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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 COSMOLOGY 31 January - 7 February, 2010,   Dubna , Russia. Content.

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Core-Collapse Supernovae: explosions mechanism and jet formation


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    1. 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

    2. 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.

    3. Supernova is one of the most powerful explosion in the Universe, energy (radiation and kinetic) about 10^51 egr End of the evolution of massive stars, with initial mass more than about 8 Solar mass.

    4. Tracks in HR diagram of a representative selection of stars from the main sequence till the end of the evolution Iben (1985)

    5. 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

    6. W.Baade and F.Zwicky, Phys.Rev., 1934, 45, 138 (Jan. 15)

    7. Astrophysical Journal, vol. 143, p.626 (1966) The Hydrodynamic Behavior of Supernovae Explosions S.Colgate, R.White

    8. 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

    9. Most of supernova explosions and ejections are not spherically symmetrical. A lot of stars arerotating 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. .

    10. Soviet Astronomy, Vol. 14, p.652 (1971) The Explosion of a Rotating Star As a Supernova Mechanism. G.S.Bisnovatyi-Kogan

    11. 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.

    12. alpha=0.01, t=8.5 1-D calculations of magnetorotational explosion .

    13. 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 alpha=0.1t=30

    14. Angular velocity distribution at different time moments. 1-D calculations B.-K., Popov, Samokhin (1976)

    15. 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  0.1М,Explosion energy 1051 ergEjected mass and explosion energy depend very weekly on the parameter Explosion time strongly depends on  . tвзрыва~ Explosion time = • Small is difficult for numerical calculations with EXPLICIT numerical schemesbecause of the Courant restriction on the time step, “stiff” system of equations: • determines a “stiffness”. In 2-D numerical IMPLICIT schemes have been used.

    16. Astrophysical Journal, vol. 161, p.541 (1970) A Numerical Example of the Collapse of a Rotating Magnetized Star J.LeBlanc, J.Wilson

    17. First 2-D calculations. Jets from collapse of rotating magnetized star: density and magnetic flux LeBlanc and Wilson (1970) Astrophys. J. 161, 541.

    18. 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., KosmachevskiiK.V., Moiseenko S.G., 1996, Astron. Astrophys. Supl.Ser., 115, 573

    19. Grid reconstruction (example)

    20. 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.

    21. 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

    22. Initial State Spherically Symmetric configuration, Uniform rotation with angular velocity 2.519 (1/сек). Temperature distribution: + 20%Grid Density contours

    23. Maximal compression state

    24. Shock wave does not produce SN explosion :

    25. Distribution of the angular velocity The period of rotation at the center of the young neutron star is about 0.001 sec

    26. 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-Koganand N. V. ArdeljanMNRAS 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 (z=0).

    27. Initial toroidal current Jφ (free boundary) Biot-Savarat law

    28. Initial magnetic field –quadrupole-like symmetry

    29. Toroidal magnetic field amplification. pink – maximum_1 of Hf^2 blue – maximum_2 of Hf^2 Maximal values of Hf=2.5 10(16)G The magnetic field at the surface of the neutron star after the explosion is H=4 1012 Gs

    30. Temperature and velocity field Specific angular momentum

    31. Rotational energy Magnetic poloidal energy Magnetic toroidal energy Kinetic poloidal energy Neutrino losses

    32. Particle is considered “ejected” if its kinetic energy is greater than its potential energy (alpha=10^{-6}) Ejected energy Ejected mass 0.14M 0.6 10 эрг

    33. Jet formation in MRE Moiseenko et al. Astro-ph/0603789 Dipole-like initial magnetic field

    34. Jet formation in MRE: entropy evolution Jet formation in MRE: velocity field evolution

    35. Jet formation in MRE:(dipole magnetic field) Energy of explosion0.6·1051эрг Ejected mass  0.14M

    36. 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).

    37. Magnetorotational explosion at different

    38. Magnetorotational instabilityexponential growth of magnetic fields. Dungey 1958,Velikhov 1959, Spruit 2002, Akiyama et al. 2003

    39. Dependence of the explosion time on 2-D calculattions: Explosion time 1-D calculattions: Explosion time (for small)

    40. Inner region: development of magnetorotational instability (MRI) Toroidal (color) and poloidal (arrows) magnetic fields (quadrupole)

    41. 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.

    42. Why time of MRE depends logarithmically on alpha in presence of MRI

    43. Toroidal magnetic field (color) and poloidal velocity field (dipole)

    44. 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 RADIATIONHYDRODYNAMIC SIMULATIONS OF PROTONEUTRON STARCONVECTION L. Dessart, A. Burrows, E. Livne, C.D. Ott PNS convection is thus found to be a secondary feature of the core-collapse phenomenon, ratherthan a decisive ingredient for a successful explosion.

    45. Violation of mirror symmetry of magnetic field (Bisnovatyi-Kogan, Moiseenko, 1992 Astron. Zh., 69, 563 (SvA, 1992, 36, 285) • Initial toroidal field • Initial dipole field • Generated toroidal field • Resulted toroidal field

    46. 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)

    47. Bisnovatyi-Kogan, 1993, Astron. Ap. Transactions 3, 287 Interaction of the neutrino with asymmetric magnetic field

    48. Dependenceof the week interaction cross-section on the magnetic fieldstrength lead to the asymmetricneutrino flux and formation of rapidlymooving pulsars due to the recoil action as well asrapidly moving black holes. Neutrino heat conductivity neutrino opacity energy flux The anisotropy of the flux Kick velocity along the rotational axis