1. Моделирование магниторотационных процессов в коллапсирующих сверхновых и развитие Магнито-Дифференциально- Ротационной неустойчивости Сергей Моисеенко, Геннадий Бисноватый-Коган Институт космических исследований, Москва

2. Core-collapsed supernovae are brightest events in the Universe. Crab nebula Cas A SN1987A

3. Magnetorotational mechanism for the supernova explosion was suggested by Bisnovatyi-Kogan (1970) Amplification of magnetic fields due to differential rotation, angular momentum transfer by magnetic field. Part of the rotational energy is transformed to the energy of explosion

4. Basic equations: MHD +self-gravitation, infinite conductivity: Axis symmetry ( ) and equatorial symmetry (z=0) are supposed. Notations: Additional condition divH=0

5. Magnetorotational supernova in 1D Example: Bisnovaty-Kogan et al. 1976, Ardeljan et al. 1979

6. (Thanks to E.A.Skiba) (Thanks to E.A.Skiba)

7. Presupernova Core Collapse Equations of state take 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 radiation pressure and an ideal gas. Neutrino losses were taken into account in the energy equations. A cool white dwarf was considered at the stability limit with a mass equal to the Chandrasekhar limit. To obtain the collapse we increase the density at each point by 20% and we also impart uniform rotation on it.

8. Operator-difference scheme (finite volumes) Ardeljan & Kosmachevskii Comp. and Math. Modeling 1995, 6, 209 and references therein Method of basic operators (Samarskii) – grid analogs of basic differential operators: GRAD(scalar) ( differential ) ~ GRAD(scalar) ( grid analog ) DIV(vector) ( differential ) ~ DIV(vector) ( grid analog ) CURL(vector) ( differential ) ~ CURL(vector) ( grid analog ) GRAD(vector) ( differential ) ~ GRAD(vector) ( grid analog ) DIV(tensor) ( differential ) ~ DIV(tensor) ( grid analog ) Implicit scheme. Time step restrictions are weaker for implicit schemes (no CFL condition). The scheme is Lagrangian=> conservation of angular momentum. Lagrangian, implicit, triangular grid with rezoning, completely conservative

9. Operator-difference scheme for hydro equations where

10. Example of calculation with the triangular grid

11. Initial magnetic field –quadrupole-and dipole-like symmetries

12. Temperature and velocity field Specific angular momentum Magnetorotational explosion for the quadruppole-like magnetic field

13. Magnetorotational explosion for the dipole-like magnetic field

14. Time evolution of different types of energies

15. Ejected energy and mass Ejected energy Particle is considered “ejected” – if its kinetic energy is greater than its potential energy Ejected mass 0.14M 

16. Magnetorotational explosion for the different Magnetorotational instability  mag. field grows exponentially (Dungey 1958,Velikhov 1959, Chandrasekhar1970,Tayler 1973, Balbus & Hawley 1991, Spruit 2002, Akiyama et al. 2003…)

17. Dependence of the explosion time from (for small  ) Example:

18. MRI in 2D – Tayler instability Tayler, R. MNRAS 1973

19. Toy model for MDRI in the magnetorotational supernova beginning of the MRI => formation of multiple poloidal differentially rotating vortexes in general we may approximate: Assuming for the simplicity that is a constant during the first stages of MRI, and taking as a constant we come to the following equation: at the initial stage of the process

20. B_0=10(9)GB_0=10(12)G MDRI No MDRI

21. Toroidal to poloidal magnetic energy relation MDRI development

22. recently P.Mosta et al. MR supernovae in 3D ApJL 2014, 785, L29 Authors observe no runaway explosion by the end of the full 3D simulation at 185 ms after bounce. Detailed 3D MR supernova simulations are necessary. Mikami H., Sato Y., Matsumoto T.,Hanawa, T. ApJ 2008, 683, 357 ( no neutrino) 3D simulations

23. 3D thetrahedral grid 3D – work in progress

24. Conclusions Magnetorotational mechanism (MRM) produces enough energy for the core collapse supernova. The MRM is weakly sensitive to the neutrino cooling mechanism and details of the EoS. MR supernova shape depends on the configuration of the magnetic field and is always asymmetrical. MRDI is developed in MR supernova explosion.