dark matter and its detection— a concept introduction 毕效军 (bi xiao-jun)...

Dark Matter and its Detection—a concept introduction

毕效军 (Bi Xiao-Jun)

中国科学院高能物理研究所 (IHEP)

International summer Institute onParticle physics, Astrophysics and Cosmology16 August 2005, HangZhou

Outline

Evidences of dark matter Related problems on dark matter

Astrophysics Particle physics

Thermal production Detection of dark matter

Direct detection of WIMP Indirect detection of WIMP

Other candidates Conclusion

Evidences — cluster scale

1933, Zwicky found the first evidence for the presence of dark matter in the Coma cluster.A system at dynamical equilibrium obeys the virial th

eorem: K+U/2=0. Zwicky found that the kinetic term estimated by measuring the proper velocities of the individual galaxies was

much larger than the potential

term due to luminous galaxies:

M/L=300M⊙ /L⊙

Coma cluster


Cluster contains hot gas which is at hydro static equilibrium. It’s temperature follows,

However, X-ray emission measures the temperature and M/Mvisible=20


Weak lensing measures the distortion of images of background galaxies by the foreground cluster, which measures the cluster mass.

Sunyaev-Zeldovich distortion measures the distortion of CMB passing through cluster, which measure the temperature of the gas and therefore the mass of the cluster.

…other measurements

Evidences — galaxy scale

From the Kepler’s law, for r much larger than the luminous terms, you should have v r∝ -1/2 However, it is flat or rises slightly.

r

rGMvcirc

)(

The most direct evidence of the existence of dark matter.

Corbelli & Salucci (2000); Bergstrom (2000)

Evidences — cosmological scale WMAP measures the anisotropy of CMB, whi

ch includes all relevant cosmological information. A global fit combined with other measurements gives

the cosmological

paramters precisely.mh2=0.135+-0.009

m=0.27+-0.04

Spergel et al 2003

Non-baryonic DM

From BBN and CMB, it has Bh2=0.02+-0.002. Therefore, most dark matter should be non-baryonic. DMh2=0.113+-0.009

Non-baryonic dark matter dominates the matter contents of the of the Universe.

Evidences — not from the gravitational effects Up to now no solid experimental evidences

other than the gravity effects indicate the existence of dark matter.

There are hints from DAMA, HEAT, EGRET and HESS experiments which may implies the existence of dark matter. However, all the result are not definite. We will introduce these results later.

Outline






Nature of the dark matter—Hot or cold

Hot dark matter is relativistic at the collapse epoch and free-streaming out the galaxy-sized over density. Larger structure forms early and fragments to smaller ones.

Cold DM is non-relativistic at de-coupling, forms structure in a hierarchical, bottom-up scenario. HDM is tightly bound from

observation and LSS forma-tion theory

Distribution of the dark matter N-body simulation is extensively adopted to study

the evolution of structure with non-linear gravitational clustering from the initial conditions.

The reliability of an N-body simulation is measured by its mass and force resolution.

Simulations suggest a universal dark matter profile, same for all masses, epochs and initial power spectra.

Distribution of the dark matter Two widely adopted density profiles are the NFW

and Moore:

Both profiles have the same behavior at large radius, however, they are different at small radius

2s

1)(

)(

ss rr

rr

r ＝

5.15.1

s

1)(

)(

ss rr

rr

r ＝

10 rrNFW 5.10 rr

Moore

Distribution of the dark matter

Figure shows the profiles of the Milky Way.

The density profiles agree with each other at large scales. Large uncertainty at the small scale.

Local density of dark matter

Determined by measurement of the rotation curves of the Milky Way. However large uncertainties are introduced due to our special position.

Velocity is also determined by the rotation curves.

Bahcall (83), ρ 0 =0.34GeV/cm3, Caldwell (81)ρ 0 =0.23GeV/cm3, Turner(86)ρ 0 =0.3-0.6GeV/cm3

Some recent developments

The slope at the inner most radius is under debate. The most recent simulations seem indicate that the slope is between the NFW and Moore profiles [Navarro, 0311231, Reed, 0312544]. The slope may even be not universal, depending on the mass scale [Reed].

The central super massive black hole will affect the central cusp heavily depending on the its initial mass and adiabatic growth.

Distribution of the dark matter The profile is specified by the two scale para

meters ρs, rs. They are determined by the virial mass of the structure and the concentration parameter by c=rvir/rs.

The concentration parameter represents how the dark matter centrally concentrated. The larger concentration the more centrally concentrated.

The concentration parameter is determined by the evolution of the structure.

How does structure form?

For CDM, structure form hierarchically bottom up ， i.e., smaller object forms earlier (at smaller scale, the fluctuation is larger), they merges to form bigger and bigger structures.

The smaller object have larger concentration parameter, since earlier epoch has greater density.

δρ/ρδρ/ρ

thresholdthreshold

How does structure form?

Objects at each mass scale corresponds to a collapse epoch zc. The collapsing epoch is determined by the condition as σ(M)=δsc, where σis the rms density fluctuation at the comoving scale encompassing M and δsc is the critical over density for collapse.

A semi-analytic model is described by two free parameters: the collapse epoch is determined by the collapsing time of a fraction of the object mass, σ(M*=FM)=δsc; The concentration parameter is determined by another free parameter c(M,z)=K(1+zc)/(1+z).

The model is determined completely by the cosmological parameters.

Concentration parameter via the virial mass

3.0m

72.0h0m

From the figure, the concentration parameter decreases with the virial mass. It is determined once the cosmological parameters are specified.

9.08＝

Substructure Will the smaller objects for

med earlier survive today in the dark halo?

A wealth of subhalos exist due to high resolution simulations.

The number density is as:

Moore et al

Problems of CDM on sub-galactic scale The simulation over-predicts the number of subhalo

s. 11 dwarf satellites of the MW are observed, which is an order of magnitude smaller than predicted.

Solutions are proposed, including inflation potential suppressing the small scale fluctuation, star formation suppressed in small subhalos, and new form of dark matter candidates, such as self-interacting dark matter, non-thermal production, warm dark matter and so on.

Milli-lensing by halo substructure seems favor the CDM scenario. It is still controversial.

The first generation object

Diemand, Moore & Stadel, 2005: Depending on the nature of the

dark matter: for neutralino-like dark matter, the first structures are mini-halos of 10-6 M⊙.

There would be zillions of them surviving and making up a sizeable fraction of the dark matter halo.

The dark matter detection schemes may be quite different!

Outline






Candidates of the dark matter Good candidates which independently motivated in p

article physics, such as neutralino, axion.

Other subjects

What theory is responsible for dark matter? SUSY, extra-dimension, little Higgs, mirror world

How to discriminate the nature of DM among a large amount of candidates?

How does the dark matter produced? Thermally or non-thermally?

How to detect WIMP dark matter other than the gravitational effect? Direct or indirect?

How to detect superWIMP particles? Can we produce the DM particles at the colliders?

Outline






Thermal production of dark matter

Assuming a new, stable particle ， its mass and weak interaction with the SM particles.

At the early Universe of temperature T, is at thermal equilibrium through , for the number density is , while for the number density is

As the cooling of the Universe, when the reaction rate equates to expanding rate ， the particle decouples from the thermal equilibrium. Dark matter as thermal relics freeze in. the comoving number density is then a contant. Introducing ， with s the entropy density 。

M

ll

MT MT

3Tn TmemTn /2/3)(

Hvn

0TTs

n

s

nY

f

Hot dark matter

At decoupling, if is relativistic, both number density of and s are , the ratio is independent of temperature, therefore . The relic density of hot dark matter is porp to its mass.

the mass is therefore constrained by cosmology.

Neutrino is hot dark matter, its abundance and it mass are constrained by SDSS and WMAP

(Tegmark et al 2003)

MTYsMnM f const)(000＝

3T

eV

Mhh

4.942

tot

2

eVmhhi i

7.112.0 2CDM

2

Cold dark matter

The CDM is non-relativistic at decoupling, its number density is exponentially suppressed, therefore the ratio to S depends strongly on its decoupling temeperature, applying the relations

we get

Here determines the strength of the interaction.

fTff vTHTn /)()(

plMTgH /66.1 22/1* 3

*4.0 Tgs 20/MT f

n

fT

f

v

scmh

MTYsh

Mnh

13272

tot

02

tot

02 103)(

v

Density via interaction strength

We have to solve the Boltzmann equation numerically, taking into account the threshold and co-annihilation Tm

Why WIMP (Weak interacting massive particles) From ， we have

for

fTv

scmh

13272 103

13252weak

2

10~~ scmM

210～

Therefore, WIMP is the most nature dark matter candidate if we take DM as thermal relics of the big bang.

Conversely, precise cosmological measurements of the dark matter abundance constrain the particle physics model strong.

GeVM 100weak～

20/22 cv 132610~ scmv

Constrains on the SUSY parameter space The blue stripe is allowed by WMAP

J. Ellis et al (2004)

mSUGRA or CMSSM: simplest (and most constrained) model for supersymmetric dark matter

R-parity conservation, radiative electroweak symmetry breaking

Free parameters (set at GUT scale): m0, m1/2, tan A0, sign()

4 main regions where neutralino fulfills WMAP relic density:

• bulk region (low m0 and m1/2)

• stau coannihilation region m mstau

• hyperbolic branch/focus point (m0 >> m1/2)

• funnel region (mA,H 2m)

• (5th region? h pole region, large mt ?)However, general MSSM model versions give more freedom. At least 3 additional parameters: , At, Ab (and perhaps several more…)

H. Baer, A. Belyaev, T. Krupovnickas, J. O’Farrill, JCAP

0408:005,2004

From the talk given by Bergstrom at SUSY 2005

Outline






Direct detection of WIMP Detect the signal when a WIMP collides with the nuclei. The inte

raction is related with annihilation via a cross symmetry.

Therefore we expect small but non-zero interaction between the WIMP and nuclei.

The scattering includes elastic and inelastic. The inelastic process is extremely weak and radiation from excited nuclei is hard to distinguish from the background. At present theexperiments measure the elastic scattering.

The energy deposited in the detector is measured. For typical and velocity of the WIMP, the energy is at the order of KeV.

llll

M

Elastic scattering

The effective coupling between and quark can be divided to the scalar, pseudo-scalar, vector, axial-vector and tensor types. For the extreme non-relativistic Majorana neutralino, the interaction is simplified to two cases: spin-dependent and spin-independent coupling.

For the SD coupling WIMP couples to the spin of the nucleus; while the SI coupling WIMP couples to the mass of the nucleus.

SD coupling

SD coupling induced by the

axial-vector coupling in the

quark level The SD coupling depends on

the spin of the nucleus

The cross section if given by ， F is the form factor and

qFvmqd

d

r

222

02 4

2220

132nnpprF SaSa

J

JmG

＝

SI coupling

Similarly we get the cross

section of the SI scattering

The cross section is proportional to the mass square, therefore the cross section is greatly enhanced for heavy nucleus, in general it is greater the SD cross section for

Most experiments try to detect the SI interaction

Q4

222

02 F

vmqd

d

r

22

,

22

2

0

4)(

4Af

mfZAZf

mnp

rnp

r

＝

30A

Dependence on the distribution of the velocity The energy deposit rate for elastic scattering

It is , but not can be measured. The deposit energy depends on the velocity distribution near

the earth, the lower limit depends on the material of the detector

It should be noted that the detector adopting different material may be sensitive to different WIMP velocity space.

Additionally there are uncertainties associated with the wave function of the nucleus, it is generally difficult to compare between different experiments.

22/2

203

target

)(

2

)()(

rmMEvr

dvv

vf

m

QFnvdvnvf

dE

dN

dE

dR ＝

00n

Annual modulation signal in DAMA

A model independent way for direct detection of WIMP is to measure the annual modulation effect. A 6.3 σ modulation signal has been observed at the DAMA experiment. However, the interpretation as SI interaction with EM has not been confirmed.

Sensitivity of direct detection experiments Actually the parameter spa

ce due to DAMA has been excluded by new CDMS result.

As the convention, all the experimental results are normalized to SI WIMP-proton cross section assuming Maxwellian velocity distribution

Due to some special velocity distribution form or special DM model there is narrow space for DAMA to reconcile with other experiments.

Outline






Indirect detection of WIMP

Indirect detection detectsthe annihilation productsof the dark matter. The annihilation rate is proportional to th

e square of the dark matter density . For the average density of DM in the Universe the anni

hilation is negligible. However the DM density at somewhere is very high the annihilation rate is also high.

According to the source the experiments are divided in to: detection of neutrinos from the sun or the earth; cosmic rays from the MW or extra-galaxies; products near the black hole in the halo center or from the subhalos.

2

22

ann 22

m

vnv

ll

Flux of the annihilation products

Flux is determined bythe products of two factors

The first factor is the strength of the interaction, determined completely by particle physics

The second by the distribution of DM

The flux depends on both the astrophysics and the particle aspects.

)()( cos moSUSY

EdE

d

dE

d

f

fSUSY

BdE

dN

m

v

dE

d224

1

dlrddVrd sol

mo )()(1

..

2

)(

22

cos

Uncertainties due to the SUSY parameter space

The uncertainty is small. The annihilation is correlated with the early decoupling process.

Uncertainties from the distribution of the DM

Gamma rays

Monoenergetic line

Continuous spectrum

mE

0Z

m

MmE Z

4

2

A smoking gun of DM ann. The flux is suppressed due to loop production.

0 Larger flux. Need careful analysis of the background

Gamma ray detection experiments

ground space

cherenkov EAS

angular reso exce （ <0.1o) good(1o) exce(~0.1o)

obser time short (10%) long (~90%) long(~100%)

effective area large(104M) large(104M2) small(~1M2)

field of view small(<5o) large(π) large （ >2π ）

bkg good （ ~99.9% ） bad(<70%) good

energy reso good(~20%) not bad (~100%) good(<10%,

small syst error ）

Simulation on the GLAST

GLAST Science

Brochure

Gamma lines at the GLAST

Brgstrom et al, 97

Neutrinos from the sun or the earth Density at the solar center is determined by t

he scattering, insensitive to the local density The present data gives

constraints on the

parameter space IceCube can cover most

paramter space

Constraints from the neutrino detection From the Sun and the Earth

Gondolo 2000 Ahrens et al. 2002

Cosmic rays from the halo of the MW—some weak hints on DM Some astrophysics obse

rvations can not be explained by the canonical physics. They may indicate the signal of DM, however, no conclusion can be drawn now.

One of such experiments is the HEAT. (The HEAT signal may indicate the non-thermal production or the subhalo nearby)

Baltz et al. 2002

Excess of gamma rays beyond 1 GeV by EGRET

Cesarini et al. 2003

High energy gamma rays from the GC by HESS and CANGROO

Horns 2004

From the central black hole

The SMBL of mass

will affect the distribution of DM at the GC. The annihilation flux can be either enhanced or decreased.

Synchrotron radiation from the GC excludes the central spike

solM6104～

Flux from the subhalos2sigma upper median

ARGO sensitivity

Outline






Some other candidates superWIMP

Its interaction strength is much smaller than the weak scale, such as gravitino, quintessino

They can not be generated efficiently through the thermal interaction, however they be produced through non-thermal production, such as via decay of heavy relics

If the decay is later than BBN, it will affect the BBN and CMB observations

In SUSY model, the NLSP can be either the neutralino or the stau, they have long life time (as long as 107sec due to suppression)

This kind of dark matter can not be detected as WIMP, there are some interesting prediction of this kind of models and can then be tested

XQ~0 Q

~~

plM

SUSY partner of Quintessence as DM The quintessence interacts with matter, its super part

ner can be the dark matter In order not to destroy the flatness of the potential of

quintessence, we introduce the derivative coupling and its supersymmetric form

It is produced non-thermally

..|ˆ 2 cheQc gV

L

Effects of Quintessino DM

Due to large velocity of non-thermal production, the matter power spectrum at subgalactic scales is suppressed

Affect BBN ， suppress 7Li abundance

Predicts a massive, long life time and charged particel

Lin, Huang, Zhang, Brandberg 01

Bi, Li, Zhang, 2004

~

production by cosmic rays

High energy cosmic neutrinos interacts with the earth matter, the supersymmetric particle and finally the NLSP particle is produced

L3+C or IceCube can detect the

~

~

Bi, wang, zhang, zhang 04

production at collider

If is the NLSP, all the susy particle will finally decay to it and leave a track of charged particle

Collect and study its decay, we can learn gravity even in the laboratory

At LHC/ILC at most

is produced

in one year

~

~

~

65 1010 ～ ~

Buchmuller et al 2004

Kuno et al., 2004

Feng et al., 2004

Conclusion

The existence of dark matter has been firmly established. CDM is favored.

Almost a hundred of DM models have been built, however the nature of the DM is still unclear.

DM is a interdisciplinary field where its astrophysics and its particle physics aspects are closely related.

Both direct and indirect detection of DM as well as the relic density measurement are complementary to colliders to constrain the parameter space of new physics strongly. Some may even reach deeper parameter space than LHC.

Maybe the DM problem is near its solution.

dark matter and its detection— a concept introduction 毕效军 (bi xiao-jun)...

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