Global Crustal Dynamics of Magnetars in Relation to their Bright X-ray Outbursts

Abstract

This paper considers the yielding response of a neutron star crust to smooth, unbalanced Maxwell stresses imposed at the core-crust boundary, and the coupling of the dynamic crust to the external magnetic field. Stress buildup and yielding in a magnetar crust is a global phenomenon: an elastic distortion radiating from one plastically deforming zone is shown to dramatically increase the creep rate in distant zones. Runaway creep to dynamical rates is shown to be possible, being enhanced by in situ heating and suppressed by thermal conduction and shearing of an embedded magnetic field. A global and time-dependent model of elastic, plastic, magnetic, and thermal evolution is developed. Fault-like structures develop naturally, and a range of outburst timescales is observed. Transient events with time profiles similar to giant magnetar flares (millisecond rise, $\sim$ 0.1 s duration, and decaying power-law tails) result from runaway creep that starts in localized sub-km-sized patches and spreads across the crust. A one-dimensional model of stress relaxation in the vertically stratified crust shows that a modest increase in applied stress allows embedded magnetic shear to escape the star over $\sim$ 3-10 ms, dissipating greater energy if the exterior field is already sheared. Several such zones coupled to each other naturally yield a burst of duration $\sim$ 0.1 s, as is observed over a wide range of burst energies. The collective interaction of many plastic zones forces an overstability of global elastic modes of the crust, consistent with QPO activity extending over $\gtrsim$ 100 s. Giant flares probably involve sudden meltdown in localized zones, with high-frequency ($\gg$ 100 Hz) QPOs corresponding to standing Alfv\'en waves within these zones.