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