Disk Topics: Black Hole Disks, Planet Formation

1. Disk Topics: Black Hole Disks, Planet Formation 12 May 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low

2. 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?

3. 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

4. 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?

5. 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

6. 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!

7. Non-Radiative Accretion Flow • Hawley & Balbus (2002) simulate non-radiative MHD flow numerically, finding outflow and unsteady, slow, accretion

8. And now for something completely different...

9. 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

10. 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

11. 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):

12. 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

13. 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

14. 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

15. 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.

16. 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.

17. 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)

18. 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)

19. 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