The Propagation and Eruption of Relativistic Jets from the Stellar

Progenitors of Gamma-Ray Bursts

W. Zhang, S. E. Woosley, & A. Heger2004, 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

• 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 （ isotropi

c ）• Afterglow ： seen after GRB events (lon

g burst only)

– Power law decay （ from ｘ -ray to radio ）– Continue over 100 days

light curve of GRB970228

Afterglow light curve

T(s)

log10(day)

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

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 struct

ure, it is possible

day

GRB990510

GRB-SN connection• “long-soft” GRBs are a phenomenon associated with the de

aths of massive stars.– Observation association with star-forming region in galaxies (Vrees

wijk 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 (Mir

abal et al. 2002)– The association of GRB 980425 with SN1998bw (Galama et al. 199

8) 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

Variety of GRBs• The general class of high-energy transients once generally c

alled “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 phenomen

a 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 fa

ctor?

Previous collapsar simulations• Jets inside massive stars have been studied numerically in b

oth 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 charact

eristics 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

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/cm

3 at R=1011cm)

← mass-loss rate of ~ 1*10-5 Msun/yr for a wind velocity ~1000 km/s at 1011cm

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 198

8) • Approximate Riemann solver (Aloy et al. 1999) using Marquina’s al

gorithm: 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

Model• The mass interior to 1.0*1010cm is removed from the presupernova st

ar and replaced by a point mass• No self-gravity• Jet are injected along the rotation axis (the center of the cylindrical axi

s) through the inner boundary• Each jet: power Edot, initial Lorentz factor 0, Etot/Ekin :f0

• 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, Lor

entz factor ←internal energy, density, power

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

Snapshot of Model 2A5s

10s

12s

Just as the jet is erupting from the star (0.89*1011cm)

20s

40s

70s

ParameterEdot: 1.0*1050 erg/s0: 10f0: 20

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

ParameterEdot: 3.0*1050 erg/s0: 5f0: 40

Snapshot of Model 2C

8s

16s

18s

28s

48s

70s

Model 2C is a less energetic jet and takes longer to reach the surface

ParameterEdot: 0.5*1050 erg/s0: 5f0: 40

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 fitEiso = 1.5*1054*(/2°)-3 ergs

Eiso = 4.5*1054*(/2°)-3 ergs

Eiso = 6.8*1053*(/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°

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 ～ 10-20

５ °

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

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*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>tanx (=40°), otherwise 1% less

• Model 3BL: ±10% imbalance in power• Propagation vector inclined to the z-axis b

y 3°(model 3P3), 5°(model 3P5), and 10°(model 3P10)

Breakout in 3D2T⇔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

Stability of the JetA study to test their survivability against nonradial instabilitiesJets 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

Discussion• Calculations show a relativistic jet can traverse a Wolf-Rayet s

tar 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 factor >20, angle

s 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

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 af

terglows (keV) to hard X-ray transients (10keV), to GRBs (1000kev)– Observations: a correlation for bursts with Epeak from 80 keV to over 1M

eV (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 phen

omenon sharing many properties• They should be associated with supernovae

– XRFs are typically visible at angles about 3 times greater than GRBs

Movie ３ Aperfect symmetry of the cylindrical initial condition

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

Movie ３ BL±10% imbalance in power