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

We investigate the dynamics of an injected outflow propagating in a progenitor in the context of the collapsar model for gamma-ray bursts (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 to be 10{sup 51} ergs s{sup -1} and radius of the injected outflow to be 7 x 10{sup 7} cm while varying its bulk Lorentz factor, {Lambda}{sub 0} = 1.05 {approx} 5, and its specific internal energy, {epsilon}{sub 0}/c{sup 2} 30 (with c being speed of light). The injected outflow propagates in the progenitor and drives a large-scale outflow or jet. We find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models. The opening angle of the outflow ({theta}{sub sim}) is sensitive to {Lambda}{sub 0}; we find {theta}{sub sim} 3. The maximum Lorentz factor is, on the other hand, sensitive to both of {Lambda}{sub 0} and {epsilon}{sub 0}; roughly {Lambda}{sub max} {approx} {Lambda}{sub 0}(1 + {epsilon}{sub 0}/c{sup 2}). In particular, a very high Lorentz factor of {Lambda}{sub max} {approx}> 100 is achievedmore » in one model. A variety of opening angles can arise by changing {epsilon}{sub 0}, even when the maximum Lorentz factor is fixed. The jet structure totally depends on {Lambda}{sub 0}. When {Lambda}{sub 0} is high, a strong bow shock appears and generates a back flow. High pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow, relativistic jet. A number of internal oblique shocks within the jet are generated by the presence of the back flow and/or shear instability. When {Lambda}{sub 0} 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 {epsilon}{sub 0} values.« less

[1]  Ryo Yamazaki,et al.  A Unified Model of Short and Long Gamma-Ray Bursts, X-Ray-rich Gamma-Ray Bursts, and X-Ray Flashes , 2004, astro-ph/0401142.

[2]  M. Putten.  Maxwell's equations in divergence form for general media with applications to MHD , 1991 .

[3]  T. Sakamoto,et al.  A giant γ-ray flare from the magnetar SGR 1806–20 , 2005, Nature.

[4]  G. Bodo,et al.  An HLLC Riemann solver for relativistic flows ¿ I. Hydrodynamics , 2005, astro-ph/0506414.

[5]  J. A. Miralles,et al.  Stability analysis of relativistic jets from collapsars and its implications on the short-term variability of gamma-ray bursts , 2002 .

[6]  Ryo Yamazaki,et al.  X-Ray Flashes from Off-Axis Gamma-Ray Bursts , 2002 .

[7]  C. McKee,et al.  Relativistic Hydrodynamics in One Dimension , 1971 .

[8]  Katsuhiko Sato,et al.  Explosive Nucleosynthesis in GRB Jets Accompanied by Hypernovae , 2006, astro-ph/0601111.

[9]  E. Müller,et al.  Numerical Hydrodynamics in Special Relativity , 1999, Living reviews in relativity.

[10]  Particle Acceleration and Magnetic Field Generation in Electron-Positron Relativistic Shocks , 2004, astro-ph/0409702.

[11]  K. Nomoto,et al.  Precursors and Main Bursts of Gamma-Ray Bursts in a Hypernova Scenario , 2005, astro-ph/0509750.

[12]  Gamma-ray bursts and the fireball model , 1998, astro-ph/9810256.

[13]  Davide Lazzati,et al.  Internal shocks in the jets of radio-loud quasars , 2001 .

[14]  Caltech,et al.  Relativistic Jets in Collapsars , 2002, astro-ph/0207436.

[15]  C. Kouveliotou,et al.  The submillimetre properties of gamma-ray burst host galaxies , 2004 .

[16]  Weiqun Zhang,et al.  RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code , 2005, astro-ph/0505481.

[17]  S. Mereghetti,et al.  Are the hosts of gamma-ray bursts sub-luminous and blue galaxies? , 2003, astro-ph/0301149.

[18]  M. Rees,et al.  Unsteady outflow models for cosmological gamma-ray bursts , 1994, astro-ph/9404038.

[19]  O. Koike,et al.  Nucleosynthesis inside supernova-driven supercritical accretion disks , 2001 .

[20]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[21]  Gregory Y. Prigozhin,et al.  Global Characteristics of X-Ray Flashes and X-Ray-Rich Gamma-Ray Bursts Observed by HETE-2 , 2005 .

[22]  A. H. Taub,et al.  Relativistic Rankine-Hugoniot Equations , 1948 .

[23]  N. Bucciantini,et al.  An efficient shock-capturing central-type scheme for multidimensional relativistic flows , 2002 .

[24]  F. Frontera.  Gamma Ray Bursts in the Afterglow Era , 2003 .

[25]  Masanori Iye,et al.  An Asymmetric Energetic Type Ic Supernova Viewed Off-Axis, and a Link to Gamma Ray Bursts , 2005, Science.

[26]  日本物理学会,et al.  Progress in Theoretical Physics , 1946, Nature.

[27]  J. G. Jernigan,et al.  Global characteristics of X-ray flashes and X-ray rich GRBs observed by HETE-2 , 2004, astro-ph/0409128.

[28]  S. E. Woosley,et al.  The propagation and eruption of relativistic jets from the stellar progenitors of gamma-ray bursts , 2004 .

[29]  T. Piran,et al.  Can Internal Shocks Produce the Variability in Gamma-Ray Bursts? , 1997, astro-ph/9705013.

[30]  A. MacFadyen,et al.  Collapsars: Gamma-Ray Bursts and Explosions in “Failed Supernovae” , 1998, astro-ph/9810274.

[31]  V. Urpin.  Instability of relativistic sheared jets and distinction between FRI and FRII sources , 2002 .

[32]  Nakamura.  Multiple Sub-Jet Model of Gamma-Ray Bursts and Possible Origin of X-Ray Precursors and Postcursors. , 2000, The Astrophysical journal.

[33]  S. Woosley,et al.  Nucleosynthesis in Gamma-Ray Burst Accretion Disks , 2002, astro-ph/0209412.

[34]  Y. Sekiguchi,et al.  Magnetohydrodynamics in full general relativity: Formulation and tests , 2005, astro-ph/0507383.

[35]  B. Paczyński.  Are Gamma-Ray Bursts in Star-Forming Regions? , 1997, astro-ph/9710086.

[36]  S. Woosley,et al.  Gamma-Ray Bursts and Type Ic Supernova SN 1998bw , 1998, astro-ph/9806299.

[37]  D. Fugazza,et al.  Evidence for supernova signatures in the spectrum of the late-time bump of the optical afterglow of GRB 021211 , 2003, astro-ph/0306298.

[38]  N. Langer,et al.  Which massive stars are gamma-ray burst progenitors? , 2005, astro-ph/0504175.

[39]  Explosive Nucleosynthesis Associated with Formation of Jet-induced Gamma-Ray Bursts in Massive Stars , 2003, astro-ph/0306417.

[40]  M. Aloy,et al.  Relativistic MHD simulations of extragalactic jets , 2005 .

[41]  Effects of Jetlike Explosion in SN 1987A , 1999, astro-ph/9907109.

[42]  M. Hashimoto.  Supernova Nucleosynthesis in Massive Stars , 1995 .

[43]  W. F. Noh.  Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux , 1985 .

[44]  Ashley F. Emery,et al.  An Evaluation of Several Differencing Methods for Inviscid Fluid Flow Problems , 1968 .

[45]  J. Hawley,et al.  A Numerical Method for General Relativistic Magnetohydrodynamics , 2002, astro-ph/0210518.

[46]  T. Totani.  A Failed Gamma-Ray Burst with Dirty Energetic Jets Spirited Away? New Implications for the Gamma-Ray Burst-Supernova Connection from SN 2002ap , 2003, astro-ph/0303621.

[47]  E. Muller,et al.  GENESIS: A High-Resolution Code for Three-dimensional Relativistic Hydrodynamics , 1999, astro-ph/9903352.

[48]  A New Multidimensional Relativistic Hydrodynamics code based on Semidiscrete Central and WENO schemes , 2005, astro-ph/0512246.

[49]  L. Rezzolla,et al.  New relativistic effects in the dynamics of nonlinear hydrodynamical waves. , 2002, Physical Review Letters.

[50]  Rosa Donat,et al.  A Flux-Split Algorithm applied to Relativistic Flows , 1998 .

[51]  Philip A. Hughes,et al.  Simulations of Relativistic Extragalactic Jets , 1994 .

[52]  S. R. Kulkarni,et al.  The Observed Offset Distribution of Gamma-Ray Bursts from Their Host Galaxies: A Robust Clue to the Nature of the Progenitors , 2000, astro-ph/0010176.

[53]  Ewald Müller,et al.  Extension of the Piecewise Parabolic Method to One-Dimensional Relativistic Hydrodynamics , 1996 .

[54]  Alexander Heger,et al.  The Progenitor Stars of Gamma-Ray Bursts , 2005, astro-ph/0508175.

[55]  S. Koide.  Magnetic extraction of black hole rotational energy: Method and results of general relativistic magnetohydrodynamic simulations in Kerr space-time , 2003 .

[56]  Katsuhiko Sato,et al.  Matter Mixing from Axisymmetric Supernova Explosion , 1997, astro-ph/9709152.

[57]  Norbert Langer,et al.  Evolution of rapidly rotating metal-poor massive stars towards gamma-ray bursts , 2005 .

[58]  J. A. Miralles,et al.  Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach , 1997 .

[59]  S. Komissarov,et al.  A Godunov-type scheme for relativistic magnetohydrodynamics , 1999 .

[60]  P. Vreeswijk,et al.  A hypernova model for the supernova associated with the γ-ray burst of 25 April 1998 , 1998, Nature.

[61]  H. Takabe,et al.  Propagation and Dynamics of Relativistic Jets , 2004, astro-ph/0402355.

[62]  M. Rees,et al.  Relativistic fireballs: energy conversion and time-scales , 1992 .

[63]  Warren R. Brown,et al.  Spectroscopic Discovery of the Supernova 2003dh Associated with GRB 030329 , 2003, astro-ph/0304173.

[64]  Dinshaw S. Balsara,et al.  Total Variation Diminishing Scheme for Relativistic Magnetohydrodynamics , 2001 .

[65]  K. Pedersen,et al.  A very energetic supernova associated with the γ-ray burst of 29 March 2003 , 2003, Nature.

[66]  M. Norman,et al.  Propagation and morphology of pressure-confined supersonic jets , 1983 .

[67]  Antonio Marquina,et al.  Morphology and Dynamics of Relativistic Jets , 1997 .

[68]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[69]  Charles F. Gammie,et al.  HARM: A NUMERICAL SCHEME FOR GENERAL RELATIVISTIC MAGNETOHYDRODYNAMICS , 2003 .

[70]  Antonio Marquina,et al.  Capturing Shock Reflections , 1996 .

[71]  S. Woosley.  Gamma-ray bursts from stellar mass accretion disks around black holes , 1993 .

[72]  K. Nomoto,et al.  Bipolar Supernova Explosions: Nucleosynthesis and Implications for Abundances in Extremely Metal-Poor Stars , 2003, astro-ph/0304172.

[73]  S. Djorgovski,et al.  The bright optical afterglow of the nearby γ-ray burst of 29 March 2003 , 2003, Nature.

[74]  Taichi Kato,et al.  Structure in the early afterglow light curve of the γ-ray burst of 29 March 2003 , 2003, Nature.

[75]  The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics , 2000, Journal of Fluid Mechanics.