1. The neutrino mass hierarchy and supernova n
Cristina VOLPE
(AstroParticule et Cosmologie -APC)

2. Core-collapse supernovae
Massive stars (M > 6-8 Msun) emit 1057 neutrinos in 10 seconds,
during the gravitational collapse and cooling of the neutron star.
Neutrino fluxes encode imprints of the explosion.
cooling
accretion
Time after bounce (s)
Hüdepohl et al. PRL 104 (2010)
Supernova n fluxes from simulations NS ne nt nm ne nt nm NS

3. Supernova observations
Time and energy signal from a supernova explosion. In our
galaxy, 1-3 events/century; one explosion/year at 4 Mpc.
The Diffuse Supernova Neutrino Background (DSNB) :
The SN fluxes integrated over cosmological redshift.
Solar abundance of heavy elements
Element nucleosynthesis
(r-process, np-process,
n-nucleosynthesis).
log Y(A)
with n-n A
Duan, Friedland, McLaughlin, Surman JPG 38 (2010)

4. SN1987A et SN simulations SN1987A events Star radius (km) Time (ms)
A. Suzuki, J. of Physics, Conf. (2008)
SN1987A events
(LMC, 50 kpc)
see e.g. Pagliaroli et al,
Astropart. Phys. 31 (2009)
SN simulations have reached a
high degree of complexity :
2D-3D, convection, realistic
neutrino transport, SASI.
Marek & Janka, ApJ (2009)
Star radius (km)
Time (ms)

5. n flavour conversion in supernovaenm ne
neutrinosphere
shock waves
n-e
(MSW)
the n interaction with matter – MSW effect – and with n .
dynamical aspects - shock waves and turbulence.
Numerous aspects require investigation.
In fact, flavour conversion effects arise because of
Novel conversion phenomena discovered in the last years.

6. The MSW effect ne Hmatter GF re =ne n2 =nm n1 e
Neutrino interaction with matter
induces a resonant flavour conversion.
Wolfenstein PRD (1978)
Mikheev and Smirnov, Sov. J. Nucl. Phys. (1985) n2 n1
MSW resonance
location
Effective mass
matter basis
=ne
=nm
high density
flavour basis
vacuum
detection
on earth
DENSITY

7. The MSW effect : established
Borexino coll, PRL 108 (2012)
n e Survival Probability
Neutrino Energy (MeV)
pep pp
MSW solution
7Be n
8B n
the beautiful explanation of the
« solar neutrino deficit » problem !

8. The MSW in supernovae The MSW effect is encountered twice :
Dighe, Smirnov, PRD62 (2000)
n-fluxes at the
neutrinosphere
Effective mass
detection
on earth
DENSITY
vacuum
Low r
High r
SN core
FLAVOUR CONVERSION at the H-RESONANCE DEPENDS
ON THE NEUTRINO MASS HIERARCHY - either n or anti-n.

9. Distance in the star (a.u.)
The MSW in supernovae
At MSW resonance(s) efficient (adiabatic) conversion depends on :
star density profile
neutrino energy
mixing angles, Dm2
sign
Distance in the star (a.u.)
n e Survival Probability
full
conversion
(adiabatic)
no conversion
(non-adiabatic)
ne -> nm
ne -> ne
Well understood.

10. depending on the hierarchy.
The shock wave effects
Dasgupta and Dighe, PRD 75 (2007).
Kneller, McLaughlin, Brockman, PRD 77 (2008).
Profile with shock waves
Neutrino conversion in MSW region
non-adiabatic
t=1s
t=1.5s
density (g/cm3)
anti-n e Survival Prob.
inverted
hierarchy
E=20 MeV
adiabatic
distance in SN (cm)
Time (s)
before the shock - adiabatic conversion
It occurs either in ne
or in anti-ne channel
depending on the hierarchy.
the shock arrives - non-adiabatic
multiple MSW (phase effects)
the shock has gone

11. Turbulence effects Potential (a.u.) distance in SN (cm)
Kneller and Volpe, PRD 82 (2010)
Profile with turbulence
Matter density fluctuations
induce multiple MSW resonances
and phase effects.
Potential (a.u.)
distance in SN (cm)
Same imprint as shock waves

12. The impact of the n-n interaction
Neutrino conversion near the neutrinosphere
Spectral-split
Neutrino Fluxes
Neutrino Energy (MeV)
n-fluxes after 200 km
Distance in SN
n e Survival Probability 1- 2- 3-
all neutrinos stick together - synchronization
instability in flavour - bipolar regime
Duan,Fuller,Qian PRD74 (2006) 76 (2007), Hannestad, et al. PRD 74 (2006),
Galais, Kneller, Volpe JPG 39 (2012)
full or no conversion depending on energy - spectral split
Duan, Fuller, Qian, PRD76(2007); Meng and Qian, PRD (2011); Raffelt and Smirnov
PRD 76 and PRL (2007); Pehlivan et al, PRD 84 (2011); Galais and Volpe, PRD 84 (2011)

13. The impact of the n-n interaction
Large matter densities appear to suppress n-n effects
during the accretion phase.
Further work is needed to test some of the approximations,
either geometrical
or inherent to the equations commonly used, such as the
mean-field approximation.
see e.g. Chakraborty, et al. PRL 107 (2011)
Cherry et al, PRL 108 (2012)
Volpe, Vaenaeaenen, Espinoza,
n-anti-n pairing
correlations

14. Current SN observatories
Borexino
Baksan
SK (104)
LVD
HALO
Daya-Bay
MiniBOONE
KamLAND (400)
IceCube (106)
Different detection channels available :
scattering of anti-ne with p, ne with nuclei, nx with e, p

15. The Diffuse Supernova n Background
Calculation that treats both the n-n
and shock wave effects :
Malek et al.
PRL (2003)
NH IH
MEMPHYS (440 kton)
GLACIER (100 kton)
LENA (50 kton)
Events/y/22.5 kton/4 MeV
Neutrino Energy (MeV)
Galais, Kneller, Gava, Volpe, PRD 81 (2010)
Upper limits on DSNB fluxes :
anti-ne /cm2/s
ne/cm2/s
THE HIERARCHY effect small.
Lunardini and Peres, JCAP (2008)
Difficult to have unambiguous information seen
astrophysical uncertainties (star formation rate).

16. n mass hierarchy with SN n
The mass hierarchy signatures studied so far are roughly
of three kinds. They exploit :
either earth matter effects with one or two-detectors ;
or the early time signal ;
or the full time and energy signal of the explosion.

17. Predictions for the time rise
From the early time signal
SN n fluxes at accretion phase
Predictions for the time rise
in Icecube
The hierarchy appear
to be distinguishable.
Serpico, Chakraborty, Fischer, Hudepohl,
Janka, Mirizzi, PRD 85 (2012).

18. From late time and energy signal
ne + p n + e+
Time signal (s)
Prediction including
the n-n interaction and
shock wave effects.
inverted hierarchy
e+ flux (/MeV/s/ton)
29 MeV
ON EARTH
adiabatic
non-adiabatic
anti-n e fluxes
Energy (MeV)
15 MeV
15 MeV
29 MeV
Gava, Kneller, Volpe, McLaughlin,
PRL 103 (2009) .
Bump (dip) at 3.5 (1) sigma in Super-Kamiokande
if a supernova at 10 kpc explodes...

19. Combining information
Vaeaenaenen, Volpe, JCAP 1110 (2011) .
(CC+NC) events in HALO-2
(1 kton lead) for a SN at
10 kpc
Predictions include nn
and n-matter interaction
Two-neutron events
One-neutron events
Detection channels with different energy
thresholds allow to identify solutions.

20. Conclusions Simulations of core-collapse supernovae and of neutrino
flavour conversion in supernovae are steadily progressing.
Several features established but various aspects needs
further studies.
For the mass hierarchy :
- the effect in the DSNB too small to be disentagled from
astrophysical uncertainties;
- the measurement of the early time rise and late time
and energy signal in water Cherenkov or scintillator
detectors are promising.

21. Danke.
Gracias
Thank you
Grazie
Life tree
Merci

22. Core-collapse supernovae
Massive stars (M > 8 Msun) emit 1057 neutrinos in 10 seconds,
during the gravitational collapse and cooling of the neutron star.
Hüdepohl et al.PRL 2010.
Neutrino fluxes encode imprints of the explosion. NS ne nt nm ne nt nm NS