Collimated Jet or Expanding Outflow: Possible Origins of Gamma‐Ray Bursts and X‐Ray Flashes

Abstract

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-1) and radius of the injected outflow (7 × 107 cm) while varying its bulk Lorentz factor, Γ0 = 1.05-5, and its specific internal energy, 0/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 (θsim) is sensitive to Γ0; we find θsim < 2° for Γ0 ≳ 3. The maximum Lorentz factor is, on the other hand, sensitive to both Γ0 and 0: roughly Γmax ~ Γ0(1 + 0/c2). In particular, a very high Lorentz factor of Γmax ≳ 100 is achieved in one model. A variety of opening angles can arise by changing 0, even when the maximum Lorentz factor is fixed. The jet structure totally depends on Γ0. When Γ0 is high, high-pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow, relativistic jet. When Γ0 is 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 0 values.