The Collapsar Model for GammaRay Bursts

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The Collapsar Model forGamma-Ray Bursts
S. E. Woosley (UCSC) Weiqun Zhang (UCSC) Alex
Heger (Univ. Chicago) Andrew MacFadyen (Cal
Tech)
Harvard CfA Meeting on GRBs, May 21, 2002
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Requirements on the Central Engine and its
Immediate Surroundings (long-soft bursts)

• Provide adequate energy at high Lorentz factor
  (G gt 200 KE 5 x 1051 erg)
• Collimate the emergent beam to approximately 0.1
  radians
• Make bursts in star forming regions
• In the internal shock model, provide a beam
  with rapidly variable Lorentz factor
• Allow for the observed diversity seen in GRB
  light curves
• Last approximately 20 s, but much longer in some
  cases
• Explain diverse events like GRB 980425
• Produce a (Type Ib/c) supernova in some cases
• Make x-ray lines

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Collapsars
A rotating massive star whose core collapses to a
black hole and produces an accretion disk.
Type Mass/sun BH Time
Scale Distance Comment
I 15-40 He prompt
20 s all z neutrino-dominated
disk II 10-40 He delayed
20 s 1 hr all z black hole by fall
back III gt130 He prompt
20 s zgt10? time dilated,
redshifted
(1z)
very energetic, pair

instability, low Z
Type I is what we are usually talking about. The
40 solar mass limit comes from assuming that all
stars above 100 solar masses on the main
sequence are unstable (except Pop III).
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Quasar 3C 175 as seen in the radio
Quasar 3C273 as seen by the Chandra x-ray
Observatory
Artists conception of SS433 based on
observations
Microquasar GPS 1915 in our own Galaxy time
sequence
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Collapsar Progenitors
Two requirements

• Core collapse produces a black hole - either
  promptly or very shortly thereafter.
• Sufficient angular momentum exists to form a
  disk outside the black hole (this virtually
  guarantees that the hole is a Kerr hole)

Fryer, ApJ, 522, 413, (1999)
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Black hole formation may be unavoidable for low
metallicity
Solar metallicity
Low metallicity
With decreasing metallicity, the binding energy
of the core and the size of the silicon core
both increase, making black hole formation more
likely at low metallicity. Woosley, Heger,
Weaver, RMP, (2002)
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The more difficult problem is the angular
momentum. This is a problem shared by all current
GRB models that invoke massive stars...
In the absence of mass loss and magnetic fields,
there would be abundant progenitors. Unfortunatel
y nature has both.
15 solar mass helium core born rotating rigidly
at f times break up
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Heger, Woosley, Spruit in prep. for ApJ
note models a-d (with B-fields) and e
(without)
Spruit, (2001), AA, 381, 923
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followed here
.
Heger and Woosley (2002) using prescription for
magnetic torques from Spruit (2001)
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Some implications ....

• The production of GRBs may be favored in metal-
  deficient regions, either at high red shift or
  in small galaxies (like the SMC). The
  metallicity- dependence of mass loss rates
  for RSGs is an important source of
  uncertainty. (Kudritzsky (2000) Vink, de
  Koters, Lamers AA, 369, 574, (2001))
• But below some metallicity Z about, 0.1,
  single massive stars will not make GRBs
  because they do not lose their hydrogen
  envelope.
• GRBs may therefore not track the total star
  formation rate, but of some special set of
  stars with an appreciable evolutionary
  correction.

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Progenitor Winds
Massive Wolf-Rayet stars during helium
burning - are known to have large mass loss
rates, approximately 10-5 solar masses/yr or
more. This wind may be clumpy and
anisotropic and its metallicity dependence is
uncertain. The density dependence of matter
around a single star in vacuum could be
approximately 1000 (1016 cm/R)2 cm-3 composed of
carbon, oxygen, and helium, BUT During
approximately the last 100 1000 years of its
life, the star burns carbon (mainly) and heavier
fuels. The mass loss rate of the star during
these stages is unknown. No WR star has ever
knowingly been observed in such a state. This
means that the mass distribution inside 1017 -
1018 cm is unknown (100 yrs at 1000 km/s).
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Given the necessary angular momentum, black hole
formation is accompanied by disk formation...
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The Star Collapses (log j gt 16.5)
alpha 0.1
alpha 0.001
7.6 s
7.5 s
Neutrino flux low
Neutrino flux high
MacFadyen Woosley ApJ, 524, 262, (1999)
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In the vicinity of the rotational axis of the
black hole, by a variety of possible processes,
energy is deposited.
It is good to have an energy deposition mechanism
that proceeds independently of the density and
gives the jet some initial momentum along the
axis
7.6 s after core collapse high viscosity case.
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The Neutrino-Powered Model (Type I Collapsar
Only)
Given the rather modest energy needs of current
central engines (3 x 1051 erg?) the
neutrino-powered model is still quite viable and
has the advantage of being calculable. A
definitive calculation of the neutrino transport
coupled to a realistic multi- dimensional
hydrodynamical model is still lacking.
Optimistic nu-deposition
a0.5
a0.5
a0
Neutrino annihilation energy deposition rate (erg
cm 3 s-1)
Fryer (1998)
MacFadyen Woosley (1999)
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MHD Energy Extraction
Blandford Znajek (1977) Koide et al. (2001) etc.
The efficiencies for converting accreted matter
to energy need not be large. B 1014 1015
gauss for a 3 solar mass black hole. Well below
equipartition in the disk.
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Jet Initiation - 1
The jet is initially collimated by the density
gradient left by the accretion. It will not
start until the ram pressure has declined below
a critical value.
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Jet Initiation -2
High disk viscosity (7.6 s 0.6 s)
Low disk viscosity (9.4 s 0.6 s)
MacFadyen, Woosley, Heger, ApJ, 550, 410,
(2001)
(Energy deposition of 1.8 x 1051 erg/s commenced
for 0.6 s opening angle 10 degrees)
log rho
5 - 11.5
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The Production of 56Ni

• Needed to power the light curve of the supernova
  if one is to be visible. Need 0.1 to 0.5
  solar masses of it.
• A bigger problem than most realize The
  jet doesnt do it too little mass
  Forming the black hole depletes the innermost
  core of heavy elements Pulsars may
  have a hard time too if their time scale is gt 1
  sec
• In the collapsar model the 56Ni is made by a
  wind off of the accretion disk. Its
  abundance is related to how much mass
  accretes into the hole

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The disk wind MacFadyen Woosley (2001)
Neglecting electron capture in the disk
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The Jet-Star Interaction
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Relativistic Jet Propagation Through the
Star Zhang, Woosley, MacFadyen (2002)
Zoom out by 10
480 radial zones120 angular zones 0 to 30
degrees 80 angular zones 30 to 90 degrees
15 near axis
Initiate a jet of specified Lorentz factor (here
50), energy flux (here 1051 erg/s), and internal
energy (here internal E is about equal to kinetic
energy), at a given radius (2000 km) in a given
post-collapse (7 s) phase of 15 solar mass helium
core evolved without mass loss assuming an
initial rotation rate of 10 Keplerian. The stars
radius is 8 x 1010 cm. The initial opening angle
of the jet is 20 degrees.
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Pressure in the same model
The pressure in the jet is greater than in the
star through which it propagates.
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The jet can be divided into three regions 1) the
unshocked jet,

2) the shocked jet, and
3)
the jet head.
jet head at 4.0 s
For some time, perhaps the duration of the burst,
the jet that emerges has been shocked and has
most of its energy in the form of internal
energy. Information regarding the central engine
is lost.
Zhang, Woosley, MacFadyen ApJ, to be submitted
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Independent of initial opening angle, the
emergent beam is collimated into a narrow beam
with opening less than 5 degrees (see also Aloy
et al. 2000)
Initial opening angle 5 degrees 1051 erg/s
Initial opening angle 20 degrees 1051 erg/s
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The previous calculation was 2D in spherical
coordinates. This puts all the resolution near
the origin and also spends a lot of zones
following the unshocked star. Repeat using
cylindrical coordinates and study the just the
jets interactions with finer zoning but
keeping the same density and temperature
structure as in the star along its rotational
axis. Carry 80,000 km 10 of the star.
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Lorentz factor
Density
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Density structure at 2.2 seconds inner 80,000 km
(star radius is 800,000 km).
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Pressure at 2.2 seconds
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Lessons Learned

• Even a jet of constant power is strongly
  modulated by its passage through the star.
• The variations in Lorentz factor and density can
  be of order unity.
• An initially collimated jet stays collimated.
• There may be important implications for the
  light curve especially its time structure.

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The Jet Explodes the Star
Continue the spherical calculation for a long
time, at least several hundred seconds. See how
the star explodes,the geometry of the supernova,
and what is left behind.
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Density and radial velocity at 80 s (big picture)
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Zoom in by 5... The shock has wrapped around and
most of the star is exploding. Outer layers and
material along the axis moves very fast. Most
of the rest has more typical supernova like
speeds 3000 10,000 km s-1
80 seconds
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(Zoom in 100)
t 80 seconds
Shown on a magnified scale, there is still a lot
of dense low velocity material near the black hole
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at 240 seconds
radial velocity/c
The shock has wrapped around and the whole star
is exploding (initial radius was less than one
tick mark here). A lot of matter in the
equatorial plane has not achieved escape velocity
though and will fall back. Continuing polar
outflow opens a channel along the rotational axis.
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240 seconds
By this time the star has expanded to over ten
times its initial radius the expansion has become
(very approximately) homologous. Provided
outflow continues along the axis as assumed, an
observer along the axis (i.e., one who saw a
GRB) will look deeper into the explosion and
perhaps see a bluer supernova with broader lines
(e.g., SN2001ke Garnavich et al.
2002). Continued accretion is occurring in the
equatorial plane.
Caution Effect of disk wind not included here
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Spreading of jets after they exit the star
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10 seconds 35 seconds
Zhang, Woosley, and MacFadyen (2002)
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The jet properties are shown 35 seconds after
its initiation. Lines give properties at
6.0, 7.5, and 9.0 x 1011 cm. At 15 degrees in
Model W1, the equivalent isotropic energy flux
is about 1046 erg s -1 (solid line).
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GRB
G 200
5o , internal shocks
GRB 980425
G 10 - 100
Hard x-ray bursts
30o , external shocks?
G 1
Unusual supernova (polarization, radio source)
A Unified Model for Cosmological Transients
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Some Conclusions

• The light curves of (long-soft) GRBs may reflect
  more the interaction of the jet with the star
  than the time variability of the engine
  itself.
• The emergent jet in the collapsar model may still
  contain a large fraction of its energy as
  internal energy. Expansion after break out of
  material with Lorentz factor of order 10 can
  still give final Lorentz factors over 100.
• Much weaker bursts are expected off axis (GRB
  980425?, x-ray flashes?)
• Jet powered supernovae may have significant
  equatorial fall back. Jet may continue with
  a declining power for a long time
• Circum-burst mass distribution highly uncertain
• 56Ni synthesis given by disk wind. May be
  related to total mass accreted.