Research Note

Incomplete-exclusion statistical mechanics in violent relaxation

¹ International Space Science Institute, 3012 Bern, Switzerland
e-mail: Wolfgang.Baumjohann@oeaw.ac.at
² Department of Geophysics, Munich University, 80333 Munich, Germany
³ Space Research Institute, Austrian Academy of Sciences, 8042 Graz, Austria

Received: 24 June 2013
Accepted: 27 August 2013

Abstract

Violent relaxation was proposed half a century ago as responsible for non-collisional dynamics in gravitationally bound systems of extended celestial objects after reaching an equilibrium state that can be described thermodynamically. It is based on a complete spatial exclusion principle that formally leads to a distribution function resembling the Fermi distribution. We extend this theory to incomplete spatial exclusion by assuming that Fermi states can only be partially occupied. This is made possible by analogy to Fermi statistics. A new form of distribution function has been obtained. Formally it does not resemble the Fermi distribution. It consists of a difference of two Bose distributions but has the same properties as the Fermi distribution. Using it in the violent relaxation equation for the global gravitational potential extends the violent relaxation theory to incomplete exclusion. Though this refines violent relaxation theory, it does not resolve its basic deficiencies: the mass problem and those problems related to the mean field assumption.