Do non-relativistic neutrinos constitute the dark matter ?

Europhysics Letters 86 (2009) 59001

Theo M. Nieuwenhuizen Institute for Theoretical Physics

University of Amsterdam

CSNSM Orsay 23-5-2009

Outline

A modeling in virial equilibrium

Comparison to a galaxy supercluster

Mass, properties, name of DM particle

Introduction: What is dark matter DM

Nucleosynthesis

About virial equilibrium

Dark matter condensation on cluster; reionization

Conclusion

Dark matter in the Universe

• Studied by Jan Hendrik Oort 1932 for our galaxy

• Zwicky 1933: for rotation galaxy clusters• V. Rubin 1980: for rotation around galaxies

• Needed to explain stability of galaxies• Needed to explain cosmology

Dark matter ring around massive galaxy cluster

detected by Hubble Space Telescope HST

Bullet cluster Two galaxy clusters crossed each other.

And so did their dark matter.

• White: galaxies and foregrounds• Red: X ray emitted by hot gas• Blue: dark matter inferred from lensing

The two types of dark matter• MACHOs: Massive Astrophysical Compact Halo Objects• Most baryons are dark (non-luminous).• A fraction is in ionized hydrogen clouds.• A fraction is locked up in frozen H-He planets of earth weight.• These planets occur in clumps of 100,000 solar masses.• Some clumps developed into globular star clusters• These clumps act as ideal gas particles around galaxies.• This explains galactic dark matter, its rotation curves.• Too small for detection in Eros II (Dapnia)

• WIMPs Weakly Interacting Massive Particles: this talk• The dark matter of galaxy clusters is non-baryonic.• Detected by lensing (galaxies have banana-shape)• About 20-25% of total mass of the Universe.• May or may not be detectable in sky searches (e.g. Edelweiss)

• Not MACHOs or WIMPs but MACHOs and WIMPs !!

• Abell 1689 galaxy cluster

• Nearby z = 0.184

• Total mass

• Luminous mass

• Baryon poor

• Einstein ring

M 10 31 15

M 10 4.4 11

IncompleteEinstein ringat 100/h kpc

Abell 1689center

Abell 1689

X-rayemitting gas

T=10 keV =1.16 10^8 K

Dark matterGalaxies

Gas

• Against slavery• How to prevent despotism?

• Trias politica• American, French, (Dutch,…) constitution• woman can head a government,

but not be effective as the head of a family

1689: birth of Montesquieu

Charles Louis de Secondat, baron de La Brède et de Montesquieu (1689-1755)

Theory • Assume that DM comes from quantum particles

in their common gravitational potential U(r)

• Mass m, degeneracy g = 2 (2s+1) #families

• Mass density for fermions in equilibrium at T

• Gravitational potential U(0)=0

• Poisson eqn (spherical symmetry)

• Together they give closed problem for U(r)

Dark matter (x), Galaxies (G) and gas (g)

• Hydrostatic equilibrium

• Ideal gas laws

• Result

• Virial equilibrium:

equal velocity dispersions

M(r) total mass inside r

Dimensionless shaperadius, potential

thermal length, scale

Dark density

Poisson eqn

dark matter + Galaxies + gas

Virial equilibrium: Galaxies gas (ionized H, He, 30% solar metallicity)

Observed quantity in strong and weak lensing

Integrated mass along line-of-sight

Average in (0, r)

Average in (r, r_m)

Contrast function

From the model

Fit to A1689 lensing data of Tyson and Fischer ApJ 1995 Limousin et al, ApJ 2007

The mass of the dark matter particle

reduced Hubble parameter

small error, 2.0%

Previous estimates: keV, MeV, GeV, TeV: excluded

Cosmic density of g occupied modes that once were thermal

Cosmic matter fraction

= number of available modes

What is the dark matter particle?The dark matter fraction

matches WMAP5 for g=12

(anti) neutrinos, left+right handed, 3 families 2*2*3=12 mass = 1.455 eV

Not: axions, gravitinos, neutralinos, X-inos (early decouplers have small occupation)

Typical speed is non-relativistic, v = 490 km/s

Local density can be enormous: in Abell center: one billion in a few cc

Thermal length visible to the eye

Temperature is low

The biggest quantum structure

# neutrinos

per (thermal wavelength)^3

per degree of freedom

N=1: quantum-to-classical crossover

at r = 505 kpc = 1.6 million light year d = 2r = 3.2 million light yearThat is pretty big …

Baryons are poor tracers of dark matter density,even though they dotrace the enclosed mass

Temperature of gas: 10 keV=10^8 K

Log(Mass)

Log(r/kpc)

Cluster radiates like a star. Radiated energy supplied by contraction.Radiation helps to keep virial equilibrium.

Virial T of alpha-particles

Virial equilibrium assumed; only amplitude adjusted

Right handed neutrinos and nucleosynthesis

• Extra neutrino ``families’’

• Extra matter causes enhanced expansion

• Faster expansion: too few neutron decays, too much He-4• Neutrino asymmetry: more neutrinos than anti-neutrinos

• Thus more reactions for neutron decay • These effects can compensate each other• So nucleosynthesis can accommodate right-handed neutrinos

NSSSHH 1351.01 ,' ,' 2

epe

n

kT/

3N

Effect on data Steigman IJMP E, 2005

=0=

==0==

===0=====

Adjusting He-4 to WMAP

Why virial equilibrium?

• Lynden Bell: violent relaxation.• Relaxation in time-dependent potential exchanges

energy of a given particle with

the gravitational energy of the whole cluster• Iff phase space density uniform, then Fermi-Dirac

distribution• Iff not, it is probably a “good” approximation.• X-ray radiation helps to maintain the virial state

CDM or HDM?• Cold Dark Matter: it is already clumped at decoupling z=1100

• But neutrinos are free streaming until trapped by galaxy cluster

• Crossover when Newton force matches Hubble force

• Free streaming

• At cluster center

• They match at crossover: Voids loose neutrinos at z=28, T=77 L, age 120 Myr.

• This heats the intracluster gas up to 10 keV, so it reionizes

• Hot Dark Matter is the proper paradigm; Agrees with gravito-hydrodynamics

What about galactic dark matter?

• Proto globolar clusters: Clumps of H-He planets, of weight 1 million M_sun each,

act as ideal gas particles

• In virial equilibrium due to mutual collisions

• polylog linearizes

• gets absorbed by a shift: unique shape of profile

• Virial speed

ex/'2''

/ )('/)()( RrxxxVrrGMrv

Galaxy rotation curves

Summary • Observed DM of Abell supercluster explained by thermal fermions.

• Fitting with global dark matter: g=12, m=1.45 eV

• Corresponds to neutrinos+antineutrinos, left+right, 3 families

• Free flow into potential well occurs at z = 28. Causes reionization

• Neutrino mass should be seen in Katrin expt (2012-2012+0.0001)

• Dark matter particle was not (should not) be observed in searches ADMX, ANAIS, ArDM, ATIC, BPRS, CAST, CDMS,CLEAN, CRESST, CUORE,

CYGNUS, DAMA, DEEP, DRIFT, EDELWEISS,ELEGANTS, EURECA, GENIUS, GERDA, GEDEON, GLAST, HDMS, IGEX, KIMS,LEP, LHC, LIBRA, LUX, NAIAD, ORPHEUS, PAMELA, PICASSO, ROSEBUD,SIGN, SIMPLE, UKDM, XENON, XMASS, ZEPLIN.

• CDM is out. Neutrinos are hot.

Psalm 118:22

The stone which the builders refused

is become the head stone of the corner

KArlsruhe TRItium Neutrino Experiments