Monte-Carlo Simulation of Solar Active-Region Energy |
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Mike Wheatland Submitted: 2009-02-06 18:49
A Monte-Carlo approach to solving a stochastic jump
transition model for active-region energy (Wheatland and
Glukhov, Astrophys. J. 494, 1998; Wheatland,
Astrophys. J. 679, 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 modelling 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 (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 (delta ), which defines the
dependence of the jump transition rates on active-region
energy, and a non-dimensional ratio (overline{r}) of
total flaring rate to rate of energy supply. For
overline{r}ll 1 the non-dimensional mean energy langle
overline{E}
angle of the active-region satisfies langle
overline{E}
angle gg 1, resulting in a power-law
distribution of flare events over many decades in energy.
The Monte-Carlo method is used to explore the behavior of
the waiting-time distributions for the flare-like models.
The models with deltaeq 0 are found to have waiting
times which depart significantly from simple Poisson
behavior when langle overline{E}
angle gg 1. The
original model from Wheatland and Glukhov (1998), with
delta=0 (no dependence of transition rates on
active-region energy), is identified as being most
consistent with observed flare statistics.
Authors: M.S. Wheatland
Projects: None
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Publication Status: Accepted for publication in Solar Physics
Last Modified: 2009-02-07 09:40
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