Flaring shape

jets

Outflows disappearbefore the disks do

(on the other hand, in debris disks which don’t have a lotof gas and much less dust as well, both the opacity of dust and thesurface density of matter are much lower, so that the optical depthis tau_0 << 1 in every direction.)

High!

[accretion heating active disks;illumination heating passive disks]

Since the flux F also equals sigma * T^4, and c ~ T^(1/2),we have that in disks where Sigma*nu = const. (stationary thin disks far from the stellar surface)F ~ r^(-3) ~ T^4 ==> T ~ r^(-3/4)z/r ~ c / v_K ~ r^(+1/8), a slightly flaring disk.

[accretion heating active disks;illumination heating passive disks]

Diffusion equation for the viscous evolution of an accretion disk

cf. Pringle (1981 in Ann Rev Astr Astoph)

The ratio of viscous to dynamical time is called Reynolds numberand denoted Re. It always is a very large number in astrophysics.

The analytical solutions (Pringle 1981)

***

*** - there is another solution…which??

ANOMALOUS VISCOSITY IN DISKS

Problem: convectiontransports angularmomentum inwards

l = Specific angular momentum

c = soundspeedz = disk scale height

Non-dimensional parameter

Idea: gather all uncertainties in alpha-parameter:

Reynolds number:

(spiralling of gas very much slower than v_k, Keplerian vel.)

Shakhura-Sunyayev (1973)

because

- disks

Magneto-rotational instability (MRI) as a source of viscosity in astrophysical disks.Velikhov (1959), Chandrasekhar (1960), and re-discovered by Balbus and Hawley (1991). Disk conditions: gas ionized; magnetic field dragged with gas magnetic field energy and pressure << gas energy,pressure differential rotation (angular speed drops with distance)

2-D and 3-D simulations of Magnetic turbulence inside the disk

Charles Gammie et al.

Chris Reynolds et al.

Results: alpha computed ab initio,sometimes not fully self-consistently often not in full 3-D disk:alpha ~ several * 1e-3

VISCOUS EVOLUTION SEEN IN DISKS

Observations of dM/dt as a function of log age [yr]

PPIV = Protostars and Planets IV book (2000)

M_sun/yr

log age [yr]

Observed dM/dt ~ 1e-6 M_sun/yr for ~0.1 Myr time==> total amount accreted ~0.1 M_sunObserved dM/dt ~ 1e-7 M_sun/yr for ~Myr time==> total amount accreted ~0.1 M_sun

Mass of the dust in disks (around A-type and similar stars)

Natta (2000, PPIV)

Primordial solar nebulae

Debris disks = beta Pic disks, zodiacal light disks

log age [yr]dM/dt [M_sun/yr]

(T Tau stars)gas

PPIV = Protostars and Planets IV book (2000)

Observations

Modeling ofobservations

Ab-initiocalculations(numerical)

Compares OK

Percentage of optically thick “outer disks” (at~3AU)

From: M. Mayers,S. Beckwith et al.

Conclusion:Major fraction of dust cleared out to several AU in 3-10 Myr

0.1 1 100 1000 MyrAge

10

If part of the disk missing => SED may show a dip=> possible diagnosticof planets.

If thisring missing

flux

frequency

SED = Spectral En. Distrib.

Z0

Summary of the most important facts about accretion disks: Found in: • quasars’ central engines, • active galactive nuclei (AGNs), galaxies, • around stars (Cataclysmic Var., Dwarf Novae, T Tauri, b Pic), • around planets.

Drain matter inward, angular momentum outside. Release gravitational energy as radiation, or reprocess radiation.

Easy-to-understand vertical structure with z/r ~ c/v_K Radial evolution due to some poorly known viscosity,

parametrized by alpha <1. Best mechanism for viscosity is MRI (magneto-rotational instability), an MHD process of growth of tangled magnetic fields at the cost of mechanical energy of the disk. Simulations give alpha= a few * 1e-3