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

-angular momentum -Centrifucal and tidal forces -gravitatianal potential energy to thermal energy

Viscosity  Converts shear to heat  Heat radiated away  Energy being lost  Gas sinks deeper in the potential well Viscosity Gravitational potential energy Radiation Disc+ viscosityAccretion Disc

Differential Rotation Shearing rate

Young disk in Taurus

*Active galactic nucleus

*X-ray Binary

Gas orbits around a black hole at 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 disk High/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 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 ⇒ E mag < E gas ≪ E grav ～ E rad RIAF/corona ⇒ E mag < E gas ～ E grav ≫ E rad ～ ～

Magnetic dynamo in accretion disks Magneto-rotational instability (MRI) ： B , B z  B r Differential rotation ： B r  B  Magnetic buoyancy ： B r, B   B z (c) Y. Kato Differential Rotation

Hawley & Balbus (2002) Poloidal fields initially  3-phase structure poloidal fields

Accretion energy to radiation reconnection Magnetic loops Disk Dynamo action in disk: Gravitational energy to B. Magnetic loops emerge and reconnect in the corona. Compton scattering radiation. 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=  c s 2 Kinematic Viscosity =  c s 2 /    P/   Steady state and axisymmetric Assumptions : d  dt=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

Thank you !