dark matter in the milky way alexey gladyshev (jinr, dubna & itep, moscow) small triangle...
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DARK MATTER IN THE MILKY WAYDARK MATTER IN THE MILKY WAY
ALEXEY GLADYSHEVALEXEY GLADYSHEV
(JINR, DUBNA & ITEP, MOSCOW)(JINR, DUBNA & ITEP, MOSCOW)
SMALL TRIANGLE MEETING 2005SMALL TRIANGLE MEETING 2005
A Gladyshev (JINR & ITEP) Small Triangle 2005 3
Outlook
Introduction.
Evidence for Dark Matter. Types of Dark Matter. Direct
searches for the Dark Matter.
EGRET data: an excess of the diffuse gamma ray flux
Dark matter distribution in the Milky Way. Halo density
profile. Halo substructure. The Milky Way rotation curve.
Positrons and antiprotons in the cosmic rays
WMAP and EGRET constraints in Constrained Minimal
Supersymmetric Standard Model
Conclusions
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Basic cosmological parameters
Density parameters – ratios of contributions of different components (matter, radiation, etc.) to the critical density
Consider the Friedmann equation in the most general form (including the cosmological constant)
203
8i
i cc
H
G
2
2
8
3 3
a k G
a a
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Basic cosmological parameters
Then we can define density parameters corresponding to the matter, radiation, cosmological constant, and even spatial curvature
The Friedmann equation can be rewritten then in the form
2 20 0
2 2 20 0 0
8 8
3 3
3
M RM R
k
G G
H H
k
H a H
4 3 22 2 0 0 0
0 4 3 2( ) R M K
a a aH a H
a a a
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Basic cosmological parameters
For today (a= a0 , H = H0 ) it corresponds to the cosmic sum rule
In the context of the Friedmann-Robetrson-Walker metric the total fraction of radiation, matter, curvature and cosmological constant densities must add up to unity
4 3 22 2 0 0 0
0 4 3 2( ) R M K
a a aH a H
a a a
A Gladyshev (JINR & ITEP) Small Triangle 2005 7
Basic cosmological parameters
In the year 2000, two CMBR missions, BOOMERANG and MAXIMA confirmed that the Universe’s geometry should be very close to flat.
The BOOMERANG result in 2001 gave
The WMAP data released in February 2003 were consistent with
0.050.051.02
0.020.021.02
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Basic cosmological parameters
The radiation component R, corresponding to relativistic
particles from the density of the cosmic microwave background radiation is
which gives R= 2.4 10-5 h-2 = 4.8 10-5. Three massless
neutrinos contribute an even smaller amount.
Therefore one can safely neglect the contribution of relativistic
particles to the total density of the Universe
2
4 3 34 3/ 4.5 10 g/cm15CMBR CMBRkT c
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Matter in the Universe
The matter contribution to the total density of the Universe can
be independently estimated in different ways
Estimation from the dynamics of clusters. A cluster mass Mcl
can be defined by consideration of galaxy motion within the
cluster and/or by gravitational lensing by a cluster gravitational
potential. An estimate of the mass of matter in the
Universe would be then
L are luminosities of a cluster and of the Universe as a whole.
A Gladyshev (JINR & ITEP) Small Triangle 2005 10
Matter in the Universe
This gives the estimate
Another estimate comes from the baryon fraction in matter
Yet another estimate comes from consideration of cluster
abundances
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WMAP
WMAP mission has provided
the first detailed full-sky
map of the microwave
background radiation in the
Universe
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A Gladyshev (JINR & ITEP) Small Triangle 2005 13
WMAP
Results of WMAP
Combination with other
cosmic experiments gives
2 0.113 0.009DM h
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Evidence for the Dark Matter
First evidence for the dark matter – motion of galaxies within
clusters (F.Zwicky, 1933)
The most direct evidence for the existence of large amount of the
dark matter are the flat rotation curves of spiral galaxies (the
dependence of the linear velocity of stars on the distance to the
galactic center)
Spiral galaxies consist of
a rather thin disc and
a spherical bulb in the
galactic center
A Gladyshev (JINR & ITEP) Small Triangle 2005 15
Evidence for the Dark Matter
From the equality of forces one
gets
Assuming spherical distribution of mass in the core one gets
inner part outer part
3
1/ 2
4
3( )
( )
rM r
v r r
v r r
2
2
( )
rgrav centr
r
G M M M vF F
r r
G Mv r
r
Solar system rotation curve
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Evidence for the Dark Matter
Observation tell us that for large radii r
which means linear distribution of mass
This points to the existence of
the huge amount of dark matter
surrounding the visible part of
the galaxy
( )v r const
rM r
Contributionof the dark matter halo alone
Contribution of the disc (visible stars) alone
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Evidence for the Dark Matter
Nowadays, thousands of galactic rotation curves are known, and
they all suggest the existence
of about ten times more
mass in the halos than
in the stars of the disc
Elliptic galaxies and cluster of galaxies
also
contain a large amount of the dark
matter
A Gladyshev (JINR & ITEP) Small Triangle 2005 18
Evidence for the Dark Matter
The Milky Way rotation curve
has been measured and
confirms the usual picture
Measurements of velocities of
Magellanic Clouds tells that the
Milky Way has very large and
massive halo
VIRGOHI21 object – a galaxy,
consisting only of dark matter
A Gladyshev (JINR & ITEP) Small Triangle 2005 19
Matter content of the Universe
The matter content of the Universe is determined by the mass
density parameter M . the possible contributions are
, ,M B lum B dark CDM HDM
The luminous baryonic matter (stars in galaxies)
The dark baryonic matter (MAssive Compact Halo Objects - MACHOs ? )
The hot dark matter(massive neutrinos ? )
The cold dark matter (Weakly Interacting Massive Particles - WIMPs - neutralinos ? )
A Gladyshev (JINR & ITEP) Small Triangle 2005 20
Matter content of the Universe
All the luminous matter in the Universe from galaxies, clusters of
galaxies, etc. is
and is very far from the critical density
Deuterium from the primordial nucleosynthesis provides a good test
for the matter density (Large density - Fast interactions - Lower
abundance)
Observation of primordial deuterium abundance gives
Thus, besides luminous matter there exist invisible baryonic matter,
with a mass more than ten times larger.
2,0.002 0.006B lumh
0.04 0.008B
A Gladyshev (JINR & ITEP) Small Triangle 2005 21
Dark Matter candidates
Baryonic Dark Matter (MACHOs – MAssive Compact Halo Objects)
Normal stars No, since they would be luminous
Hot gas No, since it would shine
Burnt-out stellar remnants
seems implausible, since
they would arise from a population of normal
stars of which there is no trace in the halo
Neutron stars No, since they would arise from supernova
explosions and thus eject heavy
elements into the galaxy
A Gladyshev (JINR & ITEP) Small Triangle 2005 22
Dark Matter candidates
Baryonic Dark Matter (MACHOs – MAssive Compact Halo Objects)
White dwarfs (stars with a mass which is not enough to reach
the supernova phase): possible, since white dwarfs are
known to exist and to be plentiful.
Maybe they could be plentiful enough to explain the Dark Matter
if young galaxies that produced white dwarfs cool more rapidly
than present theory predicts. But the production of large numbers
of white dwarfs implies the production of a large amount of
helium, which is not observed
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Dark Matter candidates
Baryonic Dark Matter (MACHOs – MAssive Compact Halo Objects)
Brown dwarfs (stars ten times lighter than the Sun) possible
Astronomers have found some
objects that are either brown
dwarf stars or very large planets.
However, there is no evidence
that brown dwarfs are anywhere
near as abundant as they would
have to be to account for the
Dark Matter in our galaxy
A Gladyshev (JINR & ITEP) Small Triangle 2005 24
Dark Matter candidates
Non-baryonic “hot” dark matter
Massive neutrinos
Today we have a convincing evidence of neutrino oscillations.
This means that neutrinos have a mass. The measurable
quantity – mass-squared difference.
If neutrino mass is as large as , their
contribution to the total density of the Universe is comparable
to the contribution of the luminous baryonic matter!
2 3 210m eV
0.1m eV
2( )0.001 0.018HDM h
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Dark Matter candidates
Non-baryonic “cold” dark matter
The most reasonable explanation –
weakly interacting massive particles (WIMP’s)
WIMP’s could have been produced in the Big Bang
origin of the Universe in the right amounts and with
the right properties to explain the Dark Matter
BUT: we do not know WHAT the WIMP IS
A Gladyshev (JINR & ITEP) Small Triangle 2005 26
Direct searches for the Dark Matter
Optical observations from the Earth (EROS, MACHO, … )
Underground searches (DAMA, EDELWEISS, CDMS, … )
Underwater searches (ANTARES, … )
Searches in space (AMS, … )
A Gladyshev (JINR & ITEP) Small Triangle 2005 27
Direct searches for the Dark Matter
MACHO experiment
(MAssive Compact Halo Object)
Location - Mount Stromlo
Observatory, Canberra, Australia
Main goal - search for objects
like brown dwarfs or planets
(Massive Compact Halo Objects
- MACHOs)
Signature - occasional
amplification
of the light by the
gravitational
lens effect
A Gladyshev (JINR & ITEP) Small Triangle 2005 28
Direct searches for the Dark Matter
The effect is large and easily detectable: the amplification could be as large as 0.75m
The phenomenon has a very symmetric light curve, characterized by only 3 parameters (brightness in the maximum, time and duration of the light amplification)
The amplification is the same for all wavelenghts
For the particular star the effect can take place only once
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Direct searches for the Dark Matter
Different collaborations have seen the signal (1993-1996)
OGLE 18 candidates in the direction to the galactic centre
MACHO 120DUO 10
Gravitional lens effect has been detected also in the direction to the Large Magellanic Cloud
MACHO 8EROS 2
The most probable mass of the lens
However, MACHOs can only account for less than ~ 50 % of the halo
0.3
0.20.5M M
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Direct searches for the Dark Matter
DAMA experiment (DArk MAtter)
Location - Gran Sasso National
Laboratory of I.N.F.N.
Main goal - search for dark
matter particles: WIMPs
Main process – WIMP elastic
scattering on the target nuclei
Measured quantity - nuclear
recoil energy in the keV range
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Direct searches for the Dark Matter
Positive evidence for a WIMP signal
could arise from the kinematics of
the Earth withing non-rotating WIMP halo.
The sun is orbiting about the galactic
centre with a velocity of ~ 220 km/s.
The Earth is orbiting about the Sun
with a velocity of ~ 30 km/s.
The resulting relative Earth-halo velocity is modulated, thus
the WIMP flux is also modulated which should lead to the
modulation of the count rate.
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Direct searches for the Dark Matter
DAMA group claim they do observe the modulation of their
count rate (results of 4 years running - 57986 kgd)
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Direct searches for the Dark Matter
This result is compatible
with a signal from WIMPs
with a mass
and a WIMP-nucleon cross
section of
10
852WIMP GeVm
60.4
0.9pb7.2 10
A Gladyshev (JINR & ITEP) Small Triangle 2005 34
Direct searches for the Dark Matter
Severe criticism has arisen in the community, ascribing the observed annual modulation rater to systematics than to a WIMP signature.
DAMA insists on their model-independent analysis: presence of annual
modulation with the proper features;
neither systematics nor side reactions able to mimic the signature
A Gladyshev (JINR & ITEP) Small Triangle 2005 35
Direct searches for the Dark Matter
1st data taking: Fall 20002nd data taking: 1st semester 20023rd data taking :October 2002 -
March 2003
EDELWEISS new limits
DAMA best fit exclusion at > 99.8 % C.L confirmed with 3 new detectors and extended exposure
Exclusion limits are astrophysical model independent
A Gladyshev (JINR & ITEP) Small Triangle 2005 36
Direct searches for the Dark Matter
EDELWEISS II
New run started : improved energy
threshold
Expect further factor > 2 in
exposure with improved sensitivity
September 2003 : EDELWEISS I
stops and EDELWEISS II
installation begins with 21×320g
Ge
Sensitivity will be improved by
a factor of 100 8 pb10
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Searches for the Dark Matter
AMS-02 experiment
(AntiMatter in Space)
Location - International
Space Station (Hopes it’ll
be launched in 2007,
scheduled to be
launched 15 Oct 2005,
planned 4 Sep 2003)
Main Goal - search for
dark matter, missing
matter & antimatter in
space
Indirect searches for the Dark Matter
A Gladyshev (JINR & ITEP) Small Triangle 2005 39
EGRET Excess
EGRET Data on diffuse Gamma Rays show excess in all sky directions with the same energy spectrum from monoenergetic quarks
9 yrs of data taken (1991-2000)
Main purpose: sky map of point sources above diffuse background.
A Gladyshev (JINR & ITEP) Small Triangle 2005 40
EGRET Excess
A: Inner Galaxy (l=±300, |b|<50)
B: Galactic plane avoiding A (30-3300)
C: Outer Galaxy (90-2700)
D: Low latitude (10-200)
E: Intermediate lat. (20-600)
F: Galactic poles (60-900)
Excess has the same shape implying the same source everywhere in the galaxy
A Gladyshev (JINR & ITEP) Small Triangle 2005 41
EGRET Excess
A: Inner Galaxy (l=±300, |b|<50)
B: Galactic plane avoiding A (30-3300)
C: Outer Galaxy (90-2700)
D: Low latitude (10-200)
E: Intermediate lat. (20-600)
F: Galactic poles (60-900)
Excess has the same shape implying the same source everywhere in the galaxy
EGRET gamma excess aboveextrapolated backgroundfrom data below 0.5 GeV
A Gladyshev (JINR & ITEP) Small Triangle 2005 42
EGRET Excess
A: Inner Galaxy (l=±300, |b|<50)
B: Galactic plane avoiding A
C: Outer Galaxy
D: Low latitude (10-200)
E: Intermediate lat. (20-600)
F: Galactic poles (60-900)
A Gladyshev (JINR & ITEP) Small Triangle 2005 43
EGRET Excess vs WIMP annihilation
The excess of diffuse gamma rays is compatible with WIMP mass of 50 -100 GeV
Region A: inner Galaxy (l=±300, |b|<50)
BackgroundWIMP contribution
A Gladyshev (JINR & ITEP) Small Triangle 2005 44
EGRET Excess vs WIMP annihilation
A: inner Galaxy (l=±300, |b|<50)
B: Galactic plane avoiding A
C: Outer Galaxy
D: low latitude (10-200)
E: intermediate lat. (20-600)
F: Galactic poles (60-900)
A Gladyshev (JINR & ITEP) Small Triangle 2005 45
EGRET Excess vs WIMP annihilation
3 components
(galactic background +
extragalactic
background + DM
annihilation)
fitted simultaneously
with same WIMP mass
and DM normalization
in all directions.
Blue: uncertainty from
WIMP mass
WIMP mass50 - 100 GeV
65100
WIM
PS 0
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Determination of halo profile
The differential gamma flux in a direction forming an angle ψ
with the direction of the galactic center is given by:
WIMP annihilation cross section
branching ratio into the tree-level annihilation final state f
differential photon yield for the final state f Dark matter mass density
Boostfactor WIMP mass
A Gladyshev (JINR & ITEP) Small Triangle 2005 47
Determination of halo profile
A survey of the optical rotation curves of 400 galaxies shows
that the halo distributions of most of them can be fitted either
with the Navarro-Frank-White (NFW) or the pseudo-isothermal
profile. The halo profiles can be parametrized as follows:
a is a scale radius,
define behaviour at r ≈ a, r >> a and r
<< a
, ,
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Determination of halo profile
Navarro-Frank-White profile (1,3,1) very cuspy
Moore profile(1.5,0,1.5) very cuspy
Isotermal profile
(2,2,0) less cuspy
β=2 implies flat rotation curve
A Gladyshev (JINR & ITEP) Small Triangle 2005 49
Determination of halo profile
The spherical profile can be
flattened in two directions to form
a triaxial halo. N-body simulations
suggest the ratio of the short
(intermediate) axis to the major
axis is typically above 0.5-0.7
It is not clear if the dark matter is
homogeneously distributed or has
a clumpy character. Clumps can
enhance the annihilation rate. This
enhancement (boostfactor) can be
determined from a fit to the data.
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Determination of halo profile
The possible enhancement of DM density in the disc was
parametrized by a set of Gaussian rings in the galactic plane in
addition to the expected triaxial profile for the DM halo. At least
two rings should be envisaged: one “outer” ring and one “inner”
ring. Parameters of the rings can be determined from a fit to the
data.
=2
1/r2 2 Gaussian ovals
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Determination of halo profile
Spiral structure Caustic rings
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Determination of halo profile
Parameters in halo profile fitted by requiring minimal difference
between boostfactors of various regions.
If clustering is similar in all directions (same boostfactors everywhere),
then the excess of diffuse gamma rays is ~<ρ>2 along the line of sight.
<ρ> is determined by the halo profile, which is normalized to the local
dark matter density ρ0.
ρ0 can be estimated from the rotation curve to be 0.3 GeV/cm3 for a
spherical profile and R0 = 8.5 kpc. For a non-spherical one the density
has to be rescaled.
A Gladyshev (JINR & ITEP) Small Triangle 2005 54
Determination of halo profile
Energy spectrum of diffuse
gamma rays is well described by
background + WIMP annihilation
Longitude and lattitude
distributions (different sky
directions!) of gammas are used
for determination of halo and
substructure (rings) parameters
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Gammas below 0.5 GeV (EGRET)
Longitude: azimuthal angle Latitude: angle out of the plane
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Gammas above 0.5 GeV (EGRET)
Longitude: azimuthal angle Latitude: angle out of the plane
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Fits for 1/r2 profile with/without rings
WITHOUT rings
DISC
50<b<100
100<b<200
200<b<900
WITH 2 rings
DISC
50<b<100 200<b<900
100<b<200
A Gladyshev (JINR & ITEP) Small Triangle 2005 58
Fit results for halo profile
Fit results of halo parameters
Enhancement of rings
over 1/r2 profile 2 and 7,
respectively.
Mass in rings 1.6% and
0.3% of total Dark
Matter
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Determination of halo profile
H2
H
R[kpc]
4
14 kpc coincides with ring of stars at 14-18 kpc due to infall of dwarf galaxy (Yanny, Ibata, ….., 2003)
4 kpc coincides with ring of neutral hydrogen molecules!
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The Milky Way rotation curve
Contributions to the rotation curve of the Milky Way from
Visible bulge Visible disk
Dark halo Inner dark ring Outer dark ring
Outer Ring
Inner Ring
bulge
tota
lDM
1/r2 halodisk
Rotation Curve
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Halo density at 300 kpc
Cored isothermal halo profile. Total mass: 3×1012 solar masses
Sideview Topview
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Halo density at 30 kpc
Ring halo substructure. R ~ 4 and 14 kpc.
Sideview Topview
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Possible origin of rings
In 1994 Cambridge astronomers
discovered a highly distorted
dwarf galaxy in the Sagittarius
constellation. The galaxy falls
towards the Milky Way spreading
out stars along its pass.
In 2003 Canis Major dwarf galaxy was discovered
In 2003 a giant stellar structure surrounding the Galaxy was
discovered (possibly the remnant of a galaxy “eaten” by Milky
Way very long ago)
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Positrons and antiprotons in cosmic rays
SAME halo and WIMP parameters as for gamma rays
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Supersymmetry
FERMIONS (s=1/2) BOSONS (s=0,1)
Quarks
Electron, Muon, Tau
Neutrinos
Photon
Z-boson
W-boson
Higgs
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Supersymmetry
FERMIONS (s=1/2) BOSONS (s=0,1)
Quarks Squarks
Electron, Muon, Tau Sleptons
Neutrinos Sneutrinos
Photino Photon
Zino Z-boson
Wino Charginos W-boson
Neutralnos
Higgsino 1 Higgs 1
Higgsino 2 Higgs 2
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Neutralino – SUSY dark matter
Still we know nothing about WIMP
Supersymmetry helps again
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Neutralino – SUSY dark matter
Lagrangian of the Minimal Supersymmetric Standard Model:
Yukawa interactions
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Supersymmetry is a broken symmetry.
Breaking takes place in a hidden sector.
Messengers to the visible sector can be
gravitino, gauge bosons, gauginos, …
Breaking must be soft (dimension of soft SUSY breaking operators 3)
In total one has about a hundred parameters
Neutralino – SUSY dark matter
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Neutralino – SUSY dark matter
Main uncertainties come from soft supersymmetry breaking parameters.
Universality hypothesis: soft supersymmetry breaking parameters unify at the scale of Grand Unification
As a result one has only 5 free parameters (4 + one sign)
Common scalar mass m0
Common gaugino mass m1/2
Common soft SUSY breaking parameter A0
tan = v2 / v1
A Gladyshev (JINR & ITEP) Small Triangle 2005 73
Neutralino – SUSY dark matter
Neutralino – a mixture of superpartners of photon, Z-boson and
neutral Higgs bosons
Neutral (no electric chaege, no colour)
Weakly interacting (due to supersymmetry)
The lightest supersymmetric particle
Stable (!) if R-parity is conserved
Perfect candidate for dark matter particle (WIMP)
0 0 01 21 2 3 4N N z N H N H
photino zino higgsino higgsino
3( ) 2( 1)
1, 1
B L S
p p
R
R R
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Neutralino – SUSY dark matter
Limits on neutralino mass
Heavy enough to account for cold
non-baryonic dark matter in the
Universe
Annihilation cross sections are
known (at least we know how to
calculate them)
exp 40 GeVM
40 400 GeVtheorM
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Neutralino – SUSY dark matter
Main diagrams for
neutralino annihilation
Dominant diagram for
WMAP cross section:
A bb
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Neutralino – SUSY dark matter
B-fragmentation well
studied at LEP! Yield and
spectra of positrons,
gammas and antiprotons
well known!
Galaxy = SUPER-B-factory
with luminosity some 40
orders of magnitude above
man-made B-factories
, , ,A bb X e p
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Neutralino – SUSY dark matter
Annihilation cross sections in m0-m1/2 plane (μ > 0, A0=0)
tanβ=5 tanβ=50
For WMAP cross section of <v> 2×10-26 cm3/s one needs large tanβ
bb bbt t t t
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Favoured regions of parameter space
Pre-WMAP allowed regions in the parameter space.
Fit to all constraints tanβ=50 Fit to Dark matter constraint
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Favoured regions of parameter space
WMAP data leave only very small allowed region as shown by the thin blue line which give acceptable neutralino relic density
Excluded by LSP
Excluded by Higgs searches at LEP2
Excluded by REWSB
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Favoured regions of parameter space
The region compatible with
all electroweak constraints
as well as with WMAP and
EGRET constraints are rather
small
It corresponds to the best fit
values of parameters
tanβ = 51
m0 = 1400 GeV
m1/2 = 180 GeV
A0 = 0.5 m0
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Favoured regions of parameter space
Superparticle spectrum for
m0=1400 GeV, m1/2=180 GeV
Squarks/sleptons are in TeV range
Charginos and neutralinos are light
LSP is largely Bino Dark Matter
may be supersymmetric partner
of Cosmic Microwave Background
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Comparison with direct DM searches
Spin-independent Spin-dependent
Prediction from EGRET data assuming supersymmetry
DAMA
CDMS
ZEPLIN
Edelweiss
Projections
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Summary: input
Astronomy Dark matter in clusters of galaxies and galaxies itself Rotation curve of the Milky Way
Astrophysics Gamma ray flux from the sky (EGRET) Positrons and antiprotons in cosmic rays
Cosmology Amount of the dark matter (~23%)
Particle physics Annihilation cross sections Spectrum of gamma quanta from quarks/antiquarks
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Summary: physics questions & answers
Astrophysicists:
What is the origin of “GeV excess” of diffuse galactic gamma rays?
What is the origin of “7 GeV excess” of positrons in cosmic rays?
What is the origin of “GeV excess” of antiprotons in cosmic rays?
Answer: Dark matter annihilation
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Summary: physics questions & answers
Astronomers:
Why a change of slope in the Milky Way rotation curve at
R0=8.3 kpc?
Answer: Dark matter substructure
Why ring of stars at 14 kpc so stable?
Why ring of molecular hydrogen at 4 kpc so stable?
A Gladyshev (JINR & ITEP) Small Triangle 2005 86
Summary: physics questions & answers
Cosmologists:
How is Cold Dark Matter distributed?
Answer: 1/r2 profile + substructure (two rings)
Particle physicists:
Is DM annihilating as expected in Supersymmetry?
Answer: Cross sections are perfectly consistent with SUSY
THE END