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Black Hole Accretion, Conduction and Outflows

Explore the impact of heat conduction on accretion flows in the context of black hole accretion. The research covers various solutions, implications of different flow dynamics, and future considerations for understanding this complex phenomenon.

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Black Hole Accretion, Conduction and Outflows

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  1. Black Hole Accretion, Conduction and Outflows Kristen Menou (Columbia University) In collaboration with Taka Tanaka (GS)

  2. Synopsis # Hot Accretion --> Weakly Collisional --> conduction? (modulo tangled magnetic fields) # Self-Similar ADAF solution with heat conduction: -- Spontaneous thermal outflows (for imposed inflow) -- purely hydrodynamical process, polar regions favored -- slow outflows with wide opening angles -- Bernoulli param. does not determine inflow/outflow # Additional consequences: -- Reduced Bondi capture rate?

  3. Hot Accretion Flows Chandra Image (Baganoff et al. 2003)

  4. Hot Accretion Flows M87 (Di Matteo et al. 2003) -- infer density and Temperature from X-ray profile -- apply standard bondi Theory for gas capture -- deduce low radiative efficiency

  5. Radiatively Inefficient Accretion Flows # ADAFS: radial advection a key ingredient Narayan & Yi (1994) + Ichimaru, Rees et al., Abramowicz et al. # ADIOS: positive Bernoulli constant implies powerful outflows Blandford & Begelman (1999) # CDAFs: unstable entropy gradient implies convection Narayan et al. (2000), Quataert & Gruzinov (2000) # Numerical simulations: different dynamical structure Hawley, Balbus & Stone (2001) + many others => ADAF with conduction: Tanaka & Menou (2006)

  6. Constraints on Collisionality # One-Temperature: ion and electron mean free paths are L~104 (T2/n) cm # L > 104-5 Schwarzschild radii in all cases # L/R increases as R-3/2-p for density going as R-3/2+p => Weakly Collisional Regime appears likely # Spitzer vs shakura-sunyaev suggest equally important in BH binaries

  7. Saturated (“flux-limited”) Conduction # Maximal electron conductive flux: -- thermal energy content times characteristic speed (“free-streaming”) -- independent of temperature gradient (only direction) # Occurs when mean free path is comparable to temperature “scale-height” -- L/R ~1 is plausible for accretion in nuclei just discussed # Simple Cowie & McKee (1977) scaling: Fs=5 s  cs3 (uncertain) (for equal ion and electron temperatures) Independent of temperature gradient => self-similar scaling possible (would not obtain for standard Spitzer conduction law)

  8. 1D ADAF with Saturated Conduction # Equations: Mass, momentum, energy conservation (Narayan & Yi 1994) Notation: f is the advection parameter alpha is the shakura-Sunyaev visco-turbulent parameter # Solutions of the form:

  9. Adiabatic Index Dependence Adiabatic Index: 1.5 1.1 Advection Parameter: F=1 Viscosity Parameter: =0.2 2 cs

  10. 2D ADAF Solutions with Conduction <= to preserve self-similarity <= for simplicity

  11. 2D ADAF self-similar equations Advective “cooling” Viscous Heating (>0) Latitudinal heat transport Radial heat Transport (>0 because self-similar)

  12. 2D ADAF Boundary conditions # seventh-order differential system: # Global inflow imposed: -- Differential equation for mdot vs theta actually solved -- Only integral mdot is imposed, not specific values with theta

  13. Results: dynamical I “disk-like”

  14. Results: dynamical II “ADAF-like”

  15. Inflow/Outflow geometry

  16. Outflow properties

  17. Dependence on viscosity parameter

  18. Flow Energetics Radial Conduction Takes over, Little Latitudinal contribution Latitudinal Conduction Cools poles

  19. Flow dynamical balance

  20. Bernoulli: not an outflow discriminant

  21. Bondi Problem with Conduction (Johnson & Quataert 2006) Spherical accretion With gravitational Energy release and Heat conduction Adiabatic isothermal Magnitude of conduction

  22. The future # Are magnetic fields limiting conduction? # Can other heat transport phenomena (eg. turbulent) play a role? # Can one generalize these solutions: -- non-zero latitudinal velocities -- non radially self-similar -- numerical simulations with conduction -- radiative transfer for inflow vs outflow regions # How do these relate to observational trends for outflows? # Could these be 2nd outflow components (on top of narrow MHD jets)? # Collimation agent for narrow jet?

  23. Future Diagnostics? M87 jet Junor, Biretta & Livio (1999, 2002)

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