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A Certain Discontinuous Markov Process in Stellar Dynamics

  • Werner Tscharnuter
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 31)

Abstract

The basic assumption in Chandrasekhar’s approach of statistical stellar dynamics (Chandrasekhar, 1942) is the postulate that a test star within a stellar system being stationary in the sense of collisionless continuum theory suffers random displacements in velocity space generated by the fluctuating part of the gravitational field in a manner that can be described in terms of a random walk. This is equivalent to the assertion that the increments of velocity are regarded as stochastically independent in disjoint time intervals. From this Chandrasekhar derived a diffusion process in velocity space. The equation of motion of the probability density W(r, u, t) in the whole 6-dimensional phase space is then written in the form of a Fokker-Planck-type equation:
$$\frac{{\partial W}}{{\partial t}}+u\cdot{\nabla_r}W+{\nabla_r}\Phi\cdot{\nabla_u}W={\nabla_u}\left({q{\nabla_u}W+\eta{W_u}}\right)$$
(1)
r, u = position, velocity vector; Φ = gravitational potential of the ‘smoothed out’ distribution of matter; q = diffusion coefficient; and η = coefficient of dynamical friction.

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References

  1. Chandrasekhar, S.: 1942, Principles of Stellar Dynamics,New York.Google Scholar
  2. Feller, W.: 1966, An Introduction to Probability Theory and Its Applications, Vol. II, New York.zbMATHGoogle Scholar
  3. Wielen, R.: 1967, Veröff. Astron. Rechen-Inst. Heidelberg,No. 19.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1972

Authors and Affiliations

  • Werner Tscharnuter
    • 1
  1. 1.Inst. für Theoret. AstronomieWienAustria

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