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=10 52 -10 54 erg （ isotropic ） Afterglow ： seen after GRB events (long burst only) –Power law decay （ from ｘ -ray to radio ） –Continue over 100 days light curve of GRB970228 Afterglow light curve T(s) log 10 (day)

3. Fireball Model In Fireball scenario compact central engine → relativistic outflow （  ～  ） ← 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 Shemi & Piran (1990) 他 Most contemporary explanation model of GRBs

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 10 51 erg （ Frail et al. 1999 ） → If supernova-like energy concentrate to jet-like structure, it is possible day GRB990510

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 from massive 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 M sun helium star (Heger & Woosley 2003) –The radius of the helium star : 8.8 * 10 10 cm Outside of star: stellar wind (< 2*10 12 cm) –Background density ∝ R -2 (5*10 -11 g/cm 3 at R=10 11 cm) ← mass-loss rate of ~ 1*10 -5 M sun /yr for a wind velocity ~1000 km/s at 10 11 cm

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  =4/3

10. Model The mass interior to 1.0*10 10 cm 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  0, E tot /E kin :f 0 a half-opening angle of about 5°, Lorentz factor  ~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 5s 10s 12s Just as the jet is erupting from the star (0.89*10 11 cm) 20s 40s 70s Parameter Edot: 1.0*10 50 erg/s  0 : 10 f 0 : 20

13. Snapshot of Model 2B 4s 8s 10s 18s 40s 70s Model 2B is a more energetic jet and reaches the surface in a shorter time Parameter Edot: 3.0*10 50 erg/s  0 : 5 f 0 : 40

14. Snapshot of Model 2C 8s 16s 18s 28s 48s 70s Model 2C is a less energetic jet and takes longer to reach the surface Parameter Edot: 0.5*10 50 erg/s  0 : 5 f 0 : 40

15. Equivalent isotropic energy The equivalent energy to an isotropic explosion inferred by a veiwer at angle  is plotted for various Lorentz factors Simple power-law fit E iso = 1.5*10 54 *(  /2°) -3 ergs E iso = 4.5*10 54 * (  /2°) -3 ergs E iso = 6.8*10 53 * (  /2°) -3 ergs 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 2°

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*10 53 -3*10 54 ergs At larger angles there is significant energy and Lorentz factor  ～ 10-20 ５°５°

17. Resolution study in 2D 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 High resolution Low resolution Cocoon plug

18. 3-dimensional model For the 3D models, the same helium star was remapped into a 3D Cartesian grid Parameter of jet –Model 2B:  =5, Edot= 3*10 50 erg/s, f 0 =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>tan  x (  =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 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 2D 3A 3BS 3BL

20. Stability of the Jet A study to test their survivability against nonradial instabilities Jets were made to precess 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. Stability of the Jet Is 2s a reasonable period for the jet to precess? There are many uncertainties, but the gravitomagnetic precession period of a black hole surrounded by an accretion disk is estimated by Hartle et al. (1986) to be T GM =900(M disk /0.001M sun ) -1 *(M bh /3M sun ) -1/2 (r/300km) 2.5 s For currently favored value of the alpha-viscosity ～ 0.1, the disk mass is about 0.001M sun. For the disk mass to approach 1M sun the viscosity would need to be  <0.001 Given the low mass of the accretion disk and radius of the disk ～ 300km, precession period ～ 2s are unlikely

22. 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 –10 51 -10 52 erg of equivalent isotropic energy, Lorentz factor  >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

23. Discussion Correlation between E iso, 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 E peak 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

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

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

26. Movie ３ BL ±10% imbalance in power