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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
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
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Czech double donut
Czech triple donut
test particles approximation (very low densities)
kinetic theory (low densities)
MHD (high densitites)
Basic equations
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basic GRMHD equations
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our toy model - test non-conductive charged fluid
- no selfconsistence (for now)
- axial symmetry and azimuthal motion
Pressure equations – general case
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pressure equations
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integrability condition
integrable
non-integrable
integrable
Pressure equations in RN spacetime
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Geometry
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Electric field
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Pressure equations
Equation of state – density equations
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Equation of state
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Angular momentum distribution
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Charge distribution
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Density equation
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Boundary conditions
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
Mass and charge of tori
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Total charge
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Total mass
Summary
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 ReissnerNordström 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, …)
1. We are going to include the electrostatic correction interaction into the
equation of state
2. 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
Acknowledgement
Trieste 2011 – Mignon hotel
Petr
Zdenek
John
Vladimir
Claudio
my dish