### 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 language | English (US) |
---|---|

Pages (from-to) | 1386-1392 |

Number of pages | 7 |

Journal | Astrophysical Journal |

Volume | 713 |

Issue number | 2 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal*,

*713*(2), 1386-1392. https://doi.org/10.1088/0004-637X/713/2/1386

**Superposition of stochastic processes and the resulting particle distributions.** / Schwadron, N. A.; Dayeh, M. A.; Desai, M.; Fahr, H.; Jokipii, J. Randy; Lee, M. A.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 713, no. 2, pp. 1386-1392. https://doi.org/10.1088/0004-637X/713/2/1386

}

TY - JOUR

T1 - Superposition of stochastic processes and the resulting particle distributions

AU - Schwadron, N. A.

AU - Dayeh, M. A.

AU - Desai, M.

AU - Fahr, H.

AU - Jokipii, J. Randy

AU - Lee, M. A.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Acceleration of particles

KW - Cosmic rays

KW - Methods: statistical

KW - Plasmas

UR - http://www.scopus.com/inward/record.url?scp=77950588994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950588994&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/713/2/1386

DO - 10.1088/0004-637X/713/2/1386

M3 - Article

AN - SCOPUS:77950588994

VL - 713

SP - 1386

EP - 1392

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -