Neutrinos and the Stars

Georg Raffelt, MPI Physics, Munich ISAPP 2011, 2/8/11, Varenna, Italy

Neutrinos and the Stars

Neutrinos and the Stars IStellar Evolution and Neutrinos

Georg G. RaffeltMax-Planck-Institut für Physik, München, Germany

ISAPP 2011, International School on Astroparticle Physics26th July–5th August 2011, Varenna, Italy

Where do Neutrinos Appear in Nature?

Nuclear Reactors

Particle Accelerators

Earth Atmosphere(Cosmic Rays)

Earth Crust(Natural Radioactivity)

AstrophysicalAccelerators Soon ?

Sun

Supernovae(Stellar Collapse) SN 1987A

Cosmic Big Bang (Today 330 n/cm3) Indirect Evidence


Neutrinos from the Sun

Reaction-chains

Energy26.7 MeV

Helium

Solar radiation: 98 % light 2 % neutrinosAt Earth 66 billion neutrinos/cm2 sec

Hans Bethe (1906-2005, Nobel prize 1967)Thermonuclear reaction chains (1938)


Bethe’s Classic Paper on Nuclear Reactions in Stars

No neutrinosfrom nuclear reactionsin 1938 …


Predicting Neutrinos from Stars

Phys. Rev. 58:1117 (1940)


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.


First Detection (1954 – 1956)

Fred Reines(1918 – 1998)Nobel prize 1995

Clyde Cowan(1919 – 1974)

Detector prototype

Anti-Electron Neutrinosfrom Hanford Nuclear Reactor

3 Gammasin coincidence𝝂𝐞 p

n Cd

e+¿ ¿ e−

g

g

g


First Measurement of Solar Neutrinos

600 tons ofPerchloroethylene

Homestake solar neutrino observatory (1967–2002)

Inverse beta decayof chlorine


2002 Physics Nobel Prize for Neutrino Astronomy

Ray Davis Jr.(1914–2006)

Masatoshi Koshiba(*1926)

“for pioneering contributions to astrophysics, inparticular for the detection of cosmic neutrinos”


Basics of Stellar EvolutionBasics of Stellar Evolution


Equations of Stellar StructureAssume spherical symmetry and static structure (neglect kinetic energy)Excludes: Rotation, convection, magnetic fields, supernova-dynamics, …

Hydrostatic equilibrium

Energy conservation

Energy transfer

Literature• Clayton: Principles of stellar evolution and nucleosynthesis (Univ. Chicago Press 1968)• Kippenhahn & Weigert: Stellar structure and evolution (Springer 1990)

Radius from centerPressureNewton’s constantMass densityIntegrated mass up to rLuminosity (energy flux)Local rate of energygeneration

Opacity

Radiative opacity

Electron conduction


Virial Theorem and Hydrostatic Equilibrium

Hydrostatic equilibrium 𝑑𝑃𝑑𝑟 =

𝐺𝑁𝑀 𝑟 𝜌𝑟 2

Average energy of single“atoms” of the gas

L.h.s. partial integrationwith at surface

Integrate both sides

Monatomic gas: (U density of internal energy)

∫0

𝑅

𝑑𝑟 4𝜋𝑟 3𝑃 ′=−∫0

𝑅

𝑑𝑟 4 𝜋𝑟3 𝐺𝑁𝑀𝑟 𝜌𝑟2

−3∫0

𝑅

𝑑𝑟 4𝜋𝑟 2𝑃=𝐸gravtot

𝑈 tot=− 12 𝐸gravtot

⟨ 𝐸 kin ⟩=−12 ⟨ 𝐸grav ⟩

Virial Theorem:Most important tool to studyself-gravitating systems


Dark Matter in Galaxy Clusters

Coma Cluster

A gravitationally boundsystem of many particlesobeys the virial theorem

Velocity dispersionfrom Doppler shiftsand geometric size

Total Mass


Dark Matter in Galaxy Clusters

Fritz Zwicky:Die Rotverschiebung von Extragalaktischen Nebeln(The redshift of extragalactic nebulae)Helv. Phys. Acta 6 (1933) 110In order to obtain the observed average Doppler effect of 1000 km/s ormore, the average density of the Coma cluster would have to be at least400 times larger than what is found from observations of the luminousmatter. Should this be confirmed one would find the surprising result thatdark matter is far more abundant than luminous matter.


Virial Theorem Applied to the Sun

Virial Theorem

Approximate Sun as a homogeneoussphere with Mass Radius Gravitational potential energy of aproton near center of the sphere Thermal velocity distribution Estimated temperature

Central temperature fromstandard solar models


Nuclear Binding Energy

Mass Number

Fe


Hydrogen Burning: Proton-Proton Chains

< 0.420 MeV 1.442 MeV

PP-I

< 18.8 MeV

hep

0.862 MeV 0.384 MeV< 15 MeV

PP-II PP-III

15%85%

0.02%90% 10%

0.24%100%

He❑3 + He❑

3 → He❑4 +2p He❑

3 + He❑4 → Be❑

7 +𝛾 He❑3 +p→ He❑

4 +e+¿+𝜈𝑒¿

H❑2 +p→ He❑

3 +𝛾

p+p→ H❑2 +e+¿+𝜈𝑒 ¿ p+e−+p→ H❑

2 +𝜈𝑒

Be❑7 +e−→ Li❑

7 +𝜈𝑒 Be❑7 +e−→ Li∗❑

7 +𝜈𝑒 Be❑7 +p→ B❑

8 +𝛾B❑8 → Be∗❑

8 +e+¿+𝜈𝑒 ¿

Li❑7 +p→ He❑

4 + He❑4 Be∗❑

8 → He❑4 + He❑

4


O816 F9

17

O817(𝑝 ,𝛼)

(𝑝 ,𝛾 ) (𝑝 ,𝛾 )

𝑒+¿ ¿𝜈𝑒

Hydrogen Burning: CNO Cycle

C612 N6

13

C613 N7

14 O815

N715

He❑4

(𝑝 ,𝛼)

(𝑝 ,𝛾 )

(𝑝 ,𝛾 ) (𝑝 ,𝛾 )

𝑒+¿ ¿𝜈𝑒

𝑒+¿ ¿𝜈𝑒


Thermonuclear Reactions and Gamow PeakCoulomb repulsion prevents nuclearreactions, except for Gamow tunneling

Tunneling probability

With Sommerfeld parameter

Parameterize cross section withastrophysical S-factor

LUNA Collaboration, nucl-ex/9902004

He❑3 + He❑

3 → He❑4 +2 p


Main Nuclear Burnings• Each type of burning occurs at a very different T but a broad range of densities• Never co-exist in the same location

Hydrogen burning • 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)

Helium burning

“Triple alpha reaction” because unstable,builds up with concentration

Typical temperatures: (10 keV)

Carbon burningMany reactions, for example or etc Typical temperatures:


Hydrogen Exhaustion

Hydrogen Burning

Main-sequence star Helium-burning star

HeliumBurning

HydrogenBurning


Burning Phases of a 15 Solar-Mass Star

Hydrogen 3H He 2.15.9 1.2107

Duration[years]Ln/Lg

rc

[g/cm3]

Tc

[keV]

DominantProcessBurning Phase

Lg [104 Lsun]

Helium 14He C, O 1.710-56.01.3103 1.3106

Carbon C Ne, Mg 53 1.7105 8.6 1.0 6.3103

Neon Ne O, Mg 110 1.6107 9.6 1.8103 7.0

Oxygen O Si 160 9.7107 9.6 2.1104 1.7

Silicon Si Fe, Ni 270 2.3108 9.6 9.2105 6 days

-


Neutrinos from Thermal Processes

These processes were firstdiscussed in 1961-63after V-A theory

Photo (Compton) Plasmon decay Pair annihilation

Bremsstrahlung


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”

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)

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 )• Degenerate helium core (, )

Plasmon decay


Neutrino-Photon-Coupling in a Plasma

Usuallynegligible

Neutrino effective in-medium coupling

For vector current it is analogousto photon polarization tensor


Plasmon Decay vs. Cherenkov Effect

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

Photon dispersion in a medium can be

“Time-like”

w2 - k2 > 0

“Space-like”

w2 - k2 < 0

Allowed process that is forbidden in vacuum

Plasmon decay toneutrinos

Cherenkov effect


Effective Neutrino Neutral-Current Couplings

Neutrino Fermion CV

Neutron

CA

Proton

Electron

𝜈𝑒𝜈𝜇𝜈𝜏

𝜈𝑒

E M≪ W,Z

Chargedcurrent

Neutralcurrent Effective

fourfermioncoupling

𝑍

𝑊

𝐻∫ ¿=

𝐺F

√2Ψ 𝑓 𝛾𝜇 (𝐶V−𝐶A𝛾5 )Ψ 𝑓 Ψ 𝜈𝛾

𝜇 (1−𝛾5 )Ψ 𝜈 ¿Fermi constant

Weak mixing angle


Existence of Direct Neutrino-Electron Coupling


Self-Regulated Nuclear Burning

Main-SequenceStar

Virial Theorem:

Small Contraction Heating Increased nuclear burning Increased pressure Expansion

Additional energy loss (“cooling”) Loss of pressure Contraction Heating Increased nuclear burning

Hydrogen burning at nearly fixed T Gravitational potential nearly fixed: (More massive stars bigger)


Modified Stellar Properties by Particle EmissionAssume that some small perturbation (e.g. axion emission) leads to a “homologous”modification: Every point is mapped to a new position Requires power-law relations for constitutive relations• Nuclear burning rate • Mean opacity Implications for other quantities• Density • Pressure • Temperature gradient Impact of small novel energy loss• Modified nuclear burning rate • Assume Kramers opacity law and • Hydrogen burning and • Star contracts, heats, and shines brighter in photons:


Degenerate Stars (“White Dwarfs”)Assume temperature very small No thermal pressure Electron degeneracy is pressure sourcePressure ~ Momentum density Velocity• Electron density • Momentum (Fermi momentum)• Velocity • Pressure • Density

Hydrostatic equilibrium

With we have

Inverse mass radius relationship

( electrons per nucleon)

For sufficiently large stellar mass ,electrons become relativistic• Velocity = speed of light• Pressure

No stable configuration

Chandrasekhar mass limit


Degenerate Stars (“White Dwarfs”)

( electrons per nucleon)

For sufficiently large stellar mass ,electrons become relativistic• Velocity = speed of light• Pressure

No stable configuration

Chandrasekhar mass limit


Stellar Collapse

Hydrogen Burning

Main-sequence star Helium-burning star

HeliumBurning

HydrogenBurning

Onion structure

Degenerate iron core: r 109 g cm-3

T 1010 K MFe 1.5 Msun

RFe 8000 km

Collapse (implosion)


Normal vs. Giant Stars

1𝑅⊙

depends on

of entire star

10𝑅⊙0.3𝑅⊙

depends on of core huge

depends on of core

Large surface area low temperature “red giant”Large luminosity mass loss

Envelopeconvective

Helium-burning star 1M⊙

Main-sequence star 1M⊙(Hydrogen burning)


Red Giant


Evolution of a Low-Mass Star

H

Main-Sequence

MS

HorizontalBranch

HHe

HB

Ged-Giant Branch

H

He

RGB

Asymptotic Giant Branch

HHe

C O

AGB


Planetary Nebulae

HourGlassNebula

PlanetaryNebula IC 418

PlanetaryNebula NGC 3132

EskimoNebula


Evolution of Stars

8 Msun ≲ M < ???

All burning cycles® Onion skin structure with degenerate iron core

Corecollapsesupernova

• Neutron star (often pulsar)• Sometimes black hole?• Supernova remnant (SNR), e.g. crab nebula

M < 0.08 Msun Never ignites hydrogen cools(“hydrogen white dwarf”) Brown dwarf

2 ≲ M ≲ 5-8 Msun Helium ignition non-degenerate

0.8 ≲ M ≲ 2 MsunDegenerate helium coreafter hydrogen exhaustion • Carbon-oxygen

white dwarf• Planetary nebula

0.08 < M ≲ 0.8 MsunHydrogen burning not completedin Hubble time

Low-mass main-squence star


The galacticglobular cluster M3

http://www.dartmouth.edu/~chaboyer/mwgc.html

Globular clusters on top of theFIRAS 2.2 micron map of the Galaxy

Globular Clusters of the Milky Way


Color-Magnitude Diagram for Globular Clusters

Color-magnitude diagram synthesized from several low-metallicity globular clusters and compared with theoretical isochrones (W.Harris, 2000)

Hot, blue cold, red

H

Main-Sequence

• Stars with M so large that they have burnt out in a Hubble time• No new star formation in globular clusters

Mass




Hot, blue cold, red

H

Main-Sequence

HHe

C O

Asymptotic Giant

H

He

Red Giant

HHe

Horizontal Branch

C OWhiteDwarfs


Basics of Stellar EvolutionBounds on

Particle Properties


Basic Argument: Stars as Bolometers

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?


Electromagnetic Properties of Neutrinos


Neutrino Electromagnetic Form Factors

Effectivecoupling ofelectromagneticfield to aneutral 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


Consequences of Neutrino Dipole Moments

T electron recoil energy

i 𝜕𝜕𝑡 (𝜈𝐿𝜈𝑅)=(0 𝜇𝜈𝐵⊥

𝜇𝜈𝐵⊥ 0 )(𝜈𝐿𝜈𝑅)

Γ=𝜇𝜈2

24𝜋 𝜔 pl3

Γ=𝜇𝜈2

8𝜋 (𝑚22−𝑚1

2

𝑚2)3

Spin precessionin externalE or B fields

Decay orCherenkoveffect

Plasmondecay instars

Scattering


Plasmon Decay and Stellar Energy Loss Rates

Assume photon dispersion relation like amassive particle (nonrelativistic plasma)

𝐸𝛾2−𝑝𝛾

2=𝜔pl2 =

4𝜋𝛼𝑛𝑒𝑚𝑒

Energy-loss rateof stellar plasma

Photon decay rate(transverse plasmon)

with energy Eg

Γ (𝛾→𝜈𝜈 )= 4𝜋3𝐸𝛾

× { 𝛼𝜈 (𝜔 pl2 /4 𝜋 )

(𝜇𝜈2 /2 ) (𝜔pl2 / 4𝜋 )2

(𝐶V2 𝐺F2 /𝛼 ) (𝜔 pl

2 /4𝜋 )3

Millicharge

Dipole moment

Standard model

𝑄 (𝛾→𝜈𝜈 )=∫ 2 𝑑3𝐩

(2𝜋 )3𝐸𝛾 Γ𝛾→𝜈𝜈𝑒𝐸𝛾 /𝑇−1

=8 𝜁3𝑇

3

3𝜋 ×{ 𝛼𝜈 (𝜔 pl2 /4𝜋 )

(𝜇𝜈2 /2 ) (𝜔 pl2 /4𝜋 )2

(𝐶V2 𝐺F2 /𝛼 ) (𝜔pl

2 /4𝜋 )3




Hot, blue cold, red

H

Main-Sequence

HHe

C O

Asymptotic Giant

H

He

Red Giant

HHe

Horizontal Branch

C OWhiteDwarfs

Particle emission reduces helium burning lifetime, i.e. number of HB stars

Particle emissiondelays He ignition, i.e.core mass increased


Measurements of Globular Cluster Observables

Number ratio of HB vs. RGB stars in 15 globular clusters

Brightness difference between HB (RR Lyrae stars) and brightest red giant in 26 globular clusters


Core-Mass at Helium Ignition

G.Raffelt, Stars as Laboratoriesfor Fundamental Physics (1996)

Catelan et al., astro-ph/9509062

Core mass at helium ignition established to 0.030 Msun or 6%

Primordial helium (observations & implied by CMBR acoustic peaks)


Globular Cluster Limits on Neutrino Dipole Moments

Compare magnetic-dipoleplasma emission withstandard case

For red-giant core beforehelium ignition

Require this to be < 1


Further Reading on Particle Limits from Stars

Georg Raffelt:

Stars as Laboratories for Fundamental Physics (University of Chicago Press, 1996)

Particle Physics from Stars Annu. Rev. Nucl. Part. Sci. 49 (1999) 163–216 [hep-ph/9903472]

Astrophysical Methods to Constrain Axions and Other Novel Particle Phenomena Phys. Rept. 198 (1990) 1–113

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Neutrinos and the Stars