  Neutron stars are a prime laboratory for testing physical processes under
conditions of strong gravity, high density, and extreme magnetic fields. Among
the zoo of neutron star phenomena, magnetars stand out for their bursting
behaviour, ranging from extremely bright, rare giant flares to numerous, less
energetic recurrent bursts. The exact trigger and emission mechanisms for these
bursts are not known; favoured models involve either a crust fracture and
subsequent energy release into the magnetosphere, or explosive reconnection of
magnetic field lines. In the absence of a predictive model, understanding the
physical processes responsible for magnetar burst variability is difficult.
Here, we develop an empirical model that decomposes magnetar bursts into a
superposition of small spike-like features with a simple functional form, where
the number of model components is itself part of the inference problem. The
cascades of spikes that we model might be formed by avalanches of reconnection,
or crust rupture aftershocks. Using Markov Chain Monte Carlo (MCMC) sampling
augmented with reversible jumps between models with different numbers of
parameters, we characterise the posterior distributions of the model parameters
and the number of components per burst. We relate these model parameters to
physical quantities in the system, and show for the first time that the
variability within a burst does not conform to predictions from ideas of
self-organised criticality. We also examine how well the properties of the
spikes fit the predictions of simplified cascade models for the different
trigger mechanisms.
