1. Neutrino oscillations in oxygen-neon-magnesium supernovae Cecilia Lunardini Arizona State University And RIKEN-BNL Research Center C.L., B. Mueller and H.T. Janka, arXiv:0712.3000, in press at PRD

2. A “petite” supernova: ONeMg Small progenitor: 8-10 M sun Up to 20% of all SNe! –Next galactic SN? Sharp density step at base of He shell He shellONeMg core Plot from Janka, Marek, Kitaura,JankaMarekKitaura AIP Conf.Proc.937:144-154,2007 Poelarends et al., arXiv:0705.4643 K. Nomoto, Astrophys. J. 277, 791–805 (1984).

3. Easier explosion –Little resistance from envelope Faster shockwave Kitaura, Janka, Hillebrandt, Astron. Astrophys. 450 (2006) 34 5 ONeMg, 8.8 M sun Fe, 15 M sun shock Buras, Rampp, Janka, Kifonidis, Astron. Astrophys. 447, 1049 (2006)

4. The simulation Calculates time-evolved density profile and neutrino flux Uses 8.8 M sun progenitor model from K. Nomoto Spherical symmetry PROMETHEUS/VERTEX code –variable Eddington factor solver for the neutrino transport –state-of-the-art treatment of neutrino-matter interactions. Particular effort was made to implement nuclear burning and electron capture rates with sufficient accuracy to ensure a smooth continuation, without transients, from the progenitor evolution to core collapse. K. Nomoto, Astrophys. J. 277, 791–805 (1984).

5. Electron number density, n e : –relativistic speed of shock t=0,50,100,….,700 ms 0 ms 100 ms 250 ms 700 ms post-shock pre-shock

6. Hierarchy of average energies –Oscillation effects  spectrum permutation

7. Oscillations: masses and mixings Normal hierarchy,  m 2 32 >0 Inverted hierarchy,  m 2 32 <0 Sin 2 2  13 <0.15 CHOOZ, PLB466, 1999 m

8. In medium: frequencies Kinetic: Forward scattering (refraction) –on electrons n e electron number density –On neutrinos (“self interaction”) N number density, R decoupling radius

9. Rule of thumb: scattering terms are relevant only if larger than kinetic:  e ¸  ji  ¸  ji  ¸  ji  non-linear, collective effects –indirect dependence on matter profile  e ~  ji  MSW resonance –Strong dependence on matter profile (n e ) Mikheev, Smirnov, Wolfenstein (1985,1978) Duan, Fuller, Carlson and Qian, Phys. Rev.D 74, 105014 (20 06)

10. Post-shock (t>300 ms)  decouples first: effects factorize t=0,50,100,….,700 ms  /(2 1/2 G F ) = n eff  e /(2 1/2 G F ) = n e  31 /(2 1/2 G F )  21 /(2 1/2 G F ) “Supernova” resonance,  13 “solar” resonance End of self- interaction effects

11. Self interaction effects Effects of  are negligible if:  Hierarchy is normal (  m 2 31 >0)  They decouple before the MSW resonance (  e ~  2  >>  )   13 is small Reduction to MSW resonances only! Hannestad, Raffelt, Sigl and Wong, Phys.Rev.D74:105010,2006 Raffelt and Smirnov, Phys.Rev.D76:081301,2007 Fogli, Lisi, Marrone and Mirizzi, arXiv:0707.1998

12. MSW: P H, P L as switches Eigenvalues PHPH PLPL e conversion Final e survival 01 e    3 ~0 00 e    3 ~0 10 e    2 sin 2  12 ~ 0.32 11 e    1 cos 2  12 ~ 0.68 x = ,  Dighe and Smirnov, Phys.Rev.D62:033007,2000

13. Transition probability Depends on density profile: Steeper profile, smaller mixing  more transition (non-adiabatic, less conversion) P H 1 PHPH  13 ! 0 dn e /dr ! 1

14. Pre-shock All frequencies relevant: numerical approach t=0,50,100,….,700 ms  /(2 1/2 G F ) = n eff  e /(2 1/2 G F ) = n e  31 /(2 1/2 G F )  21 /(2 1/2 G F )  e ~  ~  31 Duan, et al. arXiv:0710.1271, Dasgupta et al., arXiv:0801.1660, analytical interpretation

15. MSW-equations still valid with effective, step- like P H,P L –P L =  (E-12 MeV) –P H =  (E-15 MeV) p=cos 2  12 ~ 0.68 at E >15 MeV –Valid for any  13 P( e  1 ) P( e  2 ) P( e  3 ) sin 2  13 =0.01 Duan, Fuller, Carlson, and Qian, arXiv:0710.1271 Duan, private comm. P L =0P L =1 P H =0P H =1

16. Oscillations in the Earth e flux in a Earth-shielded detector: Production point Conversion in star Regeneration in Earth: P( 2 ! e )-sin 2  12 =+ C.L. & A.Yu. Smirnov, Nucl.Phys.B616:307-348,2001

17. What to expect: ONeMg: early (~1 s) increase of conversion (profile becomes smoother) ONeMg

18. Fe: late (~5 s) decrease of conversion (profile becomes steeper due to shock) Fe Schirato & Fuller, astro-ph/0205390

19. Intermediate: Slow (three steps) decreas e Small: No decreas e Large: Fast decreas e Fe supernova t=60 m s t=450 ms t=700 ms Results: jumping probabilites E=20 MeV sin 2  13

20. P L (20 MeV) = 1 pre-shock 0 post-shock Fe SN: P L =0 at all times

21. e survival probability: fast, slower, slowest.. sin 2  13 =10 -2 sin 2  13 =10 -5 sin 2  13 =6 10 -4 Fe-core SN

22. Earth effect: fast.. Fe SN: no effect t=60 m s t=700 m s t=450 m s (F D e -F e )/F e

23. ..slower.. Fe SN: no effect

24. ..slowest Fe SN: opposite sign at 60 ms, similar effect later

25. Observed spectra ONeMgFe t=60 m s t=700 m s t=450 m s

26. ONeMg vs Fe: differences ONeMgFe Pre-shock: ~68% e survival <32% e survival shock modulations before 1 s (faster for larger  13 ) Shock modulations only after 3-5 s Shock  progressive decrease of survival probability Shock  sudden increase of survival probability Shock  disappearance of Earth effect Shock  appearance of Earth effect

27. Why important? Unique way to test the density step (O-He transition) –Tomography! Provide progenitor identification (ONeMg or Fe) for obscured SNe Necessary to interpret data from a ONeMg SN –Test collapse models, neutrino emission, etc. –learn on  13, hierarchy, exotica, …