  Flaring activity following gamma-ray bursts (GRBs), observed in both long and
short GRBs, signals a long-term activity of the central engine. However, its
production mechanism has remained elusive. Here we develop a quantitative model
of the idea proposed by Perna et al. of a disc whose outer regions fragment due
to the onset of gravitational instability. The self-gravitating clumps migrate
through the disc and begin to evolve viscously when tidal and shearing torques
break them apart. Our model consists of two ingredients: theoretical bolometric
flare lightcurves whose shape (width, skewness) is largely insensitive to the
model parameters, and a spectral correction to match the bandpass of the
available observations, that is calibrated using the observed spectra of the
flares. This simple model reproduces, with excellent agreement, the empirical
statistical properties of the flares as measured by their width-to-arrival time
ratio and skewness (ratio between decay and rise time). We present model fits
to the observed lightcurves of two well-monitored flares, of GRB 060418 and of
GRB 060904B. To the best of our knowledge, this is the first quantitative model
able to reproduce the flare lightcurves and explain their global statistical
properties.
