Power spectrum of fluctuations in self‐gravitating systems in a statistical thermodynamics approach

For the description of a self‐gravitating system, a closed formula is found for the power spectrum of the density fluctuations within a statistical thermodynamics approach. A key point of the calculation is the evaluation of the statistical integral describing a system of “particles” interacting gravitationally in a canonical ensemble. The power spectrum turns out to have a smoothed step‐like form. A characteristic length separates two classes of distance regimes and thus t wo phases. The almost flat part of the spectrum for small wave vectors means that there is no distinguished scale of fluctuations in the self‐gravitating system for distances larger than some characteristic length.