NDLI: Monte Carlo Simulation of Solar Active-Region Energy

Content Provider	Springer Nature Link
Author	Wheatland, M. S.
Copyright Year	2009
Abstract	A Monte Carlo approach to solving a stochastic-jump transition model for active-region energy (Wheatland and Glukhov: Astrophys. J. 494, 858, 1998; Wheatland: Astrophys. J. 679, 1621, 2008) is described. The new method numerically solves the stochastic differential equation describing the model, rather than the equivalent master equation. This has the advantages of allowing more efficient numerical solution, the modeling of time-dependent situations, and investigation of details of event statistics. The Monte Carlo approach is illustrated by application to a Gaussian test case and to the class of flare-like models presented in Wheatland (Astrophys. J. 679, 1621, 2008), which are steady-state models with constant rates of energy supply, and power-law distributed jump transition rates. These models have two free parameters: an index (δ), which defines the dependence of the jump transition rates on active-region energy, and a nondimensional ratio ( $\overline{r}$ ) of total flaring rate to rate of energy supply. For $\overline{r}\ll 1$ the nondimensional mean energy $\langle \overline{E}\rangle$ of the active-region satisfies $\langle \overline{E}\rangle \gg 1$ , resulting in a power-law distribution of flare events over many decades of energy. The Monte Carlo method is used to explore the behavior of the waiting-time distributions for the flare-like models. The models with δ≠0 are found to have waiting times that depart significantly from simple Poisson behavior when $\langle \overline{E}\rangle \gg 1$ . The original model from Wheatland and Glukhov (Astrophys. J. 494, 858, 1998), with δ=0 (i.e., no dependence of transition rates on active-region energy), is identified as being most consistent with observed flare statistics.
Starting Page	211
Ending Page	227
Page Count	17
File Format	PDF
ISSN	00380938
Journal	Solar Physics
Volume Number	255
Issue Number	2
e-ISSN	1573093X
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-02-28
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Active regions, models Corona, models Flares, models Flares, microflares and nanoflares Extraterrestrial Physics, Space Sciences Meteorology/Climatology Astrophysics
Content Type	Text
Resource Type	Article
Subject	Astronomy and Astrophysics Space and Planetary Science

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