季向东 (Xiangdong Ji)Shanghai JiaoTong University

/University of Maryland

Lecture 1: Astrophysical Evidences for Dark Matter (gravity)

Lecture 2: Dark Matter Candidates and WIMPs

Lecture 3: Collider and Indirect Search for WIMPs

Lecture 4: Direct Detection of WIMPs

The world around us is made of ordinary matter! Ordinary matter is made of atoms and

molecules (19th century chemistry) Atoms are made of atomic nuclei and

electrons (beginning of 20th century) Atomic nuclei are made of protons and

neutrons (1930’s) Protons and neutrons are made of quarks and

gluons (1970’s)Atomic spectroscopy indicates the sun, the milky

way, and all stars in the sky are made of ordinary matter!

Virial theorem ： In the stationary gravitational system, the potential energy is twice the kinetic energy!

In 1933 ， Prof. Zwicky at Caltech studied the kinetic energy of the Coma cluster, he found that the kinetic energy is far bigger than the potential energy created by luminous mass. He proposed the concept of “dark matter”

According to his calcualtion, the mass of the dark matter must be as much as 300 times of the ordinary matter.

1. Galaxy Structure1. Rotational curve ， 2. Gravitational lensing

2. Clusters of Galaxy 1. Gravitational lensing2. Velocity distribution3. Hot gas (X-ray)

3. Cosmic Microwave Background4. Large Scale Structure of the Universe.

In the milky way, all stars rotates around the center of the galaxy

According to Newton’s gravitational theory ， the rotation speed of the sun depends on the mass distribution and the distance to the center

According to this formula, the Rotation speed of the sunShall be around 170km/s, howeverThe actual speed is about 220-250km/s.

v(r)r

In a galaxy ， stars rotation speed is a function of distace to the center. The result is the so-called galaxy rotation curve.

95% 质量来自暗物质！

This implies the existence of a dark halo, with mass density

ρ(r) ∝ 1/r2, i.e., M(r) ∝ r; At some point ρ will have to fall off faster (in

order to keep the total mass of the galaxy finite), but we do not know at what radius this will happen.

This leads to a lower bound on the DM mass density,

ΩDM>∼0.1, where ΩX ≡ ρX/ρcrit, ρcrit being the critical mass density to be described later (i.e., Ωtot = 1)

The DM density in the “neighborhood” of our solar system was first estimated as early as 1922 by J.H. Jeans, who analyzed the motion of nearby stars transverse to the galactic plane. He concluded that in our galactic neighborhood, the average density of DM must be roughly equal to that of luminous matter (stars, gas, dust).

Remarkably enough, the most recent estimates, based on a detailed model of our galaxy, find quite similar results

ρlocal DM = 0.3 GeV/cm3; This value is known to within a factor of two or so.

When light-ray passes through a gravitational field ， its direction will be bent. From the magnitude of the bending, we can calculate the distribution of the gravitational field, hence the dark matter.

Strong Lensing (Tyson et al.)

Dark Matter can extend as far as 200kpc and beyond!

The observation of clusters of galaxies tends to give somewhat larger values, ΩDM 0.2 to 0.3.

These observations include measurements of the peculiar velocities of galaxies in the cluster,

which are a measure of their potential energy if the cluster is virialized;

measurements of the X-ray temperature of hot gas in the cluster, which again correlates with the gravitational potential felt by the gas; and—most directly—

studies of (weak) gravitational lensing of background galaxies on the cluster.

According to the standard theoryof cosmology, the universe started 13 billion years ago with a big bang, expands and cools ever since. At about 300,000 years, the atomic nuclei and electronscombine to form neutral atoms, the light can

propagates now freely. The first light is propagating for nearly 13byAnd became the fossil of the universe. Cosmic microwave background radiation

(CMB) (Dicke, Gamow, 1946)

Hubble expansion parameter

Critical mass density

In 1965 ， Penzias & Wilson (Bell Lab) found the CMB for the first time, measured the temperature around 3K, received the 1978 Nobel Prize in physics.

1990, J. Mather through COBE satellite ， found the CMB is a perfect black-body radiation. Moreover, the temperature is almost the same in all directions.

In 1992 ， G. Smoot found, again through COBE data, that CMB temp has fluctuations at the level of 10-5.

The fluctuation can be explained using inflationary models, however, there must be 23% of dark matter ！

CMB Fluctuation

Mather 和 Smoot

我们今天的宇宙是非常不均匀的。这个不均匀是通过宇宙早期的涨落和引力的不稳定演化而来。

背景辐射的涨落

The currently most accurate determination of ΩDM comes from global fits of cosmological parameters to a variety of observations: the anisotropy of CMB and of the spatial distribution of galaxies, one finds a density of cold, non–baryonic matter

Ωnbmh2 = 0.106 ± 0.008 where h is the Hubble constant in units of 100

km/(s·Mpc). Some part of the baryonic matter density, Ωbh2 = 0.022 ± 0.001 may well contribute to (baryonic) DM, e.g.,

MACHOs or cold molecular gas clouds

In 1983, Milgrom proposed a modified Newtonian dynamics in which F=ma is modified to F=maµ, which µ is 1 for large acceleration, becomes a/a0 when a is small.

To explain the rotational curve, one can choose

Cannot fit into a framework consistent with GR. Hard to describe the expansion history, therefore

the CMB fluctuation and galaxy distribution. Hard to explain the bullet cluster. No MOND can explain all gravitational anomalies

without introducing DM.