Population synthesis of gamma-ray bursts with precursor activity and the
  spinar paradigm
  We study statistical properties of long gamma-ray bursts (GRBs) produced by
the collapsing cores of WR stars in binary systems. Fast rotation of the cores
enables a two-stage collapse scenario, implying the formation of a spinar-like
object. A burst produced by such a collapse consists of two pulses, whose
energy budget is enough to explain observed GRBs. We calculate models of spinar
evolution using results from a population synthesis of binary systems (done by
the `Scenario Machine') as initial parameters for the rotating massive cores.
Among the resulting bursts, events with the weaker first peak, namely,
precursor, are identified, and the precursor-to-main-pulse time separations
fully agree with the range of the observed values. The calculated fraction of
long GRBs with precursor (about 10 per cent of the total number of long GRBs)
and the durations of the main pulses are also consistent with observations.
Precursors with lead times greater by up to one order of magnitude than those
observed so far are expected to be about twice less numerous. Independently of
a GRB model assumed, we predict the existence of precursors that arrive up to
>~ 10^3 s in advance of the main events of GRBs.
