compact objects and relativistic astrophysics course
TRANSCRIPT
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Image Credit: NASA
DARK Cosmology Centre - Niels Bohr Institute - May 23, 2011
Martin PessahNiels Bohr International [email protected]
Compact Objects and Relativistic Astrophysics CourseLecture on ‘Accretion Disks’
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Why Are Accretion Disks Important?
Proto-star X-ray Binary Active Galactic Nucleus
Crucial for understanding- How stars and planets form- What powers the brightest X-ray sources in the sky- Why Active Galactic Nuclei (Quasars) shine- How to use flow dynamics to map black hole space-time
Release of gravitational energy in accretion disks responsible for some of the most powerful phenomena in nature!
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A Natural Outcome
* To a first approximation the gas is falling into a central potential
* Angular momentum is mostly conserved
* Gas can cool down faster than it can get rid of angular momentum
* Flattened, rotating structure (AKA disk!) forms...
Imagine a cloud of gas collapsing due to its own gravity
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Typical Masses, Sizes, and Luminosities
From ‘Black Hole Accretion Disks’, Kato, Fukue & Mineshige, 1998
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*Observational Evidence
* Basics of Accretion Disk Physics
* Modern Accretion Disk Theory & MHD Turbulence
* Numerical Simulations
Overview
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Observational Evidence
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Protoplanetary Disks
From ‘Black Hole Accretion Disks’, Kato, Fukue & Mineshige, 1998
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Remillard & McClintock, 2006
X-ray Binary Disks
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AGN Disks
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Evidence for Disks
From ‘Accretion Power in Astrophysics’; Frank, King, & Raine, 1995
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Evidence for Disks
From ‘Accretion Power in Astrophysics’; Frank, King, & Raine, 1995
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Evidence for Disks
From ‘Accretion Power in Astrophysics’; Frank, King, & Raine, 1995
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Black Hole States
Remillard & McClintock, 2006
Meyer-Hofmeister et al. 2009
Extreme changes in luminosity, spectra, &
variability !!!
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Variability at All Mass Scales!
Axelsson et al. 2006 McHardy et al. 2007
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Relativistic Iron Lines
Broad iron lines in AGN (Fabian et al.)Sensitive to ‘inner edge’
Sensitive to inclination
Detailed modeling of lineprofile allows us to ‘map’
the space-time aroundblack holes
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Basics of Accretion Disk Physics
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Why Are Accretion Disk so Hard to Understand?
Magnetic fields do not seem to influence stellar structure significantly
Gravity balanced bypressure gradient along REnergy flows along R too!
R
Magnetic fields are essential for accretion
disks to work
Rφz
MassMomentumEnergy
Non-thermal processesMostly thermal energy
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R
vK =
GM
R
ΩK =
GM
R3
Some Dynamical Considerations
If the disk were a collection of non-interacting particles there would be no accretion
Particles in a central potential move in stable Keplerian orbits
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Keplerian Disks 101
Ω(R)
R
Ω ∼ R−3/2
Ω2 =GM
R3
Matter
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R
l(R)
l = vφR = (ΩR)R = ΩR2
l ∼ R1/2
Importance of Angular Momentum Transport
Gas in the disk must lose angular momentum!!!!
Angular Momentum
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∂ρ
∂t+∇.(ρv) = 0
Importance of Stress...
∂l
∂t+∇.(lv) = −1
r
∂
∂r(r2Trφ)
If there is no stress, angular momentum for fluid elements in the disk is conserved and matter does not accrete!
Mass conservation
∂l
∂t+∇.(lv) = 0 Angular momentum
is not conserved....
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Solving the Angular Momentum Problem. I
Problem I: Transport of Angular Momentum
!!!
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Re~10Re~13Re~26Re~140Re~2000Re~10000
Guadalupe Island vortex street movie from GOES
Re =V L
ν
Courtesy of CK Chan
Reynolds numbers in accretion disks are HUGE!!!
Re =V L
ν∼ 1010 − 1016
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Solving the Angular Momentum Problem. I
Solution I: Assume some kind of “turbulent” viscosityEddies of size ‘H’ interacting with turnover velocity ‘α cs’
Shakura & Sunyaev ‘70s, α-model
tturb ∼ tobs !!!
With this enhanced stresswe can match the fast timescales observed!
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The Standard Accretion Disk Model
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Σ, vr, vφ, P, H, cs, Teff , Tc, τ, κ
The Standard Accretion Disk Model
T 4eff = T 4
c /3τ
τ = κΣ/2κ = κ(Σ, Tc)
cs =
kBTc/µmH
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Wide Range of Physical Conditions
From ‘Accretion Power in Astrophysics’; Frank, King, & Raine, 1995
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Structure of Standard Accretion Disk Model
We can now calculate the emitted spectrum...
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Spectral Energy Distribution
From ‘The Physics of Compact Objects’; Shapiro & Teukolsky’; 1983
Assume energy generated by stresses responsible for angular momentum transport is locally radiated away.
Disk can be divided in regions
1. Outer: P_gas and free-free
2. Middle: P_gas and e scattering
3. Inner: P_rad and e scattering
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Summary of Standard Accretion Disk Model
Since the early 70’s we have used this ‘viscosity’ prescription to remove angular momentum from the disk...
Matter
Angular momentum
Σ(r), P (r), T (r), vr(r), ...We can calculate the global structure of the disk
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Modern Accretion Disk Theory&
MHD Turbulence
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Solving the Angular Momentum Problem. II
Problem II: Origin of Turbulence? - Keplerian flows are very STABLE to hydrodynamic perturbations (Hawley et al. 1999, Yi et al. 2006) - Convection? (Stone & Balbus 1996, Lesur & Ogilvie 2010)
Solution II: Magnetic Fields* Velikhov & Chandrasekhar (early 60’s) Balbus & Hawley (early 90’s)
* Mechanism to disrupt laminar flows
* Numerical simulations confirm development of MHD turbulence
B
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Turbulent Magnetized Accretion Disks: MRI
We need to understand the dynamics of magnetic fields in differentially rotating plasmas!!!
Differentially rotating magnetized plasmas are unstable to the Magnetorotational Instability (MRI)
(Velikhov & Chandrasekhar, 60’s; Balbus & Hawley, 90’s)
From J. Hawley’s websiteFrom J. Stone’s website
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A Piece of Physics:The Magnetorotational Instability
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P
Restoring force: pressure gradients
δP
k
Acoustic Waves
B
Restoring force: magnetic tension
δB
k
Alfven Waves
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φ
r
MHD Waves
BzMagnetic Field
r
z
φ
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r
zBzδBφ
φ
Magnetic Field
Magnetic Tension
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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φ
r
r
zBzδBφ
φ
Magnetic Field
MHD Waves
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φ
r
r
zBzδBφ
φ
Magnetic Field
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ k
φ
Magnetic Field
φ
r
MHD Waves
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r
zBzδBφ k
φ
Magnetic Field
€
vA2 =
B2
4πρ€
ω 2 = k 2vA2
φ
r
MHD Waves
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Magnetorotational Instability
To the black hole
BzMagnetic Field
r
z
φ
Differential rotation
φ
r
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r
zBzδBφ
Magnetorotational Instability
φ
Magnetic Field
Differential rotation
φ
r
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φ
r
z
Magnetorotational Instability
Magnetic Field
Differential rotation
φ
r
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φ
r
z
Magnetorotational Instability
Magnetic Field
Differential rotation
φ
r
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φ
r
z
Magnetorotational Instability
Magnetic Field
Differential rotation
φ
r
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φ
r
z
Magnetorotational Instability
Magnetic Field
Differential rotation
φ
r
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φ
r
z
Magnetorotational Instability
Magnetic Field
Differential rotation
φ
r
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φ
r
z
Magnetorotational Instability
Magnetic Field
Differential rotation
φ
r
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r
z
BzδBφ
Magnetorotational Instability
MagneticTorques
φ
Magnetic Field
Differential rotation
Magnetorotational Instability
+
φ
rBzδBr
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r
z
BzδBφ
Magnetorotational Instability
MagneticTorques
φ
Magnetic Field
Differential rotation
Magnetorotational Instability
+
BzδBr
€
vA2 =
B2
4πρ€
k 2vAz2 < −2Ω2 d lnΩ
d ln r
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MHD Equations
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Local -shearing box- MHD Equations
Use background field and rotation rate to define characteristic scales in the problem
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Linear Mode Analysis
A→ A + δADynamical equations = 0
Dynamical equations for δ = 0
p(k, ω) = 0Obtain the dispersion relation
δρ δvNeglect 2nd order terms
Expand in Fourier Series
δA ∼ δρ, δP, δv, δB →
Ak exp[−i(k.x + ωt)]
63
ω = ω(k)Find the eigenfrequencies
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Growth Rates with Dissipation
z
r
k B
Various limits studied by Sano et al. 1998, Lesaffre & Balbus 2007, Lesur & Longaretti 2007, and many others…
Pessah & Chan, 2008
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Angular Momentum Transport: MRI & Turbulence
Sano et al. 2004
Maxwell Stress
Reynolds Stress
MRI and MHD turbulence lead to correlated fluctuations
of the PROPER sign!!!
€
∂l∂t
+∇ ⋅ (lv) = −1r∂∂r[r2(Rrφ −Mrφ )]
Angular momentum conservation
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Saturation of MRI & MHD Turbulence
-Maxwell
Reynolds
MRI growth
SaturationNon-linear
Insets from Sano et al. 2004
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Numerical Simulations
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Importance & Limitations of Numerical Simulations
1Gyr
1yr
1sec
0.1AU 1AU 1000AU
Mean Field Models
BroadLine
Region
Inside Horizon
NumericalSimulations
Viscous
Orbital Saturation
BHGrowth
BHVariability
Hubble Time
107Mo
Disk Spectrum
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MHD Turbulent Transport vs. alpha-viscosity
Pessah, Chan, & Psaltis, 2006Pessah, Chan, & Psaltis, 2008Shakura & Sunyaev, 1973
Standard prescription does not capture
physics correctly!
Need to understandturbulent MHD
angular momentum transport from first
principles...
Shakura & Sunyaev (‘70s):transport due to turbulence
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Current Focus and Future Prospects
Davis, Stone, & Pessah 2010
CK Chan & Pessah 2011
Better understanding of micro-physics. Thermodyn.
Synergy between analytical and numerical work
More realistic global simulations
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Global 3D MHD Simulations
Beckwith et al. 2011
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Global 3D MHD Simulations
Beckwith et al. 2011
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α−stress (~ P)Chan, Psaltis, & Ozel, ‘06
Global Models for Accretion onto Black Holes
Risco
RSch
Simulations showstresses DO NOTvanish inside ISCO
It is usually argued that stresses vanish
at the inner disk
Implications: * Inner disk structure * Spin measurements * Emission inside ISCO * Spin evolution
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Accretion Disks Big Picture Recap
Since early 70’s we have dealt with this problem by using a‘viscosity’ prescription proposed by Shakura & Sunyaev (1973)
Fundamental Problem in Accretion Disks: How to get rid of angular momentum…
Balbus & Hawley (1991): magnetic fields are key!Differentially rotating, magnetized plasmas are unstable to MRI
Ensuing turbulence removes angular momentum from disk!
Massive analytical and numerical efforts
to understand MHD turbulence and
simulate accretion disksFrom J. Hawley’s websiteFrom J. Stone’s website
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Bibliography:
Black holes in binary systems. Observational appearance.Shakura, N. I.; Sunyaev, R. A. 1973A&A....24..337S
Theory Of Accretion Disks I: Angular Momentum Transport Processes Papaloizou, J. C. B.; Lin, D. N. C. 1995ARA&A..33..505P
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