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Disk Topics: Black Hole Disks, Planet Formation. 12 May 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low. Black Hole Accretion Disks. In protostellar accretion disks, radiation is always efficient, and the assumption Ωr >> c s is good. thin disk approximation

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Disk topics black hole disks planet formation

Disk Topics: Black Hole Disks, Planet Formation

12 May 2003

Astronomy G9001 - Spring 2003

Prof. Mordecai-Mark Mac Low


Black hole accretion disks
Black Hole Accretion Disks

  • In protostellar accretion disks, radiation is always efficient, and the assumption Ωr >> cs is good.

    • thin disk approximation

  • Now turn to compact objects

    • deeper potential wells produce higher temperatures

    • far more energy must be lost to radiation

    • Some observed supermassive BHs have little radiation (Sag A* is the classic example)

    • How does accretion proceed?


Thin disk dissipation
Thin Disk Dissipation

  • Thin disk approximation

  • ν = αcs2/Ω (or πrφ = αP)prescription for viscosity

  • classic radiative disk (Shakura & Sunyaev 1973, Novikov & Thorne 1973)

    • viscous heating balances radiative cooling

    • steady mass inflow gives torque (Sellwood)

    • dissipation per unit area is then

    • 3 x binding energy, because of viscous dissipation


Thin disk radiation
Thin Disk Radiation

  • if dissipated heat all radiated away, then

  • this gives temperature distribution T ~ R3/4

  • Integrating over the disk gives spectrum

  • around a BH, energy release is ~

  • Observed luminosities from, e.g. Sag A* appear to be as low as

  • How is BH accreting so much mass without radiating?


Adaf cdaf
ADAF/CDAF

  • Narayan & Yi (1992) and others proposed that the energy is advected into the BH before it can be radiated: advection dominated accretion flow

  • Numerical models made clear that the extra energy produces a convectively unstable entropy gradient in the radial direction, as well as unbinding some of the gas entirely

  • convection dominated accretion flow proposed as elaboration of ADAF

    • outward convective transport balances inward viscous transport, leaving disk marginally stable

    • analogous to convective zone in stars


Problems with adaf cdaf
Problems with ADAF/CDAF

  • Balbus (2000) points out that convection and MRI cannot be treated as independent forces

    • instead a single instability criterion must be found

    • this reduces to the MRI, so no balance exists

  • Balbus & Hawley (2002) analyze non-radiative MHD flows.

    • convectively unstable modes overwhelmed by MRI

    • balanced transport implies that convection recovers energy produced by viscous dissipation, resulting in a dissipation-free flow: but this violates 2nd Law of Thermodynamics!


Non radiative accretion flow
Non-Radiative Accretion Flow

  • Hawley & Balbus (2002) simulate non-radiative MHD flow numerically, finding outflow and unsteady, slow, accretion



Planet formation in disks

Ruden

1999

Planet Formation in Disks

  • Solar planets formed from protoplanetary disk with at least 0.01 M of gas (Minimum Mass Solar Nebula)

  • Observed disks have comparable masses

  • Disk evolution determines initial conditions.

Ruden


Grain dynamics
Grain Dynamics

  • Gas moves on slightly sub-Keplerian orbits due to radial pressure gradient

  • Grains move on Keplerian orbits

    • grains with a < 1 cm feel drag FD = – (4/3) πa2ρcs(Δv)

    • coupling time tc = m Δv / FD , so small Ωtc = aρd / Σ means particles drop towards star, large remain.

  • Vertical settling also depends on Ωtc

    • vertical gravity gz = (z/r)GM* / R2 = Ω2z

    • settling time ts = z / vz = Ω-1 (Ωtc)-1 = Σ / (aρd Ω)

    • small grains with Ωtc << 1 take many orbits to settle

    • coagulation vital to accumulate mass in midplane


Planetesimals
Planetesimals

  • Big enough to ignore gas drag over disk lifetime

  • How do they accumulate from dust grains?

    • gravitational instability requires very cold disk with Δv ~ 10 cm s-1 (Goldreich & Ward)

    • shear with disk enough to disrupt most likely

    • Collisional coagulation main alternative (Cuzzi et al 93)

  • Planetesimals collide to form planets

    • gravitational focussing gives cross-section (Safronov):


Planet growth
Planet Growth

  • Orderly growth by planetesimal accretion has long time scale:

  • Velocity dispersion Δvmust remain low to enhance gravitational focussing.

  • Dynamical friction transfers energy from large objects to small ones

    • large objects have lowest velocity dispersion and so largest effective cross sections.

    • collisions between them lead to runaway growth

Ruden 99


Final stages of solid accretion
Final Stages of Solid Accretion

  • Runaway growth continues until material has been cleared out of orbits within a few Hill radii

    • Hill radius determined by balance between gravity of planet and tidal force of central star

  • Protoplanet sizes reach 5–10% of final masses

  • Final accumulation driven by orbital dynamics of protoplanets

    • major collisions of planet-sized objects an essential part of final evolution

    • random events determine details of final configuration of solid planets


Gas accretion
Gas Accretion

  • Above critical mass of 10–15 M planetary atmospheres no longer in hydrostatic equilibrium

    • heating comes from p’mal impacts

    • increasing heating required to balance radiative cooling of denser gas atmospheres (Mizuno 1980)

    • collapse of atmosphere occurs until heating from gravitational contraction balances cooling

    • rapid accretion can occur

  • Final masses determined either by:

    • destruction of disk by photoevaporation or tides

    • gap clearing in gaseous disk


Gap formation migration
Gap Formation & Migration

  • Giant planets exert tidal torques on surrounding gas, repelling it and forming a gap in disk.

  • Disk also exerts a torque on the planet, causing radial migration.


Gap formation
Gap Formation

  • Tidal torque on disk with surface densityΣ from planet at rp

  • Viscous torque

  • Gap opened if Tt > Tvwhich means

  • In solar system this is about 75 or roughly Saturn’s mass.


Observations
Observations

  • Disk Observations

    • spectral energy distributions

      • density distribution

      • gaps and inner edges

    • dust disks (β Pic, Vega)

      • Poynting-Robertson clears in much less than t*

      • presence of dust disk indicates colliding planetesimals

    • Proplyds [Protoplanetary disks], seen in silhouette

  • Indirect Dynamical Observations

    • radial velocity searches

      • need accurate spectroscopy: calibrator (iodine) in optical path

    • radial distance changes: pulsar timing

    • astrometry: next generation likely productive (SIM)


Observations1
Observations

  • Microlensing of planet

    • superposes spike on stellar amplification curve

    • can also shift apparent position of star

  • Direct detections

    • transits

      • photometry - eclipse of star (or of planet!)

      • transmission spectroscopy of atmosphere

    • direct imaging

      • adaptive optics

      • interferometry

      • coronagraphs (+ AO = Oppenheimer @ AMNH)


Search techniques
Search techniques

Lyot

  • Kepler: space-based transit search

  • COROT: same

  • Doppler: 3m/s ground-based

  • SIM = Space Interferometry Mission

  • FAME = next ESA astrometry mission

  • ground based transit search

  • Lyot = AO + coronagraph (BRO)

habitable

zone


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