Gamma-ray burst internal shocks with magnetization

We investigate Gamma-ray Burst (GRB) internal shocks with moderate magnetization, with the magnetization parameter σ ranging from 0.001 to 10. Possible magnetic dissipation in the stripped magnetized shells is also taken into account through introducing a parameter k (0 < k 6 1), which is the ratio of the electric field strength of the downstream and the upstream. By solving the general MHD jump conditions, we show that the dynamic evolution of the shock with magnetic dissipation is different from the familiar one obtained in the ideal MHD limit. As long as the relative velocity between the two magnetized shells is larger than the corresponding Alfven velocities in both shells, strong internal shocks still exist for σ ≫ 1, which can effectively tap kinetic energy into radiation. However, in the ideal MHD limit (k = 1), the upstream magnetic energy can not be converted into the downstream thermal energy so that the GRB radiation efficiency is low. This is likely inconsistent with the current GRB data. With magnetic dissipation, e.g., k 6 0.5 the range of k is constrained given a particular upstream-downstream Lorentz factor γ21 and a magnetization parameter σ), a significant fraction of the upstream magnetic energy can be converted into the prompt γ−ray emission. At the typical internal shock radius, the characteristic synchrotron emission frequency in the magnetic dissipation dominated case is however too large (∝ σ) compared with the data if σ ≫ 1. On the other hand, as long as the ordered magnetic field is stronger than or at least comparable with the random one generated in the internal shocks, a net linear polarization > 30% results. In view of the possible high degree of linear polarization of GRB 021206 and the identification of a possible highly magnetized flow in GRB 990123 and GRB 021211, we suggest that a mildly magnetized internal shock model (0.01 < σ < 1) with moderate magnetic dissipation is a good candidate to explain the GRB prompt emission data.