DARK MATTER IN THE MILKY WAY ALEXEY GLADYSHEV (JINR, DUBNA & ITEP, MOSCOW) SMALL TRIANGLE...

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

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)

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

M RM R

4 3 22 2 0 0 0

0 4 3 2( ) R M K

a a aH a H

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

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

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

4 3 34 3/ 4.5 10 g/cm15CMBR CMBRkT c

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.

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

WMAP mission has provided

the first detailed full-sky

map of the microwave

background radiation in the

Universe

Results of WMAP

Combination with other

cosmic experiments gives

2 0.113 0.009DM h

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

From the equality of forces one

Assuming spherical distribution of mass in the core one gets

inner part outer part

rgrav centr

G M M M vF F

G Mv r

Solar system rotation curve

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

Contributionof the dark matter halo alone

Contribution of the disc (visible stars) alone

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

contain a large amount of 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

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 ? )

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

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

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

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

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

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

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, … )

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

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

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

0.20.5M M

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

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.

DAMA group claim they do observe the modulation of their

count rate (results of 4 years running - 57986 kgd)

This result is compatible

with a signal from WIMPs

with a mass

and a WIMP-nucleon cross

section of

852WIMP GeVm

0.9pb7.2 10

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

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

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

Sensitivity will be improved by

a factor of 100 8 pb10

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

Indirect searches for the Dark Matter

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.

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 Excess

B: Galactic plane avoiding A (30-3300)

C: Outer Galaxy (90-2700)

Excess has the same shape implying the same source everywhere in the galaxy

EGRET gamma excess aboveextrapolated backgroundfrom data below 0.5 GeV

EGRET Excess

B: Galactic plane avoiding A

C: Outer Galaxy

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: inner Galaxy (l=±300, |b|<50)

B: Galactic plane avoiding A

C: Outer Galaxy

D: low latitude (10-200)

E: intermediate lat. (20-600)

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

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 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

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

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.

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

1/r2 2 Gaussian ovals

Spiral structure Caustic rings

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.

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

Gammas below 0.5 GeV (EGRET)

Longitude: azimuthal angle Latitude: angle out of the plane

Gammas above 0.5 GeV (EGRET)

Longitude: azimuthal angle Latitude: angle out of the plane

Fits for 1/r2 profile with/without rings

WITHOUT rings

50<b<100

100<b<200

200<b<900

WITH 2 rings

50<b<100 200<b<900

100<b<200

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

R[kpc]

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!

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

1/r2 halodisk

Rotation Curve

Halo density at 300 kpc

Cored isothermal halo profile. Total mass: 3×1012 solar masses

Sideview Topview

Halo density at 30 kpc

Ring halo substructure. R ~ 4 and 14 kpc.

Sideview Topview

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)

Positrons and antiprotons in cosmic rays

SAME halo and WIMP parameters as for gamma rays

Supersymmetry

FERMIONS (s=1/2) BOSONS (s=0,1)

Quarks

Electron, Muon, Tau

Neutrinos

Photon

Z-boson

W-boson

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

Neutralino – SUSY dark matter

Still we know nothing about WIMP

Supersymmetry helps again

Lagrangian of the Minimal Supersymmetric Standard Model:

Yukawa interactions

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

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

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)

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

Main diagrams for

neutralino annihilation

Dominant diagram for

WMAP cross section:

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

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

Favoured regions of parameter space

Pre-WMAP allowed regions in the parameter space.

Fit to all constraints tanβ=50 Fit to Dark matter constraint

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

The region compatible with

all electroweak constraints

as well as with WMAP and

EGRET constraints are rather

It corresponds to the best fit

values of parameters

tanβ = 51

m0 = 1400 GeV

m1/2 = 180 GeV

A0 = 0.5 m0

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

Comparison with direct DM searches

Spin-independent Spin-dependent

Prediction from EGRET data assuming supersymmetry

ZEPLIN

Edelweiss

Projections

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

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

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?

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

DARK MATTER IN THE MILKY WAY ALEXEY GLADYSHEV (JINR, DUBNA & ITEP, MOSCOW) SMALL TRIANGLE...

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