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~10 4 (T 2 /n) cm # L > 10 4-5 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: F s =5  s  c s 3 (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) # Solutions of the form: Notation: f is the advection parameter alpha is the shakura-Sunyaev visco-turbulent parameter

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

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 Latitudinal Conduction Cools poles Radial Conduction Takes over, Little Latitudinal contribution

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 Adiabaticisothermal 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)