Super-Giant Glitches and Quark Stars Sources of Gamma Ray Bursts(4)

When a spinning-down neutron star undergoes a phase transition that produces quark matter in its core, a Super-Giant Glitch of the order\Delta\Omega =\Omega ? ? 0:3 occurs on time scales from 0.05 seconds to a few minutes. The energy released is about 10 5

1977), s

o it will have a central density increase of about c= c ' 0:001 in its lifetime. Assuming a phase transition critical density cr, only those neutron stars born with central densities cr (1? c= c )< c< cr would have the chance to undergo the SGGs. For example, in the case of cr= 3:0 0, and assuming all neutron stars were born at the same initial period (Pi) of 20 milliseconds, the density range is 2:997 0< c< 3:0 0 . Neutron stars with lower central densities cannot reach the critical density in their whole lives. Those with higher central densities should be born as hybrid stars. Radio observations of binary pulsar systems together with statistics of neutron star mass distributions have given a strong constraint on neutron star masses, which lie in a narrow range from 1:0M to 1:6M (Finn 1994). For the EOS of Bethe& Johnson (1974), the central densities of these neutron stars range from a lower limit l ' 2:5 0 to an upper limit u ' 4:3 0 (Shapiro& Teukolsky 1983). It is apparent that we need EOSs predicting l< cr< u to make the sudden phase transition possible. We assume the neutron star central densities are evenly distributed in this range. The birth rate of GRB events in units of per year per galaxy (RGRB ) in our model will be the probability for a neutron star to undergo an SGG times the birth rate of neutron stars (RNS),RGRB

one. A sti mean eld EOS (e.g., Baym& Pethic 1979) predicts a 1.4 M neutron star with c ' 1:4 0, which does not undergo an SGG even for the largest possible c increase (30% according to Cook et al. 1994); while a soft EOS like that of Reid (e.g., Baym& Pethic 1979) gives c ' 10 0 and predicts that the star should be born as a hybrid star. If either of these EOSs is correct, there will be no SGGs at all. From equation (3), we can also give an upper limit for the SGG birth rate for the EOSs that favor the phase transition (like that of Bethe& Johnson). With limiting values, Pi 0:5 ms and RNS 0:02 per year per galaxy, RGRB can be as large as 10?2.

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