Evidence for dark matter from X-rays observations

Just as elliptical galaxies, clusters emit X-rays due to thermal bremsstrahlung produced in the highly ionised gas bound by the gravitational potential well of the cluster. This can be used to estimate the mass required to bind this gas, as we did when deriving Equation (7.13) from assuming hydrostatic equilibrium in an isothermal gas. This type of analysis again strongly suggests the presence of dark matter. From the pictures of the X-ray gas, it is also immediately clear that the X-rays come from all over the cluster, they are not obviously associated with individual galaxies.

From the X-ray intensity distribution, one can also estimate the amount of hot gas present in the cluster. From modelling the colours of the galaxies, one can estimate the mass in stars. Comparison of these two shows that hot gas is the dominant baryonic mass by a large factor. So most of the baryonic mass in a cluster of galaxies is actually in hot gas and not in galaxies at all.

The temperature of the gas is so high that it balances the gravitational force of the dark matter in the cluster. It gets to this high temperature by shock heating. This is how it works: as the cluster is accreting matter from its surroundings, newly accreted gas falls into the cluster at high velocity. The velocity is high, because the gas has been accelerated by the gravitational force from the tremendous amount of mass in the cluster. The high velocity gas slams into the stationary hot gas and converts most of its kinetic energy into thermal energy: this is an accretion shock.

Suppose a parcel of gas starts at infinity with zero velocity, and falls into a cluster with mass $M$ and radius $R$. By the time it reaches the outskirts of the cluster at radius $R$ it will have an in fall velocity

$${1\over 2}v_{\rm infall}^2 = {G\,M\over R}\,,$$ (9.5)

where I've used energy conservation. When it hits the cluster gas, it will convert this kinetic energy into thermal energy, hence it will be heated to a temperature $T$

$${3\over 2}{\hbox{${\rm k}_{\sc\rm B}$}T\over \mu}={1\over 2}\hbox{$m_{\sc\rm p}$}\,v_{\rm infall}^2\,.$$ (9.6)

Here, $\mu$ is the mean molecular weight of the gas. Combining the last two equations, we find that the temperature of the cluster will be

$${3\over 2}\,{\hbox{${\rm k}_{\sc\rm B}$}T\over \mu\hbox{$m_{\sc\rm p}$}}={G\,M\over R}\,.$$ (9.7)

This temperature is called the virial temperature.

Where does all this gas come from? The X-rays we observe from clusters imply that the hot gas is loosing energy and hence is cooling. So from the observed X-ray luminosity, we can estimate the cooling time of the gas $t_{\rm cool}$,

$${dT\over dt} \equiv {T\over t_{\rm cool}}\,.$$ (9.8)

Given the present cooling rate, $dT/dt$, the gas will have lost it's thermal energy after a cooling time, $t_{\rm cool}$. The measured values of $t_{\rm cool}$ turn out to be longer than the age of the Universe for most clusters^9.2. This means that once the gas gets hot it will remain hot, and cannot form into galaxies anymore. So clusters of galaxies are in fact regions where galaxy formation is strongly suppressed because the gas is too hot to cool and form stars.

But why did it not form galaxies before it became hot? This is actually a rather hotly debated issue at the moment, but here's a hint: