EDP Sciences
Open Access
Volume 496, Number 1, March II 2009
Page(s) 129 - 131
Section Galactic structure, stellar clusters, and populations
DOI http://dx.doi.org/10.1051/0004-6361:200810857
Published online 20 January 2009
A&A 496, 129-131 (2009)
DOI: 10.1051/0004-6361:200810857

Research Note

Estimating the size of the cosmic-ray halo using particle distribution moments

Y. E. Litvinenko

Department of Mathematics, University of Waikato, PB 3105, Hamilton, New Zealand

Received 26 August 2008 / Accepted 6 January 2009

Context. Particle transport in many astrophysical problems can be described either by the Fokker–Planck equation or by an equivalent system of stochastic differential equations.
Aims. It is shown that the latter method can be applied to the problem of defining the size of the cosmic-ray galactic halo.
Methods. Analytical expressions for the leading moments of the pitch-angle distribution of relativistic particles are determined. Particle scattering and escape are analyzed in terms of the moments.
Results. In the case of an anisotropic distribution, the first moment leads to an expression for the halo size, identified with the particle escape from the region of strong scattering. Previous studies are generalized by analyzing the case of a strictly isotropic initial distribution. A new expression for the variance of the distribution is derived, which illustrates the anisotropization of the distribution.
Conclusions. Stochastic calculus tools allow one to analyze physically motivated forms for the scattering rate, so that a detailed realistic model can be developed.

Key words: cosmic rays -- galaxies: halos -- scattering

© ESO 2009