1 Detecting Supernova Neutrinos X.-H. Guo Beijing Normal University

2 Contents I. SN neutrinos’ production and propagation II. Detection of SN neutrinos at neutrino experiments III. Possible information on small  13 from detection of SN neutrinos

3 I. SN neutrinos’ production and propagation Supernova explosion: natural laboratory to study fundamental issues of physics and astrophysics. Explosion mechanism is not understood completely. Two types of SN explosion. Type I: without lines of hydrogen; Type II: with strong lines of hydrogen. Type I: Usually a white dwarf (mainly C and O) accretes material from a companion star. Energy is from thermonuclear reactions. Gives out gigantic firework display  Disruption of the dwarf.

4 Type II: Energy from gravitational core collapse (Zwicky & Baade, 1934) when the star mass is bigger than 8 solar masses. Inner part of star collapses to neutron star or black hole. Intensive neutrinos are emitted for a very short period of time followed by an intensive electromagnetic radiation. Observation SN neutrinos can serve as an early warning for the optical emission of a type II SN. SN neutrinos have valuable information of deep inside the core; can be helpful to study of intrinsic properties of neutrinos. Total energy release: approximately gravitational binding energy of the core. Neutrinos take away about 99% of the total energy.

5 Core collapse process While evolving, stars get energy from burning hydrogen to helium. Then heavier helium settles to the core of the star. Towards the end of hydrogen burning, gravitational contraction heats up the core  helium burning to Carbon. Heavier carbon settles to center of core, H and He floating above it. Similar processes repeat, carbon  neon  oxygen  silicon  iron (most stable nucleus). When iron core grows to exceed Chandrasekhar mass, degenerate electron Fermi pressure fails to support gravitational pull of core, electron capture on Fe nuclei occurs predominantly via 56 Fe + e -  56 Mn + ν e. Absorption of electrons leads to loss of electron pressure support and begins core collapse. Core proceeds to contract under the pull of self gravitational force.

6 Core collapse process (cont.) When the central density ρ ≥ g cm -3, electron neutrinos begin to be trapped in the core (the mean free path of neutrino ( ~ ρ -5/3 ) is smaller than the size of core ( ~ ρ -1/3 ) ). The surface determining the escape or trapping of neutrinos in the core: neutrino sphere. Neutrinos produced within (outside) neutrino sphere cannot (can) escape freely from the core. When nuclear density ( ρ ≥ 3 X g cm -3 ) is reached in the collapsing core, repulsive nuclear force halt the collapse of inner core driving a shock wave into outer core. The shock propagates into outer core  dissociate nuclei into free nucleons. Electron capture process e - + p  n + ν e generates a huge amount of electron neutrinos and are liberated suddenly as shock waves pass through neutrino sphere: called neutronization burst. Duration of neutronization: less than 20ms. Breakout of electron neutrinos is almost simultaneous with appearance of all other neutrino species (last for O(10) seconds): via e + e - annihilation, electron neutrino anti-electronic neutrino annihilation, and nucleon-nucleon bremsstrahlung.

7 First observations of the type II SN: Kamiokande II (11 events) and IMB (8 events) observed in 13 seconds in (Large Magellanic Cloud, closest supernova since the galactic supernova in the 17th century. Progenitor star mass ~ 10 M sun, distance 50kpc.) Besides the information on the physical state deep inside SN, SN neutrinos can also bring information about the outer structure of SN through neutrino oscillation while neutrinos pass through mantle. Average energy of emitted neutrinos reflects temperature of matter around neutrino sphere. Interactions of electron neutrino and anti-electron neutrino are stronger than other flavor neutrinos. Since there are more neutrons than protons in the star, electron neutrino couples more strongly than anti-electron neutrinos. This leads to

8 Energy spectrum Since cross section of interactions depend on neutrino energy, the energy spectra of neutrinos are not simple blackbodies. As a result, the energy spectrum has a pinched shape compared with the Fermi-Dirac distribution. One popular way to parametrize neutrino spectrum is L α (0) (T α ): luminosity (temperature) of ν α ; η α : pinching parameter; E SN (0) : total energy release. Typical values from numerical simulations are ( ~ 3.15 T α ):

9 Level Crossing When SN neutrinos of each flavor is produced they are also mass eigenstates due to extremely high matter density environment. While they propagate to the surface of SN, they experience level crossing (neutrinos jump from one mass eigenstate to another) in the MSW (Mikheyev-Smirnov-Wolfenstein) resonance regions. These regions are far from the core. Two MSW resonance regions: determined by two pairs of neutrino mixing parameters: High resonance region (denser region): ρ H ~ g cm -3 ; Low resonance region (less dense region): ρ L ~ 20~200 g cm -3. Probability that neutrinos jump from one mass eigenstate to another at the high (low) resonance layer is denoted by P H (P L ). The large mixing angle (LMA) solution of the solar neutrino constrains P L =0. The level crossing diagrams are different for normal and inverted mass hierarchies. This leads to different forms for neutrino flux of mass eigenstates at the surface of SN.

10 Crossing probability at resonance point Using Landau-Zener formula, crossing probability was calculated at resonance region (T.K. Kuo, Rev. Mod. Phys., 1989). At high resonance region, where γ is adiabaticity parameter, βis mixing angle, F depends on density profile and mixing angle, N e is electron density. W hen γ>>1, P H =0. P H depends on neutrino energy, neutrino mass difference, neutrino mixing angle, and SN density profile.

11 SN neutrinos’ propagation in Earth After traveling through the cosmic distance, the neutrinos arrive at the surface of the Earth as incoherent fluxes of mass eigenstates. Neutrinos from SN explosion will go through some portion of the Earth before reaching detector. Earth effects have to be taken into account. Denote the original neutrino fluxes produced from core collapse as F α (0). Neutrino fluxes at Earth surface: Normal HierarchyInverted Hierarchy

12 Earth Matter Effect The treatment of the Earth matter effect has been discussed in detail in Dighe and Smirnov, Phys. Rev. D62 (2000) Ioannisian and Smirnov, Phys. Rev. Lett. 93 (2004) Ioannisian, Kazarian, Smirnov, and D. Wyler, Phys. Rev. D71 (2005) Centre of Earth Detector Incident angle AD OB X=AB R: radius of Earth h: depth of detector

13 Earth Matter Effect (Cont.) Let P ie be the probability that i-th neutrino mass eigenstate enters the surface of the Earth and arrives at detector as an electron neutrino. Then the flux of electron neutrino at the detector is F i is the flux of i-th neutrino mass eigenstate at the Earth surface, which is the same as the flux at SN surface. P ie obey the unitary condition In the case where the Earth matter effect is ignored, P ie =|U ei | 2

14 Earth Matter Effect (Cont.) After some straightforward derivations with the terms proportional to sin  13 being ignored, one obtains neutrino fluxes at detector (normal hierarchy): (inverted hierarchy):

15 Earth Matter Effect (Cont.) The probability P 2e has been calculated in Ioannisian and Smirnov, Phys. Rev. Lett. 93 (2004) by applying Schroedinger Eq. in low density matter (neglecting ): Number density of electrons in Earth

16 II. Detection of SN neutrinos at neutrino experiments Prediction of event numbers detected at neutrino detectors depend on: energy spectra of original neutrinos produced from SN core collapse, crossing probability at high resonance region in SN, Earth matter effects, and detector details. We let P H be two limiting values 0 and 1. For Earth matter effects, we use the realistic matter profile:

17 To calculate event numbers that can be observed through various reaction channels at current neutrino experiments, integrate the product of the target number N T, the cross section of each channel σ(i), and the neutrino flux function over the neutrino energy,  D: distance between SN and Earth, i: different channels At Daya Bay, liquid scintillator is Linear Alkyl Benzene (LAB), C 6 H 5 – C n H 2n+1, n=9~14. Let ratio of C and H be 0.6, then for total detector mass 300ton,

18 Cross Sections Inverse beta decay has the largest cross section: Neutrino-electron elastic scatterings: Charged-current capture of anti-electron neutrino on Carbon:

19 Cross sections (cont.) Charged-current capture of electron neutrino on Carbon: Neutral-current inelastic scattering on Carbon :

20 Event number for inverse beta decay (left) and neutrino-carbon reactions (right) at Daya Bay Maximum and minimum values: due to variations of T α and η α. Parameters: X.-H. Guo. M.-Y. Huang, & B.-L. Young, arXiv: [hep-ph] X.-H. Guo & B.-L. Young, Phys.Rev.D73:093003,2006.

21 What can be seen from Figs Earth matter effect depends on the incident angle of the neutrino, the mass hierarchy, and the flip probability P H. When the incident angle of SN neutrino is smaller than a value  0 ~ 90 o (L < 100km), Earth matter effect can be ignored for all reactions. Earth matter effect becomes large and reaches a maximum for  ~ 92 o o. When  is larger than about 100 o, the Earth matter effect is insensitive to . The inverse beta decay could have the largest Earth matter effect among all the channels: 7%. For neutrino-electron elastic scattering and reactions with 12 C, the maximum Earth matter effect could be as large as 2%. Variations of T α and η α may lead to 20~30% changes for the Earth matter effects.

22 Summary of current detectors. N (I) represents normal (inverted) hierarchy. We list types of liquid scintillator, detector masses, total numbers of targets (proton or deuterium), depth of detectors, location of detectors, and event numbers for inverse beta-decay process except for D 2 O at SNO (in this case we list the result for the heavy water reaction).

23 III. Possible information on small  13 from detection of SN neutrinos The crossing probability at high resonance region depends on neutrino energy, neutrino mass difference, mixing angle  13 and density profile of SN: Take the matter density profile of SN (at least in first few seconds of explosion) as: Then the adiabaticity parameter:

24 For small  13, F≈1. Then From the plot, when  13 =0, P H =1. When  13 varies between 0 o and 2 o, P H varies between 0 and 1. When  13 > 2 o, P H is nearly 0. The variation of P H depends on neutrino energy and parameter C.

25 At Daya Bay experiment, the sensitivity of sin 2 2  13 will reach 0.01, i.e. the sensitivity of  13 will reach about 3 o. If the actual value of  13 is smaller than 3 o, the Daya Bay experiment can only provide an upper limit for  13 as 3 o. However, if an SN explosion takes place during the operation of Daya Bay, roughly within the cosmic distance considered here, it is possible to reach a smaller value of  13.

26 For central values of T α, η α =0, and  = 30 o, the results for inverse beta-decay, neutrino-electron, and neutrino-carbon scattering. For other parameters, qualitative results are not changed. Variations of T α andη α lead to change of total event number ~ 50. For inverse beta-decay, for inverted hierarchy, event number varies between 122 and 172 when  13 changes between 0 o and 2 o. Variation of  13 due to C is small (~0.2 o ). For normal hierarchy, event number does not change with  13.

27 At the Daya Bay experiment, the event number of SN neutrinos can be measured in the inverse beta-decay. This will help us to get information about  13 smaller than 3 o if the mass hierarchy is inverted. If the actual case is the normal hierarchy, we may detect SN neutrino event numbers in the processes of neutrino-electron scattering and neutrino-carbon scattering. This, however, will be difficult for the Daya Bay experiment.

28 Other neutrino experiments For Super-K, Kamland, LVD, MiniBooNe, Double Chooze, Borexino, SNO (water), the main neutrino reactions are inverse beta-decay. For SNO (heavy water, 1000 tons of D 2 O), there are charged-current capture of electron-neutrino and anti-electron neutrino on deuteron: and neutral-current inelastic scattering of all flavors of neutrinos and anti-neutrinos:

29 Inverse beta-decay

30 SNO (heavy water) It can be seen that in the cases of both normal hierarchy and inverted hierarchy, event numbers of reactions of neutrinos with deuteron change obviously when  13 changes between 0 o and 2 o. So in both cases one can get information about small  13 by observing SN neutrinos. This is a unique advantage of SNO.

31 Concluding remarks Intensive neutrinos are emitted during SN explosion. Observation of SN neutrinos can serve as an early warning for the optical emission of a type II SN. By measuring the event numbers of reactions of SN neutrinos in various channels we can obtain information about the SN core; intrinsic properties of neutrinos; the Earth matter effect; the matter effect inside the SN; the neutrino mass hierarchy; the neutrino mixing angle  13 when it is between 0 o and 2 o.