Ramanath Cowsik and Benjamin Burch
Physics Department
McDonnell Center for the Space Sciences
Washinton University in St. Louis, USA 63130
WHEPP XII: Mahabaleshwar, India
January 4-5
Thanks to Professor Sreerup Raychaudhuri & Professor Utpal Sarkar
Density Distribution Of Dark Matter
Friedman-Robertson-Walker Cosmologies
3H 02
 1.9 x 10-29 h2 g cm-3
c 
8G
 104 h2 eV cm-3


c
1
Einstein-de Sitter Model
Preferred On the basis of
a)
Observations
b) Structure formation
c)
Inflation (temporal Copernicus principle)
Spectrum of the thermal microwave background at ~2.73 K.
Cowsik, McCleland, Zeldovich Bound
(PRL 29, 669, 1972)
;
After annihilation of e+ e-,
,
Zwicky - Evidence for unseen gravitating mass in clusters (1933)
Cowsik & McClelland – ‘Impossible to see’ –” weakly interacting” particles from big bang generally lead
to halos of Dark-Matter surrounding galactic systems. (1973). Recently, Nieuwenhuizen has ressurected
this idea.
Evidence for the presence of dominant mass in
invisible “dark matter”
M100 A Galaxy
Notice the beautifully formed spiral arms. The speed of
stars in their circular path increases from the center
and reaches a constant value just beyond the nucleus.
We need a halo of invisible dark matter to counteract
the centrifugal force
Dark Energy in the
Universe
Insert WMAP picture
The microwave sky: The radiation that fills the universe is highly
isotropic- almost the same intensity whichever way we look. This
necessarily implies that dark matter is needed for the formation of
galaxies and other visible structures in the universe.
Multipole power spectrum of the CMB temperature fluctuations of WMAP and other CMB anisotropy experiments.
Position of the first peak at l≈200 indicates the flatness of the Universe; height of the first peak determines the
matter density, and the ratio of the first to second peaks determines the baryon density. Together with SDSS largescale structure data, the CMB measurements have determined the shape and composition of the Universe:
Ωtot=1.003±0.010, ΩM=0.24±0.02, ΩB=0.042±0.002, and ΩΛ=0.76±0.02. The curve is the theoretical prediction of
the “concordance cosmology”, with a band that indicates cosmic variance.
A New Order
Tytler astro-ph 0001318
“Metals”
0.01%
Visible
H, He
0.5%
Dark Matter
27%
Dark Energy
Cosmological Constant 
72%
J. Primack
Einstein’s equations for a homogeneous
and isotropic universe
Friedman equations for expanding universe using
the cosmological principle:
r-r Component :
t-t Component :
Weakly interacting particles adequately survive annihilation to constitute dark
matter in the Universe. (From Kolb and Turner)
Early ‘mass-models’ of the Galaxy. The need for a “Corona” (of dark matter)
to explain the rotation curve of the Galaxy was well recognized. The Keplarian
fall-off vc~r-1/2 of the ‘bulge’ may be noted. This is an adaptation of the model
by Schmidt (1985).
Sketch of the Galaxy based on radio, infrared and optical observations.
(Churchwell et al. 2009)
NIR surface brightness of the inner Galaxy from IRAS and COBE/DIRBE observations.
(Launhardt, Zylka, and Mezger 2002)
Dynamical model for the dark matter halo
• density→potential→orbits →velocities→density
• potential gets contribution from visible matter and dark matter
• Visible matter
– Central Bulge:
– Thin and Thick disk:
(Burch and Cowsik 2011)
Dark Matter -
satisfies the stationary collisionless Boltzmann
equation. Jeans theorem applies:
Reduced isothermal phase space distribution
Coupled non-linear differential equation, solved iteratively using eigenfunction
expansion method
Comparison of theory with observed
rotation curve
Parameters for ΦDM:
truncation radius of the
dark matter distribution
•It may be difficult to distinguish between dark matter described by a King
distribution (thin lines) and a NFW distribution (thick line).
•From the square of the dark matter density, we may be able to estimate the
expected gamma-ray and e± flux from dark matter annihilation.
•Knowing the dark matter density also allows us to estimate the capture of dark
matter by stars.
•
•
Here we see that the inner rotation curve is easily fit with a Plummer-type density distribution
and the outer rotation curve is dominated by the Galactic disk, modeled by a double-exponential.
The difference between the calculated rotation curve from visible matter and the observations
allows us to determine the distribution of dark matter in the Galaxy.
(Burch and Cowsik 2011)
•It is clear that in the inner bulge region of the Milky Way (r<1.5 kpc), dark
matter contributes negligibly to the rotation speed of the Galaxy.
A sample of theoretically calculated rotation curves of the Galaxy
based on our self-consistent model, including lower bounds derived
from the study of dynamics of dwarf spheroidals. That dark matter
is modeled as having a lowered (truncated) isothermal distribution.
The density of dark at the Galactic center is less than 25% of the stellar
density. (Cowsik, Ratnam, Bhattacharjee, Majumdar, and Burch)
Gamma-ray flux from the galactic disk-ascribed to cosmic ray interactions. We may expect
1-100 GeV gamma rays from the annihilations of dark matter particles.
Gamma-ray flux from the galactic disk-ascribed to cosmic ray interactions. We may expect
1-100 GeV gamma rays from the annihilations of dark matter particles, which are to be
detected against a strong background generated by molecular interactions and inverse
Compton scattering of cosmic rays.
Dynamical model for the dark matter halo
• density→potential→orbits →velocities→density
• potential gets contribution from visible matter and dark matter
• Visible matter
– Central Bulge:
– Thin and Thick disk:
(Burch and Cowsik 2011)
Dark Matter -
satisfies the stationary collisionless Boltzmann
equation. Jeans theorem applies:
Reduced isothermal phase space distribution
Coupled non-linear differential equation, solved iteratively using eigenfunction
expansion method
weakly interacting
10-41cm2
CDMS compares phonon (WIMP)
yield to ionization (background) in
Ge detectors. (arXiv 0802:3530)
CDMS-II
XENON10
SUSY
103 GeV
signal region
After cut to remove surface events
massive
Summary
•
•
•
•
•
•
NFW profiles may arise as self-consistent solutions to reduced isothermal distributions in the
presence of baryonic matter.
Self-consistent solutions yield local dispersion velocities for DM particles.
Accurate astronomical measurements of rotation curves at galactocentric distances > 10 kpc
are needed for accurate modeling of galactic dark matter.
Astrophysical considerations for identifying the missing baryons in our galactic neighborhood
are called for.
The self-consistent solutions allow a wide range of DM densities at the galactic center: this
leads to even wider range of predictions for gamma ray and other astronomical signatures of
DM annihilations; the DM density is at most 10% of the stellar density at the galactic center,
which would therefore dominate the accretion by the black hole.
The possibility of neutrino as DM is being reconsidered. The standard constraint on neutrino
masses from their role in erasing small scale perturbations in the density of cold DM, from
laboratory measurements and from their role in generating baryon asymmetry and dark
energy condensates etc. should revisited.
Thanks to WHEPP XII
organizers & participants