NeutrinoPowered Explosions

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Lecture 14 Neutrino-Powered Explosions Mixing,
Rotation, and Making Black Holes
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Baade and Zwicky, Proceedings of the National
Academy of Sciences, (1934)
With all reserve we advance the view that a
supernova represents the transition of an
ordinary star into a neutron star consisting
mainly of neutrons. Such a star may possess a
very small radius and an extremely high density.
As neutrons can be packed much more closely than
ordinary nuclei and electrons, the gravitational
packing energy in a cold neutron star may become
very large, and under certain conditions, may
far exceed the ordinary nuclear packing fractions
...
Chadwick discovered the neutron in 1932 though
the idea of a neutral massive particle had been
around since Rutherford, 1920.
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For the next 30 years little progress was made
though there were speculations Hoyle (1946)
- supernovae are due to a rotational
bounce!! Hoyle and Fowler
(1960) Type I supernovae are due to
the explosions
of white dwarf stars Fowler and Hoyle (1964)
other supernovae are due to thermonuclear
burning in
massive stars aided by
rotation and magnetic fields
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The explosion is mediated by neutrino energy
transport ....
Colgate and White, (1966), ApJ, 143, 626 see
also Arnett, (1966), Canadian J Phys, 44,
2553 Wilson, (1971), ApJ, 163, 209
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But there were fundamental problems in the
1960s and early 1970s that precluded a
physically complete description

• Lack of realistic progenitor models (addressed
  in the 80s)
• Neglect of weak neutral currents discovered
  1974
• Uncertainty in the equation of state at
  super-nuclear densities (started to be addressed
  in the 80s)
• Inability to do realistic multi-dimensional
  models (still in progress)
• Missing fundamental physics (still discussed)

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BBAL 1979

• The explosion was low entropy
• Heat capacity of excited states kept
  temperature low
• Collapse continues to nuclear density and
  beyond
• Bounce on the nuclear repulsive force
• Possible strong hydrodynamic explosion
• Entropy an important concept

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What is the neutrino emission of a young neutron
star?
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Time-integrated spectra Woosley, Wilson, Mayle
(1984)
Typical values for supernovae electron
antineutrinos only
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Wilson 20 M-sun
Myra and Burrows, (1990), ApJ, 364, 222
Neutrino luminosities of order 1052.5 are
maintained for several seconds after an initial
burst from shock break out. At late times the
luminosities in each flavor are comparable though
the ??- and ? - neutrinos are hotter than the
electron neutrinos.
Woosley et al. (1994), ApJ,, 433, 229
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K II 2140 tons H2O IMB 6400 tons Cerenkov
radiation from n (p,n)e - dominates
n(e-,e-)n - relativistic e
all flavors n
less than solar neutrino flux but neutrinos
more energetic individually.
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Neutrino Burst Properties
Time scale
Very approximate
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Temperature
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See also conference proceedings by Wilson
(1982)
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20 Solar Masses Mayle and Wilson (1988)
rbounce 5.5 x 1014 g cm-3
Explosion energy at 3.6 s 3 x 1050 erg
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Mayle and Wilson (1988)
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Herant and Woosley, 1995. 15 solar mass star.
successful explosion. (see also Herant, Benz,
Colgate (1992), ApJ, 395, 642)
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Energy deposition here drives convection Bethe,
(1990), RMP, 62, 801 (see also Burrows,
Arnett, Wilson, Epstein, ...)
Velocity
gain radius
radius
Neutrinosphere
Infall
Accretion Shock
Inside the shock, matter is in approximate
hydrostatic equilibrium. Inside the gain radius
there is net energy loss to neutrinos.
Outside there is net energy gain from neutrino
deposition. At any one time there is about 0.1
solar masses in the gain region absorbing a few
percent of the neutrino luminosity.
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Burrows (2005)
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8.8-Solar mass Progenitor of Nomoto
Neutrino-driven Wind Explosion
Dessart, Burrows et al. 2007 Burrows 1987
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Burrows, Hayes, and Fryxell, (1995), ApJ, 450, 830
15 Solar masses exploded with an energy of
order 1051 erg. see also Janka and Mueller,
(1996), AA, 306, 167
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At 408 ms, KE 0.42 foe, stored dissociation
energy is 0.38 foe, and the total explosion
energy is still growing at 4.4 foe/s
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Mezzacappa et al. (1998), ApJ, 495, 911. Using
15 solar mass progenitor WW95. Run for 500
ms. 1D flux limited multi-group neutrino
transport coupled to 2D hydro. No explosion.
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Beneficial Aspects of Convection

• Increased luminosity from beneath the
  neutrinosphere
• Cooling of the gain radius and increased
  neutrino absorption
• Transport of energy to regions far from the
  neutrinosphere (i.e., to where the shock is)

Also Helpful

• Decline in the accretion rate and accompanying
  ram pressure as time passes
• A shock that stalls at a large radius
• Accretion sustaining a high neutrino luminosity
  as time passes (able to continue at some
  angles in multi-D calculations even as the
  explosion develops).

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Scheck et al. (2004)
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Challenges

• Tough physics nuclear EOS, neutrino opacities
• Tough problem computationally must be 3D
  (convection is important). 6 flavors of
  neutrinos out of thermal equilibrium
• (thick to thin region crucial). Must be
  follwoed with multi-energy group and
  multi-angles
• Magnetic fields and rotation may be important
• If a black hole forms, problem must be done
  using relativistic (magnto-)hydrodynamics
  (general relativity, special relativity,
  magnetohydrodynamics)

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When Massive Stars Die, How Do They Explode?
Neutron Star Neutrinos
Neutron Star Rotation
Black Hole Rotation
Colgate and White (1966) Arnett Wilson Bethe Janka
Herant Burrows Fryer Mezzacappa etc.
Bodenheimer and Woosley (1983) Woosley
(1993) MacFadyen and Woosley (1999) Narayan (2004)
Hoyle (1946) Fowler and Hoyle (1964) LeBlanc and
Wilson (1970) Ostriker and Gunn
(1971) Bisnovatyi-Kogan (1971) Meier Wheeler Usov
Thompson etc
All of the above?
10 20
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The answer depends on the mass of the core of
helium and heavy elements when the star dies and
on its angular momentum distribution.
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Rotationally Powered Models
Common theme Need iron core rotation at
death to correspond to a pulsar of lt 5 ms
period if rotation and B-fields are to matter.
This is much faster than observed in common
pulsars.A concern If calculate the
presupernova evolution with the same efficient
magnetic field generating algorithms as used in
some core collapse simulations, will it be
rotating at all?
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e.g. Wheeler, Yi, Hoeflich, Wang (2001)
Usov (1992, 1994, 1999)
The ms Magnetar Model
But now there exist magnetars and AXPs
But this much angular momentum is needed in all
modern GRB models
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The ms Magnetar Model
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What is the distribution of j(m) when the star
dies?
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no mass loss or B-field
with mass loss
At its equator, j for the Crab pulsar is 2 x 1014
cm2 s-1
with mass loss and B fields
These results are from Heger et al (2000) and
(2005).
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B-fields
The magnetic torques are also important for this.
The magnitude of the torque is approximately
Spruit and Phinney, Nature, 393, 139, (1998)
Assumed Br approximately equal Bf and
that Bf was from differential
winding. Got nearly stationary
helium cores after red giant formation. Pulsars
get rotation from
kicks. Spruit, AA, 349, 189, (1999) and 381,
923, (2002) Br given by currents
from an interchange instability. Much
smaller than Bf. Torques greatly
reduced Heger, Woosley, and Spruit, ApJ, in
press (2005) implemented these in stellar
models.
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Magnetic torques as described by Spruit, AA,
381, 923, (2002)
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Aside Note an interesting trend. Bigger stars
are harder to explode using neutrinos because
they are more tightly bound and have big iron
cores. But they also rotate faster when they die.
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Some older calculations with and without magnetic
torques.
He core 4 6 9
Magnetic torques as prescribed by Spruit,
(2001), AA, 381, 923
1.3 for bug fix
note models b d (with B-fields) and e
(without)
note dependence on mass
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Mixing During the Explosion
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The Reverse Shock and Rayleigh-Taylor Instability
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Example
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Mixing by Rayleigh-Taylor Instability
As the shock ,oves though regions of increasing
rr3, it slows. The deceleration is communicated
back towards the center by pressure waves. The
density increases as one goes towards the center.
The situation is thus RT unstable.
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Diagnosing an explosion
Kifonidis et al. (2001), ApJL, 531, 123
Left - Cas-A SNR as seen by the Chandra
Observatory Aug. 19, 1999 The red material on
the left outer edge is enriched in iron. The
greenish-white region is enriched in silicon.
Why are elements made in the middle on the
outside? Right - 2D simulation of explosion
and mixing in a massive star - Kifonidis et al,
Max Planck Institut fuer Astrophysik
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25 solar mass supernova, 1.2 x 1051 erg explosion
2D
Shock
log r
RT-mixing
Calculation using modified FLASH code Zingale
Woosley
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Prompt Black Hole Formation
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PreSN Models
Black hole formation may have been more frequent
early in the universe
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Woosley and Weaver (1995)
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Fryer, ApJ, 522, 413, (1999)
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Fryer (1999)
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100 Solar Masses
Woosley, Mayle, Wilson, and Weaver (1985)
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Fall-Back and Delayed Black Hole Formation
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Gravitational Binding Energy of the Presupernova
Star
solar
low Z
This is just the binding energy outside the iron
core. Bigger stars are more tightly bound and
will be harder to explode. The effect is
more pronounced in metal-deficient stars.
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Solar Metallicity Supernovae
Woosley and Weaver (1995)
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mass cut at Fe-core
(after fall back)
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