Disk Topics: Black Hole Disks, Planet Formation12 May 2003Astronomy G9001 - Spring 2003Prof. Mordecai-Mark Mac Low

Black Hole Accretion DisksIn protostellar accretion disks, radiation is always efficient, and the assumption r >> cs is good.thin disk approximationNow turn to compact objectsdeeper 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 DissipationThin disk approximation = cs2/ (or r = P) prescription for viscosityclassic radiative disk (Shakura & Sunyaev 1973, Novikov & Thorne 1973)viscous heating balances radiative coolingsteady mass inflow gives torque (Sellwood)

dissipation per unit area is then

3 x binding energy, because of viscous dissipation

Thin Disk Radiationif dissipated heat all radiated away, then

this gives temperature distribution T ~ R3/4Integrating over the disk gives spectrumaround 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/CDAFNarayan & Yi (1992) and others proposed that the energy is advected into the BH before it can be radiated: advection dominated accretion flowNumerical 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 entirelyconvection dominated accretion flow proposed as elaboration of ADAFoutward convective transport balances inward viscous transport, leaving disk marginally stableanalogous to convective zone in stars

Problems with ADAF/CDAFBalbus (2000) points out that convection and MRI cannot be treated as independent forcesinstead a single instability criterion must be foundthis reduces to the MRI, so no balance existsBalbus & Hawley (2002) analyze non-radiative MHD flows. convectively unstable modes overwhelmed by MRIbalanced 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 FlowHawley & Balbus (2002) simulate non-radiative MHD flow numerically, finding outflow and unsteady, slow, accretion

And now for something completely different...

Planet Formation in DisksSolar planets formed from protoplanetary disk with at least 0.01 M of gas (Minimum Mass Solar Nebula)Observed disks have comparable massesDisk evolution determines initial conditions.RudenRuden1999

Grain DynamicsGas moves on slightly sub-Keplerian orbits due to radial pressure gradientGrains move on Keplerian orbitsgrains with a < 1 cm feel drag FD = (4/3) a2cs(v)coupling time tc = m v / FD , so small tc = ad / means particles drop towards star, large remain.Vertical settling also depends on tcvertical gravity gz = (z/r)GM* / R2 = 2zsettling time ts = z / vz = -1 (tc)-1 = / (ad )small grains with tc

PlanetesimalsBig enough to ignore gas drag over disk lifetimeHow do they accumulate from dust grains?gravitational instability requires very cold disk with v ~ 10 cm s-1 (Goldreich & Ward)shear with disk enough to disrupt most likelyCollisional coagulation main alternative (Cuzzi et al 93)Planetesimals collide to form planetsgravitational focussing gives cross-section (Safronov):

Planet GrowthOrderly growth by planetesimal accretion has long time scale:

Velocity dispersion v must remain low to enhance gravitational focussing.Dynamical friction transfers energy from large objects to small oneslarge objects have lowest velocity dispersion and so largest effective cross sections.collisions between them lead to runaway growthRuden 99

Final Stages of Solid AccretionRunaway growth continues until material has been cleared out of orbits within a few Hill radiiHill radius determined by balance between gravity of planet and tidal force of central star

Protoplanet sizes reach 510% of final massesFinal accumulation driven by orbital dynamics of protoplanetsmajor collisions of planet-sized objects an essential part of final evolutionrandom events determine details of final configuration of solid planets

Gas AccretionAbove critical mass of 1015 M planetary atmospheres no longer in hydrostatic equilibriumheating comes from pmal impactsincreasing heating required to balance radiative cooling of denser gas atmospheres (Mizuno 1980)collapse of atmosphere occurs until heating from gravitational contraction balances coolingrapid accretion can occurFinal masses determined either by:destruction of disk by photoevaporation or tidesgap clearing in gaseous disk

Gap Formation & MigrationGiant 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 FormationTidal torque on disk with surface density from planet at rp

Viscous torque

Gap opened if Tt > Tv which means

In solar system this is about 75 or roughly Saturns mass.

ObservationsDisk Observationsspectral energy distributionsdensity distributiongaps and inner edgesdust disks ( Pic, Vega)Poynting-Robertson clears in much less than t*presence of dust disk indicates colliding planetesimalsProplyds [Protoplanetary disks], seen in silhouetteIndirect Dynamical Observationsradial velocity searchesneed accurate spectroscopy: calibrator (iodine) in optical pathradial distance changes: pulsar timingastrometry: next generation likely productive (SIM)

ObservationsMicrolensing of planetsuperposes spike on stellar amplification curvecan also shift apparent position of starDirect detectionstransitsphotometry - eclipse of star (or of planet!)transmission spectroscopy of atmospheredirect imagingadaptive opticsinterferometrycoronagraphs (+ AO = Oppenheimer @ AMNH)

Search techniquesKepler: space-based transit searchCOROT: sameDoppler: 3m/s ground-basedSIM = Space Interferometry MissionFAME = next ESA astrometry missionground based transit searchLyot = AO + coronagraph (BRO)habitable zoneLyot