Core-Collapse Supernovae: explosions mechanism and jet formation

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Core-Collapse Supernovae explosions mechanism
and jet formation

• G.S.Bisnovatyi-Kogan,
• Space Research Institute, Moscow

VIII  Winter School on Theoretical Physics FROM
NUCLEAR PHYSICS TO ASTROPHYSICS AND COSMOLOGY31
January - 7 February, 2010,  Dubna, Russia
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Content

• 1. Presupernovae
• 2. Development of SN theory
• 3. Magnetorotational mechanism of explosion
• 4. Core collapse and formation of rapidly
  rotating neutron star.
• 5. Magnetorotational supernova explosion
• 6. Magnetorotational instability
• 7. Jet formation in magnetorotational explosion
• 8. Mirror symmetry breaking Rapidly moving
  pulsars.

.
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Supernova is one of the most powerful explosion
in the Universe, energy (radiation and kinetic)
about 1051 egr End of the evolution of massive
stars, with initial mass more than about 8 Solar
mass.
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Tracks in HR diagram of a representative
selection of stars from the main sequence till
the end of the evolution Iben (1985)
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• Explosion mechanisms of
• spherically symmetric star
• Thermonuclear explosion of C-O degenerate core
  (SN Ia)
• Core collapse and formation of a neutron star,
  neutrino deposition
• gravitational energy release up to 5 10 erg,
  carried away by neutrino (SN II, SN Ib,c)

Equal to binding energy of the neutron star
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W.Baade and F.Zwicky, Phys.Rev., 1934, 45, 138
(Jan. 15)
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Astrophysical Journal, vol. 143, p.626 (1966)
The Hydrodynamic Behavior of Supernovae
Explosions
S.Colgate, R.White
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In a simple 1-D model neurino deposition cannot
give enough energy to matter (heating) for SN
explosion Neutrino convection leads to emission
of higher energy neutrino, may transfer more
energy into heating Results are still
controversial
Transformation of the neutrino energy into
kinetic one - ???
1968 PULSARS rapidly rotating, strongly
magnetized neutron stars
Magnetorotational explosion (MRE) transformation
of the rotational energy of the neutron star into
explosion energy by means of the magnetic field
in core collapse SN
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Most of supernova explosions and ejections are
not spherically symmetrical. A lot of stars are
rotating and have magnetic fields. Often we can
see one-side ejections.
Magnetorotational mechanism transforms
rotational energy of the star to the explosion
energy.
In the case of the differential rotation the
rotational energy can be transformed to the
explosion energy by magnetic fields.
.
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Soviet Astronomy, Vol. 14, p.652 (1971)
The Explosion of a Rotating Star As a Supernova
Mechanism.
G.S.Bisnovatyi-Kogan
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The magnetohydrodynamic rotational model of
supernova explosion
Astrophysics and Space Science, vol. 41, June
1976, p. 287-320
Calculations of supernova explosion are made
using the one-dimensional nonstationary equations
of magnetic hydrodynamics for the case of
cylindrical symmetry. The energy source is
supposed to be the rotational energy of the
system (the neutron star in the center and the
surrounding envelope). The magnetic field plays
the role of a mechanism of the transfer of
rotational momentum. The calculations show that
the envelope splits up during the dynamical
evolution of the system, the main part of the
envelope joins the neutron star and becomes
uniformly rotating with it, and the outer part of
the envelope expands with large velocity,
carrying out a considerable part of rotational
energy and rotational momentum. These results
correspond qualitatively with the observational
picture of supernova explosions.
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alpha0.01, t8.5
1-D calculations of magnetorotational explosion .
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1-D calculations of magnetorotational explosion
B.-K., Popov, Samokhin (1976).
Ardeljan, Bisnovatyi-Kogan, Popov (1979), Astron.
Zh., 56, 1244 ?10-2, 10-4, 10-8
?10-2- dashed line, ?10-4- full line
alpha0.1t30
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Angular velocity distribution at different time
moments. 1-D calculations B.-K., Popov, Samokhin
(1976)
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The main results of 1-D calculations
Magneto-rotational explosion (MRE) has an
efficiency about 10 of rotational energy.For
the neutron star mass the ejected mass ?
0.1??,Explosion energy ? 1051 ergEjected mass
and explosion energy depend very weekly on the
parameter ?Explosion time strongly depends on ? .

t??????
Explosion time

• Small ? is difficult for numerical calculations
  with EXPLICIT numerical schemes because of the
  Courant restriction on the time step, stiff
  system of equations
• determines a stiffness.
• In 2-D numerical IMPLICIT schemes have been used.

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Astrophysical Journal, vol. 161, p.541 (1970)
A Numerical Example of the Collapse of a Rotating
Magnetized Star
J.LeBlanc, J.Wilson
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First 2-D calculations.
Jets from collapse of rotating magnetized star
density and magnetic flux LeBlanc and Wilson
(1970) Astrophys. J. 161, 541.
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Difference scheme (Ardeljan, Chernigovskii,
Kosmachevskii, Moiseenko) Lagrangian, on
triangular reconstructing grid, implicite, fully
conservative
Ardeljan N.V, Kosmachevskii K.V., Chernigovskii
S.V., 1987, Problems of construction and research
of conservative difference schemes for
magneto-gas-dynamics, MSU, Moscow (in
Russian) Ardeljan N.V, Kosmachevskii K.V. 1995,
Computational mathematics and modeling, 6,
209 Ardeljan N.V., Bisnovatyi-Kogan G.S.,
Kosmachevskii K.V., Moiseenko S.G., 1996, Astron.
Astrophys. Supl.Ser., 115, 573
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Grid reconstruction (example)
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Presupernova Core Collapse
Ardeljan et. al., 2004, Astrophysics, 47, 47
Equations of state takes into account degeneracy
of electrons and neutrons, relativity for the
electrons, nuclear transitions and nuclear
interactions. Temperature effects were taken into
account approximately by the addition of the
pressure of radiation and of an ideal gas.
Neutrino losses and iron dissociation were taken
into account in the energy equations. A cool iron
white dwarf was considered at the stability
border with a mass equal to the Chandrasekhar
limit. To obtain the collapse we increase the
density at each point by 20 and switch on a
uniform rotation.
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Gas dynamic equations with a self-gravitation,
realistic equation of state, account of neutrino
losses and iron dissociation
F(?,T) - neutrino losses
-iron dissociation energy
Neutrino losses URCA processes, pair
annihilation, photo production of neutrino,
plasma neutrino
Approximation of tables from Ivanova, Imshennik,
Nadyozhin,1969
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Initial State Spherically Symmetric
configuration, Uniform rotation with angular
velocity 2.519 (1/???). Temperature distribution
20 Grid
Density contours
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Maximal compression state
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Shock wave does not produce SN explosion
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Distribution of the angular velocity
The period of rotation at the center of the young
neutron star is about 0.001 sec
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2-D magnetorotational supernova
N.V.Ardeljan, G.S.Bisnovatyi-Kogan, S.G.Moiseenko
MNRAS, 359, 333 (2005)
A magnetorotational core-collapse model with jets
S. G. Moiseenko, G. S. Bisnovatyi-Kogan and N. V.
Ardeljan MNRAS 370, 501 (2006)
Different Magneto-rotational Supernovae G. S.
Bisnovatyi-Kogan, S. G. Moiseenko, and N. V.
Ardelyan Astronomy Reports (2008) 52, No. 12,
997-1008.
Equations MHD self-gravitation, infinite
conductivity.

Axial symmetry ( ) , equatorial symmetry (z0).
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Initial toroidal current Jf
(free boundary)
Biot-Savarat law
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Initial magnetic field quadrupole-like symmetry
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Toroidal magnetic field amplification.
pink maximum_1 of Hf2
blue maximum_2 of Hf2
Maximal values of Hf2.5 10(16)G
The magnetic field at the surface of the neutron
star after the explosion is H4 ?1012 Gs
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Temperature and velocity field
Specific angular momentum
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Rotational energy Magnetic poloidal
energy Magnetic toroidal energy Kinetic poloidal
energy
Neutrino losses
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Particle is considered ejected if its kinetic
energy is greater than its potential energy
(alpha10-6)
Ejected energy
Ejected mass 0.14M?
0.6 10 ???
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Jet formation in MRE
Moiseenko et al. Astro-ph/0603789
Dipole-like initial magnetic field
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Jet formation in MRE entropy evolution
Jet formation in MRE velocity field evolution
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Jet formation in MRE (dipole magnetic field)
Energy of explosion?0.61051???
Ejected mass ? 0.14M?
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MR supernova different core masses BK, SM, Ard
(2008)
Dependence of the MR supernova explosion energy
on the core mass
Energy of the explosion of an MR supernova as a
function of the initial mass of the core for
various specific rotational energies before the
start of the evolution of the magnetic field
(before the collapse), Erot/Mcore (0.39-0.40) x
1019 erg/g (solid curve) and Erot/Mcore
(0.19-0.23) x 1019 erg/g (dashed curve).
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Magnetorotational explosion at different
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Magnetorotational instability? exponential growth
of magnetic fields. Dungey 1958,Velikhov 1959,
Spruit 2002, Akiyama et al. 2003
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Dependence of the explosion time on
2-D calculattions Explosion time
1-D calculattions Explosion time
(for small ?)
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Inner region development of magnetorotational
instability (MRI)
Toroidal (color) and poloidal (arrows) magnetic
fields (quadrupole)
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Toy model of the MRI development expomemtial
growth of the magnetic fields
at initial stages
MRI leads to formation of multiple poloidal
differentially rotating vortexes. Angular
velocity of vortexes is growing (linearly) with a
growth of H?.
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Why time of MRE depends logarithmically on alpha
in presence of MRI
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Toroidal magnetic field (color) and poloidal
velocity field (dipole)
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CP violation in week processes in regular
magnetic field does not work, because MRI leads
to formation of highly chaotic field.
Astro-ph/0510229 MULTI-DIMENSIONAL RADIATION
HYDRODYNAMIC SIMULATIONS OF PROTONEUTRON STAR
CONVECTION L. Dessart, A. Burrows, E. Livne, C.D.
Ott
PNS convection is thus found to be a secondary
feature of the core-collapse phenomenon, rather
than a decisive ingredient for a successful
explosion.
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Violation of mirror symmetry of magnetic
field (Bisnovatyi-Kogan, Moiseenko, 1992 Astron.
Zh., 69, 563 (SvA, 1992, 36, 285)

1. Initial toroidal field
2. Initial dipole field
3. Generated toroidal field
4. Resulted toroidal field

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In reality we have dipole quadrupole other
multipoles
Wang J.C.L., Sulkanen M.E., Lovelace R.V.L.
Asymmetry of Solar magnetic field
The North-South Coronal Asymmetry with Inferred
Magnetic Quadrupole Osherovich, V. A. et al..
Solar Wind Nine, Proceedings of the Ninth
International Solar Wind Conference, Nantucket,
MA, October 1998. AIP Conference Proceedings,
471, 721 (1999)

In magnetorotational supernova Kick velocity,
along the rotational axis, due to the asymmetry
of the magnetic field up to 300km/sec
Kich along the rotational axis even in the case
of inclined dipole jets along rotational axis.
Hanawa et al. AIP Conf. Series 359, 158 (2006)
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Bisnovatyi-Kogan, 1993, Astron. Ap. Transactions
3, 287
Interaction of the neutrino with asymmetric
magnetic field
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Dependence of the week interaction cross-section
on the magnetic field strength lead to the
asymmetric neutrino flux and formation of rapidly
mooving pulsars due to the recoil action as well
as rapidly moving black holes.
Neutrino heat conductivity
neutrino opacity
energy flux
The anisotropy of the flux
Kick velocity along the rotational axis
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Approximate estimation
Important to do Numerical simulations without
mirror symmetry Accurate formulae for neutrino
processes at high magnetic field
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S. Johnston et al. astro/ph 0510260 (MNRAS, 2005,
364, 1397)
Evidence for alignment of the rotation and
velocity vectors in pulsars
We present strong observational evidence for a
relationship between the direction of a pulsar's
motion and its rotation axis. We show carefully
calibrated polarization data for 25pulsars, 20
of which display linearly polarized emission from
the pulse longitude at closest approach to the
magnetic pole we conclude that the velocity
vector and the rotation axis are aligned at
birth.

W.H.T. Vlemmings et al. astro-ph/0509025 (Mm.
SAI, 2005, 76, 531)
Pulsar Astrometry at the Microarcsecond Level
Determination of pulsar parallaxes and proper
motions addresses fundamental astrophysical
questions. We have recently finished a VLBI
astrometry project to determine the proper
motions and parallaxes of 27 pulsars, thereby
doubling the total number of pulsar parallaxes.
Here we summarize our astrometric technique and
present the discovery of a pulsar moving in
excess of 1000 kms, PSR B150855.
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Astro-ph/0708.4251
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Conclusions

• In the magnetorotational explosion (MTE) the
  efficiency of transformation of rotational energy
  into the energy of explosion is 10. This is
  enough for producing core collapse SN from
  rapidly rotating magnetized neutron star.
• Development of magneto-rotational instability
  strongly accelerate MRE, at lower values of the
  initial magnetic fields.
• The new born neutron star has inside a large
  (about 1014 Gauss) chaotic magnetic field.
• 4. Jet formation is possible for dipole-like
  initial topology of the field possible relation
  to cosmic gamma-ray bursts equatorial ejection
  happens at prevailing of the quadrupole-like
  component.
• 5. Violation of mirror symmetry of magnetic
  field lead to asymmetry in MRE explosion, and in
  the neutrino flux, producing kick.
• ..
• .