Subject will be restored when possible
Mike Wheatland Submitted: 2008-02-26 16:45
A stochastic model for the energy of a flaring solar
active region is presented, generalising and extending the approach
of Wheatland & Glukhov (1998). The probability distribution for the free energy of an
active region is described by the solution to a master equation involving
deterministic energy input and random jump
transitions downwards in energy (solar flares). It is shown how two
observable distributions, the flare frequency-energy distribution and
the flare waiting-time distribution, may be derived from the
steady-state solution to the master equation, for given choices for the
energy input and for the rates of flare transitions. An efficient method
of numerical solution of the steady-state master equation is presented.
Solutions appropriate for flaring, involving a constant rate of energy
input and power-law distributed jump transition rates, are
numerically investigated. The flare-like solutions exhibit power-law
flare frequency-energy distributions below a high energy rollover,
set by the largest energy the active region is likely to have.
The solutions also exhibit approximately exponential (i.e. Poisson)
waiting-time distributions, despite the rate of flaring depending on the
free energy of the system.
Authors: M.S. Wheatland
Publication Status: To appear in the Astrophysical Journal
Last Modified: 2008-09-23 21:22