Preprint typeset using LATEX style emulateapj v. 5/2/11 OPENING ANGLES OF COLLAPSAR JETS

We investigate the jet propagation and breakout from the stellar progenitor for gamma-ray burst (GRB) collapsars by performing two-dimensional relativistic hydrodynamic simulations and analytical modeling. We find that the jet opening angle is given by θj ∼ 1/5Γ0 and infer the initial Lorentz factor of the jet at the central engine, Γ0, is a few for existing observations of θj. The jet keeps the Lorentz factor low inside the star by converging cylindrically via collimation shocks under the cocoon pressure, and accelerates at jet breakout before the free expansion to a hollow-cone structure. In this new picture the GRB duration is determined by the sound crossing time of the cocoon, after which the opening angle widens, reducing the apparent luminosity. Some bursts violating the maximum opening angle θj,max ∼ 1/5 ∼ 12 ◦ imply the existence of a baryon-rich sheath or a long-acting jet. We can explain the slopes in both Amati and Yonetoku spectral relations using an off-centered photosphere model, if we make only one assumption that the total jet luminosity is proportional to the initial Lorentz factor of the jet. We also numerically calibrate the pre-breakout model (Bromberg et al.) for later use. Subject headings: (stars:) gamma-ray burst: general — hydrodynamics — ISM: jets and outflows — methods: analytical numerical — methods: numerical 1