SELF-SIMILAR SOLUTIONS OF VISCOUS RESISTIVE ACCRETION FLOWS Jamshid Ghanbari Department of Physics, School of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran Department of Physics and Astronomy, San Francisco State University , 1600 Holloway, Francisco, CA 94132
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SELF-SIMILAR SOLUTIONS OF V ISCOUS RESISTIVE ACCRETION FLOWS
SELF-SIMILAR SOLUTIONS OF V ISCOUS RESISTIVE ACCRETION FLOWS. Jamshid Ghanbari. Department of Physics, School of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. Department of Physics and Astronomy, San Francisco State University , 1600 Holloway, San Francisco, CA 94132. Outline. - PowerPoint PPT Presentation
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SELF-SIMILAR SOLUTIONS OF
VISCOUS RESISTIVE ACCRETION FLOWS
Jamshid Ghanbari
Department of Physics, School of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Physics and Astronomy, San Francisco State University , 1600 Holloway, San Francisco, CA 94132
Outline• Accretion Disk
– (1) Descriptions , (2) Models
• Magnetic Fields In Accretion Flows
• Analysis
• Numerical Solutions
• Conclusion
The formation of the accretion disc
In circumstellar
Through mass transfer or stellar wind in the binary system
2
1
3
r
GM
-angular momentum
-Centrifucal and tidal forces
-gravitatianal potential energy to thermal energy
ViscosityViscosity
Converts shear to heat
Heat radiated away
Energy being lost
Gas sinks deeper in the potential well
Viscosity
Gravitationalpotential energy
Radiation
Disc+ viscosityAccretion Disc
Differential Rotation 2v d
R dR
2
1
3
r
GM
Shearing rate 0d
A RdR
Young disk in Taurus
*Active galactic nucleus
*X-ray Binary
Gas orbits around a black holeat the center of the galaxy M87.As it spirals into the hole it heats up and shines brightly.
*Around Black Hole
Accretion Flow (Disk) Models
• Start from Kepler Motion– Optically Thick Standard Disk
– Optically Thin Disk • Irradiation Effect, Relativistic Correction, Advection etc.
– Slim Disk (Optically Thick ADAF)
– Optically Thin ADAF
• Start from Free Fall– Hydrodynamic Spherical Accretion Flow=Bondi
Accretion … transonic flow
Standard Accretion Disk Model• Shakura and Sunyaev (1973)• Optically Thick• Geometrically Thin (r/H>>1)• Rotation = Local Keplerian • Steady, Axisymmetric• Viscosity is proportional to Pressure
Cooling-Dominated Flows: describe the viscous heating of the gas is balanced by local radiative cooling.
Thin accretion disk model was first developed by Shakura & Sunyaev (1973), Novikov & Thorne (1973) to study black holes in binary systems
Global models of thin accretion disk developed by Paczynski &Bisnovatyi-Kogan (1981), Muchotrzeb & Paczynski (1992) which include effects such as the radial pressure and radial energy transfer to study transonic accretion flows around black holes.
Advection-Dominated Accretion Flow
• The advection-dominated accretion flow (ADAF)
the solution was discovered by Ichimaru (1977)some aspects of it were discussed by Rees et al. (1982)
• The key feature of an ADAF
The heat energy released by viscous dissipation is not radiated immediately, as in a thin disk, but is stored in the gas as thermal energy and advected with the flow
ADAFs and X-ray Binaries
The low-dM/dt, two-temperature ADAF model has three properties which make it attractive for applications to X-ray:
• high electron temperature
• low density
• thermal stability
ADAF (Optically Thick and Thin)
Summary
Accretion disk solution
Optically thin
Optically thick
Abramowicz et al. (1995)
Standard diskHigh/Soft state
Advection Dominated Accretion Flow (ADAF)Low/Hard state
Slim disk
unstable
Optically thick ADAF
Real Disks are Magentized
• Magnetorotational Instability
d/ dr
X
Hawley et al
Magnetic fields in accretion flowMagnetic fields in accretion flow
Important roles of magnetic fields• Source of viscosity
• Disk corona (and RIAF) heating
• Cause of flares, producing variability
• Source of radiation (via synchrotron)
• Jet & outflow formation
More important in hot accretion flow
• Standard disk ⇒ Emag < Egas ≪ Egrav ~ Erad
• RIAF/corona ⇒ Emag < Egas ~ Egrav ≫ Erad
~~
Magnetic dynamo in accretion disks
• Magneto-rotational instability (MRI) : B, Bz Br
• Differential rotation : Br B
• Magnetic buoyancy : Br, B Bz
(c) Y. Kato
Differential Rotation
Hawley & Balbus (2002)
Poloidal fields initially 3-phase structure
)8//( 2 BnkT
poloidal fields
Accretion energy to radiationAccretion energy to radiation
reconnection
Magnetic loops
Disk
Dynamo action in disk: Dynamo action in disk: Gravitational energy to B.Gravitational energy to B.
Magnetic loops emerge and Magnetic loops emerge and reconnect in the corona.reconnect in the corona.