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