Download Do non-relativistic neutrinos constitute the dark matter

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
Introduction: What is dark matter DM
A modeling in virial equilibrium
Comparison to a galaxy supercluster
Mass, properties, name of DM particle
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
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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)
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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
Incomplete
Einstein ring
at 100/h kpc
Abell 1689
center
Abell 1689
X-ray
emitting gas
T=10 keV =
1.16 10^8 K
Dark matter
Galaxies
Gas
1689: birth of Montesquieu
Charles Louis de Secondat,
baron de La Brède et de Montesquieu
(1689-1755)
•! 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
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
M(r) total mass inside r
•! Ideal gas laws
•! Result
•! Virial equilibrium:
equal velocity dispersions
Dimensionless shape
radius, 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
= number of available modes
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
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)
Thermal length visible to the eye
Temperature is low
Typical speed is non-relativistic,
v = 490 km/s
Local density can be enormous:
in Abell center: one billion in a few cc
The biggest quantum structure
# neutrinos
per (thermal
wavelength)^3
per degree of freedom
Baryons are poor tracers
of dark matter density,
even though they do
trace the enclosed mass
N=1: quantum-to-classical crossover
at r = 505 kpc = 1.6 million light year
d=
2r
= 3.2 million light year
That is pretty big …
Temperature of gas: 10 keV=10^8 K
Virial T of alpha-particles
Log(Mass)
Virial equilibrium assumed;
only amplitude adjusted
Log(r/kpc)
Cluster radiates like a star.
Radiated energy supplied by contraction.
Radiation helps to keep virial equilibrium.
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
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
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polylog linearizes
gets absorbed by a shift: unique shape of profile
•! Virial speed
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