Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...244.1039k&link_type=abstract
Astrophysical Journal, Vol.244, P.1039, 1981
Astronomy and Astrophysics
Astrophysics
18
Scientific paper
Chandrasekhar and von Neumann developed a completely stochastic formalism to analyze the complexion of forces acting upon a test star situated in an infinite, homogeneous distribution of field stars. This formalism is generalized here to allow for more realistic inhomogeneous and anisotropic systems. It is demonstrated that the forces acting upon a test star decompose "naturally" into the incoherent sum of a mean force associated with the average spatial inhomogeneity and a fluctuating force associated with stochastic deviations from these mean conditions. Moreover, as in the special case considered by Chandrasekhar and von Neumann, one can apparently associate the fluctuating forces with the effects of particularly proximate field stars, thereby motivating the "nearest neighbor" interpretation first introduced by Chandrasekhar.
This description of fluctuations as local phenomena contradicts conventional wisdom. Therefore, an attempt has been made to isolate the origin of this "localization" of fluctuations in the stochastic formalism. The possibility of such an interpretation is related to properties of the interaction potential and the density profile. A simple one-dimensional example is constructed which does not admit a nearest neighbor interpretation. This example yields a Gaussian distribution of fluctuating forces and consequently agrees with conventional arguments.
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