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)