Neutron starquake models for gamma-ray bursts

We assess neutron starquake models for γ-ray bursts. The elastic energy the crust can store is sufficient to account for that radiated in a single burst, but it is insufficient to supply the ≳ 10^6 bursts each star produces over its lifetime, and so it must be replenished. Seismic waves are radiated if shear stress is relieved by brittle fracture. However they cannot propagate directly to the surface but are temporarily trapped below a reflecting layer. Between the reflecting layer and the surface the displacement amplitude of the wave is nearly constant and the strain is very small. At low frequencies, ≾ 10^4 Hz, the reflection is associated with an evanescent zone. At high frequencies, ≳ 10^4 Hz, the reflection occurs where the magnetic field stress starts to dominate the crustal rigidity. The shaking of the stellar surface couples the seismic waves to Alfén waves which propagate out into the magnetosphere. At low frequencies, the coupling coefficient, T, is proportional to the square of the magnetic field, B, and increases with the seventh power of the wave frequency, v. At high frequencies, T is proportional to B^(4/7)v^(3/7). Alfvén wave luminosities sufficient to power Galactic γ-ray bursts are possible if magnetic fields ≳ 10^(11) G cover at least part of the stellar surface. The conversion of Alfvén waves into γ-rays may occur if the waves are charge-starved or if their amplitudes approach that of the background magnetic field