Neutrinos and the stars
Neutrinos and the Stars
Georg Raffelt, MPI for Physics
Lectures at the Topical Seminar
Neutrino Physics & Astrophysics
17-21 Sept 2008, Beijing, China
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Where do Neutrinos Appear in Nature?

Earth Crust
(Natural
Radioactivity)
Sun

Nuclear Reactors
Supernovae
(Stellar Collapse)
SN 1987A 

Particle Accelerators
Cosmic Big Bang
(Today 330 n/cm3)
Indirect Evidence

Earth Atmosphere
(Cosmic Rays)

Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Astrophysical
Accelerators
Soon ?
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Where do Neutrinos Appear in Nature?
Neutrinos from nuclear
reactions:
Energies 1-20 MeV
Quasi thermal sources
Supernova: T ~ few MeV
“Beam dump neutrinos”
• High-energy protons hit
matter or photons
• Produce secondary p
• Neutrinos from pion
decay
p  m + nm
m  e + nm + ne
• Energies ≫ GeV
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Big-Bang Neutrinos:
Very small energies today
(cosmic red shift)
Like matter today
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Where do Neutrinos Appear in Nature?
Low-energy
neutrino astronomy
(including geo-neutrinos)
Energies ~ 1-50 MeV
Long-baseline
neutrino oscillation
experiments with
• Reactor neutrinos
• Neutrino beams from
accelerators
• Precision cosmology &
limit on neutrino mass
• Big-bang nucleosynthesis
• Leptogenesis
High-energy
neutrino astronomy
Closely related to
cosmic-ray physics
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from the Sun
Helium
Reactionchains
Energy
26.7 MeV
Solar radiation: 98 % light
2 % neutrinos
At Earth 66 billion neutrinos/cm2 sec
Hans Bethe (1906-2005, Nobel prize 1967)
Thermonuclear reaction chains (1938)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Bethe’s Classic Paper on Nuclear Reactions in Stars
No neutrinos
from nuclear reactions
in 1938 …
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Gamow & Schoenberg, Phys. Rev. 58:1117 (1940)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Gamow & Schoenberg 2
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Sun Glasses for Neutrinos?
8.3 light minutes
Several light years of lead
needed to shield solar
neutrinos
Bethe & Peierls 1934:
“… this evidently means
that one will never be able
to observe a neutrino.”
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
First Detection (1954 - 1956)
Clyde Cowan
(1919 – 1974)
Anti-Electron
Neutrinos
from
Hanford
Nuclear Reactor
Fred Reines
(1918 – 1998)
Nobel prize 1995
n
ne
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Detector prototype
Cd
g
g
p
e+
e-
3 Gammas
in coincidence
g
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
First Measurement of Solar Neutrinos
Inverse beta decay
of chlorine
600 tons of
Perchloroethylene
Homestake solar neutrino
observatory (1967-2002)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from the Sun
Solar Neutrinos
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Hydrogen burning: Proton-Proton Chains
p + p  2H + e+ + ne
< 0.420 MeV
p + e- + p  2H + ne
1.442 MeV
100%
2
PP-I
85%
3
3
He + 3 He  4 He + 2p
0.24%
H + p  3 He + g
Be + e -  7 Li + n e
0.862 MeV
PP-II
7
7
10%
3
He + p  4 He + e + + n e
< 18.8 MeV
0.02%
Be + e -  7 Li* + n e
0.384 MeV
Li + p  4 He + 4 He
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
hep
He + 4 He  7 Be + g
90%
7
15%
PP-III
7
Be + p  8 B + g
8
B  8 Be* + e + + n e
< 15 MeV
8
Be*  4 He + 4 He
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Solar Neutrino Spectrum
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Hydrogen Burning: CNO Cycle
4 He
17
8O
(p,a)
e+
ne
15
7N
(p,a)
(p,g)
16
8O
(p,g)
17
9F
e+
ne
13
6C
(p,g)
14
7N
(p,g)
15
8O
e+
ne
12
6C
(p,g)
13
6N
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Missing Neutrinos from the Sun
Homestake
Chlorine
8B
Calculation of expected
experimental counting
rate from various
source reactions
John Bahcall
1934 - 2005
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
CNO
7Be
Measurement (1970 – 1995)
Raymond Davis Jr.
1914 - 2006
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Results of Chlorine Experiment
Average
Rate
Average (1970-1994) 2.56  0.16stat  0.16sys SNU
(SNU = Solar Neutrino Unit = 1 Absorption / sec / 1036 Atoms)
Theoretical Prediction 6-9 SNU
“Solar Neutrino Problem” since 1968
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrino Flavor Oscillations
Two-flavor mixing
 n e   cos  sin    n1 
   
 
n
 m   - sin  cos    n 2 
Each mass eigenstate propagates as e ipz
2
m
with p  E2 - m2  E 2E
m2
z implies flavor oscillations
Phase difference
2E
Probability
ne  nm
sin2(2)
z
2
Oscillation 4 pE  2.5 m  E   eV 

 2 
2
Length
MeV

  m 
m
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Bruno Pontecorvo
(1913 – 1993)
Invented nu oscillations
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Cherenkov Effect
Elastic scattering
or CC reaction
Light
Electron or Muon
(Charged Particle)
Light
Cherenkov
Ring
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Water
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Super-Kamiokande Neutrino Detector
42 m
39.3 m
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Super-Kamiokande: Sun in the Light of Neutrinos
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
2002 Physics Nobel Prize for Neutrino Astronomy
Ray Davis Jr.
(1914 - 2006)
Masatoshi Koshiba
(*1926)
“for pioneering contributions to astrophysics, in
particular for the detection of cosmic neutrinos”
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Solar Neutrino Spectrum
7-Be line measured
by Borexino (since 2007)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Solar Neutrino Spectroscopy with BOREXINO
• Neutrino electron scattering
• Liquid scintillator technology
(~ 300 tons)
• Low energy threshold
(~ 60 keV)
• Online since 16 May 2007
• Expected without flavor
oscillations
75 ± 4
counts/100t/d
• Expected with oscillations
49 ± 4
counts/100t/d
• BOREXINO result (May 2008)
49 ± 3stat ± 4sys cnts/100t/d
arXiv:0805.3843 (25 May 2008)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Next Steps in Borexino
• Collect more statistics of Beryllium line
• Seasonal variation of rate
(Earth orbit eccentricity)
• Measure neutrinos from the CNO reaction chain
• Information about solar metal abundance
Measure geo-neutrinos
(from natural radioactivity in the Earth crust)
Approx. 7-17 events/year
Main background: Reactors ~ 20 events/year
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Geo Neutrinos: Why and What?
We know surprisingly little about
the interior of the Earth:
• Deepest bore hole ~ 12 km
• Samples from the crust are
available for chemical analysis
(e.g. vulcanoes)
• Seismology reconstructs density
profile throughout the Earth
• Heat flow from measured
temperature gradients 30-44 TW
(BSE canonical model, based on
cosmo-chemical arguments,
predicts ~ 19 TW from crust and
mantle, none from core)
• Neutrinos escape freely
• Carry information about chemical composition, radioactive heat production,
or even a putative natural reactor at the core
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Expected Geo Neutrino Fluxes
S. Dye, Talk 5/25/2006
Baltimore
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Geo Neutrinos
Predicted geo neutrino flux
KamLAND scintillator detector (1 kton)
Reactor background
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Kamland Observation of Geoneutrinos
• First tentative observation of geoneutrinos
at Kamland in 2005 (~ 2 sigma effect)
• Very difficult because of large background
of reactor neutrinos
(is main purpose for neutrino oscillations)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from the Sun
Solar Models
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Equations of Stellar Structure
Assume spherical symmetry and static structure (neglect kinetic energy)
Excludes: Rotation, convection, magnetic fields, supernova-dynamics, …
Hydrostatic equilibrium
G M 
dP
- N r
dr
r2
Energy conservation
dLr
 4 pr 2
dr
Energy transfer
4 pr 2 d(aT 4 )
Lr 
3 dr
r
P
GN

Mr
Lr


Literature
• Clayton: Principles of stellar evolution and
nucleosynthesis (Univ. Chicago Press 1968)
• Kippenhahn & Weigert: Stellar structure
and evolution (Springer 1990)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Radius from center
Pressure
Newton’s constant
Mass density
Integrated mass up to r
Luminosity (energy flux)
Local rate of energy
generation [erg/g/s]
  nuc + grav -  n
Opacity
 -1   -g1 +  c-1
 g Radiative opacity
-1
g   g
Rosseland
 c Electron conduction
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Convection in Main-Sequence Stars
Sun
Kippenhahn & Weigert, Stellar Structure and Evolution
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Virial Theorem and Hydrostatic Equilibrium
Hydrostatic equilibrium
GNMr 
dP
dr
r2
R
Integrate both sides
R
3 
3 GNMr 
dr
4
p
r
P

dr
4
p
r


2
r
0
0
R
L.h.s. partial integration
with P = 0 at surface R
tot
- 3  dr 4 pr 2 P  Egrav
Classical monatomic gas: P  2 U
3
(U density of internal energy)
tot
Utot  - 21 Egrav
Average energy of single
“atoms” of the gas
0
Ekin  - 21 Egrav
Virial Theorem
Most important tool to understand
self-gravitating systems
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Virial Theorem Applied to the Sun
Ekin  - 21 Egrav
Virial Theorem
Approximate Sun as a homogeneous
sphere with
Mass
M sun  1.99  1033 g
Radius R sun  6.96  1010 cm
Gravitational potential energy of a
proton near center of the sphere
3 GNM sunmp
Egrav   -3.2 keV
2
R sun
Thermal velocity distribution
Ekin  32 kB T  - 21 Egrav
Estimated temperature
T = 1.1 keV
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Central temperature from
standard solar models
Tc  1.56  10 7 K
 1.34 keV
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Constructing a Solar Model: Fixed Inputs
Solve stellar structure equations with good microphysics, starting from a
zero-age main-sequence model (chemically homogeneous star) to present age
Fixed quantities
Solar mass
M⊙ = 1.989  1033 g
0.1%
Kepler’s 3rd law
Solar age
t⊙ = 4.57  109 yrs
0.5%
Meteorites
Quantities to match
Solar luminosity
Solar radius
Solar metals/hydrogen
ratio
L⊙ = 3.842  1033 erg s-1
0.4%
Solar constant
R⊙ = 6.9598  1010 cm
0.1%
Angular diameter
(Z/X)⊙ = 0.0229
Photosphere and
meteorites
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Constructing a Solar Model: Free Parameters
3 free parameters
• Convection theory has 1 free parameter:
Mixing length parameter aMLT
determines the temperature stratification where convection
is not adiabatic (upper layers of solar envelope)
• 2 of the 3 quantities determining the initial composition:
Xini, Yini, Zini (linked by Xini + Yini + Zini = 1).
Individual elements grouped in Zini have relative abundances
given by solar abundance measurements (e.g. GS98, AGS05)
• Construct a 1 M⊙ initial model with Xini, Zini, (Yini = 1 -Xini - Zini)
and aMLT
• evolve it for the solar age t⊙
• match (Z/X)⊙, L⊙ and R⊙ to better than one part in 105
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Standard Solar Model Output Information
Eight neutrino fluxes:
production profiles and integrated values.
Only 8B flux directly measured (SNO) so far
Chemical profiles X(r), Y(r), Zi(r)
 electron and neutron density profiles
(needed for matter effects in neutrino studies)
Thermodynamic quantities as a function of radius:
T, P, density (), sound speed (c)
Surface helium abundance Ysurf
(Z/X and 1 = X + Y + Z leave 1 degree of freedom)
Depth of the convective envelope, RCZ
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Standard Solar Model: Internal Structure
Temperature
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Density
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from the Sun
Helioseismology
and the
New Opacity Problem
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Helioseismology: Sun as a Pulsating Star
•
•
•
•
Discovery of oscillations: Leighton et al. (1962)
Sun oscillates in > 105 eigenmodes
Frequencies of order mHz (5-min oscillations)
Individual modes characterized by
radial n, angular l and longitudinal m numbers
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Helioseismology: p-Modes
• Solar oscillations are acoustic waves
(p-modes, pressure is the restoring force)
stochastically excited by convective motions
• Outer turning-point located close to temperature inversion layer
• Inner turning-point varies, strongly depends on l
(centrifugal barrier)
Credit: Jørgen Christensen-Dalsgaard
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Examples for Solar Oscillations
+
+
=
http://astro.phys.au.dk/helio_outreach/english/
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Helioseismology: Observations
• Doppler observations of spectral
lines measure velocities of
a few cm/s
• Differences in the frequencies
of order mHz
• Very long observations needed.
BiSON network (low-l modes)
has data for  5000 days
• Relative accuracy in frequencies
10-5
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Helioseismology: Comparison with Solar Models
• Oscillation frequencies depend on , P, g, c
• Inversion problem:
From measured frequencies and from a reference solar model
determine solar structure
• Output of inversion procedure: c2(r), (r), RCZ, YSURF
Relative sound-speed
difference between
helioseismological model
and standard solar model
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
New Solar Opacities (Asplund, Grevesse & Sauval 2005)
• Large change in solar composition:
Mostly reduction in C, N, O, Ne
• Results presented in many papers by the “Asplund group”
• Summarized in Asplund, Grevesse & Sauval (2005)
Authors
(Z/X)⊙
Main changes (dex)
Grevesse 1984
0.0277
Anders & Grevesse 1989
0.0267
Grevesse & Noels 1993
0.0245
Grevesse & Sauval 1998
0.0229
DC = -0.04, DN = -0.07, DO = -0.1
0.0165
DC = -0.13, DN = -0.14, DO = -0.17
DNe = -0.24, DSi = -0.05
(affects meteoritic abundances)
Asplund, Grevesse & Sauval
2005
DC = -0.1, DN = +0.06
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Origin of Changes
Spectral lines
from solar
photosphere
and corona
• Improved modeling
3D model atmospheres
MHD equations solved
NLTE effects accounted for in most cases
• Improved data
Better selection of spectral lines
Previous sets had blended lines
(e.g. oxygen line blended with nickel line)
• Volatile elements
do not aggregate easily into solid bodies
e.g. C, N, O, Ne, Ar only in solar spectrum
Meteorites
• Refractory elements,
e.g. Mg, Si, S, Fe, Ni
both in solar spectrum and meteorites
meteoritic measurements more robust
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Consequences of New Element Abundances
• Much improved modeling
What is good
• Different lines of same element give
same abundance (e.g. CO and CH lines)
• Sun has now similar composition
to solar neighborhood
New problems
• Agreement between helioseismology
and SSM very much degraded
• Was previous agreement a coincidence?
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Standard Solar Model 2005: Old and New Opacity
Sound Speed
Density
Old: BS05 (GS98)
New: BS05 (ASG05)
Helioseismology
RCZ
0.713
0.728
0.713 ± 0.001
YSURF
0.243
0.229
0.2485 ± 0.0035
<c>
0.001
0.005
---
<r>
0.012
0.044
---
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Old and New Neutrino Fluxes
Old: BS05 (GS98)
New: BS05 (AGS05)
Measurement (SNO)
Flux
cm-2 s-1
Error
%
4.99  106
 6.6
Flux
cm-2 s-1
Error
%
Flux
cm-2 s-1
Error
%
pp
5.99  1010
0.9
6.06  1010
0.7
pep
1.42  108
1.5
1.45  108
1.1
hep
7.93  103
15.5
8.25  103
15.5
7Be
4.84  109
10.5
4.34  109
9.3
8B
5.69  106
+17 -15
4.51  106
+13 -11
13N
3.05  108
+36 -27
2.00  108
+15 -13
15O
2.31  108
+37 -27
1.44  108
+17 -14
17F
5.84  106
+72 -42
3.25  106
+17 -14
Cl (SNU)
8.12
6.6
Ga (SNU)
126.1
118.9
Bahcall, Serenelli & Basu (astro-ph/0412440 & astro-ph/0511337)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from the Sun
Very Low-Energy
Solar Neutrinos
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from Thermal Plasma Processes
Photo (Compton)
Plasmon decay
Pair annihilation
Bremsstrahlung
These processes first
discussed in 1961-63
after V-A theory
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Solar Neutrinos from Compton Process
Cross section (non-relativistic limit)
4
2 2
E


32 aGF me 2
g


(C V + 5C2A ) 
2
105 (4 p)
 me 
Photo (Compton)
4
E


g

   1.34  10 -55 cm2 
 10 keV 
flavors
Volume energy loss rate

 2 d3p g E g  
Q n n  ne 
 (2p)3 Eg T
e
-1

Energy loss rate per unit mass
erg  T 8
Q nn
8
 nn    2.5  10
Ye 

g s  keV 
To be compared with nuclear energy generation rate in the Sun
L sun 4  1033 erg / s
erg
Watts 200 Watts
nuc 

2
 2  10 - 7

33
M sun
gs
g
kilo - ton
2  10 g
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Thermal vs. Nuclear Neutrinos from the Sun
Haxton & Lin, The very low energy solar flux of electron and
heavy-flavor neutrinos and anti-neutrinos, nucl-th/0006055
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from the Sun
Search for
Solar Axions
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Search for Solar Axions
Axion Helioscope (Sikivie 1983)
Axion-Photon-Oscillation
Primakoff
production
a
g
Axion flux
N
a
Magnet
g
S
Sun
 Tokyo Axion Helioscope (“Sumico”)
(Results since 1998, up again 2008)
 CERN Axion Solar Telescope (CAST)
(Data since 2003)
Alternative technique:
Bragg conversion in crystal
Experimental limits on solar axion flux
from dark-matter experiments
(SOLAX, COSME, DAMA, ...)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Tokyo Axion Helioscope (“Sumico”)
~3m
S.Moriyama, M.Minowa, T.Namba, Y.Inoue, Y.Takasu
& A.Yamamoto, PLB 434 (1998) 147
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
LHC Magnet Mounted as a Telescope to Follow the Sun
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
CAST at CERN
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Limits from CAST-I and CAST-II
CAST-I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010
CAST-II results (He-4 filling): preliminary
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from the Sun
High-Energy Neutrinos
from the Sun
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Search for WIMP Dark Matter
Direct Method (Laboratory Experiments)
Galactic
dark matter
particle
(e.g.neutralino)
Crystal
Energy
deposition
Recoil energy
(few keV) is
measured by
• Ionisation
• Scintillation
• Cryogenic
Indirect Method (Neutrino Telescopes)
Galactic dark
matter
particles
are accreted
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Annihilation
Sun
High-energy
neutrinos
(GeV-TeV)
can be measured
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
IceCube Neutrino Telescope at the South Pole
• 1 km3 antarctic ice, instrumented
with 4800 photomultipliers
• 40 of 80 strings installed (2008)
• Completion until 2011 foreseen
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Muon Flux from WIMP Annihilation in the Sun
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
High-Energy Neutrinos from the Sun
Ingelman & Thunman, High Energy Neutrino Production by
Cosmic Ray Interactions in the Sun [hep-ph/9604288]
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos (and other Particles) from the Sun
Thermal plasma reactions
E ~ 1 eV - 30 keV
No apparent way to measure
Nuclear burning reactions
E ~ 0.1 - 18 MeV
Routine detailed measurements
Cosmic-ray interactions in the Sun
E ~ 10 - 109 GeV
Future high-E neutrino telescopes (?)
Dark matter annihilation in the Sun
E ~ GeV - TeV (?)
Future high-E neutrino telescopes (?)
New particles, notably axions
Are searched with CAST & Sumico
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Basics of Stellar Evolution
Basics of Stellar Evolution
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Equations of Stellar Structure
Assume spherical symmetry and static structure (neglect kinetic energy)
Excludes: Rotation, convection, magnetic fields, supernova-dynamics, …
Hydrostatic equilibrium
G M 
dP
- N r
dr
r2
Energy conservation
dLr
 4 pr 2
dr
Energy transfer
4 pr 2 d(aT 4 )
Lr 
3 dr
r
P
GN

Mr
Lr


Literature
• Clayton: Principles of stellar evolution and
nucleosynthesis (Univ. Chicago Press 1968)
• Kippenhahn & Weigert: Stellar structure
and evolution (Springer 1990)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Radius from center
Pressure
Newton’s constant
Mass density
Integrated mass up to r
Luminosity (energy flux)
Local rate of energy
generation [erg/g/s]
  nuc + grav -  n
Opacity
 -1   -g1 +  c-1
 g Radiative opacity
-1
g   g
Rosseland
 c Electron conduction
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Nuclear Binding Energy
Fe
Mass Number
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Thermonuclear Reactions and Gamow Peak
Coulomb repulsion prevents nuclear
reactions, except for Gamow tunneling
Tunneling probability
p  E-1 2e - 2p
With Sommerfeld parameter
12
m
   
 2E 
Z1Z2e 2
Parameterize cross section with
astrophysical S-factor
S(E)  (E) E e2p (E)
LUNA Collaboration, nucl-ex/9902004
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Main Nuclear Burnings
Hydrogen burning 4p + 2e-  4He + 2ne
• Proceeds by pp chains and CNO cycle
• No higher elements are formed because
no stable isotope with mass number 8
• Neutrinos from p  n conversion
• Typical temperatures: 107 K (~1 keV)
• Each type of burning occurs
at a very different T but a
broad range of densities
• Never co-exist in the same
location
Helium burning
4He + 4He + 4He  8Be + 4He  12C
“Triple alpha reaction” because 8Be unstable,
builds up with concentration ~ 10-9
12C + 4He  16O
16O + 4He  20Ne
Typical temperatures: 108 K (~10 keV)
Carbon burning
Many reactions, for example
12C + 12C  23Na + p or 20Ne + 4He etc
Typical temperatures: 109 K (~100 keV)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Hydrogen Exhaustion in a Main-Sequence Star
Main-sequence star
Hydrogen Burning
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Helium-burning star
Helium
Burning
Hydrogen
Burning
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Burning Phases of a 15 Solar-Mass Star
Burning Phase
Dominant
Process
Hydrogen
H  He
Helium
He  C, O
Carbon
Tc
c
[keV] [g/cm3]
Ln/Lg
-
Duration
[years]
1.2 107
5.9
2.1
14
1.3103
6.0 1.7 10-5
1.3 106
C  Ne, Mg
53
1.7105
8.6
1.0
6.3 103
Neon
Ne  O, Mg
110
1.6107
9.6
1.8 103
7.0
Oxygen
O  Si
160
9.7107
9.6
2.1 104
1.7
Silicon
Si  Fe, Ni
270
2.3108
9.6
9.2 105
6 days
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
3
Lg [104 Lsun]
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from Thermal Plasma Processes
Photo (Compton)
Plasmon decay
Pair annihilation
Bremsstrahlung
These processes first
discussed in 1961-63
after V-A theory
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrino Energy Loss Rates
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Existence of Direct Neutrino-Electron Coupling
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Self-Regulated Nuclear Burning
Virial Theorem
Ekin  - 21 Egrav
Small Contraction
 Heating
 Increased nuclear burning
 Increased pressure
 Expansion
Main-Sequence Star
Additional energy loss (“cooling”)
 Loss of pressure
 Contraction
 Heating
 Increased nuclear burning
Hydrogen burning at a nearly fixed T
 Gravitational potential nearly fixed:
GNM/R ~ constant
 R  M (More massive stars bigger)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Degenerate Stars (“White Dwarfs”)
Assume T very small
 No thermal pressure
 Electron degeneracy is pressure source
Pressure ~ Momentum density x Velocity
• Electron density ne  pF3 (3p 2 )
• Momentum pF (Fermi momentum)
• Velocity
• Pressure
v  pF me
P  pF5  5 3  M5 3R -5
-3
• Density
  MR
(Stellar mass M and radius R)
Hydrostatic equilibrium
G M 
dP
- N r
dr
r2
With dP/dr ~ -P/R we have approximately
P  GNMR -1  GNM 2R - 4
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Inverse mass-radius relationship
for degenerate stars: R  M-1/3
13
 0.6 M sun 
R  10,500 km 

M


(2 Ye )5 3
(Ye electrons per nucleon)
For sufficiently large mass,
electrons become relativistic
• Velocity = speed of light
• Pressure
P  pF4   4 3  M 4 3R - 4
No stable configuration
Chandrasekhar mass limit
M Ch  1.457 M sun (2Ye )2
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Degenerate Stars (“White Dwarfs”)
Inverse mass-radius relationship
for degenerate stars: R  M-1/3
Chandrasekhar mass limit
M Ch  1.457 M sun (2Ye )2
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Stellar Collapse
Main-sequence
Onion structure
star
Degenerate iron core:
  109 g cm-3
Hydrogen
Burning
T  1010 K
MFe  1.5 Msun
RFe  8000 km
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Collapse
Helium-burning
(implosion)
star
Helium
Burning
Hydrogen
Burning
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Evolution of Stars
M < 0.08 Msun
Never ignites hydrogen  cools
(“hydrogen white dwarf”)
Brown dwarf
0.08 < M ≲ 0.8 Msun
Hydrogen burning not completed
in Hubble time
Low-mass
main-squence star
0.8 ≲ M ≲ 2 Msun
Degenerate helium core
after hydrogen exhaustion
2 ≲ M ≲ 5-8 Msun
Helium ignition non-degenerate
6-8 Msun ≲ M < ???
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
All burning cycles
 Onion skin
structure with
degenerate iron
core
Core
collapse
supernova
• Carbon-oxygen
white dwarf
• Planetary nebula
• Neutron star
(often pulsar)
• Sometimes
black hole?
• Supernova
remnant (SNR),
e.g. crab nebula
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Evolution of a Low-Mass Star
H
H
He
C
O
H
He
H
He
MS
Main-Sequence
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
RGB
HB
Ged-Giant Branch
AGB
Horizontal
Branch
Asymptotic
Giant Branch
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Planetary Nebulae
Hour
Glass
Nebula
Planetary
Nebula IC 418
Eskimo
Nebula
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Planetary
Nebula NGC 3132
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Globular Clusters of the Milky Way
http://www.dartmouth.edu/~chaboyer/mwgc.html
Globular clusters on top of the
FIRAS 2.2 micron map of the Galaxy
The galactic globular cluster M3
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Color-Magnitude Diagram for Globular Clusters
• Stars with M
so large that
they have burnt
out in a Hubble
time
• No new star
formation in
globular
clusters
H
Hot, blue
cold, red
Main-Sequence
Color-magnitude diagram synthesized from several low-metallicity globular
clusters and compared with theoretical isochrones (W.Harris, 2000)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Color-Magnitude Diagram for Globular Clusters
H
He
H
C
O
He
Asymptotic Giant
Red Giant
H
H
He
C
O
Horizontal Branch
White
Dwarfs
Hot, blue
cold, red
Main-Sequence
Color-magnitude diagram synthesized from several low-metallicity globular
clusters and compared with theoretical isochrones (W.Harris, 2000)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Basics of Stellar Evolution
Bounds on
Neutrino Properties
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Basic Argument
Flux of weakly interacting particles
Star
• Low-mass weakly-interacting particles can be emitted from stars
• New energy-loss channel
• Back-reaction on stellar properties and evolution
• What are the emission processes?
• What are the observable consequences?
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Bernstein et al.
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Color-Magnitude Diagram for Globular Clusters
H
He
H
Particle emission
delays He ignition, i.e. He
core mass increased
C
O
Asymptotic Giant
Red Giant
H
H
He Particle emission reduces
helium burning lifetime,
C
i.e. number of HB
O stars
White
Dwarfs
Horizontal Branch
Hot, blue
cold, red
Main-Sequence
Color-magnitude diagram synthesized from several low-metallicity globular
clusters and compared with theoretical isochrones (W.Harris, 2000)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrinos from Thermal Plasma Processes
Photo (Compton)
Plasmon decay
Pair annihilation
Bremsstrahlung
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Plasmon Decay in Neutrinos
Propagation in vacuum:
• Photon massless
• Can not decay into other
particles, even if they
themselves are massless
Plasmon decay
Propagation in a medium:
• Photon acquires a “refractive index”
• In a non-relativistic plasma
(e.g. Sun, white dwarfs, core of red
giant before helium ignition, …)
behaves like a massive particle:
2
2 - k 2  pl
2  4pane
Plasma frequency
pl
me
(electron density ne)
• Degenerate helium core pl  18 keV
( = 106 g/cm3, T = 8.6 keV)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Interaction in vacuum:
• Massless neutrinos do
not couple to photons
• May have dipole moments
or even “millicharges”
Interaction in a medium:
• Neutrinos interact coherently with
the charged particles which
themselves couple to photons
• Induces an “effective charge”
• In a degenerate plasma
(electron Fermi energy EF and
Fermi momentum pF)
en
 16 2 C V GFEFpF
e
• Degenerate helium core (and CV = 1)
e n  6  10 -11e
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Plasmon Decay vs. Cherenkov Effect
Photon dispersion in
a medium can be
Refractive index n
(k = n )
Example
Allowed process
in medium
that is forbidden
in vacuum
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
“Time-like”
“Space-like”
2 - k2 > 0
2 - k2 < 0
n<1
n>1
• Ionized plasma
• Normal matter for
large photon energies
Water (n  1.3),
air, glass
for visible frequencies
Plasmon decay to
neutrinos
g  nn
Cherenkov effect
e e+ g
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrino-Photon-Coupling in a Plasma
Neutrino effective
in-medium coupling
L eff  - 2GF g a 1 (1 - g 5) aA 
2
For vector-current
analogous to photon
polarization tensor

3


 (PK)2 gmn + K 2PmP n - (PK)(PmK n + K mP n )
d p
mn
 V (K)  4 eCV 
[f (p) + f + (p)]
3 ee
(PK)2 - 41 (K 2 )2
 2E(2p)
C
 V  mn
(K)
V
e

2P K
3
K



d
p
Usually
a 
mn
 A (K)  2ieCA  mna
[f - (p) - f + (p)]
3 e
e
negligible
(PK)2 - 41 (K 2 )2
 2E(2p)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutral-Current Couplings and Plasmon Decay
Standard-model
plasmon decay
process  C2V
sin2  W  41
Standard-model
plasmon decay
produces almost
exclusively n e n e
A neutral-current process that was
never useful for “neutrino counting”
unlike big-bang nucleosynthesis
(of course today Z0-decay width
fixes Nn = 3)
G
Hint  F f g m (C V - C A g 5)f n g m (1 - g 5)n
2
Neutrino
ne
GF 
1.166  10 - 5 GeV - 2
2
sin  W  0.231
nm , n 
n e, nm , n 
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Fermion
CV
CA
+ 21 + 2 sin2  W  1
+ 21
- 21 + 2 sin2  W  0
- 21
Proton
+ 21 - 2 sin2  W  0
+ 1.226
Neutron
- 21
- 1.226
Electron
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrino Electromagnetic Form Factors
Effective
L eff  - F1  g m  A m
coupling of
electromagnetic
- G1  g m g 5  nF mn
field to a
neutral fermion
- 1 F2  mn F mn
2
Charge en = F1(0) = 0
Anapole moment G1(0)
Magnetic dipole moment m = F2(0)
- 1 G2  mng 5 Fmn Electric dipole moment  = G2(0)
2
• Charge form factor F1(q2) and anapole G1(q2) are short-range interactions
if charge F1(0)  0
• Connect states of equal helicity
• In the standard model they represent radiative corrections to weak interaction
• Dipole moments connect states of opposite helicity
• Violation of individual flavor lepton numbers (neutrino mixing)
 Magnetic or electric dipole moments can connect different flavors
or different mass eigenstates (“Transition moments”)
• Usually measured in “Bohr magnetons” mB = e/2me
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Standard Dipole Moments for Massive Neutrinos
In standard electroweak model,
neutrino dipole and
transition moments
are induced at higher order
Massive neutrinos ni (i = 1,2,3),
mixed to form weak eigenstates
Explicit evaluation for Dirac
neutrinos
(Magnetic moments mij
electric moments ij)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
3
n    Uin i
i1
 m 
e 2GF
*

m ij 
(mi + mj)  UjUi f 
2
(4 p)
 mW 
  e,m,
 ij  ... (mi - mj) ...
2
4

 m 




m
m
  - 3 + 3    + O    
f 
2 4 m
  mW  
 mW 
 W


Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Standard Dipole Moments for Massive Neutrinos
Diagonal case
(Magnetic moments
of Dirac neutrinos)
m ii 
3e 2GF
m
mi  3.20  10 -19 mB i
eV
(4 p)2
mB  e
 ij  0
Off-diagonal case
(Transition moments)
First term in
f(mℓ/mW) does not
contribute
(“GIM cancellation”)
2me
2
m 
3e 2GF
*  m 
m ij 
(mi + mj)  
U
U
 j i  
2
m
4(4 p)
 W    e,m,
 m 
 3.96  10 - 23 mB
mi + mj
eV
*  m 
U
U
 j i  
 m 
  e,m,
2
2
 ij  ... (mi - mj) ...
Largest neutrino mass eigenstate 0.05 eV < m < 0.2 eV
For Dirac neutrino expect
1.6  10 -20 mB < m n < 0.6  10 -19 mB
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Consequences of Neutrino Dipole Moments
Spin
precession
in external
E or B fields
m nB  nL 
  nL   0
i  
 
0  nR 
t  nR   m nB
2
d GF me

dT
2p
Scattering

me T 
T 2

2
2
2
2
(C V + C A ) + (C V - C A ) 1 -  + (C V - C A ) 2 
 E
E 

1 1
+ am2n  + 
 T E
T electron recoil energy
Plasmon
decay in
stars
Decay or
Cherenkov
effect
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
m 2n 3


24 p pl
3
2  m2 - m2 
m
1
 n 2
8p  m2 


Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Plasmon Decay and Stellar Energy Loss Rates
Assume photon dispersion relation like a
massive particle (nonrelativistic plasma)
2 
E2g - p2g  pl
4 pane
me
Photon decay rate
(transverse plasmon)
with energy Eg
 a (2 4 p)
 n pl
4 p  m 2n 2
(g  nn) 

(pl 4 p)2
3E g  2
2 2
CVGF (2 4 p)3
 a
pl
Energy-loss rate
of stellar plasma
(temperature T
and plasma
frequency pl)
 a (2 4 p)
 n pl

 2d3p E g g  nn 8 3 T 3  m 2n 2
Q(g  nn)  


(pl 4 p)2
2
3 E T
3p
 (2p) e g - 1
 2 2
CVGF (2 4 p)3
 a
pl
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Millicharge
Dipole moment
Standard model
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Globular Cluster Limits on Neutrino Dipole Moments
Compare magnetic-dipole
plasma emission with
standard case
Qm
Q SM

2pam2n
2
C2V GF2pl
For red-giant core before
helium ignition pl = 18 keV
Qm
2
m 
 9  10 22  n 
Q SM
 mB 
Require this to be < 1
m n < 3  10 -12 mB
Globular-cluster limit on neutrino dipole moment
m n < 3  10 -12 mB
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Neutrino Radiative Lifetime Limits
Radiative
decay
n  n + g
Plasmon
decay
g pl  n + n
n  ng 
g  nn 
m 2eff
8p
m 2eff
24 p
m3n
3
pl
For low-mass
neutrinos,
plasmon decay
in globular
cluster stars
yields most
restrictive limits
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China
Limits on Milli-Charged Particles
Davidson,
Hannestad &
Raffelt
JHEP 5 (2000) 3
Globular
cluster limit
most restrictive
for small masses
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany
Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China

Neutrinos - MPP Theory Group