  We propose a model for short duration gamma-ray bursts (sGRBs) based on the
formation of a quark star after the merger of two neutron stars. We assume that
the sGRB central engine is a proto-magnetar, which has been previously invoked
to explain the plateau-like X-ray emission observed following both long and
short GRBs. Here, we show that: i) a few milliseconds after the merger it is
possible to form a stable and massive star made in part of quarks; ii) during
the early cooling phase of the incompletely formed quark star, the flux of
baryons ablated from the surface by neutrinos is large and it does not allow
the outflow to achieve a bulk Lorentz factor high enough to produce a GRB; iii)
after the quark burning front reaches the stellar surface, baryon ablation
ceases and the jet becomes too baryon poor to produce a GRB; iv) however,
between these two phases a GRB can be produced over the finite timescale
required for the baryon pollution to cease; a characteristic timescale of the
order of $\sim 0.1 $ s naturally results from the time the conversion front
needs to cover the distance between the rotational pole and the latitude of the
last closed magnetic field line; v) we predict a correlation between the
luminosity of the sGRB and its duration, consistent with the data; vi) our
model also predicts a delay of the order of ten seconds between the time of the
merger event and the sGRB, allowing for the possibility of precursor emission
and implying that the jet will encounter the dense cocoon formed immediately
after the merger.
