Roles of statistical mechanics in determining the density profile of mild relaxation |
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| Authors: | Dong-Biao Kang |
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| Institution: | 1. Xinjiang Astronomical Observatory, Chinese Academy of Sciences, 830011, Urmuqi, China
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| Abstract: | The r ?4 law of cold collapse has been explained in other work. Here we try to explain the density profile of mild relaxation by statistical mechanics. In this paper we first generate many kinds of initial conditions with the same mass and energy to see whether there are other initial factors that can change the density profile of an isolated equilibrium self-gravitating system; then for a more general initial condition we discuss the role of mass and energy in determining the final density profile. Next we use our previous results obtained from statistical mechanics to fit these simulations, and find that when the masses of the particles in clumps are less than 5 % of the total mass, or the initial density is shallower than r ?2, the whole virialized density profile (VDF) can be fitted well by our equation of state with three parameters, and some other cases can be explained by the theory with the r ?4 law. We conclude that statistical physics may play an important role in determining the shape of VDF in the mild relaxation, mass and energy can control the values of the central density and the system’s radius, but there are still other initial configurations that can affect the VDF. |
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