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.

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.

•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

Analysis

State equation P=cs 2

Kinematic Viscosity =cs 2/P/

Steady state and axisymmetric

Assumptions :

ddt=0 , d/d

resistivity

Magnitude field

Basic Equations of Viscous-Resistive ADAFs

Self Similar Solution:

Boundary conditions

Non-rotating accretion flow

Rotating accretion flow

Non-rotating accretion flow

Rotating accretion flow

Non-rotating accretion flow

Rotating accretion flow

Rotating accretion flow

Thank you !