Gamma-ray bursts from X-ray binaries

A weakly magnetized ($\sim 10^7$G) neutron star, slowly spun up by accretion in an X-ray binary, crosses the instability boundary for r-mode instability at P=1--2 msec. The amplitude of the oscillation, which initially increases only at the spinup time scale, is secularly unstable due to the negative temperature dependence of the viscosity in neutron star matter, and diverges after a few hundred years. Angular momentum loss by the gravitational wave causes strong differential rotation, in which the magnetic field is wound up to $10^{17}$G on a time scale of a few months. When this field becomes unstable to buoyancy instability, a surface field strength of a few $10^{16}$G is produced on a time scale of seconds, which then powers a GRB with energies of $\sim 1-8\times 10^{51}$ and duration of 1--100 sec.