Los elementos de la acción colectiva

Evidences for dark matter can be found at all astrophysical scales: from the rotation curves of galaxies, over the luminosity of galaxy clusters up to the cosmological scale of the microwave background, there are many dierent hints for the existence of additional matter in our universe. Rotation curves The rst hint for the existence of 'invisible matter' came from the observation of the rotation curves of galaxies [91, 92]. While the velocity v of stars should drop according to

0 0 10 20 30 50 100 150 gas dark matter disk r [kpc] v [k m /s ]

Figure 1.6.: Schematic picture of the rotation curve of a galaxy. The dotted line is the contribution of gas, the dashed line of the disk and the dash-dotted line of a dark matter halo. The sum of all three contributions reproduces the observed, at curve (solid line).

Newton's law like v(r) =

r

GM (r)

r (1.72)

as a function of the distance r to the center of the galaxy, it was observed that v is constant over a large range of r. This behavior is not an eect of general relativity and not explainable by the visible amount of matter in the galaxy without changing the physical laws. There are models trying to explain this observation with modied Newtonian dynamics (MOND) [93]. However, such models have often severe problems explaining other observations. Another explanation for the atness of the rotation curves are new sources of gravitational attraction in form of dark matter halo as depicted in Fig. 1.6.

Cosmic microwave background The most precise measurement of the amount of dark matter comes from the observation of the cosmic microwave background (CMB). The CMB is an echo of the decoupling of the photons from matter in the early universe. This eect was rst predicted by Gamow in 1948 [95] and accidentally discovered by Penzias and Wilson 1965. While the CMB looks at rst glance very isotropic with a temperature of T = 2.726 K, satellite experiments have detected a distortion of these isotropy at the 10−5 _{level. The anisotropies are usually}

parametrized by an expansion in spherical harmonics Y (Θ, Φ): δT T = +∞ X l=2 +l X m=−l almYlm(Θ, Φ) . (1.73)

All measurements show that the anisotropies are Gaussian-like distributed and the power spec- trum can be expressed as a function of 1

2πl(l + 1)Cl. Cl is the variance of alm Cl =h|alm|2i = 1 2l + 1 +l X m=−l |alm|2 . (1.74)

1.2. DARK MATTER

Figure 1.7.: Picture of the bullet cluster [94]. The pink areas show X-ray emission observed by the Chandra X-Ray telescope. At this region the luminosity matter is located. The blue areas are the region where most of the mass is located according to gravitational lensing. The explanation for this large separation of visible and dark matter is that dark matter can pass the collision area much faster because of its weak interaction.

Fig. 1.8 shows the result of the power spectrum based on the 7-year data of the Wilkinson Mi- crowave Anisotropy Probe (WAMP). The dierent peaks are an eect of the dierent constituents of the universe building the potential of the photons at the time of decoupling. Therefore, this power spectrum can be translated into the matter and energy content of the universe. The result is normally expressed in units of Ωh2_{. The best t value for the amount of baryonic and dark}

matter from the 7-year data of WMAP together with results of Baryon Acoustic Oscillations (BAO) and Hubble constant measurements is [86]

Ωbh2= 0.02260± 0.00053 , ΩDMh2 = 0.1123± 0.0035 . (1.75)

Remarkably, the largest contribution to the energy density in the universe with

ΩΛ= 0.728± 0.015 (1.76)

comes from the so called 'Dark Energy', which is still poorly understood.

Bullet Cluster Finally, we show a picture of the galaxy cluster 1E 0657-56, called 'the bullet cluster' in Fig. 1.7. This picture is often referred to as the rst direct detection of dark matter [97]: it shows the merging of two galaxies. The combination of the X-ray image taken by the Chandra X-Ray telescope together with optical and weak lensing observation shows that the mass center of the collision doesn't coincide with the visible mass distribution. Thus, most of the matter has passed the collision area much faster. This can only happen if a high amount of matter in these galaxies is only weakly interacting.

This was just a small extract of the clues and evidences for dark matter. We have here skipped, for instance, the results of weak lensing (see [98] and references therein) or simulations of structure formation of the universe like the well-known millennium project [99].

Figure 1.8.: 7-year result of WMAP mission for the power spectrum of the universe [96]. The tem- perature anisotropies of the CMB are expressed as function of the multipole moment l. Assuming a cosmological scenario, the best t parameters to this curve are related to the amount of matter and energy in the universe at the time of decoupling.