Magnetar Driven Bubbles and the Origin of Collimated Outflows in Gamma-ray Bursts

We model the interaction between the wind from a newly formed rapidly rotating magnetar and the surrounding supernova shock and host star. The dynamics is modeled using the two-dimensional, axisymmetric thin-shell equations. In the first ~10-100 seconds after core collapse the magnetar inflates a bubble of plasma and magnetic fields behind the supernova shock. The bubble expands asymmetrically because of the pinching effect of the toroidal magnetic field, just as in the analogous problem of the evolution of pulsar wind nebulae. The degree of asymmetry depends on E_mag/E_tot. The correct value of E_mag/E_tot is uncertain because of uncertainties in the conversion of magnetic energy into kinetic energy at large radii in relativistic winds; we argue, however, that bubbles inflated by newly formed magnetars are likely to be significantly more magnetized than their pulsar counterparts. We show that for a ratio of magnetic to total power supplied by the central magnetar L_mag/L_tot ~ 0.1 the bubble expands relatively spherically. For L_mag/L_tot ~ 0.3, however, most of the pressure in the bubble is exerted close to the rotation axis, driving a collimated outflow out through the host star. This can account for the collimation inferred from observations of long-duration gamma-ray bursts (GRBs). Outflows from magnetars become increasingly magnetically dominated at late times, due to the decrease in neutrino-driven mass loss as the young neutron star cools. We thus suggest that the magnetar-driven bubble initially expands relatively spherically, enhancing the energy of the associated supernova, while at late times it becomes progressively more collimated, producing the GRB.