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The Propagation and Eruption of Relativistic Jets from the Stellar Progenitors of Gamma-Ray Bursts

The Propagation and Eruption of Relativistic Jets from the Stellar Progenitors of Gamma-Ray Bursts. W. Zhang, S. E. Woosley, & A. Heger 2004, ApJ, 608, 365 Yosuke Mizuno Plasma semiar 2004.6.22. Observational Properties of GRBs. Gamma-Ray Bursts (GRBs) are one of the most energetic explosion

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The Propagation and Eruption of Relativistic Jets from the Stellar Progenitors of Gamma-Ray Bursts

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  1. The Propagation and Eruption of Relativistic Jets from the Stellar Progenitors of Gamma-Ray Bursts W. Zhang, S. E. Woosley, & A. Heger 2004, ApJ, 608, 365 Yosuke Mizuno Plasma semiar 2004.6.22

  2. Observational Properties of GRBs • Gamma-Ray Bursts (GRBs) are one of the most energetic explosion • Duration (millisec - 100sec) • Various Light curves • Rapid time variability （～millisec） • 2 population (long-soft, short-hard) • Happen a few / a day • Cosmological distance(z～1） Total energy=1052-1054 erg （isotropic） • Afterglow ：seen after GRB events (long burst only) • Power law decay （from ｘ-ray to radio） • Continue over 100 days T(s) light curve of GRB970228 log10(day) Afterglow light curve

  3. Fireball Model Most contemporary explanation model of GRBs Shemi & Piran (1990)他 • In Fireball scenario • compact central engine • → relativistic outflow（G～100） • 　← From compactness problem • （Avoid to be optical thick） • Convert to radiation by shock scenario • Internal shock : GRB • External shock : afterglow • It doesn’t know the central engine of GRBs (most fundamental problem) Schematic figure of Fireball model

  4. GRB is Relativistic Jet? • Achromatic break in GRB afterglow→It indicates GRB is collimated outflow • Θ～a few degree • Total energy ～narrowly clustered around 1051erg（Frail et al. 1999） → If supernova-like energy concentrate to jet-like structure, it is possible GRB990510 day

  5. GRB-SN connection • “long-soft” GRBs are a phenomenon associated with the deaths of massive stars. • Observation association with star-forming region in galaxies (Vreeswijk et al, 2001; Grosabel et al. 2003…) • “bumps” observed in the afterglows (Reichart 1999;…) • Spectral features like a WR-star in the afterglow of GRB021004 (Mirabal et al. 2002) • The association of GRB 980425 with SN1998bw (Galama et al. 1998) and GRB 030329 with SN 2003dh (Stanek et al. 2003…) • Some GRBs are produced when the iron core of a massive star collapses to a black hole (Woosley 1993) (or very rapidly rotating highly magnetized neutron star (Wheeler et al. 2000)), producing a relativistic jet : collapsar model

  6. Variety of GRBs • The general class of high-energy transients once generally called “gamma-ray bursts” has been diversifying • X-ray flashes (XRFs; Heise et al. 2001; Kippen et al. 2003) • Long, faint gamma-ray bursts (in’t Zand et al. 2004) • Lower energy events like GRB 980425 (Galama et al. 2004) • Is a different model required for each new phenomenon? Or is some unified model? • Observable properties vary with its environment, the angle at which it is viewed, Its redshift • The answer is probably “both” • Not all jets are the same, and even if they were, different phenomena would be seen at different angles → Consider the observational consequences of highly relativistic jets as they propagate through, and emerge frommassive star • What would they look like if seen from different angles? • What is the distribution with polar angle of the energy and Lorentz factor?

  7. Previous collapsar simulations • Jets inside massive stars have been studied numerically in both Newtonian (MacFadyen & Woosley 1999 etc.) and relativistic simulations (Aloy et al. 2000; Zhang et al. 2003) • The collapsar model is able to explain many of the observed characteristics of GRBs • Require further examination, especially with higher resolution • The emergence of the jet and its interaction with the material at the stellar surface and the stellar wind could lead to some sort of precursor activity • There is the question of whether jets calculated in 2D are stable when studied in 3D → 2 and 3D numerical studies, the interaction of relativistic jets with the outer layers of the Wolf-Rayet stars thought responsible for GRBs

  8. Progenitor Star • We are concerned with the propagation of relativistic jets and their interactions with the star and stellar wind • Initial stellar model • Presupernova star : 15 Msun helium star (Heger & Woosley 2003) • The radius of the helium star : 8.8 * 1010 cm • Outside of star: stellar wind (< 2*1012cm) • Background density ∝R-2 (5*10-11 g/cm3 at R=1011cm) ← mass-loss rate of ~ 1*10-5 Msun/yr for a wind velocity ~1000 km/s at 1011cm

  9. Computer code • Multidimensional relativistic hydrodynamics code • Explicit Eulerian Godunov-type shock-capturing method (Aloy et al. 1999) • relativistic hydrodynamic equations • Time integration: high-order Runge-Kutta sheme (Shu & Osher 1988) • Approximate Riemann solver (Aloy et al. 1999) using Marquina’s algorithm: to compare the numerical fluxes from physical variables (pressure, rest mass density and velocity at the cell interface) • The values of physical fluid variables at the cell interface are interpolated using reconstruction schemes • Conserved variables → physical variables: Newton-Raphson iteration • Cartesian, cylindrical, or spherical coordinates • Approximate Newtonian gravity: including source terms • Gamma-law equation of state with g=4/3

  10. Model • The mass interior to 1.0*1010cm is removed from the presupernova star and replaced by a point mass • No self-gravity • Jet are injected along the rotation axis (the center of the cylindrical axis) through the inner boundary • Each jet: power Edot, initial Lorentz factor G0, Etot/Ekin :f0 • a half-opening angle of about 5°, Lorentz factor G~5-10 • Jet power: constant for first 20s, then turned down linearly during the next 10s • During the declining phase, pressure, density remained constant, Lorentz factor ←internal energy, density, power

  11. Results in Two Dimensions • In agreement with previous studies (Aloy et al. 2000; Zhang et al. 2003), the jet consists of a supersonic beam, a shocked cocoon, and a bow shock, and it is narrowly collimated

  12. Snapshot of Model 2A 20s 5s Parameter Edot: 1.0*1050 erg/s G0: 10 f0: 20 10s 40s 70s 12s Just as the jet is erupting from the star (0.89*1011cm)

  13. Snapshot of Model 2B 4s 18s Parameter Edot: 3.0*1050 erg/s G0: 5 f0: 40 Model 2B is a more energetic jet and reaches the surface in a shorter time 40s 8s 10s 70s

  14. Snapshot of Model 2C 8s 28s Parameter Edot: 0.5*1050 erg/s G0: 5 f0: 40 48s 16s Model 2C is a less energetic jet and takes longer to reach the surface 18s 70s

  15. Equivalent isotropic energy Eiso = 4.5*1054*(q/2°)-3 ergs The equivalent energy to an isotropic explosion inferred by a veiwer at angle q is plotted for various Lorentz factors 2° • The equivalent isotropic energy at larger angles (>2°) for all 3 models can be fitted well by a simple power-law • 1.5: 4.5: 0.68 are very close to those of the energy deposition rates 1.0: 3.0: 0.5 • Inside 2°, the distributions of energy and Lorentz factor are roughly flat Eiso = 6.8*1053*(q/2°)-3 ergs Simple power-law fit Eiso = 1.5*1054*(q/2°)-3 ergs

  16. Fraction of energy • The high Lorentz factor characteristic of common GRB is confined to a narrow angne of about 3°-5°with a maximum equivalent isotropic energy in highly relativistic matter along the axis of ~3*1053-3*1054 ergs • At larger angles there is significant energy and Lorentz factor G～10-20 ５°

  17. Resolution study in 2D High resolution plug • Qualitatively the results are similar • the jet emerges from the star with a cocoon surrounding the jet beam and a dense “plug” at the head of the jet • The distributions of equivalent isotropic energy versus angle for the jet core (<3°) are very similar Cocoon Low resolution

  18. 3-dimensional model • For the 3D models, the same helium star was remapped into a 3D Cartesian grid • Parameter of jet • Model 2B: G=5, Edot= 3*1050 erg/s, f0=40 • Grid: Cartesian 256 zones (x,y) and 512 zones (z) • Model 3A: perfect symmetry of the cylindrical initial condition • Model 3BS: pressure and density: 1% more if y>tanax (a=40°), otherwise 1% less • Model 3BL: ±10% imbalance in power • Propagation vector inclined to the z-axis by 3°(model 3P3), 5°(model 3P5), and 10°(model 3P10)

  19. Breakout in 3D • 2T⇔3A • The answer is insensitive to the dimensionality of the grid • 3A⇔3BS, 3BL • The properties of jets were nearly identical • The structure of the emergent jet and cocoon is strikingly different 2D 3BS 3A 3BL • More dramatic is the difference in the high-density “plug” • 3BS, 3BL: the plug has a much lower density and is not prominent • 3A: the plug is held by a concave surface of the highly relativistic jet core • ← the plug cannot easily escape and is pushed forward by the jet beam • presence or absence may have important implication for the production of short GRB

  20. Stability of the Jet A study to test their survivability against nonradial instabilities Jets were made toprecess with a period equal to 2s • 3°: jet escapes the star with its relativistic flow at least partly intact • 5°, 10°: the break-up of the jet • Because these is no well-focused highly relativistic jet beam, more baryon mass is mixed into the jet • → it will be very difficult for these jets to make a common GRB • The critical angle for jet precession is about 3° • The constraint on the angle of precession will be reduced if the jet bears more power or is powered longer

  21. Discussion • Calculations show a relativistic jet can traverse a Wolf-Rayet star while retaining sufficient energy and Lorentz factor to make a GRB. This conclusion is robust in 3D as well as 2D • As it breaks out, the jet is surrounded by a cocoon of mildly relativistic, energy-laden matter • 1051-1052 erg of equivalent isotropic energy, Lorentz factorG>20, angles about 3 times greater than a GRB • Whatever transient will be an orders of magnitude more frequently observable in the universe, but 2 orders of magnitude less energetic than a GRB • Weaker transients can be obtained at still larger angles • Might there be observable counterparts to these large-angle, low Lorentz factor explosions? • Too low a Lorentz factor to make a common GRBs • By external shock interaction with the progenitor wind, a hard transient of some sort should result

  22. Discussion • Correlation between Eiso, Lorentz factor, and angle • GRB outflows have a narrow highly relativistic jet beam and a wide mildly relativistic jet wing • Recent observations and afterglow modeling support this nonuniform jet model (Berger et al. 2003 etc.) • Lorentz factor is correlated with peak energy observed in the burst → a continuum of high-energy transients spanning the range from X-ray afterglows (keV) to hard X-ray transients (10keV), to GRBs (1000kev) • Observations: a correlation for bursts with Epeak from 80 keV to over 1MeV (Amati et al. 2002) • Many XRFs are the off-axis emissions of GRBs, made in the lower energy wings of the principal jet • XRFs and GRBs should be continuous classes of the same basic phenomenon sharing many properties • They should be associated with supernovae • XRFs are typically visible at angles about 3 times greater than GRBs

  23. Movie ３A perfect symmetry of the cylindrical initial condition

  24. Movie ３BS pressure and density: 1% more if y>tanax (a=40°), otherwise 1% less

  25. Movie ３BL ±10% imbalance in power

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