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)
# 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?
Hot Accretion Flows
Chandra Image(Baganoff et al. 2003)
Hot Accretion Flows
M87 (Di Matteo et al. 2003)
-- infer density andTemperature from X-rayprofile
-- apply standard bondi Theory for gas capture
-- deduce low radiativeefficiency
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)
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
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)
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
Adiabatic Index Dependence
AdvectionParameter:F=1
ViscosityParameter:=0.2
AdiabaticIndex:
1.5 1.1
2
cs
2D ADAF Solutions with Conduction
<= to preserve self-similarity
<= for simplicity
2D ADAF self-similar equations
Advective“cooling” Viscous
Heating (>0)
Latitudinal heat transport
Radial heat Transport (>0 because self-similar)
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
Results: dynamical I
“disk-like”
Results: dynamical II
“ADAF-like”
Inflow/Outflow geometry
Outflow properties
Dependence on viscosity parameter
Flow Energetics
LatitudinalConductionCools poles
Radial ConductionTakes over, Little Latitudinal contribution
Flow dynamical balance
Bernoulli: not an outflow discriminant
Bondi Problem with Conduction
(Johnson & Quataert 2006)
Spherical accretionWith gravitationalEnergy release andHeat conduction
Adiabatic isothermal
Magnitude of conduction
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?
Future Diagnostics? M87 jet
Junor, Biretta & Livio (1999, 2002)
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