  The critical brain hypothesis has emerged as an attractive framework to
understand neuronal activity, but it is still widely debated. In this work, we
analyze data from a multi-electrodes array in the rat's cortex and we find that
power-law neuronal avalanches satisfying the crackling-noise relation coexist
with spatial correlations that display typical features of critical systems. In
order to shed a light on the underlying mechanisms at the origin of these
signatures of criticality, we introduce a paradigmatic framework with a common
stochastic modulation and pairwise linear interactions inferred from our data.
We show that in such models power-law avalanches that satisfy the crackling
noise relation emerge as a consequence of the extrinsic modulation, whereas
scale-free correlations are solely determined by internal interactions.
Moreover, this disentangling is fully captured by the mutual information in the
system. Finally, we show that analogous power-law avalanches are found in more
realistic models of neural activity as well, suggesting that extrinsic
modulation might be a broad mechanism for their generation.
