2006ApJ...651..960M

We investigate the dynamics of an outflow propagating in a progenitor in the context of the collapsar model for GRBs through two-dimensional axisymmetric relativistic hydrodynamic simulations. Initially, we locally inject an outflow near the center of a progenitor. We calculate 25 models, in total, by fixing its total input energy (10⁵¹ ergs/s) and radius of the injected outflow (7x10⁷ cm) while varying its bulk Lorentz factor, Γ₀=1.05-5, and its specific internal energy, ε₀/c²=0.1-30 (with c being speed of light). We find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models. The half opening angle of the outflow (θ_sim) is sensitive to Γ₀; we find θ_sim<2° for Γ₀≳3. The maximum Lorentz factor is, on the other hand, sensitive to both Γ₀and ε₀: roughly Γ_max~Γ₀(1+ε₀/c²). In particular, a very high Lorentz factor of Γ_max≳100 is achieved in one model. A variety of opening angles can arise by changing ε₀, even when the maximum Lorentz factor is fixed. The jet structure totally depends on Γ₀. When Γ₀is high, high-pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow, relativistic jet. When Γ₀is low, on the contrary, the outflow expands soon after the injection, since the bow shock is weak and thus the pressure of the progenitor gas is not high enough to confine the flow. Our finding will explain a smooth transition between the GRBs, X-ray-rich GRBs (XRRs), and X-ray flashes (XRFs) by the same model but with different ε₀values.