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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. ONeMg core. He shell. A “petite” supernova: ONeMg.

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## Neutrino oscillations in oxygen-neon-magnesium supernovae

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**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**ONeMg core**He shell A “petite” supernova: ONeMg Plot from Janka, Marek, Kitaura , AIP Conf.Proc.937:144-154,2007 • Small progenitor: 8-10 Msun • Up to 20% of all SNe! • Next galactic SN? • Sharp density stepat base of He shell Poelarends et al., arXiv:0705.4643 K. Nomoto, Astrophys. J. 277, 791–805 (1984).**Easier explosion**• Little resistance from envelope • Faster shockwave Fe, 15 Msun ONeMg, 8.8 Msun shock Buras, Rampp, Janka, Kifonidis, Astron. Astrophys. 447, 1049 (2006) Kitaura, Janka, Hillebrandt, Astron. Astrophys. 450 (2006) 345**The simulation**• Calculates time-evolved density profile and neutrino flux • Uses 8.8 Msun 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).**Electron number density, ne:**• relativistic speed of shock 0 ms t=0,50,100,….,700 ms 100 ms 250 ms 700 ms post-shock pre-shock**Hierarchy of average energies**• Oscillation effects spectrum permutation**Sin2 213<0.15**CHOOZ, PLB466, 1999 Normal hierarchy, D m232>0 Inverted hierarchy, D m232<0 Oscillations: masses and mixings m**In medium: frequencies**• Kinetic: • Forward scattering (refraction) • on electrons • ne electron number density • On neutrinos (“self interaction”) • N number density, R decoupling radius**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 (ne) Duan, Fuller, Carlson and Qian, Phys. Rev.D 74, 105014 (2006) Mikheev, Smirnov, Wolfenstein (1985,1978)** decouples first: effects factorize**Post-shock (t>300 ms) “Supernova” resonance, 13 t=0,50,100,….,700 ms e/(21/2 GF) = ne /(21/2 GF) = neff 31/(21/2 GF) 21/(21/2 GF) End of self-interaction effects “solar” resonance**Self interaction effects**• Effects of are negligible if: • Hierarchy is normal ( m231>0) • They decouple before the MSW resonance (e ~ 21 >> ) • 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**MSW: PH, PL as switches**Eigenvalues x = , Dighe and Smirnov, Phys.Rev.D62:033007,2000**PH**Transition probability • Depends on density profile: • Steeper profile, smaller mixing more transition (non-adiabatic, less conversion) PH 1 13! 0 dne/dr !1**All frequencies relevant: numerical approach**Pre-shock Duan, et al. arXiv:0710.1271, Dasgupta et al., arXiv:0801.1660, analytical interpretation e/(21/2 GF) = ne t=0,50,100,….,700 ms e ~ ~ 31 31/(21/2 GF) 21/(21/2 GF) /(21/2 GF) = neff**PL=0**PH=0 PL=1 PH=1 • MSW-equations still valid with effective, step-like PH,PL • PL = (E-12 MeV) • PH=(E-15 MeV) • p=cos212 ~ 0.68 at E >15 MeV • Valid for any 13 P(e 1) P(e 2) P(e 3) sin213=0.01 Duan, Fuller, Carlson, and Qian, arXiv:0710.1271 Duan, private comm.**Oscillations in the Earth**• e flux in a Earth-shielded detector: = + Production point Regeneration in Earth: P(2!e)-sin212 Conversion in star C.L. & A.Yu. Smirnov, Nucl.Phys.B616:307-348,2001**What to expect:**• ONeMg:early (~1 s)increase of conversion (profile becomes smoother) ONeMg**Fe:late (~5 s)decrease of conversion (profile becomes**steeper due to shock) Schirato & Fuller, astro-ph/0205390 Fe**Intermediate:**Slow (three steps) decrease Large: Fast decrease Small: No decrease Results: jumping probabilites t=60 ms E=20 MeV t=450 ms t=700 ms Fe supernova sin213**PL (20 MeV) = 1 pre-shock**0 post-shock • Fe SN: PL=0 at all times**e survival probability: fast, slower, slowest..**sin213=10-5 sin213=6 10-4 Fe-core SN sin213=10-2**t=700 ms**t=450 ms t=60 ms Earth effect: fast.. (FDe-Fe)/Fe Fe SN: no effect**..slower..**Fe SN: no effect**..slowest**Fe SN: opposite sign at 60 ms, similar effect later**Observed spectra**ONeMg Fe t=60 ms t=450 ms t=700 ms**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, …

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