Properties of Clusters and scaling relations

X-ray imaging of clusters directly provide a map of the hot gas distribution, while the spectroscopy of this gas provide its temperature. Typical temperatures are found in the range between 1 and 15 keV. Bolometric luminosities can be very different from one cluster to an other and range from 1043 erg/s to nearly from 1046 erg/s. There is a well established correlation between luminosities and temperature, although it is widely dispersed. The following relation can be used for most applications  

Recent and detailed reanalysis can be found in Arnaud and Evrard (1999) and Markevitch (1998). The X-ray bremsstrahlung emission of clusters can generally be fitted by the emission of a gas distributed accordingly to the so called 

The scaling argument holds on the idea that different clusters are geometrically identical. This means that clusters at a given epoch can be entirely described by only one quantity, their mass to which an unique scale is associated the virial radius llv. We have seen already how velocity dispersion and temperature can be related to the mass in the previous section4 A further assumption is that the gas fraction does not vary with mass neither with redshift. For instance, self similarity implies  

One can therefore predict the expected scaling of the luminosity-temperature relation, a well observed quantity  

This conflicts with the observed relation. The origin of this discrepancy is not yet entirely understood. It is reasonable to believe that additional non-gravitational physics is necessary, which results in gas heating. Important scaling laws in clusters properties have been found however from numerical simulations in the dark matter distribution. From several numerical simulations, Navarro, Frenk White (1995) noticed that, at least for regular clusters, the dark matter profile follows a law commonly called the NFW profile  

---