Supernovae,

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Supernovae, Gamma-Ray Bursts, and Stellar
Rotation
S. E. Woosley (UCSC) A. Heger (Univ. Chicago)
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When a massive star (M gt 8 solar masses) dies,
what is the angular momentum of its iron core?
In terms of the resulting pulsar period or its
equivalent. Is it lt 1 ms needed
for current GRB models lt 5 ms will
necessarily influence the supernova
kinematics gt 20 ms
with considerable variability - as is implied
by observed pulsars
all values between?
3
The answer depends on following a massive star
- including all forms of magnetic and
non-magnetic torques through six major nuclear
burning stages and including mass loss (plus the
possible effects of binary membership)
The answer is critically important to
understanding
Baade Zwicky (1939) Hoyle (1946)

• How supernovae explode
• How gamma-ray bursts work
• The strength of potential sources of
  gravitational radiation
• The nature of pulsars and supernova remnants
• Nucleosynthesis
• ....

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The current paradigm for supernova explosion
powered by neutrino energy deposition gives
ambiguous results.Rotation could alter this by

• Providing extra energy input
• Creating ultrastrong B fields and jets
• Changing the convective flow pattern

Burrows, Hayes, and Fryxell (1995)
Ostriker and Gunn 1971
LeBlanc and Wilson 1970Wheeler et al 2002
Fryer and Heger 2000
Mezzacappa et a l (1998)
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1/day in BATSE
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Paciesas et al (2002) Briggs et al (2002)
Koveliotou (2002)
Shortest 6 ms GRB 910711
Longest 2000 s GRB 971208
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The majority consensus

• Long-soft bursts are at cosmological distances
  and are associated with star forming regions

Djorgovski et al (2002)
27 Total
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Djorgovski et al (2002)
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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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• GRBs are produced by highly relativistic flows
  that have been collimated into narrowly
  focused jets

Quasar 3C273 as seen by the Chandra x-ray
Observatory
Quasar 3C 175 as seen in the radio
Artists conception of SS433 based on
observations
Microquasar GPS 1915 in our own Galaxy time
sequence
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It is a property of matter moving close to the
speed of light that it emits its radiation in a
small angle along its direction of motion. The
angle is inversely proportional to the Lorentz
factor
This offers a way of measuring the beaming angle.
As the beam runs into interstellar matter it
slows down.
Measurements give an opening angle of about 5
degrees.
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• GRBs have total energies not too unlike
  supernovae

Frail et al. ApJL, (2001), astro/ph 0102282
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).
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• There may be several hundred unusual explosions
  for
• every gamma-ray burst we see

Very approximately 1 of all supernovae make
GRBs but we only see about 0.5 of all the
bursts that are made a rare phenomenon

• If typical GRBs are produced by massive stars,
  the star must have lost its hydrogen envelope
  before it died.

A jet that loses its power source after the mean
duration of 10 s can only traverse 3 x 1011 cm.
This is longenough to escape a Wolf-Rayet star
but not a giant.
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There may even be an observational connection
between supernovae and GRBs

• Bumps seen in the optical afterglows of at
  least three GRBs - 970228, 980326, and 011121
  at the time and with a brightness like
  that of a Type I supernova

Bloom et al (2002)
note SN 56Ni
A spectrum please!!
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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)
Type Ic supernova, d 40 Mpc Modeled as the 3 x
1052 erg explosion of a massive CO
star (Iwamoto et al 1998 Woosley, Eastman,
Schmidt 1999) GRB 8 x 1047 erg 23 s
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• It is the consensus that the root cause of
  these energetic phenomena is star death that
  involves an unusually large amount of angular
  momentum (j 1015 1016 cm2 s-1) and quite
  possibly, one way or another, ultra-strong
  magnetic fields (1015 gauss).
• These are exceptional circumstances required,
• in part, to get relativistic jets.

Prompt models Millisecond
magnetars Delayed models (seconds to years)
Supranova Collapsar
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Wheeler, Yi, Hoeflich, and Wang (2001) Usov
(1992, 1994, 1999)
The ms Magnetar Model
Problems with Alfven radius at
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Supranovae
Vietri Stella, 1998, ApJL, 507, L45 Vietri
Stella, 1999, ApJL, 527, L43

• First an otherwise normal supernova occurs
  leaving behind a neutron star whose existence
  depends on a high rotation rate.

Shapiro (2000) Salgado et al (1994)

• The high rotation rate ( 1 ms) is braked by
  pulsar- like radiation until a critical
  angular momentum is reached
• The neutron star then collapses on a dynamic
  time scale
• to a black hole leaving behind a disk
• (this may be sensitive to the EOS)
• Accretion of this disk produces a delayed GRB
  (time scales of order a year after the
  supernova)

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Collapsars
A rotating massive star whose core collapses to a
black hole and produces an accretion disk.
Bodenheimer and Woosley (1982) Woosley
(1993) MacFadyen and Woosley (1999)
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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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Basics

• Wolf-Rayet Star no hydrogen envelope about 1
  solar radius.
• Collapse time scale tens of seconds
• Rapid rotation j 1016 erg s
• Black hole 3 solar masses accretes several
  solar masses

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The star collapses and forms a disk (log j gt 16.5)
In the vicinity of the rotational axis of the
black hole, by a variety of possible processes,
energy is deposited.
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.
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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Blandford Znajek (1977) Koide et al. (2001) van
Putten (2001) Lee et al (2001) etc.
MHD Energy Extraction
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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Lorentz factor
Density
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To summarize
All currently favored massive star models
for GRBs require a collapsing iron core to have
sufficient angular momentum to make a millisecond
pulsar (j 6 x 1015 cm2 s-1). The collapsar
model may need even more (2 x 1016 cm2 s-1).
Do current views regarding the evolution
of massive stars with helium cores over 10 solar
masses allow this to happen? (need not be a
common phenomena)

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- red supergiants at death. Pulsar periods 3 to
15 ms
Heger, Woosley, Spruit, in prep. for ApJ
Spruit, (2001), AA, 381, 923
note models b (with B-fields) and e (without)
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(probably in a binary)
.
Heger and Woosley (2002) using prescription for
magnetic torques from Spruit (2001)
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The difficult problem is the angular momentum.
This is a problem shared by all current GRB
models that invoke massive stars...
no mass loss or B-field
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
with mass loss
with mass loss and B-fields
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Suppose all neutron stars are born rotating very
rapidly. What processes can brake them?
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Neutrino Braking (an invisible sink for E and j)
Upon birth, a neutron star radiates about 20
30 of its rest mass as neutrinos. These carry
away angular momentum as well as energy,
especially since their last interaction is at the
edge of the neutron star. Thomas Janka estimates
that the total angular momentum of the collapsing
iron core is reduced by about 30. So for
example, 7 ms in the earlier table becomes 9 ms.
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r-Mode Instability (Gravity Waves)
Arras et al (astroph 0202345) submitted to
ApJ find that the r-mode waves saturate at
amplitudes fall lower than obtained in
(erroneous) previous numerical calculations that
assumed an unrealistically large driving force.
Much less gravitational radiation.
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The Neutrino Powered Wind
Duncan, Shapiro, and Wasserman (1986) Qian and
Woosley (1996)
A magnetic stellar wind? (Mestel and Spruit
(1987)
Wind magnetically confined until at rcrit
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Results
Depend on w and how magnetic field strength
scales with radius (r-2 or r-3 ?) Case b) (high
mass loss rate- early on) requires extremely
large fields (gt 1016 gauss) if P 5 ms. Case a)
(low mass loss rate- later) can brake the
rotation of neutron stars in about 10 s but only
if the rotation rate is already pretty slow (P gt
50 ms) and the surface field is gt 1014 gauss and
B scales as r-2.
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Fall back and the propeller mechanism
25 solar mass supernova explosions with various
final energies
MacFadyen, Woosley, and Heger, (2001)
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Propeller Mechanism
Illarionov and Sunyaev (1975) Alpar (2001)
coupled to fallback
Chevalier (1989) Lin, Woosley and Bodenheimer
(1991) MacFadyen Woosley, and Heger (2001)
Fallback accretion rate
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Alfven Radius
So long as the calculated Alfven radius is
smaller than the neutron star radius (10 km), the
magnetic field will be pushed to the surface of
the star and no braking can occur. For B 1012
gauss it takes of order one day until the
accretion rate subsides to the point that rA gt
10 km.
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Additionally there is a critical accretion rate,
for a given field strength and rotation rate,
above which the corotation speed at the Alfven
radius will be slower than the Keplerian orbit
speed. In this case the matter will accrete
rather than be ejected and magnetic braking will
be inefficient until.
This turns out to be very restrictive and will
only allow appreciable braking (of w3 1) if m30
100, that is B 1014 gauss.
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When the necessary restrictions on the accretion
rate and magnetic field apply, the torque is
given by
Putting it all together, a neutron star can be
braked to a much slower rotational rate provided
m30 gt 78, 43, 25 for initial periods of 6, 21,
and 60 ms respectively. If the field is much
weaker than 5 x 1013 gauss, braking by the
propeller mechanism will be negligible in most
interesting situations. The ejection of
material by the propeller also shuts off the
accretion, so the process is self limiting.
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To summarize
It is very difficult to brake the rotation of
neutron stars born with periods less than about 5
ms but slower rotaters can be braked to almost
arbitrarily slow rates by fallback - if the
surface dipole field is 1014 gauss or more. So,
if the rotation period at birth is 10 ms (Heger
et al) then there may be other ways to slow it
down to an arbitrarily low value. But what about
the much faster values needed for GRBs?
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Question to the Community
How can we have it both ways? Can a few massive
Wolf-Rayet stars die with cores rotating at
nearly the break up speed, while pulsars (in red
supergiants) are still born rotating
slowly? Anisotropic mass loss? Accretion in a
binary? Mergers? It helps to have the WR star
itself rotate rapidly, but this is not the only
problem. WR mass loss rates too high? Heger,
Woosley, and Spruit off by 5? Fall back? Large
B-fields in the explosion?