Mathematics – Logic
Scientific paper
Aug 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005jrasc..99q.138h&link_type=abstract
Journal of the Royal Astronomical Society of Canada, Vol. 99, No. 4, p.138
Mathematics
Logic
Scientific paper
In 1967 Lynden-Bell presented a statistical mechanical theory for the relaxation of collisionless systems. Since then this theory has been studied numerically and theoretically by many authors. Nakamura in 2000 gave an alternate theory that differed from that of Lynden- Bell by predicting a Gaussian equilibrium distribution function rather than Fermi-Dirac. More recently Henriksen in 2004 has used a coarsegraining technique on cosmological infall systems that also predicts a Gaussian equilibrium distribution function. These relaxed states are thought to occur from the centre of the system outwards. Simulations of cosmological cold dark-matter halos however persist in finding central density cusps (the NFWprofile), which are inconsistent with the predicted distribution functions and perhaps with the observations of some galaxies. Some numerical studies (e.g.Merrall & Henriksen 2003) that attempt to measure the distribution function of dark matter do find Gaussian functions, provided that the initial asymmetry is not too great. Moreover recent work at Queen's reported here by MacMillan, suggests that it is the growth of asymmetry during the infall that produces the cusped behaviour. So put briefly, the essential physics of dark-matter relaxation remains "obscure" as does the validity of the theoretical predictions. "Violent virialization" occurs rapidly, well before subscale relaxation, but the scale at which the relaxation stops (and why) remains unclear. I will present some results that argue for wave-particle relaxation (Landau damping as frequently suggested by Kandrup) and in addition I will suggest that the evolution of isolated systems is very different from that of systems constantly disturbed by infall. Isolated systems may become trapped in an unrelaxed state by the development or existence of multipolar internal structure. Nevertheless a suitable coarse graining of the system may restore the predicted distribution functions.
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