Neutrinos from Supernovae

Proc Indian Natn Sci Acad, 70, A No. 1, January 2004, pp. 123–133 c Printed in India.

a †

SANDHYA CHOUBEY ¡ AND KAMALES KAR

¡ Department of Physics and Astronomy, University of Southampton, Highﬁeld, Southampton S017 1BJ (UK) †Theory Group, Saha Institute of Nuclear Physics, Kolkata 700 064 (India)

(Received 10 January 2003; Accepted 17 July 2003)

In this review, the effect of ﬂavor oscillations on the neutrinos released during supernova explosion after core collapse is described. In some scenarios there is a large enhancement of the number of events compared to the no oscillation case. Various other features associated with supernova neutrinos are also discussed.

Key Words: Core Collapse Supernova; Neutrino Mass and Mixing; Neutrino Detection

1 Introduction Sudbury Neutrino Observatory (SNO) through electron scattering and charged/neutral current dissocia- February 23, 1987 saw the birth of a new era in tion of heavy water respectively. The recent results an- astrophysics-extra-solar system neutrino astronomy. nounced by the KamLAND reactor experiment gives The supernova explosion in the Large Magellanic for the first time conclusive evidence for neutrino os- Cloud (LMC) at a distance of about 50 kpc was not cillation using a terrestrial neutrino source and con- only the closest visual supernova since Kepler but was firms the Large Mixing Angle (LMA) solution to the also the source of neutrinos detected at the terrestrial solar neutrino problem. Thus the present day interest detectors of Kamiokande (KII) and IMB giving rise to in supernova neutrinos lies around the question: if you 11 and 8 events respectively. have a galactic supernova event today what would be The next few years saw great excitement in this the number of events and their time and energy dis- field. Astrophysics interacted with particle physics tributions in the large number of neutrino detectors intimately. From the number and the energy dis- in operation. The other related question is whether tribution of the observed neutrinos one tried to ex- one can get a signature of neutrino oscillation mecha- tract information about the stellar core and check nism from the observed data and also how other neu- them with model predictions. On the other hand trino properties get constrained. Information about the these neutrinos also gave particle physics constraints mechanisms of the supernova explosion is also an area on neutrino properties. In the last few years inter- of huge interest. est in this area got rejuvenated by the finding that In this review we survey some of these issues. neutrinos do have non-zero mass and the flavors do In section 2 we give a brief overview of the physics mix when they travel. This conclusion was reached of type II supernovae and the emission of neutrinos through the analysis of the atmospheric neutrinos de- from them. Section 3 introduces the subject of neu- tected at the Superkamioka (SK) along with their trino oscillation and the impact of vacuum and matter zenith angle dependence and the observation of the enhanced oscillation on the supernova neutrinos from deficit of detected solar neutrinos by the Chlorine the core. Section 4 describes the expected number of and Gallium radiochemical detectors and at SK and events in the terrestrial detectors for the different mass and mixing scenarios. Finally section 5 briefly states a Now at INFN Sezione di Trieste and Scuola Internazionale the other connected issues of supernova neutrino de- Superiore di Studi Avazanti, I-34014, Trieste, Italy. tection. 124 SANDHYA CHOUBEY AND KAMALES KAR

2 Type II Supernovae and Neutrino Emission and so the νe “neutrinosphere” has the largest radius and smallest temperature. In this article we shall as-

Stars of masses larger than 8M ¢ after burning for sume that the three types of neutrino gas have Fermi- millions of years collapse when the nuclear reac- Dirac distributions with temperatures 11, 16 and 25 tions in the core stop with matter consisting mostly MeV for νe, ν¯e and νx respectively. of 56Fe like nuclei. This collapse proceeds very fast An important role played by neutrinos in type (timescale of the order of tens of milliseconds) and II supernovae is in the process of “delayed neutrino stops in the central region when its density goes be- heating”5 . In almost all simulations for large mass yond the nuclear matter density with a strong shock stars one sees that the shock wave moving outward starting to travel outward1. This shock wave, even- fast loses energy in dissociating the nuclei in the over- tually hitting the outer mantle in a few seconds and lying matter and soon becomes an accretion shock. supplying the explosion energy of a few times 1051 This shock gets revitalized over the much longer ergs, is believed to be the cause of type II supernova timescale of seconds through the absorption of a small explosion. During this process, the binding energy re- fraction of the thermal neutrinos that radiate out with leased comes out almost completely as neutrinos and each neutrino depositing energy of the order of 10 antineutrinos of three different ﬂavors (e, µ and τ) in MeV. Large convection in the central regions also the “cooling phase” with the total energy release of helps this process. the order of 1053 ergs. Let us discuss the emission of the neutrinos in some more detail. Firstly during 3 The Neutrino Oscillation Probabilities the early stage of the collapse (densities less than 1012 g/cc) neutrinos are produced through neutronization

να The ﬂavor eigenstate created inside the super-

ν nova can be expressed as a linear superposition of the £¥¤§¦ ¨ © ¦ ¤ ¨ ©¤

e N Z N 1 Z 1 e (1) ν ν

α ∑ mass eigenstates such that i Uαi i , where U is the unitary mixing matrix and the sum is over N ν α

ν neutrino states. After time t, the initial evolves

£¤ ¤

e p n e (2)

iEit

¦ © ν ν

α ∑ £ to t i e Uαi i where Ei is the energy of th where only ν (not ν¯) are produced. At lower densi- the i mass eigenstate. Then the probability of ﬁnd- e e ν ν ties these neutrinos have mean free path much larger ing a ﬂavor β in the original α beam after traveling than the core radius and hence escape. But the to- a distance L in vacuum is given by tal energy of these neutronization neutrinos is much δ

Pαβ αβ

smaller than that in the cooling phase. Even then it ∆ 2

is possible to detect them for nearby galactic super- 2 mi jL

¨ 2 4 ∑ UαiUβiUα jUβ j sin 1 27 (3) novae at distances within 1 kpc . These neutrinos can E j i give information about the temperature and composi-

∆ 2 2 2 tion of the core. where mi j mi m j is the mass squared difference. The main neutrino emission is during the cooling Over the last few years the idea that neutrinos are phase where the thermal ν/ν¯ are produced through not massless but have small masses has become estab- pair production and other processes3 . Out of these lished as a result of Super-Kamiokande (SK) and SNO νµ , ντ , ν¯µ and ν¯τ , called collectively as νx, interact which have ﬁrm evidence for atmospheric and solar

6 11 with matter only through neutral current whereas νe neutrino oscillations . The SK atmospheric neu-

2 3 2 ν ∆ and ¯ have both charged current and neutral current trino data demand m 3 10 £ eV and almost e 32 interaction with matter. As the matter is neutron-rich maximal mixing (sin2 2θ 1) 6 while the global so- 23

ν ν ∆ 2

the ’s interact more with matter than the ¯’s. These lar neutrino data is best explained if m 6 1 e e 21

5 2 2 θ 10, 12 £

neutrinos deep inside the core are in equilibrium with 10 eV with large mixing angles (tan 0 41) . the ambient matter and their energy distributions are Very recently the KamLAND reactor antineutrino dis- close to Fermi-Dirac as seen through simulations and appearance experiment 13 provided conclusive con- through the analysis of 1987A neutrinos4 . As the stel- ﬁrmation of the LMA solution to the solar neutrino lar core has a strong density gradient, electron type problem, with mass and mixing parameters absolutely neutrinos can stay in equilibrium upto larger radius consistent with the solar neutrino results. The global NEUTRINOS FROM SUPERNOVAE 125

14 n

' ρ &

analysis of the solar and the KamLAND data gives very well approximated by a power law r Cr "

∆ 2 5 2 2 θ 18 ! " m 7 17 10 eV and tan 0 44. The with n 3 in the core . 2

CHOOZ reactor experiment restricts sin θ 0 1 for Neutrino oscillation probabilities may also be sig- 13 #

∆ 2 $ 3 215 m 10 " eV . The only other positive signal for niﬁcantly affected inside Earth as the neutrinos tra- neutrino oscillations comes from the accelerator ex- verse the Earth matter19. Thus the neutrino oscillation periment LSND which requires ∆m2 % eV2 and mix- probability is given by

2 θ % 3 ing angle small (sin 2 10 " ). To include LSND N

in the framework of oscillation one needs to extend m P ∑ Pα P + β (6) the number of neutrino generations to four, or in other αβ i i , i * 1 words, include a sterile neutrino. However with the latest SNO data on solar neutrinos and the ﬁnal data where from SK on atmospheric neutrinos, both the “2+2” N 2 2 m m m

and “3+1” 4-generation scenarios fail to explain the Pα ∑ Uα ν ν (7) 1

i j i 0 j

- - - -

global neutrino data. While “3+1” is inadequate in j * 1

- - -/. - explaining the combined accelerator-reactor data in-

is the probability that a να (α e µ τ) produced in- , cluding LSND, “2+2” cannot accommodate the solar , ν 16 side the supernova core would emerge as a i (i and atmospheric neutrino data together . m

1 2 3) at the surface of the supernova, Uα are the ele- , Since galactic supernova neutrinos with energies , j

ments of the mixing matrix at the point of production

% % % 20

10 MeV travel distances 10 Kpc ( 3 ! 10

and ν νm 2 is the probability that a ν m state in

1 1

0 0 0 m), the coherent term in eq.3 becomes important only 0 i j j

matter appears as the state ν at the supernova sur-

% 0 ∆ 2 19 2 . i for m 10 " eV . Thus supernova neutrinos can i j face in vacuum. This is the so called “jump probabil- be used as probes for mass squared differences, not ν ity”. P + is the probability that the mass eigenstate possible to detect with any known terrestrial source. iβ i arriving at the surface of the Earth is detected as a ν However for the solar and atmospheric mass scales β ﬂavor state in the detector. Depending on whether the given above the oscillatory term would average out to

neutrinos cross the Earth or not, P + maybe different 1/2. iβ

from U 2, where U is the element of the mixing 0 The expression (3) would have been correct/exact 0 βi βi if the neutrinos were traveling in vacuum. However matrix in vacuum. for the supernova neutrinos things are a little compli- Since to a good approximation the average energy cated since they are created deep inside the core and and the total ﬂuxes of νµ , ν¯µ , ντ and ν¯τ are same, for traverse through extremely dense matter before they mixing between only active neutrino ﬂavors the only ν come out into the vacuum. As the neutrinos move relevant oscillation probability that we need is the e

in matter they undergo scattering with the ambient survival probability Pee which is given by eq.6 with α β electrons. While all the active neutrino flavors scat- e. ter electrons by the neutral current process, only the Two Flavor Oscillations νe (and ν¯e) have charged current interactions as well. This significantly affects neutrino oscillations param- To begin with let us for simplicity assume that ν eters as the e picks up an additional matter induced there are just two neutrino flavors, νe and another ac- 17 mass term tive flavor νa which may be νµ or ντ . The effective

mixing angle in matter is given by

' ( & ' A & r 2 2GF NAne r E (4) where G is the Fermi constant, N the Avogadro’s ∆m2 sin2θ

F A

tan2θm & r (8) '

& ∆ 2 θ

& ' number, ne r the ambient electron density in the su- m cos2 2 A r pernova at radius r and E the energy of the neutrino beam. In appropriate units Since the density inside the supernova core where the

∆ 2 '3

ρ neutrinos are created is extremely high, A & rs m ' & ' A & r r E

! & ' θ π ) 2 15 14 10 Ye r 3 (5) and m 4 2. Hence the survival probability Pee eV gm ) cm MeV

given by eqs.6 and 7 reduces to

' & '

where Ye & r is the electron fraction and ρ r is the

& 2 ' + matter density proﬁle in the supernova which can be P P P + 1 P P (9)

ee 5 J 1e J 2e , 126 SANDHYA CHOUBEY AND KAMALES KAR

where P ν νm 2 is the jump or the crossing the Earth) and ∆m2 are the mixing angle and the mass

7 ;<7 J 687:9 1 2 e probability from one neutrino mass eigenstate to the squared difference inside the Earth’s mantle. If the other at resonance. If P 0 the neutrino propaga- neutrinos cross both the mantle as well as the core of J = tion in matter is called adiabatic, otherwise it is non- the Earth then adiabatic. When P 1 then we encounter the ex-

J > G G ψM ψC M i k M C i i A I ∑ U e Uα Uα e

treme non-adiabatic situation. In ref.[20] it is shown 2e 6 ek k i

O O

that the double-exponential parametrization of P de- i O j k P J α P β σ

rived in ref.[21] and used extensively for the solar neu- G ψM C M i j M

trinos, works extremely well even for the supernova UβiUβ je Uσ jUσ2 (16)

D EEE density proﬁle. In this parametrization the jump prob-

where (i j k) denotes mass eigenstates and (α β σ)

D D D ability is expressed as D denotes ﬂavor eigenstates, U, U M and UC are the

γ 2 θ γ mixing matrices in vacuum, in the mantle and the

BC@ ?A@ B exp ?A@ sin exp P (10) M C

J 6 core respectively and ψ and ψ are the correspond-

?A@ B D EEE 1 @ exp γ ing phases picked up by the neutrinos as they travel where γ is given by through the mantle and the core of the Earth. Then the

G probability is given by ∆m2 dln n 1 γ π e (11)

6 2

E EEE

F F I E dr I

r H r P A (17) 7

mva 6Q7 F

F 2e 2e

E EEE

F F

G F F 1 dln ne The additional mass term picked up by the ν¯e

The density scale factor dr gives a measure of

F F

? B

as it moves in matter is @ A r . Since the crucial F

the deviation from adiabaticityF and is calculated at the F position where we have F maximum violation of adia- combination which decides matter effects is the ratio

2 BR ? ∆ ¯ baticity (mva)20, 22. That is where A r m , the antineutrino survival probability Pee is identical to that for the neutrinos if we change the sign

2 ∆ 2 B A ? r ∆m (12) of m , which is equivalent to swapping of the mass

mva 6 EEE E 20 labels 1 S 2 . Then the expression for P¯ee is similar Note that the position of mva (rmva) is different from to that for Pee and is given by

the position of resonance (rres) which is given by the

I I

? B condition P¯ P¯P¯ 1 @ P¯ P¯ (18)

ee 6 J 1e J 2e

D EEE

2 B A ? r ∆m cos2θ (13)

res 6 where

E EEE

γ θ BT@ ?A@ γ B The form of the probability P depends crucially exp ?A@ cos exp ie P¯ (19)

on the trajectory of the neutrinos inside the earth and J 6

EEE

γ D ?A@ B 1 @ exp hence on the direction of the supernova. If the direc- 2 2 tion is such that the neutrinos cross only the mantle of where we replace cos θ with sin θ (swapping 1 S 2) the Earth then the amplitude is given by and γ is calculated at rmva given by the same eq.12. ¯ G φ e The expressions for the oscillation probabilities P e i j e 2e

A I ∑U e ν ν (14)

9 7 ;

2e 6 e j j i EEE

D are again similar to those for the neutrinos j

e 2 P¯I sin θ where Ue j is the mixing matrix elements in the Earth’s 2e 6 mantle and φ e is the phase. Therefore the expression ∆¯ J m L

j θ¯ θ¯ θ 2 K e

@ B

sin2 e sin ? 2 e 2 sin 1 27 (20)

? @ B I

for P I 1 P is given by

E DUEEE 2e 6 1e E

2 P I sin θ 2e 6 where eq.20 is for transition probability in Earth for ∆ θ¯ J m L one slab approximation, with the mixing angle e

2 K e

@ B

sin2θe sin ? 2θe 2θ sin 1 27 (15) LMDNEEE E E given by where L is the distance traversed inside Earth and θ ∆ 2 θ e θ¯ m sin 2 tan2 J (21)

(given by eq.8) but with A calculated in the mantle of e 6 ∆ 2 θ

BVE EEE m cos2 A ? r NEUTRINOS FROM SUPERNOVAE 127

¯W The expression for P2e for two slabs can also be ing the double exponential forms with

similarly derived from eq.17 with the corresponding 2

^ γ θ ^ γ _

exp sin _ exp

] ]

changes for the antineutrinos. P ] L 12 L (25) \

L g

^ γ _

1 exp aaa ] ] L

γ θ ^ γ

Three Flavor Oscillations ^ _

exp sin _ exp

] ]

P ] H 13 H (26) \

H g

^ γ aaa

1 exp _ ] We now consider a more realistic scenario with ] H mixing between three active neutrinos, with one of where γ is calculated using eq.11 at the position of L h H the mass squared differences corresponding to the so- maximum violation of adiabaticity corresponding to 2 5 2 lar scale (∆m 10 Y eV ) and the other one corre- 21 X the lower (r ) and the higher scales (r ) respectively ∆ 2 3 2 L H sponding to the atmospheric scale ( m 10 Y eV ). 31 X given by the relations In this case the neutrinos encounter two resonances,

2 2

θ ^ ∆

the ﬁrst one corresponding to the higher scale at a cos A r _ m (27) \ 13 L 21 g

higher density in the supernova and the next one cor- ∆ 2 aaa ^

A r _ m (28)

H \ 31 aaa responding to the lower mass scale further out in the a mantle. Though from solar neutrino data we know For the antineutrinos ν¯e the matter term is nega-

that the sign of ∆m2 ∆m2[ is positive10 (∆m2 tive so as in the two-generation case the mixing angle \ 21 Z i j m2 m2), there is still an ambiguity in the sign of for the antineutrinos in matter is given by i ] j ∆m2 ∆m2 . It would be hard to determine the sign 2

Z ∆ θ 32 atm ¯m m21 sin2 12

2 θ ^

∆ tan2 r _ (29)

of m in any of the current and planned long base- 12 \ 2 2

32 ∆ θ θ ^ _ m cos2 cos A r aaa line oscillation experiments and only a neutrino fac- 21 12 f 13 ∆ 2 θ

tory would be able to resolve this ambiguity. However ¯m m31 sin 2 13 θ ^

tan2 r _ (30) 13 \ 2

2 2 ∆ θ ^ _ m cos2 A r aaa for the supernova neutrinos the sign of ∆m ∆m 31 13 f 32 X 31 is crucial and thus the supernova neutrinos can be used which implies that at the point of production

very effectively to give us the neutrino mass hierarchy. cos2θ¯m 1 cos 2θ¯m (θ¯m 0 θ¯m ) and the an-

d d d 12 dif 13 12 13 νm Direct Mass Hierarchy Since the density at the neutrino tineutrinos are created in pure ¯1 state. Thus for the 2 2 20

^ ∆ ∆ antineutrinos the survival probability is given by ` source (rs) is very high, A rs _C` m31 m21 and we

can solve the eigenvalue problem perturbatively to get

W W

¯ ^ ¯ ¯ ¯ ¯

P 1 P _ P P P (31)

] g

the mixing angles for neutrinos20, 23, 24, 25 in matterb ee L 1e f L 2e aaa where the jump probability P¯ for the antineutrinos is ∆ 2 θ L

m m21 sin2 12 given by θ ^

tan2 r _ (22)

12 \ ∆ 2 θ 2 θ ^

m cos2 cos A r _baaa 12 ] 13

21 γ 2 θ γ ^ ^ _

exp cos _ exp

] ] ∆m2 sin2θ P¯ L 12 ] L (32)

m 31 13 L \

θ ^

^ γ

tan2 r _ (23)

\ aaa

13 1 exp _ ]

∆ 2 θ ] L ^ aaa m cos2 A r _ 31 13 ] γ with L deﬁned by eq.27 and eq.11.

∆ 2 ^ ` At the point of production since A r _c` m s 31 Inverse Mass Hierarchy If ∆m2 ∆m2 is negative, the 2 m m 31 d 32

∆m from eqs.22 and 23 we see that θ π e 2 θ d 21 12 d 13 ν m mixing angles for the neutrinos are still given by the and neutrinos are created in almost pure 3 states ∆ 2 c eqs.22 and 23 but with the sign of m31 reversed. At and the expression for the survival probability for this θ m π θ m

the production point then e 2 while 0 and d 12 d 13 three-generation scenario is ν ν m e j s are thus in almost pure 2 states and the neutrino

survival probability is

W W W

^ ^ _

P P P P P 1 P _ P 1 P P (24)

] ]

f g

ee H L 1e f H L 2e H 3e

aaa

W W ^

P P P 1 P _ P (33)

\ ] ee L 1e f L 2e where PH and PL are the jump probabilities for the aaa high and low density transitions respectively. Just like with the jump probability PL given by eqs.25, 27 and in the two-generation case they can be calculated us- 11. b θ ν If we choose the standard parametrization of the mixing matrix, the mixing angle 23 does not affect the e survival probability and thus we can either choose to rotate it away or even put it to zero without loss of generality. c ∆ 2 12 Note that we take the sign of m21 as k ve in accordance with currently favored LMA MSW solutions to the solar neutrino problem . 128 SANDHYA CHOUBEY AND KAMALES KAR

With inverse hierarchy the antineutrino mixing an- for the neutrino with the target particle, D is the dis- ∆ 2 gles are given by eqs.29 and 30 with the sign of m31 tance of the neutrino source from the detector (taken ν νm reversed. Therefore ¯e are created in pure ¯3 states as 10kpc for galactic supernovae considered here), n is and their survival probability is20 the number of detector particles for the reaction con-

sidered and fν m Eν is the energy spectrum for the

α p

q q o q

¯ o ¯ ¯ ¯ ¯ ¯ m

P lnm 1 P P P P P P 1 P P (34) ε

r r p sss ee p

L H 1e L H 2e H 3e neutrino species involved, while m Eν is the detector p efﬁciency as a function of the neutrino energy. with P¯ given by eq.32 and P by eq.26. L H The main reaction process by which the water Cerenk˘ ov detectors like SK would observe the super-

4 Event Rates in Terrestrial Detectors nova neutrinos is |

Neutrinos are created deep inside the supernova core ν¯ p { e n (40)

r sss e r ν ν as o ¯pairs. They stream out through the supernova core, mantle and envelope and reach the Earth However the other neutrino species are also observ- 17

t ν after traveling distances 10 km. In the presence able in SK through the o e elastic scattering pro- of neutrino oscillations there is a modiﬁcation of the cesses

neutrino ﬂuxes as they oscillate into one another and }

ν e }~{ ν e (41)

r sss the resultant neutrino beam at Earth is given by i r i

0 0 0

m m m m m m

Nν l P E Nν t Pµ E Nν t Pτ E Nν t

pVr p pVr p p e ee p e e µ e τ In addition to the above two reactions, super-

0 0 nova neutrinos can also be traced in the water

m m m m m

l P E Nν t 1 P E Nν t (35)

pr pp p sss ee p e ee x ˘ 16 0 0 Cerenkov detectors through reactions involving O.

¯ o ¯

m m m m m

N l P E Nν t 1 P E Nν t (36)

pVr pp p sss ν p ¯e ee ¯e ee x The oxygen nuclei in water are doubly closed shell 1 1

0 0 and have a very high threshold (Eth) for excitation. o

m m m m m m

Nν l 1 P E Nν t 1 P E Nν t

pVr r pp p ee pp ee x 2 e 2 x Thus solar neutrinos are unable to have charged or (37) sss neutral current reactions on oxygen. But supernova 1 0 1 0 neutrinos with much larger energy range can trigger

o ¯ ¯

m m m m m m

N l 1 P E Nν t 1 P E Nν t

pVr r pp p ν¯ ee pp ¯ ee x 2 e 2 x charged current reactions26

(38) sss

16 16 }

ν O { e F (42)

r sss ¯ ν ν¯ e r

where Pee and Pee are the e and e survival probabili- 16 16 ν |

0 ¯ O { e N (43)

r sss

e r

ties given in the previous section and Nν m t is the neu- α p trino ﬂux produced inside the supernova core given 27

0 and neutral current reaction

l m m m

by Nν m t Lν t Eν t , where Lν t is the neu-

puwv px p α p α α α

trino luminosity and Eν m t is the average energy. px

v α 16 16

ν O { ν O (44)

sss r In the above expressions we have used the fact that x r x

the νµ ν¯µ beam is indistinguishable from the ντ ν¯τ 16 u u γ where O decays by n, p or emission. The reaction ν beam in ﬂux and energy and call them x. thresholds for the charged current reactions (42) and The current and planned terrestrial detectors are (43) are 15.4 MeV and 11.4 MeV respectively26 . The capable of observing the supernova neutrinos through electrons from the charged current reactions on 16O various charged and neutral current processes. The can be distinguished in principle from the positrons differential number of neutrino events at the detector from ν¯e capture on protons (cf. reaction (40)) by for a given reaction process is their angular distribution. While the 16O events are backward peaked and electron scattering events are 2 strongly forward peaked, the ν¯p events are mostly

d S n σ ε e

m m m

l ∑ Nν fν Eν Eν Eν (39)

p pzysss 2 α α p isotropic. Thus even though all these processes are dEν dt α 4πD detected via the Cerenk˘ ov , it is possible to disentan- where α runs over the neutrino species concerned (e, gle them. µ τ , ), Nνα is the neutrino ﬂux at the detector given by In heavy water (D2O) detectors like SNO, in ad- σ

eqs. 35)–(38 and m Eν is the reaction cross-section dition to the reactions involving elastic scattering off p NEUTRINOS FROM SUPERNOVAE 129 electrons and reactions on 16O, neutrinos can be ob- Table I served by the charged and neutral current breakup of [Signal from a galactic supernova for complete conversion] The expected deuteron number of neutrino events in SNO. To get the number of events in SK, one has to scale the number of events in H2O given here to its ﬁducial mass

of 32 kton. The column A corresponds to massless neutrinos, column B to

e d p p e (45)

neutrinos with complete ﬂavor conversion (P 0). The mixing angle

ν ee

¯e d n n e (46) 12 is considered to be very small corresponding to the SMA solution and ¯ ν

hence Pee 1. The i here refers to all the six neutrino species.

ν ν

x d p n x (47) A B

The charged current reactions are detected by the ν

reactions e d p p e 75 239

˘ ν

Cerenkov radiation from the electron/positron. The in ¯e d n n e 91 91

ν ν

1 kton i d n p i 544 544

neutral current reaction, which will give us informa-

ν ν

D2O e e e e 4 6

ν ν

tion about the total neutrino ﬂux from the supernova, ¯e e ¯e e 1 1

ν ν ν ν

¯ ¯

τ µ τ µ τ µ τ

irrespective of whether they oscillate or not, is de- µ e e 4 3

16 16

νe O e F 1 55

tected by the capture of the released neutron, either 16 16 ν

¯e O e N 4 4 35 ν 16 ν γ

on deuteron or on Cl (salt). In the last phase of SNO i O i X 21 21

the neutral current process will be detected by directly reactions ν¯e p n e 357 357

ν ν

in e e e e 6 9

observing the neutrons in helium proportional coun- ν ν

1.4 kton ¯e e ¯e e 2 2

ν ν¯ ν ν¯

µ τ µ τ µ τ µ τ

ters. H2O e e 6 5

ν 16 16

e O e F 2 86

There have been various attempts before to esti- 16 16

ν¯e O e N 6 6

mate the effect of non-zero neutrino mass and mixing 16 ν ν γ

i O i X 33 33

on the expected neutrino signal from a galactic supernova. With vacuum oscillations we can expect an in- 28, 29 crease in both the νe and ν¯e signal . Some special Hence the νe ﬂux though depleted in number, gets cases where the matter effects inside the supernova are enriched in high energy neutrinos and since the de- negligible and one has almost pure vacuum oscilla- tection cross-sections are strongly energy dependent, tions have been considered in ref.[29]. However for this results in the enhancement of the charged cur- the currently most preferred neutrino mass spectrum rent signal29. Since the cross-section for the 16O re- one expects to have substantial matter effects. Mat- actions have the strongest dependence on energy, they

ter enhanced resonant flavor conversion has been ob- are most affected by neutrino oscillations and can be 28 30 35 served to have a large effect on the νe signal . used as an effective way to study neutrino properties Table I gives the calculated number of events ex- from supernova neutrino detection. For the neutral pected from the main reactions in H2O and D2O, for current sector the number of events remain unchanged a typical galactic supernova with a total luminosity of as the interaction is flavor blind. 53 about 3 10 ergs. The numbers here correspond to a From a comparison of the predicted numbers in three-flavor oscillation scenario with complete flavor Table I it is evident that neutrino oscillations play θ conversion. The 13 considered here is large so that a significant role in supernova neutrino detection. νµ ντ both PL and PH are almost zero, the propagation is al- As the average energy of the is greater than θ ν most adiabatic and hence Pee 0. The 12 considered the average energy of the e, neutrino flavor mix- ¯ d

is very small and hence Pee 1 . For the cross-section ing modiﬁes their energy spectrum. Figure 1 taken

z z

ν ν ν ν

of the e d ¯e d x d and ¯e p reac- from ref.[33], shows the comparison between the to- tions we refer to Burrows3. The cross-section of the tal charged current events as a function of the elec-

ν ν ν ν

e ¯e e and x e scattering has been taken tron/positron energy observed in H2O ( ¯e p events)

ν ν ν from ref.[36] while the neutral current x O scat- and D2O (sum of ed and ¯ed events) for small and 2 θ ω θ tering cross-section is taken from ref.[37]. For the large values of the mixing angle sin 2 12 ( 12).

16 16 16 16 2

ν ν θ ε O e e F and O ¯e e N reactions we refer The value of sin 13 is large ( 0 08) which to [26] where we have used the cross-sections for the implies that the neutrino propagation is fully adia- detector with perfect efﬁciency. batic. Figure 2 also taken from ref.[33], shows the d The Table I is just for the purpose of illustration only. For the LMA solution the νe events would still remain the same, while the ν¯e events would be slightly enhanced. 130 SANDHYA CHOUBEY AND KAMALES KAR

0 12

0 0 20 40 60 0 20 40 60

Fig. 1 Total event rates (from combining the individual νe d and νe d) are shown as a function of the electron/positron energy, Ee, for

ω θ ε 2 θ

two different values of , and for sin 0 08 so that the propagation is fully adiabatic. The solid lines represent 12 13 the no mixing case. The dotted and dashed lines are due to the effects of 3- and 4-ﬂavour mixing. Results from a 1 kton water

detector (from νe p alone) are shown on the right, for comparison. This ﬁgure is taken from ref.[33].

0 12

0 0 20 40 60 0 20 40 60

Fig. 2 Same as Fig. 1 but for ε 0 so that non-adiabatic effects are included. This ﬁgure is taken from ref.[33]. NEUTRINOS FROM SUPERNOVAE 131

2 θ ε ν ν corresponding plots when sin is small ( 0), the ¤ ¯direction for each event was also measured. 13 which implies that the neutrino propagation is non- There were also 5 events at Mt. Blanc and 3 in Baksan adiabatic. In both the figures the solid lines give the no at the same time4. A number of analyses were done in oscillation distribution and the dotted line the events the next few years and the results more-or-less agreed for three-generation scenario, while the dashed lines with the typical values given in section 2 for the lumi- correspond to the distribution for a four-generation nosities, average energies and spectra of the neutrinos, schemee. The figures show that for the LMA solu- though the IMB events gave average energy and tem- tion (upper panels) there is a shift in the spectral peak perature consistently higher40, 41. in D2O for both three as well as four generations, the Also with such small samples there were large er- shift being more pronounced for the high ε (adiabatic) rors in the extraction of the SN parameters. However case. The corresponding shifts in H2O are less. The even though the statistics were poor the SN1987A SMA cases shown in the lower panels are of less in- data was used extensively to study the neutrino mass terest now since SMA solution is now ruled out. The and mixing patterns. In the context of two flavors such figures show that by comparing the signal in SK and analysis was done by Smirnov et al42 and Jegerlehner SNO one can distinguish between the three and four- et al43 and recently it was extended to three flavors generation scenario. But again the four-generation in44. The authors of ref.[44] claim that the inverse θ schemes are largely disfavored by the global solar and mass hierarchy is disfavored by the data unless 13 16 2 4 atmospheric neutrino data . is very small, sin θ 10 . However the authors 13 ¦ The potential for detecting supernova neutri- of ref.[45]dispute this observation and conclude that nos in scintillation detectors like Borexino38 and the SN1987A data cannot distinguish between the MiniBOONE39 have been recently considered. The direct and inverted mass hierarchies. In ref.[46]the 12C in these detectors can be excited through charged SN1987A data is combined with the global solar neu- current and neutral current interactions with the su- trino data and it is found that while all the other large pernova neutrinos. The charged current reaction mixing angle solutions (LOW-QVO and VO) are dis-

12 12

( C e e N) has a threshold of 17.34 MeV while favored, the LMA solution remains the only allowed

12 ν 12

¡¢ that for ( C ¯e e B) has a threshold of 14.4 MeV. solution which can explain the SN1987A and the so- But here again the cross-sections have a strong en- lar neutrino observations simultaneously. Nowadays ergy dependence and these events show a dramatic after the evidence of neutrino mass and mixing one increase with large conversion with oscillations com- has to work on the “inverse problem” using SN 1987A pared to the no oscillation case. The neutral current data to extract the original neutrino spectra using real-

12 ν ν 12

£ events through ( C x x C ) can be used to put di- istic (Large Mixing Angle solution) scenario of neu- rect limits on the neutrino masses using the time delay trino oscillation47, 48. techniques briefly discussed in the following section. b) Detection of Neutronisation Neutrinos: The neutrinos emitted during the collapse phase due to the 5 Other Effects of Neutrino Mass and Mixing neutronisation give rise to a luminosity small compared to the thermal post-bounce neutrinos discussed In this section we briefly touch upon a number of ar- above, but for close enough (1 kpc) galactic super- eas where the mass and mixing of supernova neutrinos novae they can still be detected by SK and SNO2. can lead to interesting effects: The measurement of the fluence of these neutrinos at a) SN 1987A: The eleven SN 1987A events at KII SNO and the distortion of the spectrum detected at were observed within a timespan of 5.6 secs and with SK, in particular the ratio of the calorimetric detection an energy range of the positron/electron released in of the neutrino fluence via the neutral current chan- the water Cerenkov detector from 7.5 MeV to 35.4 nel to the total energy integrated fluence observed via MeV. Similarly IMB had the eight events within a time the charged current channel at SNO can yield valu- of 12.4 secs and with the electron energy range of 20 able information about the mass squared difference

4 49 MeV to 40 MeV . The angle of the e ¡¥¤ e path to and mixing . e We have not considered the four-generation scenario in this review. For a detailed discussion on the four-generation neutrino mass spectrum and its effects on supernova neutrino detection refer to34, 33. 132 SANDHYA CHOUBEY AND KAMALES KAR c) Delay of Massive Supernova Neutrinos: For a neutrino signal in present and future neutrino detec- neutrino of mass m (in eV) and energy E (in MeV) tors can give valuable information about the mecha- the delay (in sec) in traveling a distance (in 10 kpc) is nism of shock propagation and the delayed neutrino 52

2 heating . When the shock front moves through the

MSW conversion region the µ ¬ τ to e type neutrino neglecting small higher order terms. If we assume conversion gets stopped during that time leading to a that the mass of the νx is much larger than those of detectable dip in the neutrino energy/count rate. νe and ν¯e then the neutral current events will have a e) r-process nucleosynthesis: The neutrino-driven- delay compared to the charged current events. This wind environment in the late time (about 3–15 secs difference due to time-of-ﬂight for neutral current sig- after bounce) of core collapse supernova is consid- nal compared to the charged current signal in SNO ered to be a very promising site for the rapid neutron can determine νµ and ντ mass down to 30 eV, an im- capture process (r - process) for producing neutron- provement by many orders of magnitude over current rich heavy elements. The capture rate of νe and ν¯e on estimates37. One also sees that one can construct50 use- neutrons and protons respectively determine the elec- ful diagnostic tools for neutrino mass and mixing us- tron fraction, Ye and for successful r-process Ye must ing the charged and neutral current events as a func- be less than 0.5. This is favored by the higher aver- tion of time but only for mass squared differences of age energy of ν¯e; however if oscillations between νe 2 the order of tens of eV . and νx takes place giving a stiffer νe spectrum, the d) Effect of Neutrino Mixing on Delayed Neutrino r-process may get stopped. Thus to get r-process nu- Heating: To generate a stronger shock in the super- cleosynthesis operative one excludes53 the parameter

∆ 2 2 2 θ 5 ¯ nova models one thinks of mechanisms of extra heat- space m a few eV and sin 2 ® 10 . Recently ing in the region near the shock. As the heating rate the effect of active-sterile neutrino transformation on due to neutrino capture depends on the square of the the r-process was also considered54 and initial work neutrino temperature, if the νµ or ντ emitted from the showed that it is possible to get sufﬁciently neutron neutrino sphere can get converted to νe before reach- rich matter to activate rapid neutron capture. ing the shockfront, it heats up the shock more. Fuller et al51 in their numerical calculations got 60% more Acknowledgement ν τ heating but with the « neutrino mass of 40 eV. How- We thank G Dutta, D Indumathi, M V N Murthy and G ever with realistic solar and atmospheric mass squared Rajasekaran for allowing us to reproduce two of their ν differences one does not get this conversion to e in- ﬁgures. side the stalled shock. Recently it is proposed that the

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