Core-Collapse Supernovae: explosions mechanism and jet formation G.S.Bisnovatyi-Kogan,

Space Research Institute, Moscow

VIII Winter School on Theoretical PhysicsFROM NUCLEAR PHYSICS TO ASTROPHYSICS AND COSMOLOGY 31 January - 7 February, 2010, Dubna, Russia

Content 1. Presupernovae 2. Development of SN theory 3. Magnetorotational mechanism of explosion4. 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. .

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.

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

Explosion mechanisms ofspherically symmetric star

Thermonuclear explosion of C-O degenerate core (SN Ia)

Core collapse and formation of a neutron star, neutrino depositiongravitational energy release up to 5 10 erg, carried away by neutrino (SN II, SN Ib,c)Equal to binding energy of the neutron star

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

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

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 Transformation of the neutrino energy into kinetic one - ???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 controversial1968: PULSARS rapidly rotating, strongly magnetized neutron stars

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..

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

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.

alpha=0.01, t=8.51-D calculations of magnetorotational explosion.

1-D calculations of magnetorotational explosion B.-K., Popov, Samokhin (1976).

alpha=0.1t=30Ardeljan, Bisnovatyi-Kogan, Popov (1979), Astron. Zh., 56, 1244 =10-2, 10-4, 10-8=10-2- dashed line, =10-4- full line

Angular velocity distribution at different time moments.

1-D calculationsB.-K., Popov, Samokhin (1976)

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~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.

Explosion time =

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

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

Difference scheme (Ardeljan, Chernigovskii, Kosmachevskii, Moiseenko)

Lagrangian, on triangular reconstructing grid, implicite, fully conservativeArdeljan 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, 209Ardeljan N.V., Bisnovatyi-Kogan G.S., Kosmachevskii K.V., Moiseenko S.G., 1996, Astron. Astrophys. Supl.Ser., 115, 573

Grid reconstruction (example)

Presupernova Core CollapseEquations 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. Ardeljan et. al., 2004, Astrophysics, 47, 47

-iron dissociation energy F(,T) - neutrino lossesGas dynamic equations with a self-gravitation, realistic equation of state, account of neutrino losses and iron dissociationNeutrino losses:URCA processes, pair annihilation, photo production of neutrino, plasma neutrino Approximation of tables from Ivanova, Imshennik, Nadyozhin,1969

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

Maximal compression state

Shock wave does not produce SN explosion :

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

2-D magnetorotational supernovaEquations: MHD + self-gravitation, infinite conductivity.Axial symmetry ( ) , equatorial symmetry (z=0). N.V.Ardeljan, G.S.Bisnovatyi-Kogan, S.G.Moiseenko MNRAS, 359, 333 (2005)A magnetorotational core-collapse model with jetsS. 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.

Initial toroidal current JBiot-Savarat law(free boundary)

Initial magnetic field quadrupole-like symmetry

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

Temperature and velocity fieldSpecific angular momentum

Neutrino losses Rotational energyMagnetic poloidal energyMagnetic toroidal energy Kinetic poloidal energy

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

Dipole-like initial magnetic fieldJet formation in MREMoiseenko et al. Astro-ph/0603789

Jet formation in MRE: velocity field evolutionJet formation in MRE: entropy evolution

Jet formation in MRE: (dipole magnetic field)Energy of explosion0.61051 Ejected mass 0.14M

MR supernova different core massesBK, SM, Ard (2008)Dependence of the MR supernova explosion energy on the core massEnergy 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).

Magnetorotational explosion at different

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

Dependence of the explosion time on(for small )1-D calculattions:Explosion time2-D calculattions:Explosion time

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

Toy model of the MRI development: expomemtial growth of the magnetic fieldsMRI leads to formation of multiple poloidal differentially rotating vortexes. Angular velocity of vortexes is growing (linearly) with a growth of H. at initial stages

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

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

CP violation in week processes in regular magnetic field: does not work, because MRI leads to formation of highly chaotic field. PNS convection is thus found to be a secondary feature of the core-collapse phenomenon, rather than a decisive ingredient for a successful explosion.Astro-ph/0510229MULTI-DIMENSIONAL RADIATION HYDRODYNAMIC SIMULATIONS OF PROTONEUTRON STAR CONVECTIONL. Dessart, A. Burrows, E. Livne, C.D. Ott

Violation of mirror symmetry of magnetic field(Bisnovatyi-Kogan, Moiseenko, 1992 Astron. Zh., 69, 563 (SvA,1992, 36, 285)Initial toroidal fieldInitial dipole fieldGenerated toroidal fieldResulted toroidal field

In magnetorotational supernovaKick velocity, along the rotational axis, due to the asymmetry of the magnetic field ~ up to 300km/secIn reality we have dipole + quadrupole + other multipoles Wang J.C.L., Sulkanen M.E., Lovelace R.V.L.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) Asymmetry of Solar magnetic fieldKich along the rotational axis even in the case of inclined dipole jets along rotational axis. Hanawa et al. AIP Conf. Series 359, 158 (2006)

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

Kick velocity along the rotational axisDependence 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 conductivityenergy fluxneutrino opacityThe anisotropy of the flux

Approximate estimationImportant to do:

Numerical simulations without mirror symmetry

Accurate formulae for neutrino processes at high magnetic field

S. Johnston et al. astro/ph 0510260 (MNRAS, 2005, 364, 1397) Evidence for alignment of the rotation and velocity vectors in pulsarsWe 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 B1508+55.

Astro-ph/0708.4251

ConclusionsIn 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 10^14 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.

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