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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.

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SELF-SIMILAR SOLUTIONS OF V ISCOUS RESISTIVE ACCRETION FLOWS

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  1. 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

  2. Outline • Accretion Disk • (1) Descriptions , (2) Models • Magnetic Fields In Accretion Flows • Analysis • Numerical Solutions • Conclusion

  3. In circumstellar The formation of the accretion disc Through mass transfer or stellar wind in the binary system

  4. -angularmomentum -Centrifucalandtidalforces -gravitatianal potential energy to thermal energy

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

  6. Differential Rotation Shearingrate

  7. Young disk in Taurus

  8. *Active galactic nucleus

  9. *X-ray Binary

  10. *Around Black Hole 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.

  11. 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

  12. 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-DominatedFlows: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.

  13. 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 ADAFThe 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

  14. 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

  15. ADAF (Optically Thick and Thin)

  16. Summary

  17. Optically thin Slim disk Advection Dominated Accretion Flow (ADAF) Low/Hard state Standard disk High/Soft state Optically thick unstable Accretion disk solution Optically thick ADAF Abramowicz et al. (1995)

  18. dW / dr X Real Disks are Magentized • Magnetorotational Instability Hawley et al

  19. 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 ⇒ Emag< Egas ≪ Egrav ～ Erad • RIAF/corona ⇒ Emag < Egas ～ Egrav ≫ Erad ～ ～

  20. Magnetic dynamo in accretion disks • Magneto-rotational instability (MRI)：Bf, Bz Br • Differential rotation：Br Bf • Magnetic buoyancy：Br, Bf Bz Differential Rotation 　(c) Y. Kato

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

  22. Magnetic loops Disk reconnection Accretion energy to radiation Dynamo action in disk: Gravitational energy to B. Magnetic loops emerge and reconnect in the corona. Magnetic energy is transferred to thermal energy. Evaporation of gas at disk surface. Compton scattering radiation.

  23. Viscous ADAFs angular momentum transfer and energy dissipation Turbulence viscosity The magnetic fields are regarded as of turbulence origin b =P(magnetic)/P(gas) • Resistive ADAFs Angular momentum transfer The magnetic stress of a large scale magnetic field Energy dissipation The electric resistivity

  24. Analysis Assumptions : • State equation P=r cs 2 Kinematic Viscosity n =acs 2/Wk=aP/rWk Steady state and axisymmetric d/dt=0 , d/df=0 resistivity Magnitude field

  25. Basic Equations of Viscous-Resistive ADAFs

  26. Self Similar Solution:

  27. Boundary conditions

  28. Non-rotating accretion flow

  29. Rotating accretion flow

  30. Non-rotating accretion flow

  31. Rotating accretion flow

  32. Non-rotating accretion flow

  33. Rotating accretion flow

  34. Rotating accretion flow

  35. Thank you !

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