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Jiří Kovář, Petr Slan ý, Vladimír Karas , Zdeněk Stuchlík Claudio Cremaschini and John Miller

Vznik této prezentace byl podpořen projektem CZ.1.07/2.3.00/09.0138 Tato prezentace slouží jako vzdělávací materiál . Charged tori near compact objects. Institute of Physics Silesian University in Opava Czech Republic. Astronomical Institute Czech Academy of Sciences Prague.

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Jiří Kovář, Petr Slan ý, Vladimír Karas , Zdeněk Stuchlík Claudio Cremaschini and John Miller

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  1. Vznik této prezentace byl podpořen projektem CZ.1.07/2.3.00/09.0138Tato prezentace slouží jako vzdělávací materiál.

  2. Charged tori near compact objects Institute of Physics Silesian University in Opava Czech Republic Astronomical Institute Czech Academy of Sciences Prague International School for Advanced Studies, SISSA and INFN, Trieste, Italy Jiří Kovář, Petr Slaný, Vladimír Karas, Zdeněk Stuchlík Claudio Cremaschini and John Miller

  3. Beginning of the story Halo orbits existence and basic properties Kovář, Stuchlík and Karas, 2008, Class. Quantum Gravity Kovář, Kopáček, Karas and Stuchlík, 2010, Class. Quantum Gravity Kopáček, Karas, Kovář and Stuchlík, 2010, The Astrophysical Journal

  4. Effective potential and halo orbits Neutron star

  5. The crazy idea CHARGED OFF-EQUATORIAL TORI Polish donut Czech double donut Czech triple donut • test particles approximation (very low densities) • kinetic theory (low densities) • MHD (high densitites)

  6. Basic equations • basic GRMHD equations • our toy model - test non-conductive charged fluid • - no selfconsistence (for now) • - axial symmetry and azimuthal motion

  7. Pressure equations – general case • pressure equations • integrability condition integrable integrable non-integrable

  8. Pressure equations in RN spacetime • Geometry • Electric field • Pressure equations

  9. Equation of state – density equations • Equation of state • Angular momentum distribution • Charge distribution • Density equation • Boundary conditions

  10. Pressure and density profiles Positively charged torus

  11. Correction function and charge density Positively charged torus

  12. Pressure and density profiles Negatively charged torus

  13. Correction function and charge density Negatively charged torus

  14. Mass and charge of tori • Total charge • Total mass

  15. Summary • We have built a GR toy model of charged thick dielectric torus rotating in gravitational and electromagnetic fields • We have tested it and presented it on the background of charged Reissner-Nordström black hole, considering physically relevant (astrophysically unsuitable) parameters of the fluid • We are going to test it in more astrophysically relevant cases (dipole magnetic field, reasonable parameters of the fluid, …) • We are going to include the electrostatic correction interaction into the equation of state • We are going to construct the off-equatorial charged tori (for now, realizing it in the Newtonian way – talk by Petr Slaný) • Kovář, Slaný, Stuchlík, Karas, Cremaschini, Miller, 2011, Physical Review D

  16. Acknowledgement Trieste 2011 – Mignon hotel Petr Zdenek John Vladimir Claudio my dish

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