Cluster temperatures and non-extensive thermo-statistics
  We propose a novel component to the understanding of the temperature structure of galaxy clusters which does not rely on any heating or cooling mechanism. The new ingredient is the use of non-extensive thermo-statistics which is based on the natural generalization of entropy for systems with long-range interactions. Such interactions include gravity and attraction or repulsion due to charges. We explain that there is growing theoretical indications for the need of this generalization for large cosmological structures. The observed pseudo temperature is generally different from the true thermodynamic temperature, and we clarify the connection between the two. We explain that this distinction is most important in the central part of the cluster where the density profile is most shallow. We show that the observed pseudo temperature may differ up to a factor 2/5 from the true thermodynamic temperature, either larger or smaller. In general the M-T and L-T relations will be affected, and the central DM slope derived through hydrostatic equilibrium may be either more shallow or steeper. We show how the true temperature can be extracted correctly either from the spectrum or from the shape of the Doppler broadening of spectral lines. 
Steen H. Hansen