The Central Engine for GammaRay Bursts

1
The Central Engine forGamma-Ray Bursts
S. E. Woosley (UCSC) Alex Heger
(UCSC/Chicago) Andrew MacFadyen
(UCSC/CIT) Weiqun Zhang (UCSC)
Woods Hole GRB Meeting Nov. 6, 2001
2
Requirements on the Central Engine and its
Immediate Surroundings (long-soft bursts)

• Provide adequate energy at high Lorentz factor
• Collimate the emergent beam to approximately 0.1
  radians
• In the internal shock model, provide a beam
  with rapidly variable Lorentz factor
• Allow for the observed diverse GRB light curves
• Last approximately 10 s, but much longer in some
  cases
• Explain diverse events like GRB 980425
• Produce a (Type Ib/c) supernova in some cases
• Make bursts in star forming regions

3
Despite their large inferred brightness, it is
increasingly believed that GRBs are
not inherently much more powerful than
supernovae. From afterglow analysis, there is
increasing evidence for a small "beaming angle"
and a common total jet energy near 3 x 1051 erg
(for a conversionefficiency of 20).
Frail et al. ApJL, (2001), astro/ph 0102282
See also Freedman Waxman,
ApJ, 547, 922 (2001) Bloom,
Frail, Sari AJ, 121, 2879
(2001) Piran et al. astro/ph
0108033 Panaitescu Kumar,
ApJL, 560, L49 (2000)
4
Minimum Lorentz factors for the burst to be
optically thin to pair production and to avoid
scattering by pairs. Lithwick Sari, ApJ, 555,
540, (2001)
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Merging neutron star - black hole pairs
(Ruffert this session Rosswog poster
Salmonson poster Lee - poster)
Strengths a) Known event b)
Plenty of angular momentum c)
Rapid time scale d) High
energy e) Well developed
numerical models
Weaknesses a) Outside star forming regions
b) Beaming and energy may be
inadequate for long
bursts c) Uncertain disk
physics
Needed a) Locations of short hard
bursts b) Calculations that
include jet formation c)
Better understanding of disk physics
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Magnetar Birth
Strengths a) Star forming regions
b) Supernova association c)
Magnetars exist d) Sufficient
energy if a milliseond
pulsar is formed
Wheeler et al, ApJ, 537, 810, (2000)
Weaknesses a) Requisite dipole field strengths
very high b) Model still
very qualitative what holds up
the accreting star while the neutron
star deposits its
energy?
Needed more work
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Black Hole - He-Core Mergers
Strengths a) Plenty of angular momentum
b) Star forming regions
c) High energy
Zhang Fryer, ApJ, 550, 357, (2001)
Weaknesses a) Is star's envelope really
ejected in the merger? b)
Long time scale (gt100 s?)
c) No calculations of jet formation
d) Disk physics uncertain, not neutrino
dominated
Needed Calculations to address all of above
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Collapsars
(MacFadyen this session)
Strengths a) Found in star-forming regions
b) Large sustained accretion
rates c) Form jets naturally
d) Detailed numerical models
e) GRB makes supernova
f) Can be a common occurrence
Weaknesses a) Is there enough angular
momentum? b) Hard to
make short bursts c)
Uncertain disk physics
Needed a) Realistic evolution of stars
including magnetic torques
b) Better simulations of the full event
c) Better understanding of disk
physics
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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 Z
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 accepted.
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The real problem is the angular momentum ...
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
Heger and Woosley - poster paper and in
preparation for ApJ. Joss this session Wijers
poster paper
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Ways to improve the situation.

• Use metal deficient stars. These are both more
  likely to implode to black holes and lose less
  angular momentum to winds. Max He-core at
  death for single solar metallicity stars is
  11 Msun. For 0.3 solar metallicity stars, it
  may be 20 Msun. But too small a metallicity
  can also keep single stars from making GRBs
• Use binary systems - either common envelope
  mergers after one or both stars are already
  highly evolved or perhaps tidally induced
  co-rotation (Joss this session, Heger -
  poster)
• Find reasons that the magnetic torques may have
  been overestimated by Spruit, AA in press,
  astro/ph-0108207

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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.
• Similarly, the GRBs happening today (e.g.,
  GRB 980425) may have different properties -
  probably weaker, than GRBs at high redshift
  because the collapsing core is smaller.

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Progenitor Winds
Massive Wolf-Rayet stars are known to have
large mass loss rates, approximately 10-5 solar
masses/yror more. This wind may be clumpy
and anisotropic, but it isunavoidable and its
metallicity dependence is uncertain. The
density dependence of matter around a single star
in vacuum is thus approximately 1000 (1016
cm/R)2 cm-3 composed of carbon, oxygen, and
helium. The wind the burst interacts with was
ejected during carbon burning. At some radius
this wind will terminate due to interaction with
the ISM at 1018 /n 1/2 cm (Ramirez Ruiz et al.
MNRAS, 2001). The GRB jet will start to be
decelerated by thiswind at about 3 x 1015 cm.

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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. (Van Putten this
session Ruffini this session Vlahakis -
poster)
The exact mechanism for extracting this energy,
either from the disk or the rotation of the
black hole, is fascinating physics, but is not
crucial to the outcome, so long as the energy is
not contaminated by too much matter. It is good
to have an energy deposition mechanism that
proceeds independently of the density.
7.6 s after core collapse high viscosity case.
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The Neutrino-Powered Model
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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Gamma-Ray Bursts are Inefficient
Typical masses accreted are several solar
masses. The energy of the last stable orbit is
approximately 10 Mc2 or about 5 x 1053 erg. The
GRB jet uses less than a percentof this. Such
inefficiency is more reminiscent of
supernovae than of active galactic nuclei.Part
of the energy goes into blowing up the star, but
most islost to neutrinos or swept into the hole.
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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.
20
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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Why is the jet energy nearly constant?

• The black hole mass and the total mass accreted
  do not vary greatly from event to event.
• The explosion is self-limiting in the sense that
  the jet that makes the GRB also blows up the
  star that makes the jet.
• A minimum threshold energy is required for the
  jet to propagate out of the central regions of
  the star and not be swept into the hole by
  accretion.

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Relativistic Jet Propagation Through the Star
Zhang, Woosley, MacFadyen (poster) Aloy this
session
Ramirez-Ruiz this
session
480 radial zones120 angular zones 0 to 30
degrees 80 angular zones 30 to 90 degrees
15 near axis
Note instabilities
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
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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 all 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, in preparation.
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Independent of initial opening angle, the
emergent beam is collimated into a narrow beam
with opening less than 5 degrees
Initial opening angle 5 degrees 1051 erg/s
Initial opening angle 20 degrees 1051 erg/s
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The jet emerges with a small
opening angle (see also Aloy et al ApJL, 510,
119, (2000))
In terms of energy at least, the jet can be
"hollow", at least for the calculation initiated
with large angle (20 deg)
The opening angle gradually increases, but not
monotonically.
Energy flux at 9 x 1010 cm (just outside star)
Zhang, Woosley, MacFadyen (2002)
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The termination of the unshocked jet remains
inside the star for a long time. Note the
variability of Lorentz factor is correlated with
angle. Smaller angle means more instability.
(20 degrees)
(5 degrees)
0
4
0
1
2
8
10
20
Narrower opening angles should be correlated with
higher luminosity along the axis and with greater
variability.
28
Once the jet has broken out, the energy input at
the bottom emerges at the top as relativistic
ejecta with almost 100 efficiency.
29
Dark solid lines indicate the Lorentz factor
shortly after break out in two models. The
lighter lines indicate the Lorentz factor that
will exist at infinity when all the internal
energy has converted
Terminal Lorenz factor
Lorentz factor at break out

1010 200
30
SN 1998bw/GRB 980425
NTT image (May 1, 1998) of SN 1998bw in the
barred spiral galaxy ESO 184-G82Galama et al,
AA S, 138, 465, (1999)
WFC error box (8') for GRB 980425 and two NFI
x-ray sources. The IPN error arc is also shown.
1) Were the two events the same thing? 2) Was
GRB 980425 an "ordinary" GRB seen off-axis?
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SN 1998bw/GRB 980425
The supernova - a Type Ic - was very unusual.
Large mass of 56Ni 0.3 - 0.9 solar masses
(note jets acting alone do not make 56Ni)
Sollerman et al, ApJL, 537, 127
(2000) McKinzie Schaefer,
PASP, 111, 964, (1999) Extreme energy and
mass gt 1052 erg gt 10 Msun
Iwamoto et al., Nature, 395, 672 (1998)
Woosley, Eastman, Schmidt, ApJ,
516, 788 (1999) Mazzali et
al, ApJ, 559, 1047 (2001) Exceptionally strong
radio source Li Chevalier, ApJ,
526, 716, (1999)
Relativistic matter was ejected 1050 - 1051
erg Wieringa, Kulkarni, Frail,
AAS, 138, 467 (1999) Frail
et al, ApJL (2001), astroph-0102282
Probability favors the GRB-SN association
Pian et al ApJ, 536, 778 (2000)

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We conclude that SN 1998bw and GRB were the
same event, but was it an ordinary GRB seen
off-axis or an inherentlyweak GRB?
1051 erg/s Gamma 10, 5o high internal
energy
1051 erg/s Gamma 50, 5o low internal energy
35 s
Weak or truncated jet - only mildly relativistic
at break out. MacFadyen, Woosley, Heger (2001)
Spreading at late times in an ordinary GRB
Zhang, Woosley, MacFadyen (2001)
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After Break-Out .....
Lorentz factor and total energy flux as a
function of angle
For the models on the previous page, the energy
fluxes at 6.0, 7.5, and 9.0 x 1011 cm at a time
of 35 s after jet break out. At large angles one
will see a weak burst characterized by a
moderate (about 10) Lorentz factor. At 30
degrees in Model A2, the equivalent isotropic
energy is about 1049 erg/s. This result is very
dependent upon the artificial wayin which the
jet was turned down, but is suggestive.
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Some Conclusions

• The collapsar model is able to explain many of
  the observed attributes of GRBs. It naturally
  provides a reasonable energy and collimation
  to the jet - provided the necessary angular
  momentum and prompt black hole formation are
  achieved.
• 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.
• SN 1998bw and GRB 980425 were the same event. It
  remains unclear at this point if the burst was
  weak because of a deficiency, at all angles,
  of highly relativistic ejecta, or if it was an
  ordinary GRB viewed off axis. The latter
  hypothesis is favored. Every ordinary GRB may
  make an event like this beamed to a much
  larger fraction of the sky.
• 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.
• 3D calculations of jet propagation are needed.