1. Neutrino Burst from Supernovae and Neutrino Oscillation Katsuhiko Sato (Univ.Tokyo) Collaborators: K. Takahashi, S.Ando, T. Totani, K. Kotake, S. Yamada, T. Shimizu, S. Ebisuzaki J. Wilson, S. Dalhed, A. Burrows and T. Thompson J. Wilson, S. Dalhed, A. Burrows and T. Thompson -What is the effect of neutrino OSC on explosion and the detection? -Can we extract OSC parameters from the neutrino observations ?

2. Plan of this talk Introduction Introduction A brief review of gravitational collapse-driven supernova A brief review of gravitational collapse-driven supernova Neutrino OSC in supernova and the detection Neutrino OSC in supernova and the detection -Constraint on OSC parameters from the detection of supernova neutrino burst – -Constraint on OSC parameters from the detection of supernova neutrino burst – Effects of rotation on explosion and neutrino burst Effects of rotation on explosion and neutrino burst （ Gravitational wave from supernovae ） （ Gravitational wave from supernovae ）

3. Supernova １９８７ A in LMC ２３ Feb. ７：３５ AM （ UT ），１９８７ 10 trillion neutrinos passed through your body. Huge water Cerenkov counters could detect this neutrino burst, 11 events by Kamiokande & 8 events by IMB. Direct evidence that SN is triggered by gravitational collapse of stellar cores. Remarkable achievement which remains in history.

4. Nobel Prize was awarded to Dr. M. Koshiba, the head of Kamiokande, Professor emeritus of the Univ. of Tokyo. From http://www.nobel.se/ We have been waiting the prize more than 15 years ！

5. Now huge neutrino detectors are running! If a supernova appears at the Galactic center, then almost If a supernova appears at the Galactic center, then almost 10,000 events at SK and 350 events at SNO are expected. Total mass:10,000t, Fiducial mass:3,200t 30xKamII 1,000tD 2 O, 1.400t H 2 O Now we must consider seriously what astrophysics/physics are obtained from the detection of supernova neutrino burst. 800 events At LVD.

6. 56 Fe+e-> 56 Mn+ν e If M > 8-10 M solar, Iron core is formed. –10 9.5 g/cm 3 Unstable and begins to collapse. Neutrinos can escape from the core without scattering. –10 11 g/cm 3 The mean free path becomes shorter than the core radius, core, l mfp <R. –10 12 g/cm 3 The diffusion time τ dif = becomes longer than the characteristic collapsing time scale τ ff.. τ dif > τ ff.. ν ν l mfp Neutrinos are trapped, and are degenerate in SN cores. Collapse of Stellar Cores and Neutrino Trapping (K. Sato’75)

7. Neutrino reactions in supernova cores emission, absorption, scattering on nucleons scattering on electrons emission, absorption, scattering on nuclei -pair creations, annihilations Neutrinos are trapped by the effect of coherent scattering (Sato,’75) since the cross section proportional to A 2,and is larger.

8. How nuclei melt into supernova matter / neutron star matter ? Just after the glitches of pulsars were discovered. Coherent scattering depends on the size and shape of nuclei.

9. How nuclei melt in the course of collapse? Important for opacity “Nuclear Pasta “ Structure With increasing matter density, the shape changes from sphere,cylinder,slab, cylindrical bubble,spherical bubble and eventually becomes homogeneous. (Ravenhall & Pethick.,83, Hashimoto et al,84, Oyamatsu et al., 84,…Maruyama et al., 98, Watanabe et al., 00, and 01, Iida et al.,01) Essentially this change is described by the surface energy minimum principle. Oyamatsu,93 How the structure changes with increasing temperature? Pethick, Potekhin,98, Watanabe et al., 00 Perturbation analysis with the analogy of liquid crystal Pethick, Potekhin,98, Watanabe et al., 00 QMD method is suitable for investigating the melting by finite temperature (Maruyama et al. 98). Recently we improved this method and succeeded to construct pasta structure (Watanabe et. al.,01,02,03). From Oyamatsu et al., 84

10. Model: N= 2048 T~0.1MeVX=p/(p+n)=0.3 Results of QMD calculation (Watanabe,Sato,Yasuoka,Ebisusaki; PRC ’02) Sphere(0.1ρ ０ ） slab (0.35ρ ０ ） cylinder (0.18ρ ０ ） Cylinder hole (0. ５ ρ ０ ） Spherical hole (0.55ρ ０ ）

11. Preliminary result on the melting with increasing temperature: Model:N= 2048,ρ~0. ３５ ρ ０, X=p/(p+n)=0.5 T=1MeV T=2MeV (slab) T=3MeV T=0.1MeV (cylinder+slab) T=5MeVT=4MeV (almost homogeneous)

12. Two-point correlation function ξ of the nucleon density fluctuations δ with& uniform phase at T>4-5MeV ξ(r)=0 at larger r disappearance of long-range correlation at T=5MeV

13. Nucleon Distributions for X=p/(p+n)=0.3 and ρ=0.175ρ 0 Cylinder phase at T=0 ρ=0.175ρ 0 N=2048, N p =614, N n =1434 box size=41.394fm T=1MeV T=2MeVT=3MeV T=4MeV T=3, 4MeV : Nuclear surface cannot be identified by an isodensity surface.

14. Nucleon Distributions for x=0.3 and ρ=0.35ρ 0 Slab phase at T=0 ρ=0.35ρ 0 N=2048, N p =614, N n =1434 box size=32.85fm T=0MeVT=1MeV T=2MeV T=3MeV T=3MeV : Nuclear surface cannot be identified by an isodensity surface.

15. Phase Diagrams for ｘ＝０．３ χ > 0 ‹H› > 0 χ = 0 ‹H› > 0 χ < 0 ‹H› > 0 χ = 0 ‹H› = 0 χ < 0 ‹H› < 0 χ = 0 ‹H› < 0 χ > 0 ‹H› < 0 ｘ＝ 0.3 phase-separating region limit for identification of nuclear surface Structure with χ<0 (“intermediate” phase) : Sponge-like χ = (number of isolated regions) – (number of tunnels) + (number of cavities) Euler characteristic Still preliminary, but systematic investigation is in progress.

16. Eventually the shock revived by ν deposition, and outer shells are expelled. Delayed Explosion(Wilson) Eventually the shock revived by ν deposition, and outer shells are expelled. Delayed Explosion(Wilson) -10 15 g/cm 3 Inner core shock The core bounces and the unshocked inner core is formed.The shock is generated at the surface. Unshocked core playas a role of spring for explosion. If the shock is sufficiently strong, the star explodes; Prompt explosion However, most simulations show it is insufficient for explosion, and stalled. No prompt explosion occurs in realistic sim. If the shock is sufficiently strong, the star explodes; Prompt explosion However, most simulations show it is insufficient for explosion, and stalled. No prompt explosion occurs in realistic sim. ν Inner core ν ν ν ν ν ν νν

17. An example of delayed explosion late time explosion by ν-heating shock The stalled shock is revived by the neutrino deposition from the proto-neutron star. Wilson ‘82

18. The latest example of LLL group: the general relativistic core- collapse simulation with full νtransport calculation (Totani, Sato, Dalhed, Wilson,’98) Pre-supernova Model: Weaver & Woosley 20 Solar Mass. 108 109 Neutrino Burst from SN

19. 1.The latest neutrino burst models of the LLL group (pre- SN model:Weaver, Woosely 20 M solar ) (Totani,Sato,Dalhed, Wilson,’98). Time evolution of ν luminosity & the average energies =10MeV =15MeV =23MeV (ν μ 、 ν τ and their antiparticles)

20. Latest simulations with updated neutrino processes and sophisticated neutrino transfer show no explosion. Liebendoerfer et al. ‘01 Rampp et al. ’00,’03Thomson et al. ‘02

21. 1. Microphysics (neutrino processes, EOS etc.) are still insufficient ? Something important processes are missed? 2. Computational methods ( neutrino transfer, convection, etc) are still unreliable? 3. Spherical symmetric simulation is inadequate. Stellar rotation and/or magnetic field play essential role for explosion ? Why no explosion? In the present neutrino OSC analysis of supernova neutrino burst, We employ two models 1.LLL models (Totani et al, ’98) as the full neutrino burst model (~ 15 sec). (only one full time neutrino burst model available today) 2. Burrows’s group model (Thomson et al, ’02) as an early phase burst model (~ 0.2 sec.). (as a representative of latest simulations)

22. 2.TBP (Thompson,Burrows,Pint) Model (early 0.2 sec burst) Evolution of luminosity Evolution of average energies =12MeV =15MeV =20MeV The early phase analysis has advantage in that it is not affected whether the remnant is a neutron star or a black hole. (Takahashi, Sato, Burrows, Thompson, PRD‘03)

23. Neutrino OSC and Neutrino Burst from Supernovae 1.What is the effect on Explosion ? If we take values of oscillation parameters suggested by solar ν and atmospheric ν obs., no resonances occur in the core, but they occur in the mantle of SN (C+O shell, He shell). No effect on explosion. Note: If Δm ~10 1-2 ev, resonance happens in the hot bubble region, energy deposition is greatly enhanced because of the large cross section of high energy electron type neutrinos. Explosion is greatly strengthened (Shramm et al, …..) SK and SNO showed clearly neutrinos have masses, and oscillate.

24. 2.What are the effects on the detection? In order to get original information of cores and to extract the explosion mechanism, it is essentially important to know how the spectra of the neutrino burst are modified by neutrino OSC. 3. Can we extract osc parameters from the neutrino observation if a Galactic supernova appears ? Supernova is the strongest source of three type of neutrinos in the universe. (Sun e- type only, atmospheric neutrinos e- and μ- type) i) Can we obtain the implication on the parameter,which has not yet determined? ii) Can we solve the mass hierarchy problem ? (m>m>>m) Inverted mass hierarchy model (mν μ >mν e >>mν τ ) has not yet ruled out by experiments.

25. Resonance in Supernova Mantle –normal hierarchy model- Resonance Condition: H He C, O Ne, Mg Si Fe Dighe,Smirnov, ’ 00 Lunardini,A.Y.Smirnov,01 Minakata, Nunokawa. ’ 01 Takahashi,Sato, ’ 01 Takahashi et al, ’ 01 ………….

26. Neutrino OSC Models LMA-L 0.87 0.87 1.0 1.0 0.043 0.043 LMA-S 0.87 0.87 1.0 1.0 SMA-L 0.043 0.043 SMA-S 1.0 1.0 ： from solar neutrinos, : upper limit from nuclear : atmospheric neutrinos reactor Inverted mass hierarchy models are denoted as Inv-LMA-L, Inv-LMA-S, Inv-SMA-L, Inv-SMA-S.

27. Time evolution of conversion probability for LMA-L and LMA-S νe ντντ ντντ ντντ

28. Event rate at SK for LLL neutrino burst Model We calculate the event rate and the energy spectra at SK, assuming SN appeared at GC(10kpc). Most of events come from

29. Time evolution of event rate expected at SK

30. Time-integrated Energy spectra and Event numbers Can be distinguished from the ratio of event rate at the peak region to the tail region. Most of events come from.  effect of vacuum OSC. νe ν μ 、 τ  Models with larger mixing angle deviate from no osc model.

31. Event rate at SNO for LLL neutrino burst Model 1,000t D 2 O, （ 1.400t H 2 O ） Important reactions Electron type neutrinos can be detected efficiently by We discuss only CC, not NC.

32. Time evolution of event rate expected SNO

33. Energy spectra and Event numbers Events come from the both.  both effects, vacuum OSC and MSW. with increasing mixing angle, event number increases. Can be distinguished from the ratio of event rate at 15Mev region to the E>30Mev region.

34. Case of Normal mass hierarchy Case of Normal mass hierarchy Case of inverted mass hierarchy Case of inverted mass hierarchy Crossing diagram for antineutrinos m1m1 m2m2 m3m3 No Level crossing H-resonance H-resonance happens for anti neutrinos If the resonance is adiabatic (large ), conversion occurs effectively. conversion occurs effectively. nene Case for inverted mass hierarchy Event rate is greatly increased !

35. The time-integrated energy spectra ν e events are increased by ν e events are increased by H-resonance: ν τ  νe. 13,084 events 10,245events 68 185 237 82 190 118 111

36. In order to extract information of mixing angle, we define the ratios, R(SK) and R(SNO), R(SK) and R(SNO) are good indicators for neutrino OSC.

37. Plots on R SK- R SNO plane (Error –bars represent only statistical errors.) nor-LMA-s and inv-LMA-s are degenerate, but inv-LMA-L is clearly discriminated from nor-LMA-L. If the mixing parameter is -L, mass hierarchy problem is solved. Anti neutrino events can be subtracted by neutron detection.

38. Analysis by using the TBP burst model This simulation was done by using the updated neutrino processes and sophisticate neutrino transfer program. This simulation was done by using the updated neutrino processes and sophisticate neutrino transfer program. Available data are only the initial 0.2 second of the neutrino burst, but this early phase analysis has advantage that it is not affected whether the remnant is a neutron star or a black hole. Available data are only the initial 0.2 second of the neutrino burst, but this early phase analysis has advantage that it is not affected whether the remnant is a neutron star or a black hole. We investigated the dependence on the pre-supernova mass. We found the results are almost independent of the masses. We investigated the dependence on the pre-supernova mass. We found the results are almost independent of the masses.

39. Evolution of the burst and time-integrated energy spectra (TBP model)

40. Presupernova-mass dependence on R(SK)- R (SNO) Plots nor-LMA-s and inv-LMA-s are degenerate, but inv-LMA-L is clearly discriminated from nor-LMA-L. If the mixing parameter is -L, mass hierarchy problem is solved. Error bars come from only statistical errors, which are increased because the event numbers becomes small.

41. The Earth effects on the supernova neutrinos Supernova neutrinos oscillate and are reconverted each other in the earth. The spectra are greatly modified if they pass through the earth. Pass length when SN occurs at Galactic center. t=0 : the time at which the SN is aligned with the Greenwich meridian. (Dighe &Smirnov (00,01), Takahashi & Sato (00, 01) ) Earth SK 9500 events SNO 300 events LVD 850 events

42. In order to analyze the earth effect and to get information on OSC parameters, we need to know supernova direction, which is determined accurately by electron scattering. Electron scattering has sharp forward peak, but the fraction of is ~ 3% (282 events/total 8441 for Galactic Center Supernova at SK) Electron scattering has sharp forward peak, but the fraction of is ~ 3% (282 events/total 8441 for Galactic Center Supernova at SK) Monte Carlo Simulation of recoiled e - (e + ) direction for SK: Most of the events are by By using the least- square method, we get the direction within the accuracy 7degree (1σ ）。 Ando & Sato, ‘01

43. Modification of the spectra Spectra are greatly modified by MSW effects in the earth. Case: LMA-S, nadir angle =0 (pass through the center) Case: LMA-S, nadir angle =0 (pass through the center)

44. The spectra depend sensitively on the nadir angle and Since the nadir angle can be determined from the scattering by electrons at SK or SNO, could be determined more precisely by the earth effects. nadir angle dependence dependence

45. Supernova Relic Neutrinos Supernova Relic Neutrinos and its detectability There should be a diffuse background of neutrinos emitted from past supernovae. (Supernova Relic Neutrino Background, or SRN) Ando, Sato, Totani ’02, Ando, Sato ‘03 Flux depends on the history of supernova rate and neutrino oscillation parameters. We investigated the dependence of the flux on the OSC parameters, and effects on the detectability. Flux is increased greatly if LMA, and if inverted mass hierachy. Cosmic time We are here. z=0 z=1 z=5

46. History of Supernova Rate The SN rate model is evaluated from corresponding SFR model based on optical/UV observation by HST. Particularly, behavior at high redshift is not known well. (Luminosity function is not established and dust extinction is unknown.) However, owing to energy redshift, neutrinos emitted at high-z contribute only to low energy region (, where SK does not have sensitivity). Madau et al. (1996) The uncertainty around here is not important so much.

47. Flux for Various OSC Models We obtain the hardest spectrum for the INV-L model. The spectra for the other LMA models are degenerated. We also set upper limit for these oscillation models, by analyzing the spectrum with the SK observational result.

48. Theoretical prediction and Observational Limit (SK)model Predicted flux (cm  s  ) SK limit (90%C.L.) Prediction/ Limit NOR-S12 < 35 0.34 NOR-L11 < 34 0.33 INV-S11 0.33 INV-L9.0 < 12 0.74 No oscillation 12 < 73 0.17 The upper limit is more severe for the INV-L model. (In spite of difficult observation, SK upper limit is approaching the theoretical prediction. It is expected constraints on OSC parameters could be obtained near future.) Malek et al,’03

49. Effects of Rotation on the Supernova Explosion Massive stars have large angular momentum: Massive stars have large angular momentum: q= J/(GM 2 /C) ~ 10 q= J/(GM 2 /C) ~ 10 Implications of rotational collapse and Jet-like explosion from SN1987A observations. Implications of rotational collapse and Jet-like explosion from SN1987A observations. 1.Observation of asymmetry of expanding envelope by SPECKLE (Papalios, et. al. 89) 1.Observation of asymmetry of expanding envelope by SPECKLE (Papalios, et. al. 89) 2.Observation of linear polarization of scattered photons (Cropper et al.88) 2.Observation of linear polarization of scattered photons (Cropper et al.88) 3. Rings suggest pre-supernova was rapidly rotating. 3. Rings suggest pre-supernova was rapidly rotating.

50. Many groups have been challenging the simulation of rotational collapse of stellar cores. Mesh code 2dim. LeBranc, Wilson Symbalisty Moenchmeier et al (91) Yamada, Sato Shimizu, Yamada, Sato(94,01) ….. 3-dim. Shimizu, Yamada, Sato (94) SPH (Smoothed Particle Hydrodynamics) Herant et al (’94) Fryer (’99), Fryer et al (’01) ………… Difficulties in simulation multi-dimension neutrino transport general relativistic treatment ……… All simulations are still preliminary ones.

51. Asymmetric -heating due to rotation If oblate proto neutron stars are formed due to centrifugal forces, more neutrinos are emitted in the direction of rotation axis. Assuming an oblate proto neutron star is formed, we carried out hydrodynamic simulation, and found that -heating is enhanced near the rotation axis, and global convections are induced in heating regions. As the result, Jet like explosion is induced. Shimizu, Ebisuzaki, Sato, Yamada,’01 oblate proto neutron star

52. 2D Rotational Collapse Simulations Kotake, Yamada, Sato, ApJ595, 304 (03) t = 256ms Radius [cm] T [MeV] 0° 90° Density entropy Shape of neutrino sphere becomes spheroid. Temperature on the sphere Neutrino luminosity and the average energy depend on what direction we observe. We are investigating whether implication on OSC parameter could be obtained or not. ３ ５

53. Gravitational Radiation from Axisymmetric Rotational Core Collapse Preceding works and recent works …… Moenchmeyer et al. ’91 Yamada, Sato, ’97 Zwerger & Mueller ’97 Dimmelmeier et al. ’02 Shibata ’03 Kotake,Yamada, Sato ’03 Ott et al., ’03 Kotake, Yamada, Sato, PRD68, 044023 (03) We calculated gravitational radiation by using quadrupole radiation formula. Most preceding works took simplified EOS, i.e., p=Kρ γ, and neutrino emission/ absorption/transport are neglected. We carried out collapse simulation by using realistic EOS (Relativistic MFA; Shen et al. ‘98 ) and included neutrino processes.

54. Theoretical prediction of “h TT ” when SN appear at Galactic center and detection limit We carried out for various rotation models, and found most of them are higher than TAMA detection limit.

55. Case of Moderate rotation Example of wave pattern Wave patterns depend on rotational speed and distribution of angular momentum. Case of strong differential rotation Small fluctuations disappear because of centrifugal force in the central core region. If the gravitational wave is detected and wave pattern is observed, information on the rotation would be obtained.

56. Summary ● Now huge neutrino detectors (SK, SNO,LVD,..) and supersensitive GW detectors (TAMA,LIGO,..) are working. 1. 1.If SN appears at Galactic center, 10,000 events (SK), and 350 events (SNO) will be detected, and fruitful information on the explosion mechanism and neutrino OSC parameters would be obtained. More huge detector Hyper Kamiokande is proposed. 2.TAMA and LIGO would detect gravitational waves from Galactic supernovae if precise time of explosion is informed by SK, and implication on the rotational speed and the stiffness of EOS could be obtained. Despite almost 40 years of intensive and extensive studies, we still do not figure out how the collapse-driven supernova occurs 。 More extensive and systematic studies on gravitational collapse including realistic EOS and neutrino transfer are necessary.