Neutrinos in Astrophysics and Cosmology Title TU Darmstadt, Physik Kolloquium, 23. November 2007 Neutrinos in Astrophysics and Cosmology Georg Raffelt, Max-Planck-Institut für Physik, München

Pauli’s Explanation of the Beta Decay Spectrum (1930) Wolfgang Pauli (1900-1958) Nobel Prize 1945 “Neutron” (1930) “Neutron” (1930) “Neutrino” (E.Fermi) Niels Bohr: Energy not conserved in the quantum domain?

Periodic System of Elementary Particles Quarks Leptons Charm Top Gravitation Weak Interaction Strong Interaction (QCD) Electromagnetic Interaction (QED) Down Strange Bottom Electron Muon Tau e-Neutrino t-Neutrino 1st Family 2nd Family 3rd Family Charge +2/3 Charge -1/3 Charge -1 Charge 0 Up m-Neutrino nt ne e m t d s b c u nm Quarks Leptons Charge +2/3 Up Charge -1/3 Down Charge -1 Electron Charge 0 e-Neutrino ne e d u Neutron Proton

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

Neutrinos from the Sun Helium Solar radiation: 98 % light Hans Bethe (1906-2005, 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

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

Gamow & Schoenberg, 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) 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

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

Elastic scattering or CC reaction Cherenkov Effect Cherenkov Ring Elastic scattering or CC reaction Light Electron or Muon (Charged Particle) Neutrino Water Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Super-Kamiokande Neutrino Detector

Super-Kamiokande: Sun in the Light of Neutrinos Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Hydrogen burning: Proton-Proton Chains < 0.420 MeV 1.442 MeV 100% 0.24% 15% 85% PPI < 18.8 MeV hep 90% 10% 0.02% 0.862 MeV 0.384 MeV < 15 MeV PPII PPIII

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

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 c/100t/d Expected with oscillations 49 ± 4 c/100t/d BOREXINO result (August 07) 47 ± 7stat ± 12sys c/100t/d

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

Mixing of Neutrinos with Different Mass mass m1 mass m2 n Electron neutrino Mass m1 Mass m2 > m1 Mass m1 Mass m2 > m1 Mass m1 Mass m2 > m1 Mass m1 Mass m2 = m1 Mass m1 Mass m2 > m1 Neutrino propagation as a wave phenomenon Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Neutrino Oscillations Mass m1 Mass m2 > m1 Oscillation length Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Neutrino Oscillations Oscillation length Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Three-Flavor Neutrino Parameters Solar 75-92 Atmospheric 1400-3000 CHOOZ Solar/KamLAND 2s ranges hep-ph/0405172 Atmospheric/K2K d CP-violating phase m e t 1 Sun Normal 2 3 Atmosphere Inverted Tasks and Open Questions Precision for q12 and q23 How large is q13 ? CP-violating phase d ? Mass ordering ? (normal vs inverted) Absolute masses ? (hierarchical vs degenerate) Dirac or Majorana ?

Sanduleak -69 202 Supernova 1987A 23 February 1987 Tarantula Nebula Large Magellanic Cloud Distance 50 kpc (160.000 light years) Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Supernova Neutrinos 20 Jahre nach SN 1987A Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Crab Nebula Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

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

Stellar Collapse and Supernova Explosion Newborn Neutron Star ~ 50 km Proto-Neutron Star r  rnuc = 3  1014 g cm-3 T  30 MeV Collapse (implosion) Neutrino Cooling

Stellar Collapse and Supernova Explosion Newborn Neutron Star ~ 50 km Proto-Neutron Star r  rnuc = 3  1014 g cm-3 T  30 MeV Neutrino Cooling Gravitational binding energy Eb  3  1053 erg  17% MSUN c2 This shows up as 99% Neutrinos 1% Kinetic energy of explosion (1% of this into cosmic rays) 0.01% Photons, outshine host galaxy Neutrino luminosity Ln  3  1053 erg / 3 sec  3  1019 LSUN While it lasts, outshines the entire visible universe

Neutrino Signal of Supernova 1987A Kamiokande-II (Japan) Water Cherenkov detector 2140 tons Clock uncertainty 1 min Irvine-Michigan-Brookhaven (US) Water Cherenkov detector 6800 tons Clock uncertainty 50 ms Baksan Scintillator Telescope (Soviet Union), 200 tons Random event cluster ~ 0.7/day Clock uncertainty +2/-54 s Within clock uncertainties, signals are contemporaneous

SN 1987A Event No.9 in Kamiokande-II Kamiokande-II detector 2140 tons of water fiducial volume for SN 1987A Hirata et al., PRD 38 (1988) 448

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”

Neutrino-Driven Delayed Explosion Neutrino heating increases pressure behind shock front Picture adapted from Janka, astro-ph/0008432

Standing Accretion Shock Instability (SASI) Mezzacappa et al., http://www.phy.ornl.gov/tsi/pages/simulations.html Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

The Energy-Loss Argument Neutrino sphere SN 1987A neutrino signal Neutrino diffusion Emission of very weakly interacting particles would “steal” energy from the neutrino burst and shorten it. (Early neutrino burst powered by accretion, not sensitive to volume energy loss.) Volume emission of novel particles Late-time signal most sensitive observable

Do Neutrinos Gravitate? Neutrinos arrive a few hours earlier than photons  Early warning (SNEWS) SN 1987A: Transit time for photons and neutrinos equal to within ~ 3h Shapiro time delay for particles moving in a gravitational potential Longo, PRL 60:173,1988 Krauss & Tremaine, PRL 60:176,1988 Equal within ~ 1 - 4 10-3 Proves directly that neutrinos respond to gravity in the usual way because for photons gravitational lensing already proves this point Cosmological limits DNn ≲ 1 much worse test of neutrino gravitation Provides limits on parameters of certain non-GR theories of gravitation Photons likely obscured for next galactic SN, so this result probably unique to SN 1987A

Large Detectors for Supernova Neutrinos MiniBooNE (200) LVD (400) Borexino (100) Baksan (100) Super-Kamiokande (104) KamLAND (400) In brackets events for a “fiducial SN” at distance 10 kpc IceCube (106)

Simulated Supernova Signal at Super-Kamiokande Accretion Phase Kelvin-Helmholtz Cooling Phase Simulation for Super-Kamiokande SN signal at 10 kpc, based on a numerical Livermore model [Totani, Sato, Dalhed & Wilson, ApJ 496 (1998) 216]

IceCube Neutrino Telescope at the South Pole 1 km3 antarctic ice, instrumented with 4800 photomultipliers 22 of 80 strings installed (2007) Completion until 2011 foreseen

Global Cosmic Ray Spectrum

Core of the Galaxy NGC 4261 Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Neutrino Beams: Heaven and Earth Target: Protons or Photons Approx. equal fluxes of photons & neutrinos Equal neutrino fluxes in all flavors due to oscillations F. Halzen (2002)

3369 events from northern hemisphere AMANDA Skyplot 2000-2003 3369 events from northern hemisphere

IceCube as a Supernova Neutrino Detector Each optical module (OM) picks up Cherenkov light from its neighborhood. SN appears as “correlated noise”. About 300 Cherenkov photons per OM from a SN at 10 kpc Noise < 260 Hz Total of 4800 OMs in IceCube IceCube SN signal at 10 kpc, based on a numerical Livermore model [Dighe, Keil & Raffelt, hep-ph/0303210] Method first discussed by Pryor, Roos & Webster, ApJ 329:355 (1988) Halzen, Jacobsen & Zas astro-ph/9512080

H- and L-Resonance for MSW Oscillations R. Tomàs, M. Kachelriess, G. Raffelt, A. Dighe, H.-T. Janka & L. Scheck: Neutrino signatures of supernova forward and reverse shock propagation [astro-ph/0407132] Resonance density for Resonance density for

Shock-Wave Propagation in IceCube Inverted Hierarchy No shockwave Inverted Hierarchy Forward & reverse shock Inverted Hierarchy Forward shock Normal Hierarchy Choubey, Harries & Ross, “Probing neutrino oscillations from supernovae shock waves via the IceCube detector”, astro-ph/0604300

Core-Collapse SN Rate in the Milky Way SN statistics in external galaxies Core-collapse SNe per century 1 2 3 4 5 6 7 8 9 10 van den Bergh & McClure (1994) Cappellaro & Turatto (2000) Gamma rays from 26Al (Milky Way) Diehl et al. (2006) Historical galactic SNe (all types) Strom (1994) Tammann et al. (1994) No galactic neutrino burst 90 % CL (25 y obserservation) Alekseev et al. (1993) References: van den Bergh & McClure, ApJ 425 (1994) 205. Cappellaro & Turatto, astro-ph/0012455. Diehl et al., Nature 439 (2006) 45. Strom, Astron. Astrophys. 288 (1994) L1. Tammann et al., ApJ 92 (1994) 487. Alekeseev et al., JETP 77 (1993) 339 and my update.

SuperNova Early Warning System (SNEWS) Neutrino observation can alert astronomers several hours in advance to a supernova. To avoid false alarms, require alarm from at least two experiments. Super-K IceCube Coincidence Server @ BNL Alert LVD Supernova 1987A Early Light Curve Others ? http://snews.bnl.gov astro-ph/0406214

The Red Supergiant Betelgeuse (Alpha Orionis) First resolved image of a star other than Sun Distance (Hipparcos) 130 pc (425 lyr) If Betelgeuse goes Supernova: 6 107 neutrino events in Super-Kamiokande 2.4 103 neutron events per day from Silicon-burning phase (few days warning!), need neutron tagging [Odrzywolek, Misiaszek & Kutschera, astro-ph/0311012]

LAGUNA - Funded FP7 Design Study Large Apparati for Grand Unification and Neutrino Astrophysics (see also arXiv:0705.0116)

Title Dark Energy 73% (Cosmological Constant) Neutrinos 0.1-2% Matter 23% Normal Matter 4% (of this about 10% luminous) Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

“Weighing” Neutrinos with KATRIN Sensitive to common mass scale m for all flavors because of small mass differences from oscillations Best limit from Mainz und Troitsk m < 2.2 eV (95% CL) KATRIN can reach 0.2 eV Under construction Data taking foreseen to begin in 2009 http://www-ik.fzk.de/katrin/

“KATRIN Approaching” (25 Nov 2006)

Cosmological Limit on Neutrino Masses Cosmic neutrino “sea” ~ 112 cm-3 neutrinos + anti-neutrinos per flavor mn < 40 eV For all stable flavors A classic paper: Gershtein & Zeldovich JETP Lett. 4 (1966) 120

Strukturbildung im Universum Smooth Structured Structure forms by gravitational instability of primordial density fluctuations A fraction of hot dark matter suppresses small-scale structure

Structure Formation with Hot Dark Matter Standard LCDM Model Neutrinos with Smn = 6.9 eV Structure fromation simulated with Gadget code Cube size 256 Mpc at zero redshift Troels Haugbølle, http://whome.phys.au.dk/~haugboel

Power Spectrum of Cosmic Density Fluctuations

Some Recent Cosmological Limits on Neutrino Masses Smn/eV (limit 95%CL) Data / Priors Hannestad 2003 [astro-ph/0303076] 1.01 WMAP-1, CMB, 2dF, HST Spergel et al. (WMAP) 2003 [astro-ph/0302209] 0.69 WMAP-1, 2dF, HST, s8 Crotty et al. 2004 [hep-ph/0402049] 1.0 0.6 WMAP-1, CMB, 2dF, SDSS & HST, SN Hannestad 2004 [hep-ph/0409108] 0.65 WMAP-1, SDSS, SN Ia gold sample, Ly-a data from Keck sample Seljak et al. 2004 [astro-ph/0407372] 0.42 WMAP-1, SDSS, Bias, Ly-a data from SDSS sample Hannestad et al. 2006 [hep-ph/0409108] 0.30 WMAP-1, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly-a (SDSS) Spergel et al. 2006 [hep-ph/0409108] 0.68 WMAP-3, SDSS, 2dF, SN Ia, s8 Seljak et al. 2006 [astro-ph/0604335] 0.14 WMAP-3, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly-a (SDSS)

Weak Lensing - A Powerful Probe for the Future Distortion of background images by foreground matter Unlensed Lensed

Sensitivity Forecasts for Future LSS Observations Lesgourgues, Pastor & Perotto, hep-ph/0403296 Planck & SDSS Smn > 0.21 eV detectable at 2s Smn > 0.13 eV detectable Ideal CMB & 40 x SDSS Abazajian & Dodelson astro-ph/0212216 Future weak lensing survey 4000 deg2 σ(mν) ~ 0.1 eV Kaplinghat, Knox & Song, astro-ph/0303344 σ(mν) ~ 0.15 eV (Planck) σ(mν) ~ 0.044 eV (CMBpol) CMB lensing Wang, Haiman, Hu, Khoury & May, astro-ph/0505390 Weak-lensing selected sample of > 105 clusters σ(mν) ~ 0.03 eV

Fermion Mass Spectrum 10 100 1 meV eV keV MeV GeV TeV d s b Quarks (Q = -1/3) u c t Quarks (Q = +2/3) Charged Leptons (Q = -1) e m t All flavors n3 Neutrinos

Periodic System of Elementary Particles Matter Anti-Quarks Anti-Leptons -2/3 +1/3 +1 Strong Int’n Electromagnetic Int’n Antimatter Leptons Anti-Leptons „Majorana Neutrinos” are their own antiparticles Can explain baryogenesis by leptogenesis Why is there no antimatter in the Universe? (Problem of „Baryogenesis”) Quarks Leptons +2/3 c t Gravitation Weak Interaction Strong Int’n Electromagnetic Int’n -1/3 s b -1 m 1st Family 2nd Family 3rd Family u d e Charge

See-Saw Model for Neutrino Masses Neutrinos Charged Leptons Dirac masses from coupling to standard Higgs field f Heavy Majorana masses Mj > 1010 GeV Lagrangian for particle masses Light Majorana mass Diagonalize

See-Saw Model for Neutrino Masses ℓ 1010 GeV 1 GeV 10-10 GeV Charged leptons Ordinary neutrinos Heavy “right-handed” (no gauge interactions) Light Majorana mass

Leptogenesis by Out-of-Equilibrium Decay abundance of heavy Majorana neutrinos Created lepton-number abundance Equilibrium abundance of heavy Majorana neutrinos Real abundance determined by decay rate CP-violating decays by interference of tree-level with one-loop diagram Equilibrium abundance of heavy Majorana neutrinos Real abundance determined by decay rate M. Fukugita & T. Yanagida: Baryogenesis without Grand Unification Phys. Lett. B 174 (1986) 45 W. Buchmüller & M. Plümacher: Neutrino masses and the baryon asymmetry Int. J. Mod. Phys. A15 (2000) 5047-5086

Leptogenesis by Majorana Neutrino Decays In see-saw models for neutrino masses, out-of-equilibrium decays of right-handed heavy Majorana neutrinos provide source for CP- and L-violation Cosmological evolution B = L = 0 early on Thermal freeze-out of heavy Majorana neutrinos Out-of-equilibrium CP-violating decay creates net L Shift L excess into B by sphaleron effects Sufficient deviation from equilibrium distribution of heavy Majorana neutrinos at freeze-out Limits on Yukawa couplings Limits on masses of ordinary neutrinos Requires Majorana neutrino masses below 0.1 eV Buchmüller, Di Bari & Plümacher, hep-ph/0209301 & hep-ph/0302092

Title Dark Energy 73% (Cosmological Constant) Neutrinos 0.1-2% Matter 23% Normal Matter 4% (of this about 10% luminous) Massive neutrinos can explain presence of matter by leptogenesis mechanism Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Killing Two Birds with One Stone See-Saw mechanism explains Small neutrino masses Baryon asymmetry of the universe by leptogenesis

Leptogenesis by Majorana Neutrino Decays A classic paper

Leptogenesis as a Research Topic Citation of Fukugita & Yanagida, PLB 174 (1986) 45 or “leptogenesis” in title (SPIRES data base)

Neutrinoless bb Decay 0n mode, enabled Standard 2n mode by Majorana mass Measured quantity Best limit from 76Ge

Portion of the Hubble Ultra Deep Field Astrophysics & Cosmology Elementary Particle Physics n Cosmic Rays Georg Raffelt, Max-Planck-Institut für Physik, München Physik Kolloquium, 23. November 2007, TU Darmstadt

Gamow & Schoenberg 2

Long-Baseline Experiment K2K K2K Experiment (KEK to Kamiokande) has confirmed neutrino oscillations, to be followed by T2K (2009)

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

Matrices of Density in Flavor Space Neutrino quantum field Spinors in flavor space Destruction operators for (anti)neutrinos Variables for discussing neutrino flavor oscillations Quantum states (amplitudes) “Matrices of densities” (analogous to occupation numbers) Neutrinos Anti- neutrinos Sufficient for “beam experiments,” but confusing “wave packet debates” for quantifying decoherence effects “Quadratic” quantities, required for dealing with decoherence, collisions, Pauli-blocking, nu-nu-refraction, etc.

General Equations of Motion Vacuum oscillations M is neutrino mass matrix Note opposite sign between neutrinos and antineutrinos Usual matter effect with Nonlinear nu-nu effects are important when nu-nu interaction energy exceeds typical vacuum oscillation frequency (Do not compare with matter effect!)

Toy Supernova in “Single-Angle” Approximation Assume 80% anti-neutrinos Vacuum oscillation frequency w = 0.3 km-1 Neutrino-neutrino interaction energy at nu sphere (r = 10 km) m = 0.3105 km-1 Falls off approximately as r-4 (geometric flux dilution and nus become more co-linear) Bipolar Oscillations Decline of oscillation amplitude explained in pendulum analogy by inreasing moment of inertia (Hannestad, Raffelt, Sigl & Wong astro-ph/0608695)

Collective SN neutrino oscillations 2006-2007 “Bipolar” collective transformations important, even for dense matter Duan, Fuller & Qian astro-ph/0511275 Numerical simulations Including multi-angle effects Discovery of “spectral splits” Duan, Fuller, Carlson & Qian astro-ph/0606616, 0608050 Pendulum in flavor space Collective pair annihilation Pure precession mode Hannestad, Raffelt, Sigl & Wong astro-ph/0608695 Duan, Fuller, Carlson & Qian astro-ph/0703776 Self-maintained coherence vs. self-induced decoherence caused by multi-angle effects Raffelt & Sigl, hep-ph/0701182 Esteban-Pretel, Pastor, Tomas, Raffelt & Sigl, arXiv:0706.2498 Theory of “spectral splits” in terms of adiabatic evolution in rotating frame Raffelt & Smirnov, arXiv:0705.1830, 0709.4641 Duan, Fuller, Carlson & Qian arXiv:0706.4293, 0707.0290 Independent numerical simulations Fogli, Lisi, Marrone & Mirizzi arXiv:0707.1998

Looking forward to the next galactic supernova SN 1006 Looking forward to the next galactic supernova http://antwrp.gsfc.nasa.gov/apod/ap060430.html

Wilson, Proc. Univ. Illinois Meeting on Num. Astrophys.(1982) Delayed Explosion Wilson, Proc. Univ. Illinois Meeting on Num. Astrophys.(1982) Bethe & Wilson, ApJ 295 (1985) 14

Experimental Limits on Relic Supernova Neutrinos Super-K upper limit 29 cm-2 s-1 for Kaplinghat et al. spectrum [hep-ex/0209028] Upper-limit flux of Kaplinghat et al., astro-ph/9912391 Integrated 54 cm-2 s-1 Cline, astro-ph/0103138

DSNB Measurement with Neutron Tagging Beacom & Vagins, hep-ph/0309300 [Phys. Rev. Lett., 93:171101, 2004] Future large-scale scintillator detectors (e.g. LENA with 50 kt) Inverse beta decay reaction tagged Location with smaller reactor flux (e.g. Pyhäsalmi in Finland) could allow for lower threshold Pushing the boundaries of neutrino astronomy to cosmological distances

Neutrinos in Astrophysics and Cosmology responsible for ordinary astrophysical and cosmological phenomena Dominant radiation component in the early universe Crucial role in big-bang nucleosynthesis Dark-matter component (but subdominant) May be responsible for baryonic matter in the universe (leptogenesis) Important (sometimes dominant) cooling agent of stars May trigger supernova explosions May be crucial for r-process nucleosynthesis Heavenly laboratories for new particle physics phenomena Cosmological limit (future detection?) of nu mass scale Flavor oscillations of solar and atmospheric neutrinos Neutrino oscillations from a future galactic supernova Limits on “exotic” neutrino properties (dipole moments, right-handed interactions, decays, flavor-violating neutral currents, sterile nus, …) Neutrinos as astrophysical messengers Look into the solar interior (“measure” temperature) Watch stellar collapse directly Neutrinos from all cosmological supernovae Astrophysical accelerators for cosmic rays Annihilation signature for neutralino dark matter

Hot dark matter ruled out in 1983 1000 particle simulation [Frenk, White & Davis, ApJ 271 (1983) 417] The coherence length of the neutrino distribution […] is too large to be consistent with the observed clustering scale of galaxies […] The conventional neutrino-dominated picture appears to be ruled out. White, Frenk & Davis, ApJ 274 (1983) L1.