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.