327 research outputs found
The Origin of the Solar Flare Waiting-Time Distribution
It was recently pointed out that the distribution of times between solar
flares (the flare waiting-time distribution) follows a power law, for long
waiting times. Based on 25 years of soft X-ray flares observed by Geostationary
Operational Environmental Satellite (GOES) instruments it is shown that 1. the
waiting-time distribution of flares is consistent with a time-dependent Poisson
process, and 2. the fraction of time the Sun spends with different flaring
rates approximately follows an exponential distribution. The second result is a
new phenomenological law for flares. It is shown analytically how the observed
power-law behavior of the waiting times originates in the exponential
distribution of flaring rates. These results are argued to be consistent with a
non-stationary avalanche model for flares.Comment: 7 pages, 3 figures, accepted by ApJ Letter
Modeling a falling slinky
A slinky is an example of a tension spring: in an unstretched state a slinky
is collapsed, with turns touching, and a finite tension is required to separate
the turns from this state. If a slinky is suspended from its top and stretched
under gravity and then released, the bottom of the slinky does not begin to
fall until the top section of the slinky, which collapses turn by turn from the
top, collides with the bottom. The total collapse time t_c (typically ~0.3 s
for real slinkies) corresponds to the time required for a wave front to
propagate down the slinky to communicate the release of the top end. We present
a modification to an existing model for a falling tension spring (Calkin 1993)
and apply it to data from filmed drops of two real slinkies. The modification
of the model is the inclusion of a finite time for collapse of the turns of the
slinky behind the collapse front propagating down the slinky during the fall.
The new finite-collapse time model achieves a good qualitative fit to the
observed positions of the top of the real slinkies during the measured drops.
The spring constant k for each slinky is taken to be a free parameter in the
model. The best-fit model values for k for each slinky are approximately
consistent with values obtained from measured periods of oscillation of the
slinkies.Comment: 30 pages, 11 figure
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
Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays
We study the waiting time distributions of solar flares observed in hard
X-rays with ISEE-3/ICE, HXRBS/SMM, WATCH/GRANAT, BATSE/CGRO, and RHESSI.
Although discordant results and interpretations have been published earlier,
based on relatively small ranges ( decades) of waiting times, we find that
all observed distributions, spanning over 6 decades of waiting times ( hrs), can be reconciled with a single distribution
function, , which
has a powerlaw slope of at large waiting times ( hrs) and flattens out at short waiting times \Delta t \lapprox
\Delta t_0 = 1/\lambda_0. We find a consistent breakpoint at 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, . This waiting time
distribution can be modeled with a nonstationary Poisson process with a flare
rate that varies as . 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.Comment: Preprint also available at
http://www.lmsal.com/~aschwand/eprints/2010_wait.pd
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