Reconciliation of waiting time statistics of solar flares observed in hard Xrays 

Markus J. Aschwanden Submitted: 20100211 17:03
We study the waiting time distributions of solar flares observed
in hard Xrays with ISEE3/ICE, HXRBS/SMM, WATCH/GRANAT, BATSE/CGRO,
and RHESSI. Although discordant results and interpretations have been
published earlier, based on relatively small ranges (< 2 decades)
of waiting times, we find that all observed distributions,
spanning over 6 decades of waiting times (Delta t approx 10^{3}
10^{3} hrs), can be reconciled with a single distribution function,
N(Delta t) propto lambda_0 (1 + lambda_0 Delta t)^{2}, which has
a powerlaw slope of p approx 2.0 at large waiting times
(Delta t approx 11000 hrs) and flattens out at short waiting times
Delta t lapprox Delta t_0 = 1/lambda_0.
We find a consistent breakpoint at Delta t_0 = 1/lambda_0 = 0.80pm0.14
hours from the WATCH, HXRBS, BATSE, and RHESSI data.
The distribution of waiting times is invariant for
sampling with different flux thresholds, while the mean waiting time
scales reciprocically with the number of detected events, Delta t_0
propto 1/n_{det}.
This waiting time distribution can be modeled with a nonstationary
Poisson process with a flare rate lambda=1/Delta t that varies as
f(lambda) propto lambda^{1} exp{(lambda/lambda_0)}.
This flare rate distribution represents a highly intermittent flaring
productivity in short clusters with high flare rates, separated by
quiescent intervals with very low flare rates.
Authors: Markus J. Aschwanden and James M. McTiernan
Projects: RHESSI

Publication Status: ApJ (accepted April 15, 2010  in press)
Last Modified: 20100416 13:37


