The Solar Memory From Hours to Decades
Markus J. Aschwanden Submitted: 2021-07-29 11:43
Waiting time distributions allow us to distinguish at least
three different types of dynamical systems, such as (i) linear
random processes (with no memory); (ii) nonlinear, avalanche-type,
nonstationary Poisson processes (with memory during the exponential
growth of the avalanche rise time); and (iii) chaotic systems in the state of
a nonlinear limit cycle (with memory during the oscillatory phase).
We describe the temporal evolution of the flare rate \lambda(t) ∝ t^p
with a polynomial function, which allows us to distinguish linear
(p ≈ 1) from nonlinear (p ≳ 2) events.
The power law slopes α of observed waiting times (with full solar
cycle coverage) cover a range of α =2.1-2.4, which agrees
well with our prediction of α = 2.0+1/p = 2.3-2.5.
The memory time can also be defined with the time evolution of the
logistic equation, for which we find a relationship between the
nonlinear growth time τ_G = τrise/(4p) and
the nonlinearity index p. We find a nonlinear evolution for most
events, in particular for
the clustering of solar flares (p=2.2±0.1),
partially occulted flare events (p=1.8±0.2), and
the solar dynamo (p=2.8±0.5).
The Sun exhibits memory on time scales of
≈2 hours to 3 days (for solar flare clustering),
6 to 23 days (for partially occulted flare events), and
1.5 month to 1 year (for the rise time of the solar dynamo).
Authors: Aschwanden, M.J. and Johnson, J.R.
Publication Status: submitted
Last Modified: 2021-08-01 20:58