Charged current interactions of muon
neutrinos in supernova
Andreas Lohs (TU Darmstadt)
In collaboration with:
Gabriel Martinez-Pinedo (TU Darmstadt, GSI)
Tobias Fischer (Wroclaw)
SN&GRB 2013 - Yukawa Institute,Kyoto,Japan

October 22, 2013

-5pt

Neutrinos in core collapse supernova
A core collapse supernova releases 99% of it’s energy, up
to 1053 erg in neutrinos. Hence they affect the evolution of thesupernova and the protoneutron star in multiple ways:

Neutron to proton ratio for
nucleosynthesis
Matter ejection in neutrino
driven wind
Cooling and deleptonization

H.Th.Janka et al.,Phys.Rep.442(2007)38-74

Role of µ and τ flavor neutrinos
νµ and ντ transport energy from core of PNS (> 50%)
Charged current interactions are assumed to be negligible
Emission from higher density than νeCurrent CC-SN simulations treat νµ , ντ as a single type νx
Production of νx - ν̄x pairs only
Spectral differences between νx and ν̄x could arise fromneutral current scattering with electrons and neutrons

Hüdepohl et al., PRL 104,251101(2010)

Charged current interactions for µ-flavor
Chemical potentials 722 ms postbounceµ n − µpµe
3·T

140

In the core of PNS µe andµn − µp are of the order of mµ
Production of µ+ and τ always
suppressed

120Energy[MeV]Charged current reactions
suppressed by large Q values:mµ , mτ

100
80
60
40
20010141013

Density[g/cm3 ]1012

18M -modell from T.Fischer et al.,(2010) A&A 517 A80⇒ Charged current reactions could be a significant opacity
source for νµ .
This could induce spectral differences between νµ and other νx(potentially interesting for oscillations).

Charged current interactions for µ-flavor

Charged current weak reactions for µ-type neutrinos:νµ + n → p + µ−

nucleonic absorption

νµ + e− → νe + µ−

purely leptonic, difficult kinematics

νµ + ν̄e + e− → µ−inverse muon decayν̄e + e− → ν̄µ + µ−

production of muons without νµConcept of neutrinosphere
The neutrinosphere Rsp is the radius where emitted neutrinos
become free streaming. It is defined via the optical depth τ :Z ∞1
dr = 23
τ (Rsp ) =λ(r)Rsp tot
Scattering sphere RScat : All opacities contribute equallyP 11
1=+λtotλscattλabs

Raffelt, APJ 561(2001)840-914

Concept of neutrinosphere
The neutrinosphere Rsp is the radius where emitted neutrinos
become free streaming. It is defined via the optical depth τ :Z ∞12
τ (Rsp ) =dr=3
Rsp λtot (r )Energy sphere REff : Last energy exchanger qP

P
1
1
1
1=·+λtot
λabs
λscattλabs

Raffelt, APJ 561(2001)840-914

Mean free path and neutrino sphere
Inverse mean free path for νµ at 722 ms postbounce
103(isoscatt)νµ + n(isoscatt)νµ + p
νµ + ν̄µνµ + ν̄µ + NN(scatt)νµ + e−

102

[1/km]

101
100

10−110−210−31014

1013

Density[g/cm3 ]1012

Mean free path and neutrino sphere
Inverse mean free path for νµ at 722 ms postbounce
103(isoscatt)νµ + n(isoscatt)νµ + p
νµ + ν̄µνµ + ν̄µ + NN(scatt)νµ + e−(abs)νµ + e−(abs)νµ + nνµ + ν̄e + e−

102

[1/km]

101
100

10−110−210−31014

1013

Density[g/cm3 ]1012

Mean free path and neutrino sphere
Energy dependent REff for νµ at 722 ms postbounce
Energy dependent neutrinosphere position
old REff
new REff

Energy[MeV]

1001010141013

Density[g/cm3 ]1012

Mean free path and neutrino sphere
Energy dependent REff for νµ at 168 ms postbounce
Energy dependent neutrinosphere position
old REff
new REff

Energy[MeV]

100101014

1013

Density[g/cm3 ]

1012

1011

Mean free path and neutrino sphere103(isoscatt)νµ + n(isoscatt)νµ + pνµ + ν̄µνµ + ν̄µ + NN(scatt)νµ + e−(abs)νµ + e−(abs)νµ + nνµ + ν̄e + e−

102

Energy sphere shifted.
∆T ' 200 − 300keV[1/km]

101
100

10−1

Scattering sphere not affected10−210−31014

1013

Density[g/cm3 ]Muonic reactions are significant at the region of νµ decoupling.
This will cause a difference to the spectrum of ν̄µ .
All these reactions will produce muons, but how fast is thetimescale of muon production?

1012

Muon productionµ− production per baryon106ν̄e + e− → ν̄µ + µ−
νµ + e− → νe + µ−
νµ + n → p + µ−
νµ + ν̄e + e− → µ−105

Rate[1/s]

104
103102101
10010−110−210141013

Density[g/cm3 ]1012

Timescale for µ production faster than dynamical timescale⇒ muons are in chemical equilibrium.

muon abundance in early PNS
New composition including muons. Net muon number must be
zero inside effective νµ -sphere.
Abundances without muons
10010−110−210−3YnYpYeYµYνeYν̄eYνµYν̄µ10−410−510−61014

1013

Density[g/cm3 ]1012

muon abundance in early PNS
New composition including muons. Net muon number must be
zero inside effective νµ -sphere.
Abundances including muons
10010−110−210−3YnYpYeYµYνeYν̄eYνµYν̄µ10−410−510−610141013

Density[g/cm3 ]1012

Production of νµνµ must be produced by pair process in the first place. This has
to happen fast enough.
νµ production per baryon
106

e+ + e− → νµ + ν̄µNN → NN + νµ ν̄µνe + µ− → νµ + e−
p + µ− → n + e −µ− → e− + ν̄e + νµ105

Rate[1/s]

104
103102101
100
10−110−210141013

Density[g/cm3 ]1012

Summary and Outlook
We have calculated charged-current reactions for νµ insupernova.
At densities & 1013 g cm−3 they become one of thedominating sources of νµ opacity, manifested by anoutward shift of the energy neutrinosphere.
We expect that the spectrum of emitted νµ will be different
from ν̄µ , ντ , and ν̄τ . This should lead to a production of net
muon number in the PNS core.
Further, we find muons reach equilibrium in very shorttimescales.
PNS deleptonization timescale could be affected.
Possibile impact in collective neutrino oscillations.