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We will construct a theory which can explain the dynamics toward the steadystate self-gravitating systems (SGSs) where many particles interact via thegravitational force. Real examples of SGS in the universe are globular clustersand galaxies. The idea is to represent an interaction by which a particle ofthe system is affected from the others by a special random force. That is, wewill use a special Langevin equation, just as the normal Langevin equation canunveil the dynamics toward the steady state described by the Maxwell-Boltzmanndistribution. However, we cannot introduce the randomness into the systemwithout any evidence. Then, we must confirm that each orbit is random indeed.Of course, it is impossible to understand orbits of stars in globular clustersfrom observations. Thus we use numerical simulations. From the numericalsimulations of SGS, grounds that we use the random noise become clear. Thespecial Langevin equation includes the additive and the multiplicative noise.By using the random process, we derive the non-Maxwellian distribution of SGSespecially around the core. The number density can be obtained through thesteady state solution of the Fokker-Planck equation corresponding to the randomprocess. We exhibit that the number density becomes equal to the densityprofiles around the core by adjusting the friction coefficient and theintensity of the multiplicative noise. Moreover, we also show that our modelcan be applied in the system which has a heavier particle, corresponding to theblack hole in a globular cluster.

Stochastic Dynamics Toward the Steady State of Self-Gravitating Systems