Neutrino oscillations in oxygen-neon-magnesium supernovae Cecilia Lunardini Arizona State University...
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Transcript of Neutrino oscillations in oxygen-neon-magnesium supernovae Cecilia Lunardini Arizona State University...
Neutrino oscillations in oxygen-neon-magnesium
supernovaeCecilia Lunardini
Arizona State UniversityAnd RIKEN-BNL Research Center
C.L., B. Mueller and H.T. Janka, arXiv:0712.3000, in press at PRD
A “petite” supernova: ONeMg
• Small progenitor: 8-10 Msun
• 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 , AIP Conf.Proc.937:144-154,2007
Poelarends et al., arXiv:0705.4643K. Nomoto, Astrophys. J. 277, 791–805 (1984).
• Easier explosion– Little resistance from envelope
• Faster shockwave
Kitaura, Janka, Hillebrandt, Astron. Astrophys. 450 (2006) 345
ONeMg, 8.8 MsunFe, 15 Msun
shock
Buras, Rampp, Janka, Kifonidis, Astron. Astrophys. 447, 1049 (2006)
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
t=0,50,100,….,700 ms0 ms
100 ms250 ms
700 ms
post-shockpre-shock
Oscillations: masses and mixings
12
3
Normal hierarchy, m2
32>0
Inverted hierarchy, m2
32<0
13Sin2 213<0.15
CHOOZ, PLB466, 1999m
e
232m
221m
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)
Mikheev, Smirnov, Wolfenstein (1985,1978)
Duan, Fuller, Carlson and Qian, Phys. Rev.D 74, 105014 (2006)
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/(21/2 GF)
21/(21/2 GF)
“Supernova” resonance, 13
“solar” resonance
End of self-interaction
effects
Self interaction effects
• Effects of are negligible if:Hierarchy is normal ( m2
31>0)They decouple before the MSW
resonance (e ~ 2 >> )
13 is smallReduction to MSW resonances only!
Hannestad, Raffelt, Sigl and Wong, Phys.Rev.D74:105010,2006Raffelt and Smirnov, Phys.Rev.D76:081301,2007 Fogli, Lisi, Marrone and Mirizzi, arXiv:0707.1998
MSW: PH, PL as switches
Eigenvalues
PH PL e
conversion
Final e
survival
0 1 e3 ~0
0 0 e3 ~0
1 0 e2 sin2 12 ~ 0.32
1 1 e1 cos2 12 ~ 0.68
x = ,Dighe and Smirnov, Phys.Rev.D62:033007,2000
Transition probability
• Depends on density profile:
• Steeper profile, smaller mixing more transition (non-adiabatic, less conversion) PH 1
PH
13 ! 0dne/dr ! 1
Pre-shock• All frequencies relevant: numerical
approach
t=0,50,100,….,700 ms
/(2 1/2 G
F ) = n eff
e/(21/2 G
F) = ne
31/(21/2 GF)
21/(21/2 GF)
e ~ ~ 31
Duan, et al. arXiv:0710.1271, Dasgupta et al., arXiv:0801.1660, analytical interpretation
• MSW-equations still valid with effective, step-like PH,PL
– PL = (E-12 MeV)
– PH=(E-15 MeV)
• p=cos2 12 ~ 0.68 at E >15 MeV– Valid for any 13
P(e 1)
P(e 2)
P(e 3)
sin2 13=0.01
Duan, Fuller, Carlson, and Qian,arXiv:0710.1271Duan, private comm.
PL=0 PL=1
PH=0 PH=1
Oscillations in the Earth
• e flux in a Earth-shielded detector:
Production point
Conversion in star
Regeneration in Earth: P(2 ! e)-sin212
= +
C.L. & A.Yu. Smirnov, Nucl.Phys.B616:307-348,2001
• Fe: late (~5 s) decrease of conversion (profile becomes steeper due to shock)
Fe
Schirato & Fuller, astro-ph/0205390
Intermediate: Slow (three steps)decrease
Small: No decrease
Large: Fastdecrease
Fe supernova
t=60 ms
t=450 m
s
t=700 m
s
Results: jumping probabilites
E=20 MeV
sin2 13
e survival probability: fast, slower, slowest..
sin2 13=10-2
sin2 13=10-5
sin2 13=6 10-4
Fe-
core
SN
ONeMg vs Fe: differences
ONeMg FePre-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