Superposition of stochastic processes and the resulting particle distributions

N. A. Schwadron, M. A. Dayeh, M. Desai, H. Fahr, J. R. Jokipii, M. A. Lee

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

Many observations of suprathermal and energetic particles in the solar wind and the inner heliosheath show that distribution functions scale approximately with the inverse of particle speed (v) to the fifth power. Although there are exceptions to this behavior, there is a growing need to understand why this type of distribution function appears so frequently. This paper develops the concept that a superposition of exponential and Gaussian distributions with different characteristic speeds and temperatures show power-law tails. The particular type of distribution function, f v -5, appears in a number of different ways: (1) a series of Poisson-like processes where entropy is maximized with the rates of individual processes inversely proportional to the characteristic exponential speed, (2) a series of Gaussian distributions where the entropy is maximized with the rates of individual processes inversely proportional to temperature and the density of individual Gaussian distributions proportional to temperature, and (3) a series of different diffusively accelerated energetic particle spectra with individual spectra derived from observations (1997-2002) of a multiplicity of different shocks. Thus, we develop a proof-of-concept for the superposition of stochastic processes that give rise to power-law distribution functions.

Original languageEnglish (US)
Pages (from-to)1386-1392
Number of pages7
JournalAstrophysical Journal
Volume713
Issue number2
DOIs
StatePublished - Jan 1 2010

Keywords

  • Acceleration of particles
  • Cosmic rays
  • Methods: statistical
  • Plasmas

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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