1. Neutrinos and the stars
Georg Raffelt, MPI for Physics
Lectures at the Topical Seminar
Neutrino Physics & Astrophysics
17-21 Sept 2008, Beijing, China

2. 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) 
Astrophysical
Accelerators Soon ?

3. Where do Neutrinos Appear in Nature?
Neutrinos from nuclear
reactions:
Energies 1-20 MeV
Quasi thermal sources
Supernova: T ~ few MeV
Big-Bang Neutrinos:
Very small energies today
(cosmic red shift)
Like matter today
“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

4. 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

5. Neutrinos from the Sun Helium Solar radiation: 98 % light
Hans Bethe ( , Nobel prize 1967)
Thermonuclear reaction chains (1938)
Helium
Reaction-
chains
Energy
26.7 MeV
Solar radiation: 98 % light
2 % neutrinos
At Earth 66 billion neutrinos/cm2 sec

6. Bethe’s Classic Paper on Nuclear Reactions in Stars
No neutrinos
from nuclear reactions
in 1938 …

7. Gamow & Schoenberg, Phys. Rev. 58:1117 (1940)

8. Gamow & Schoenberg 2

9. 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.”

10. First Detection (1954 - 1956) g p n Cd e+ e- Clyde Cowan (1919 – 1974)
Fred Reines
(1918 – 1998)
Nobel prize 1995
Detector prototype
Anti-Electron
Neutrinos
from
Hanford
Nuclear Reactor
3 Gammas
in coincidence p n Cd e+ e- g

11. First Measurement of Solar Neutrinos
Inverse beta decay
of chlorine
600 tons of
Perchloroethylene
Homestake solar neutrino
observatory ( )

12. Neutrinos from the Sun
Solar Neutrinos

13. Hydrogen burning: Proton-Proton Chains
< MeV
1.442 MeV
100%
0.24%
15%
85%
PP-I
< 18.8 MeV
hep
90%
10%
0.02%
0.862 MeV
0.384 MeV
< 15 MeV
PP-II
PP-III

14. Solar Neutrino Spectrum

15. Hydrogen Burning: CNO Cycle
(p,g)
(p,a)
(p,g)
(p,a)

16. Missing Neutrinos from the Sun
Homestake
Chlorine
7Be 8B
CNO
Measurement (1970 – 1995)
Calculation of expected
experimental counting
rate from various
source reactions
John Bahcall
Raymond Davis Jr.

17. Results of Chlorine Experiment
Average
Rate
Average ( )  0.16stat  0.16sys SNU
(SNU = Solar Neutrino Unit = 1 Absorption / sec / 1036 Atoms)
Theoretical Prediction 6-9 SNU
“Solar Neutrino Problem” since 1968

18. Neutrino Flavor Oscillations
Two-flavor mixing
Each mass eigenstate propagates as
with
Phase difference implies flavor oscillations
Probability ne  nm
sin2(2q)
Bruno Pontecorvo
(1913 – 1993)
Invented nu oscillations z
Oscillation
Length

19. Elastic scattering or CC reaction
Cherenkov Effect
Cherenkov Ring
Elastic scattering or CC reaction
Light
Electron or Muon
(Charged Particle)
Neutrino
Water

20. Super-Kamiokande Neutrino Detector

21. Super-Kamiokande: Sun in the Light of Neutrinos

22. 2002 Physics Nobel Prize for Neutrino Astronomy
Ray Davis Jr.
( )
Masatoshi Koshiba
(*1926)
“for pioneering contributions to astrophysics, in
particular for the detection of cosmic neutrinos”

23. Solar Neutrino Spectrum
7-Be line measured
by Borexino (since 2007)

24. 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 ± counts/100t/d
Expected with oscillations
49 ± counts/100t/d
BOREXINO result (May 2008)
49 ± 3stat ± 4sys cnts/100t/d
arXiv: (25 May 2008)

25. 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 events/year
Main background: Reactors ~ 20 events/year

26. 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 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

27. Expected Geo Neutrino Fluxes
S. Dye, Talk 5/25/2006
Baltimore

28. Geo Neutrinos Predicted geo neutrino flux
KamLAND scintillator detector (1 kton)
Reactor background

29. 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)

30. Neutrinos from the Sun
Solar Models

31. Equations of Stellar Structure
Assume spherical symmetry and static structure (neglect kinetic energy)
Excludes: Rotation, convection, magnetic fields, supernova-dynamics, …
Hydrostatic equilibrium r P GN Mr Lr e
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]
Opacity
Radiative opacity
Electron conduction
Energy conservation
Energy transfer
Literature
Clayton: Principles of stellar evolution and
nucleosynthesis (Univ. Chicago Press 1968)
Kippenhahn & Weigert: Stellar structure
and evolution (Springer 1990)

32. Convection in Main-Sequence Stars
Sun
Kippenhahn & Weigert, Stellar Structure and Evolution

33. Virial Theorem and Hydrostatic Equilibrium
Integrate both sides
L.h.s. partial integration
with P = 0 at surface R
Classical monatomic gas:
(U density of internal energy)
Average energy of single
“atoms” of the gas
Virial Theorem
Most important tool to understand
self-gravitating systems

34. Virial Theorem Applied to the Sun
Approximate Sun as a homogeneous
sphere with
Mass
Radius
Gravitational potential energy of a
proton near center of the sphere
Thermal velocity distribution
Estimated temperature
T = 1.1 keV
Central temperature from
standard solar models

35. 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⊙ =  1033 g
0.1%
Kepler’s 3rd law
Solar age
t⊙ = 4.57  109 yrs
0.5%
Meteorites
Quantities to match
Solar luminosity
L⊙ =  1033 erg s-1
0.4%
Solar constant
Solar radius
R⊙ =  1010 cm
0.1%
Angular diameter
Solar metals/hydrogen ratio
(Z/X)⊙ =
Photosphere and meteorites
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

36. Constructing a Solar Model: 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

37. 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 (r), 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

38. Standard Solar Model: Internal Structure
Temperature
Density

39. Helioseismology and the New Opacity Problem
Neutrinos from the Sun
Helioseismology
and the
New Opacity Problem

40. 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

41. 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

42. Examples for Solar Oscillations+ + =

43. 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

44. Helioseismology: Comparison with Solar Models
Oscillation frequencies depend on r, P, g, c
Inversion problem:
From measured frequencies and from a reference solar model
determine solar structure
Output of inversion procedure: dc2(r), dr(r), RCZ, YSURF
Relative sound-speed
difference between
helioseismological model
and standard solar model

45. 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
DC = -0.1, DN = +0.06
Grevesse & Noels 1993
0.0245
Grevesse & Sauval 1998
0.0229
DC = -0.04, DN = -0.07, DO = -0.1
Asplund, Grevesse & Sauval
2005
0.0165
DC = -0.13, DN = -0.14, DO = DNe = -0.24, DSi = -0.05
(affects meteoritic abundances)
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

46. Origin of Changes Improved modeling 3D model atmospheres
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)
Meteorites
Volatile elements
do not aggregate easily into solid bodies
e.g. C, N, O, Ne, Ar only in solar spectrum
Refractory elements,
e.g. Mg, Si, S, Fe, Ni
both in solar spectrum and meteorites
meteoritic measurements more robust

47. Consequences of New Element Abundances
What is good
Much improved modeling
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

48. 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 ±
<dc>
0.001
0.005
---
<dr>
0.012
0.044
Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

49. Old and New Neutrino Fluxes
Old: BS05 (GS98)
New: BS05 (AGS05)
Measurement (SNO)
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
7Be
4.84  109
10.5
4.34  109
9.3 8B
5.69  106
4.51  106
4.99  106
 6.6
13N
3.05  108
2.00  108
15O
2.31  108
1.44  108
17F
5.84  106
3.25  106
Cl (SNU)
8.12
6.6
Ga (SNU)
126.1
118.9
Bahcall, Serenelli & Basu (astro-ph/ & astro-ph/ )

50. Very Low-Energy Solar Neutrinos
Neutrinos from the Sun
Very Low-Energy
Solar Neutrinos

51. Neutrinos from Thermal Plasma Processes
Photo (Compton)
Plasmon decay
Pair annihilation
Bremsstrahlung
These processes first
discussed in
after V-A theory

52. Solar Neutrinos from Compton Process
Photo (Compton)
Cross section (non-relativistic limit)
Volume energy loss rate
Energy loss rate per unit mass
To be compared with nuclear energy generation rate in the Sun

53. 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/

54. Search for Solar Axions
Neutrinos from the Sun
Search for
Solar Axions

55. Search for Solar Axions
Axion Helioscope (Sikivie 1983) g
Magnet S N a
Axion-Photon-Oscillation
Primakoff
production
Axion flux a g
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, ...)

56. Tokyo Axion Helioscope (“Sumico”)
S.Moriyama, M.Minowa, T.Namba, Y.Inoue, Y.Takasu
& A.Yamamoto, PLB 434 (1998) 147

57. LHC Magnet Mounted as a Telescope to Follow the Sun

58. CAST at CERN

59. Limits from CAST-I and CAST-II
CAST-I results: PRL 94: (2005) and JCAP 0704 (2007) 010
CAST-II results (He-4 filling): preliminary

60. High-Energy Neutrinos
Neutrinos from the Sun
High-Energy Neutrinos
from the Sun

61. Search for WIMP Dark Matter
Direct Method (Laboratory Experiments)
Crystal
Energy
deposition
Recoil energy
(few keV) is
measured by
Ionisation
Scintillation
Cryogenic
Galactic
dark matter
particle
(e.g.neutralino)
Indirect Method (Neutrino Telescopes)
Sun
Annihilation
High-energy
neutrinos
(GeV-TeV)
can be measured
Galactic dark
matter
particles
are accreted

62. 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

63. Muon Flux from WIMP Annihilation in the Sun

64. High-Energy Neutrinos from the Sun
Ingelman & Thunman, High Energy Neutrino Production by
Cosmic Ray Interactions in the Sun [hep-ph/ ]

65. Neutrinos (and other Particles) from the Sun
Thermal plasma reactions
E ~ 1 eV - 30 keV
No apparent way to measure
Nuclear burning reactions
E ~ MeV
Routine detailed measurements
Cosmic-ray interactions in the Sun
E ~ 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

66. Basics of Stellar Evolution

67. Equations of Stellar Structure
Assume spherical symmetry and static structure (neglect kinetic energy)
Excludes: Rotation, convection, magnetic fields, supernova-dynamics, …
Hydrostatic equilibrium r P GN Mr Lr e
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]
Opacity
Radiative opacity
Electron conduction
Energy conservation
Energy transfer
Literature
Clayton: Principles of stellar evolution and
nucleosynthesis (Univ. Chicago Press 1968)
Kippenhahn & Weigert: Stellar structure
and evolution (Springer 1990)

68. Nuclear Binding Energy
Mass Number Fe

69. Thermonuclear Reactions and Gamow Peak
Coulomb repulsion prevents nuclear
reactions, except for Gamow tunneling
Tunneling probability
With Sommerfeld parameter
Parameterize cross section with
astrophysical S-factor
LUNA Collaboration, nucl-ex/

70. Main Nuclear Burnings 12C + 12C  23Na + p or 20Ne + 4He etc
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)

71. Hydrogen Exhaustion in a Main-Sequence Star
Hydrogen Burning
Helium-burning star
Helium
Burning
Hydrogen

72. Burning Phases of a 15 Solar-Mass Star
Hydrogen 3
H  He -
2.1
5.9
1.2 107
Duration
[years]
Ln/Lg rc
[g/cm3] Tc
[keV]
Dominant
Process
Burning Phase
Lg [104 Lsun]
Helium 14
He  C, O
1.7 10-5
6.0
1.3103
1.3 106
Carbon
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

73. Neutrinos from Thermal Plasma Processes
Photo (Compton)
Plasmon decay
Pair annihilation
Bremsstrahlung
These processes first
discussed in
after V-A theory

74. Neutrino Energy Loss Rates

75. Existence of Direct Neutrino-Electron Coupling

76. Self-Regulated Nuclear Burning
Virial Theorem
Main-Sequence Star
Small Contraction
 Heating
 Increased nuclear burning
 Increased pressure
 Expansion
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)

77. Degenerate Stars (“White Dwarfs”)
Assume T very small
 No thermal pressure
 Electron degeneracy is pressure source
Inverse mass-radius relationship
for degenerate stars: R  M-1/3
Pressure ~ Momentum density x Velocity
Electron density
Momentum pF (Fermi momentum)
Velocity
Pressure
Density
(Stellar mass M and radius R)
(Ye electrons per nucleon)
For sufficiently large mass,
electrons become relativistic
Velocity = speed of light
Pressure
No stable configuration
Hydrostatic equilibrium
With dP/dr ~ -P/R we have approximately
Chandrasekhar mass limit

78. Degenerate Stars (“White Dwarfs”)
Inverse mass-radius relationship
for degenerate stars: R  M-1/3
Chandrasekhar mass limit

79. Stellar Collapse Onion structure Main-sequence star Hydrogen Burning
Collapse (implosion)
Helium-burning star
Helium
Burning
Hydrogen
Degenerate iron core:
r  109 g cm-3
T  K
MFe  1.5 Msun
RFe  8000 km

80. 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
Carbon-oxygen
white dwarf
Planetary nebula
2 ≲ M ≲ 5-8 Msun
Helium ignition non-degenerate
6-8 Msun ≲ M < ???
All burning cycles
Onion skin
structure with
degenerate iron
core
Core
collapse
supernova
Neutron star
(often pulsar)
Sometimes
black hole?
Supernova
remnant (SNR),
e.g. crab nebula

81. Evolution of a Low-Mass StarH
Main-Sequence MS
Ged-Giant Branch H He
RGB
Horizontal
Branch H He HB
Asymptotic
Giant Branch H He C O
AGB

82. Planetary Nebulae Hour Glass Nebula Planetary Nebula IC 418 Eskimo
Nebula NGC 3132

83. Globular Clusters of the Milky Way
Globular clusters on top of the
FIRAS 2.2 micron map of the Galaxy
The galactic globular cluster M3

84. Color-Magnitude Diagram for Globular Clusters
Mass
Stars with M
so large that
they have burnt
out in a Hubble
time
No new star
formation in
globular
clusters H
Main-Sequence
Hot, blue
cold, red
Color-magnitude diagram synthesized from several low-metallicity globular
clusters and compared with theoretical isochrones (W.Harris, 2000)

85. Color-Magnitude Diagram for Globular ClustersH He C O
Asymptotic Giant H He
Red Giant H He
Horizontal Branch H
Main-Sequence C O
White
Dwarfs
Hot, blue
cold, red
Color-magnitude diagram synthesized from several low-metallicity globular
clusters and compared with theoretical isochrones (W.Harris, 2000)

86. Basics of Stellar Evolution
Bounds on
Neutrino Properties

87. Basic Argument Star Flux of weakly interacting particles
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?

88. Bernstein et al.

89. Color-Magnitude Diagram for Globular ClustersH He C O
Asymptotic Giant H He
Red Giant
Particle emission
delays He ignition, i.e.
core mass increased H He
Horizontal Branch H
Main-Sequence
Particle emission reduces
helium burning lifetime,
i.e. number of HB stars C O
White
Dwarfs
Hot, blue
cold, red
Color-magnitude diagram synthesized from several low-metallicity globular
clusters and compared with theoretical isochrones (W.Harris, 2000)

90. Neutrinos from Thermal Plasma Processes
Photo (Compton)
Plasmon decay
Plasmon decay
Pair annihilation
Bremsstrahlung

91. Plasmon Decay in Neutrinos
Propagation in vacuum:
Photon massless
Can not decay into other
particles, even if they
themselves are massless
Interaction in vacuum:
Massless neutrinos do
not couple to photons
May have dipole moments
or even “millicharges”
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:
Plasma frequency
(electron density ne)
Degenerate helium core
(r = 106 g/cm3, T = 8.6 keV)
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)
Degenerate helium core (and CV = 1)

92. Plasmon Decay vs. Cherenkov Effect
Photon dispersion in
a medium can be
“Time-like”
w2 - k2 > 0
“Space-like”
w2 - k2 < 0
Refractive index n
(k = n w)
n < 1
n > 1
Example
Ionized plasma
Normal matter for
large photon energies
Water (n  1.3),
air, glass
for visible frequencies
Allowed process
in medium
that is forbidden
in vacuum
Plasmon decay to
neutrinos
Cherenkov effect

93. Neutrino-Photon-Coupling in a Plasma
Neutrino effective
in-medium coupling
For vector-current
analogous to photon
polarization tensor
Usually
negligible

94. Neutral-Current Couplings and Plasmon Decay
Standard-model
plasmon decay
process
produces almost
exclusively
A neutral-current process that was
never useful for “neutrino counting”
unlike big-bang nucleosynthesis
(of course today Z0-decay width
fixes Nn = 3)
Neutrino
Fermion CV CA
Electron
Proton
Neutron

95. Neutrino Electromagnetic Form Factors
Effective
coupling of
electromagnetic
field to a
neutral fermion
Charge en = F1(0) = 0
Anapole moment G1(0)
Magnetic dipole moment m = F2(0)
Electric dipole moment e = G2(0)
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

96. 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 eij)

97. Standard Dipole Moments for Massive Neutrinos
Diagonal case
(Magnetic moments
of Dirac neutrinos)
Off-diagonal case
(Transition moments)
First term in
f(mℓ/mW) does not
contribute
(“GIM cancellation”)
Largest neutrino mass eigenstate eV < m < 0.2 eV
For Dirac neutrino expect

98. Consequences of Neutrino Dipole Moments
Spin
precession
in external
E or B fields
Scattering
T electron recoil energy
Plasmon
decay in
stars
Decay or
Cherenkov
effect

99. Plasmon Decay and Stellar Energy Loss Rates
Assume photon dispersion relation like a
massive particle (nonrelativistic plasma)
Photon decay rate
(transverse plasmon)
with energy Eg
Millicharge
Dipole moment
Standard model
Energy-loss rate
of stellar plasma
(temperature T
and plasma
frequency wpl)

100. Globular Cluster Limits on Neutrino Dipole Moments
Compare magnetic-dipole
plasma emission with
standard case
For red-giant core before
helium ignition wpl = 18 keV
Require this to be < 1
Globular-cluster limit on neutrino dipole moment

101. Neutrino Radiative Lifetime Limits
decay
Plasmon
decay
For low-mass
neutrinos,
plasmon decay
in globular
cluster stars
yields most
restrictive limits

102. Limits on Milli-Charged Particles
Davidson,
Hannestad &
Raffelt
JHEP 5 (2000) 3
Globular
cluster limit
most restrictive
for small masses