Neutrinos and the Stars

1. ISAPP 2011, International School on Astroparticle Physics 26th July–5th August 2011, Varenna, Italy Neutrinos and the Stars Neutrinos and the Stars I Stellar Evolution and Neutrinos Georg G. Raffelt Max-Planck-Institut für Physik, München, Germany

2. Where do Neutrinos Appear in Nature?   Sun Nuclear Reactors Supernovae (Stellar Collapse) SN 1987A   Particle Accelerators Earth Atmosphere (Cosmic Rays) Astrophysical Accelerators Soon ?  Cosmic Big Bang (Today 330 n/cm3) Indirect Evidence Earth Crust (Natural Radioactivity) 

3. Neutrinos from the Sun Helium Reaction- chains 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)

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

5. Predicting Neutrinos from Stars Phys. Rev. 58:1117 (1940)

6. 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.

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

8. First Measurement of Solar Neutrinos Inverse beta decay of chlorine 600 tons of Perchloroethylene Homestake solar neutrino observatory (1967–2002)

9. 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”

10. Basics of Stellar Evolution Basics of Stellar Evolution

11. Equations of Stellar Structure Assume 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 center Pressure Newton’s constant Mass density Integrated mass up to r Luminosity (energy flux) Local rate of energy generation Opacity Radiative opacity Electron conduction

12. Virial Theorem and Hydrostatic Equilibrium Hydrostatic equilibrium Integrate both sides L.h.s. partial integration with at surface Monatomic gas: (U density of internal energy) Average energy of single “atoms” of the gas Virial Theorem: Most important tool to study self-gravitating systems

13. Dark Matter in Galaxy Clusters A gravitationally bound system of many particles obeys the virial theorem Velocity dispersion from Doppler shifts and geometric size Total Mass Coma Cluster

14. Dark Matter in Galaxy Clusters Fritz Zwicky: Die Rotverschiebung von Extragalaktischen Nebeln (The redshift of extragalactic nebulae) Helv. Phys. Acta 6 (1933) 110 In order to obtain the observed average Doppler effect of 1000 km/s or more, the average density of the Coma cluster would have to be at least 400 times larger than what is found from observations of the luminous matter. Should this be confirmed one would find the surprising result that dark matter is far more abundant than luminous matter.

15. Virial Theorem Applied to the Sun Virial Theorem 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 Central temperature from standard solar models

16. Nuclear Binding Energy Fe Mass Number

17. Hydrogen Burning: Proton-Proton Chains < 0.420 MeV 1.442 MeV 100% 0.24% 85% 15% PP-I hep < 18.8 MeV 90% 10% 0.02% 0.862 MeV 0.384 MeV < 15 MeV PP-II PP-III

18. Hydrogen Burning: CNO Cycle

19. 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/9902004

20. 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 burning Many reactions, for example or etc Typical temperatures:

21. Hydrogen Exhaustion Main-sequence star Helium-burning star Hydrogen Burning Helium Burning Hydrogen Burning

22. Burning Phases of a 15 Solar-Mass Star Lg[104 Lsun] Duration [years] Dominant Process Ln/Lg Burning Phase Tc [keV] rc [g/cm3] - Hydrogen H  He 3 5.9 2.1 1.2107 1.710-5 Helium He  C, O 14 1.3103 6.0 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 9.2105 9.6 6 days

23. Neutrinos from Thermal Processes Photo (Compton) Plasmon decay Pair annihilation Bremsstrahlung These processes were first discussed in 1961-63 after V-A theory

24. 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” 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: • Plasma frequency • (electron density ) • Degenerate helium core • (, ) • 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)

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

26. 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 that is forbidden in vacuum Plasmon decay to neutrinos Cherenkov effect

27. Effective Neutrino Neutral-Current Couplings Neutral current Effective four fermion coupling Neutrino CV Fermion CA Electron E ≪ MW,Z Charged current Proton Neutron Fermi constant Weak mixing angle

28. Existence of Direct Neutrino-Electron Coupling

29. Self-Regulated Nuclear Burning • 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) Main-Sequence Star

30. Modified Stellar Properties by Particle Emission • Assume 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:

31. Degenerate Stars (“White Dwarfs”) • Assume temperature very small •  No thermal pressure •  Electron degeneracy is pressure source • Pressure ~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

32. 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

33. Stellar Collapse Collapse (implosion) Main-sequence star Onion structure Helium-burning star Degenerate iron core: r 109 g cm-3 T  1010 K MFe 1.5 Msun RFe  8000 km Hydrogen Burning Helium Burning Hydrogen Burning

34. Normal vs. Giant Stars Main-sequence star 1M⊙ (Hydrogen burning) Helium-burning star 1M⊙ Large surface area  low temperature  “red giant” Large luminosity  mass loss Envelope convective depends on of core depends on of entire star depends on of core  huge

35. Red Giant

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

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

38. Evolution of Stars 0.8 ≲ M ≲ 2 Msun Degenerate helium core after hydrogen exhaustion 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 • Carbon-oxygen • white dwarf • Planetary nebula 2≲ M ≲ 5-8 Msun Helium ignition non-degenerate 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

39. Globular Clusters of the Milky Way Globular clusters on top of the FIRAS 2.2 micron map of the Galaxy http://www.dartmouth.edu/~chaboyer/mwgc.html The galactic globular cluster M3

40. Color-Magnitude Diagram for Globular Clusters 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 Color-magnitude diagram synthesized from several low-metallicity globular clusters and compared with theoretical isochrones (W.Harris, 2000)

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

42. Basics of Stellar Evolution Bounds on Particle Properties

43. 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?

44. Electromagnetic Properties of Neutrinos

45. Neutrino Electromagnetic Form Factors Charge en = F1(0) = 0 Effective coupling of electromagnetic field to a neutral fermion 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

46. 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

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

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

49. 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

50. Core-Mass at Helium Ignition Core mass at helium ignition established to  0.030 Msun or 6% Primordial helium (observations & implied by CMBR acoustic peaks) G.Raffelt, Stars as Laboratories for Fundamental Physics (1996) Catelan et al., astro-ph/9509062