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

• Hierarchy of average energies– Oscillation effects

spectrum permutation

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

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)

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

• PL (20 MeV) = 1 pre-shock

0 post-shock

• Fe SN: PL=0 at all times

e survival probability: fast, slower, slowest..

sin2 13=10-2

sin2 13=10-5

sin2 13=6 10-4

Fe-

core

SN

Earth effect: fast..

Fe SN: no effect

t=60 ms

t=700 ms

t=450 ms

(FD

e-F

e)/

Fe

..slower..

Fe SN: no effect

..slowest

Fe SN: opposite sign

at 60 ms, similar effect

later

Observed spectraONeMg Fe

t=60 ms

t=700 mst=450 ms

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

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, …