self-similar solutions of viscous resistive accretion flows jamshid ghanbari department of physics,...
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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
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Outline• Accretion Disk
– (1) Descriptions , (2) Models
• Magnetic Fields In Accretion Flows
• Analysis
• Numerical Solutions
• Conclusion
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The formation of the accretion disc
In circumstellar
Through mass transfer or stellar wind in the binary system
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2
1
3
r
GM
-angular momentum
-Centrifucal and tidal forces
-gravitatianal potential energy to thermal energy
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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
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Differential Rotation 2v d
R dR
2
1
3
r
GM
Shearing rate 0d
A RdR
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Young disk in Taurus
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*Active galactic nucleus
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*X-ray Binary
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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
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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
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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.
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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
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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
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ADAF (Optically Thick and Thin)
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Summary
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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
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Real Disks are Magentized
• Magnetorotational Instability
d/ dr
X
Hawley et al
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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
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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
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Hawley & Balbus (2002)
Poloidal fields initially 3-phase structure
)8//( 2 BnkT
poloidal fields
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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.
Compton scattering radiation.Compton scattering radiation.
Evaporation of gas at disk surface.Evaporation of gas at disk surface.
Magnetic energy is transferred Magnetic energy is transferred to thermal energy.to thermal energy.
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•Viscous ADAFs
•Resistive ADAFs
angular momentum transfer and energy dissipation
Turbulence viscosity
The magnetic fields are regarded as of turbulence origin
=P(magnetic)/P(gas)
Angular momentum transfer
The magnetic stress of a large scale magnetic field
The electric resistivity
Energy dissipation
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Analysis
State equation P=cs 2
Kinematic Viscosity =cs 2/P/
Steady state and axisymmetric
Assumptions :
ddt=0 , d/d
resistivity
Magnitude field
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Basic Equations of Viscous-Resistive ADAFs
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Self Similar Solution:
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Boundary conditions
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Non-rotating accretion flow
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Rotating accretion flow
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Non-rotating accretion flow
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Rotating accretion flow
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Non-rotating accretion flow
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Rotating accretion flow
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Rotating accretion flow
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Thank you !