Download The Propagation and Eruption of Relativistic Jets from the

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
• Duration (millisec - 100sec)
– Various Light curves
– Rapid time variability （～millisec）
– 2 population (long-soft, short-hard)
T(s)
•
•
Happen a few / a day
light curve of GRB970228
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
log10(day)
Afterglow light curve
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
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
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
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?
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
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
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
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
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 2A
5s
20s
10s
40s
Parameter
Edot: 1.0*1050 erg/s
G0: 10
f0: 20
12s
Just as the jet
is erupting
from the star
(0.89*1011cm)
70s
Snapshot of Model 2B
4s
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
8s
10s
18s
40s
70s
Snapshot of Model 2C
8s
28s
Parameter
Edot: 0.5*1050 erg/s
G0: 5
f0: 40
Model 2C is a less 16s
energetic jet and
takes longer to
reach the surface
48s
18s
70s
Equivalent isotropic
energy
The equivalent energy to an isotropic
explosion inferred by a veiwer at angle q is
plotted for various Lorentz factors
• 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 =
4.5*1054*
(q/2°)-3
ergs
2°
Eiso =
6.8*1053*
(q/2°)-3
ergs
Simple power-law fit
Eiso = 1.5*1054*(q/2°)-3 ergs
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°
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
Cocoon
Low
resolution
plug
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)
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
3A
3BS
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
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
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 factor G>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
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
Movie ３A
perfect symmetry of the cylindrical initial condition
Movie ３BS
pressure and density: 1% more if y>tanax (a=40°), otherwise 1% less
Movie ３BL
±10% imbalance in power