Transcript Great Migrations & other natural history tales

Flaring shape
jets
Outflows disappear
before the disks do
High!
(on the other hand, in debris disks which don’t have a lot
of gas and much less dust as well, both the opacity of dust and the
surface density of matter are much lower, so that the optical depth
is tau_0 << 1 in every direction.)
[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.
Diffusion equation for the viscous evolution
of an accretion disk
cf. Pringle (1981 in Ann Rev Astr Astoph)
[accretion heating active disks;
illumination heating passive disks]
The ratio of viscous to dynamical time is called Reynolds number
and 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: convection
transports angular
momentum inwards
- disks
Shakhura-Sunyayev (1973)
Non-dimensional parameter
c = soundspeed
z = disk scale height
Idea: gather all uncertainties in alpha-parameter:
because
l = Specific
angular
momentum
Reynolds number:
(spiralling of gas very much
slower than v_k, Keplerian vel.)
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
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
Charles Gammie et al.
VISCOUS EVOLUTION SEEN IN DISKS
Protostars and
IV book (2000)
Observations of
dM/dt as a function
of
log age [yr]
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_sun
Observed 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)
Primordial solar nebulae
Debris disks = beta Pic
disks, zodiacal light disks
Natta (2000, PPIV)
gas
dM/dt
[M_sun/yr]
PPIV = Protostars and
Planets IV book (2000)
(T Tau stars)
log age [yr]
Observations
Modeling of
observations
Compares OK
Ab-initio
calculations
(numerical)
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
10
100
1000 Myr
Age
SED = Spectral En. Distrib.
flux
If this
ring missing
If part of the disk
missing => SED
may show a dip
=> possible diagnostic
of planets.
frequency
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