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Vznik této prezentace byl podpořen projektem CZ.1.07/2.3.00/09.0138
Tato prezentace slouží jako vzdělávací materiál.
Jiří Kovář, Petr Slaný, Vladimír Karas, Zdeněk Stuchlík Claudio Cremaschini and John Miller
Institute of PhysicsSilesian University in Opava
Czech Republic
Charged tori near compact objects
Astronomical Institute Czech Academy of Sciences
Prague
International School for Advanced Studies, SISSA and INFN, Trieste, Italy
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
Effective potential and halo orbits Neutron star
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)
• our toy model - test non-conductive charged fluid - no selfconsistence (for now) - axial symmetry and azimuthal motion
• basic GRMHD equations
Basic equations
• pressure equations
• integrability condition
Pressure equations – general case
non-integrable integrable
integrable
• Geometry
• Electric field
• Pressure equations
Pressure equations in RN spacetime
• Equation of state
• Angular momentum distribution
• Charge distribution
• Density equation
• Boundary conditions
Equation of state – density equations
Pressure and density profiles Positively charged torus
Correction function and charge density Positively charged torus
Pressure and density profiles Negatively charged torus
Correction function and charge density Negatively charged torus
• Total charge
• Total mass
Mass and charge of tori
1. We have built a GR toy model of charged thick dielectric torus rotating in gravitational and electromagnetic fields
2. 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
3. We are going to test it in more astrophysically relevant cases (dipole magnetic field, reasonable parameters of the fluid, …)
4. We are going to include the electrostatic correction interaction into the equation of state
5. 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
Summary
Acknowledgement
Claudio
Vladimir
John
Zdenek
PetrTrieste 2011 – Mignon hotel
my dish
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