.g., the propagation of the shock wave
)
can be imprinted in the fina
l
n
eutrino fluxes and thus observable in experiments
(
Fogl
i
et al
., 2005
)
.
7.3.2 Matter Effects in the Supernov
a
It is well known that neutrino oscillations with the M
S
W matter e
ff
ects
c
an perfectly solve the solar neutrino problem. An immediate question is