11 research outputs found
Time-dependent Stochastic Modeling of Solar Active Region Energy
A time-dependent model for the energy of a flaring solar active region is
presented based on a stochastic jump-transition model (Wheatland and Glukhov
1998; Wheatland 2008; Wheatland 2009). The magnetic free energy of the model
active region varies in time due to a prescribed (deterministic) rate of energy
input and prescribed (random) flare jumps downwards in energy. The model has
been shown to reproduce observed flare statistics, for specific
time-independent choices for the energy input and flare transition rates.
However, many solar active regions exhibit time variation in flare
productivity, as exemplified by NOAA active region AR 11029 (Wheatland 2010).
In this case a time-dependent model is needed. Time variation is incorporated
for two cases: 1. a step change in the rates of flare jumps; and 2. a step
change in the rate of energy supply to the system. Analytic arguments are
presented describing the qualitative behavior of the system in the two cases.
In each case the system adjusts by shifting to a new stationary state over a
relaxation time which is estimated analytically. The new model retains
flare-like event statistics. In each case the frequency-energy distribution is
a power law for flare energies less than a time-dependent rollover set by the
largest energy the system is likely to attain at a given time. For Case 1, the
model exhibits a double exponential waiting-time distribution, corresponding to
flaring at a constant mean rate during two intervals (before and after the step
change), if the average energy of the system is large. For Case 2 the
waiting-time distribution is a simple exponential, again provided the average
energy of the system is large. Monte Carlo simulations of Case~1 are presented
which confirm the analytic estimates. The simulation results provide a
qualitative model for observed flare statistics in active region AR 11029.Comment: 25 pages, 9 figure