Probes of gravitational wells

2.1 Probes of gravitational wells

The existence of “dark matter” is inferred from astrophysical observations that probe gravitational potentials. The mass content required to provide the derived gravitational potential is then compared with the visible mass content. Several types of observation allow this to be done and in most cases the mismatch between the required mass and the observed mass is extreme. The following list summarises some of the evidence that has been accumulated:

Studies of the dynamics of stars in the local disk environment gave rise to the first suggestion of ‘missing matter’ nearly 70 years ago [98 , 99 ]. The kinetic energy associated with the motion of these stars normal to the plane of the Milky Way gives a measure of the restraining gravitational potential that binds them to the disk. Since the first work by Oort, a number of further studies have given conflicting results. However, even if present, this particular disk dark matter is not significant compared with the halo component.
Rotation curves for a large number of spiral galaxies have now been reliably established and it is observed that the orbital velocities of objects (stars, globular clusters, gas clouds, etc. ) tend to a constant value, independent of the radial position $r$ , even for objects out toward, and even far beyond, the edge of the visible disks. This is quite inconsistent with the $√-- 1∕ r$ behaviour expected from Newtonian mechanics, assuming most mass is in the central part of the galaxies. According to Newtonian mechanics, the mass density within these galaxies is only declining as $∼ r−2$ , leading to a total mass that actually continues to increase proportional to $r$ .
Within the Local Group of galaxies, the Milky Way and Andromeda (M31) are approaching each other at a much faster pace than can be explained by gravitational attraction of the visible mass. To explain the approach velocity, and indeed the fact that these two galaxies are not still moving away from each other as part of the Hubble expansion, requires each to have masses that are consistent with those deduced from their rotation curves.
Many clusters of galaxies show extended x-ray emission. This is usually attributed to a thin plasma of hot gas. On the assumption that the hot gas is gravitationally bound to the cluster and in equilibrium (i.e. we have a virial system), the gravitational potential energy can be inferred from the kinetic energy budget of the hot gas. The cluster mass determined in this way is much higher than that seen either visibly or in the gas itself.
Gravitational lensing by clusters of galaxies causes images of more distant galaxies to be distorted and often split into multiple images. The gravitational mass of the lens (i.e. the cluster), and its distribution, can be recovered through detailed analysis of the image pattern surrounding the cluster. The lenses show a far more extended spatial extent than the visible cluster.
Galaxy red-shift surveys have revealed large-scale galaxy-cluster streaming motions superimposed on the Hubble expansion. Attempts to explain this due to gravitational attraction resulting from the overall distribution of galaxy superclusters give the right direction of motion but need more than the observed visible masses in the superclusters to explain the speed of motion.

The next four items are not really at the same level of “simple” observational evidence as those above, as they require reliance on a more convoluted path to determine masses involved. However, the first three of these have received a great deal of effort and are now heavily used as a combined strong argument in favour of the existence of “dark matter”, and indeed have resulted in a consensus view of “standard cosmology” over the past few years.

The large scale structure (LSS) of the Universe can be studied using large surveys of distant galaxies, by measuring their spatial distribution and peculiar motions. There is an extensive industry in N-body simulations trying to explain the LSS and large-scale dynamics in terms of gravitational growth of small perturbations present in the early Universe. The only simulations that give reasonable agreement with observation are those that use a matter density somewhat higher than currently thought allowable in visible matter. Indeed, starting from the level of the COBE observations of the density fluctuations ( $∼$ 10^–5) at the time of recombination (z = 1000), for gravitational instability to lead to galaxy formation on a reasonable timescale it seems necessary to invoke a significant dark matter component, which only interacts gravitationally.
Type Ia supernovae can be used as standard candles to determine distances, independently of red-shift to high red-shift galaxies in which they occur. This allows the geometry of space-time to be studied at high red-shift. The implications of the results will be discussed later, but consistent cosmological models seem to require a dark matter component.
The COBE satellite gave us the first measurement of the amplitude of microwave background anisotropies at the time of recombination. It is these perturbations which subsequently grow through gravitational instabilities to form the large-scale structure seen today. COBE had a relatively poor angular resolution. Recently, new results have determined the angular power spectrum of the microwave background anisotropies at much finer angular scales, where enhancements are expected due to acoustic wave resonances in the early Universe. The position and amplitude of the enhancement depends on parameters of the early Universe. A clear first peak is seen in the data and its position favours a dark matter component. Even second and third peaks look to be emerging and the amplitudes and positions of these provide constraints on various cosmological parameters (this will be discussed in more detail in the following section).
For those who believe in inflation, most surviving models naturally have a density equal to the critical density, which exceeds that possible in visible matter.

With such a large volume of evidence there can be no doubt that there is a real mystery to be unravelled here. Ideally, it would be satisfying if there were a single simple solution that explained all the above. This has proven elusive so far, but recently there has been some convergence on models that address the larger scale issues to do with the Universe as a whole, and this is discussed in the next subsection. The main aim is to establish a consensus opinion on the dark matter fraction, and more specifically the cold dark matter fraction, as this motivates most of the experimental searches for dark matter. In doing this we will see that a strong argument for a standard cosmology, with cold dark matter as one of its components, is beginning to become established. However, some issues clearly hint at aspects of the cosmology that have yet to be properly resolved, and some of these do have potentially serious implications for the cold dark matter component. These will be discussed in Section 2.3.