Burst Timing of the SYM-H Index: Elementary Lifetimes, Exact Identities, and Their Solar-Cycle Variation James A. Wanliss

<jats:p>We study burst-timing statistics over 45 years of the 1-min SYM-H index with a complete timing suite: growth, recovery, quiet, burst, waiting, and interpeak lifetimes. Three lifetimes are elementary. The burst-to-waiting ratio satisfies a level-crossing identity to a residual ~0.0031. Composite scaling exponents (μ) are judged against a permutation null, which the burst exponent exceeds at every threshold, growth and recovery lengthening together as storms grow larger; the waiting-minus-interpeak difference, whose null expectation is exactly zero, isolates within-event coupling (z = 29). The median-threshold recovery exponent is stable across solar cycles 21–25, with temporal variation bounded at 1.5% of its mean. Recovery exceeds growth at every threshold (Δμ = +0.24 windowed at the median, dz = 3.4). The growth exponent rises with sunspot number (SSN) and survives conditioning on occurrence rate, on discarding the shortest events, and on excluding shock-driven onsets. The quiet exponent’s correlation instead tracks how often and how long the record dips below threshold, collapsing once that rate is held fixed. Recovery is flat (r = −0.15), the solar cycle appearing through the cutoff scale, not the exponent. The growth–recovery contrast is significant against a phase-randomised surrogate null (p = 0.001). Across storm classes growth rises by 0.15 to 0.17 per decade of threshold depth and quiet falls by 0.17, recovery and burst staying flat. The exponent values and their solar correlations are conditional on SYM-H’s 1-nT resolution and on counting every threshold crossing as a separate event. Plain Language Summary Earth’s magnetosphere generates “space weather” in response to solar driving. At low latitudes it is tracked by SYM-H, a ground-based index recorded every minute since 1981. Instead of cataloguing individual storms we study “bursts”, intervals when the index dips below a chosen level. We ask how often they start, how long they and the intervening quiet periods last, and how quickly the system loads and relaxes. In probability distributions, the mathematical “shape” of each barely changes as the Sun cycles from quiet to active across five cycles. The rule for the buildup part of each activity burst shifts slightly with solar activity. For the quiet gaps between bursts it shifts the opposite way, while the rule for the recovery part stays the same. Part of the buildup shift may reflect how the index is reported, since SYM-H is rounded to whole numbers. We describe these shifts as properties of the measured SYM-H, not necessarily a statement about the magnetosphere itself. These stable shapes provide a reference description of this index’s storm timing, against which other indices and models can be compared.</jats:p>