268 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
On the Brightness and Waiting-time Distributions of a Type III Radio Storm observed by STEREO/WAVES
Type III solar radio storms, observed at frequencies below approximately 16
MHz by space borne radio experiments, correspond to the quasi-continuous,
bursty emission of electron beams onto open field lines above active regions.
The mechanisms by which a storm can persist in some cases for more than a solar
rotation whilst exhibiting considerable radio activity are poorly understood.
To address this issue, the statistical properties of a type III storm observed
by the STEREO/WAVES radio experiment are presented, examining both the
brightness distribution and (for the first time) the waiting-time distribution.
Single power law behavior is observed in the number distribution as a function
of brightness; the power law index is approximately 2.1 and is largely
independent of frequency. The waiting-time distribution is found to be
consistent with a piecewise-constant Poisson process. This indicates that
during the storm individual type III bursts occur independently and suggests
that the storm dynamics are consistent with avalanche type behavior in the
underlying active region.Comment: 14 pages, 4 figures, 1 table. Accepted for publication in
Astrophysical Journal Letter
The Energetics of a Flaring Solar Active Region, and Observed Flare Statistics
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.Comment: 24 pages, 6 figures. Accepted for publication in the Astrophysical
Journa
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