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Black Hole Accretion, Conduction and Outflows

Black Hole Accretion, Conduction and Outflows. Kristen Menou (Columbia University) In collaboration with Taka Tanaka (GS). Synopsis. # Hot Accretion --> Weakly Collisional --> conduction? (modulo tangled magnetic fields)

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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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