The formation of stars and planets Day 3, Topic 2: Viscous accretion disks Continued... Lecture by: C.P. Dullemond

Non-stationary (spreading) disks So far we assumed an infinitely large disk In reality: disk has certain size As most matter moves inward, some matter must absorb all the angular momentum This leads to disk spreading: a small amount of outer disk matter moves outward

Non-stationary (spreading) disks Given a viscosity power-law function, one can solve the Shakura-Sunyaev equations analytically in a time-dependent manner. Without derivation, the resulting solution is: Lynden-Bell & Pringle (1974), Hartmann et al. (1998) where we have defined with r 1 a scaling radius and t s the viscous scaling time:

Non-stationary (spreading) disks Time steps of 2x10 5 year Lynden-Bell & Pringle (1974), Hartmann et al. (1998)

Formation & viscous spreading of disk

From the rotating collapsing cloud model we know: Initially the disk spreads faster than the centrifugal radius. Later the centrifugal radius increases faster than disk spreading

Formation & viscous spreading of disk A numerical model

Formation & viscous spreading of disk A numerical model

Formation & viscous spreading of disk A numerical model

Formation & viscous spreading of disk A numerical model

Formation & viscous spreading of disk A numerical model

Formation & viscous spreading of disk Hueso & Guillot (2005)

Disk dispersal Haisch et al It is known that disks vanish on a few Myr time scale. But it is not yet established by which mechanism. Just viscous accretion is too slow. - Photoevaporation? - Gas capture. by planet?

Photoevaporation of disks (Very brief) Ionization of disk surface creates surface layer of hot gas. If this temperature exceeds escape velocity, then surface layer evaporates. Evaporation proceeds for radii beyond:

Some special topics

‘Dead zone’ MRI can only work if the disk is sufficiently ionized. Cold outer disk (T<900K) is too cold to have MRI Cosmic rays can ionize disk a tiny bit, sufficient to drive MRI Cosmic rays penetrate only down to about 100 g/cm 2. full penetration of cosmic rays partial penetration of cosmic rays

‘Dead zone’ Hot enough to ionize gas Only surface layer is ionized by cosmic rays Tenuous enough for cosmic rays Above dead zone: live zone of fixed  = 100 g/cm 2. Only this layer has viscosity and can accrete.

Accumulation of mass in ‘dead zone’ Remember: Stationary continuity equation (for active layer only): For  >0 we have mass loss from active layer (into dead zone)

Gravitational (in)stability If disk surface density exceeds a certain limit, then disk becomes gravitationally unstable. Toomre Q-parameter: For Q>2 the disk is stable For Q<2 the disk is gravitationally unstable Unstable disk: spiral waves, angular momentum transport, strong accretion!!

Gravitational (in)stability Spiral waves act as `viscosity’ Rice & Armitage

Episodic accretion: FU Orionis outbursts 1.Dead zone: accumulation of mass 2.When Q<2: gravitational instability 3.Strong accretion, heats up disk 4.MRI back to work, takes over the viscosity 5.Massive dead zone depleted 6.Temperature drops 7.Main accretion event ends 8.New dead zone builds up, another cycle time (year) Armitage et al. 2001

FU Orionis stars

McNeal’s Nebula: a new FU Ori?

Effect of an external companion Augereau & Papaloizou (2004)

Observations of disks

Silhouette disks in Orion Nebula

Photoevaporation of disks: from outside Many low mass stars with disks in Orion near Trapezium cluster of O-stars. Their disks are being photoevaporated.

Images of isolated disks: scattered light C. Grady HD100546

Images of isolated disks: scattered light C. Grady HD163296

Measuring the Keplerian rotation CO, CN lines HD163296:MWC 480: Qi (PhD Thesis) 2001

Measuring the Keplerian rotation Pietu, Guilloteau & Dutrey (2005) AB Aurigae: nearly Kepler, but deviations 13 CO 2-1

AB Aurigae: spiral arms and clumps Pietu, Guilloteau & Dutrey (2005)

AB Aurigae: spiral arms and clumps Fukagawa et al Scattered light