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L 6: Circumstellar Disks
Background image: HH 30 JHK HST-NICMOS, courtesy Padgett et al. 1999, AJ 117, 1490
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L6 - Stellar Evolution II: August-September, 2004
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L 6: Circumstellar Disks
Recent reviews include:
Protostars & Planets IV, Mannings, Boss & Russell (eds.)
12 Articles on Disks
5 Articles on Outflows
Zuckerman, ARAA 2001, 39: 549
Zuckerman & Song (?), ARAA 2004, in press
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L 6: Circumstellar Disks
and Outflows
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Flattened structures - Disks
Inevitable consequence of star formation
Rotation
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Magnetic Fields
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Flattened structures - Disks
Inevitable consequence of star formation
Rotation
P.S. Laplace 1796, 1799
I. Kant 1755
Exposition du systeme du monde
Mechanique celeste
Allgemeine
Naturgeschichte und
Theorie des Himmels
Planetary System Formation
...another lecture – another time...
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L6 - Stellar Evolution II: August-September, 2004
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Mass Loss - Outflows
Inevitable consequence of star formation
Angular Momentum Loss - Redistribution
The race between mass accretion & mass loss processses
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L6 - Stellar Evolution II: August-September, 2004
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Lynden-Bell & Pringle 1974, MNRAS 168, 603:
Keplerian Disk
Differential Rotation
+
Viscosity
Mass Transport Inwards
Angular Momentum Transport Outwards
See also Gösta Gahm’s lecture
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`standard model´: e.g., Frank, King & Raine Accretion Power in Astrophysics
self-consistent structure of steady, optically thick a-disk
blackbody radiation and thin disk approximation

2 H
cs
1.  c 
2. H 
3. cs 
2
thi n disk definition
vertical hydrostati c equilibriu m
GM / R 3
P
veloci ty of sound (  1)

 kTc 4 4
4. Pc 

T
 m H 3c
4
4σTc
3GMM
5.

3
8 R 3
equation of state
1


2
R


1     
 R 


6.    
energy tra nsport
opacity relation
7
p q
e.g.,     T : Kramer opacity for p  1, q  0
2
1


2
1   R  
 R 


8.   a cs H
M
7.   
3
When / Where valid ?
mass and angular momentum conservati on
viscosity prescripti on
Shakura & Sunyaev : a  1,    turb  v turblturb
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Example:
Lin & Papaloizou opacities
(1985 PP II)
Icy grains
HMolecules
bound-free
free-free
(Cox-Stuart-Alexander)
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Grain Opacities
Beckwith et al. 2000, PP IV
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`standard model´: e.g., Frank, King & Raine Accretion Power in Astrophysics
self-consistent structure of steady, optically thick a-disk
Solve for the 8 unknowns ρ, Σ, H, cs , P, Tc , ,
as functions of M, M , R
and any parameter R , Rin , Rout , a ...
The radial drift velo city ist then found from

3   R 
v rad  
1  
2R   R 

and the spectrum
1
2
1


M
 

2 R 

4 h cos i 3 out
R dR
F  2
 
2
c D
exp( h / kT )  1
Rin
R
has the form
3  h / kT
 e
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

1
3

  2T
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40 observed SEDs of T Tauri Stars & `mean model´ of star+disk
HABE Disk Structure:
Dullemond & Dominik 2004
includes
vertical
Temperature
distribution
D´Alessio et al. 1999
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Gas Disks – Structure Models
Steady Disks around Single Stars
Boundary Conditions
Rin : boundary layer, magnetosphere?
Rout: ? , interstellar turbulence?
Viscosity
MHD/rotation
Opacity
  (, T, …, XYZ, ..., z0, ..., c ...)
Models
Adams & Shu 1986 (flat)
Kenyon & Hartmann 1987 (flared)
Malbet & Bertout 1991 (vertical structure)
D´Allessio et al. 1998,... 2003
Aikawa & Herbst 1998 (chemistry)
Nomura 2002 (2D)
Wolf 2003 (3D)
[examples]
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(Hawley & Balbus 1995)
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Observations of Keplerian Disks
JE Keeler 1895
ApJ 1: 416
The Rings of Saturn
spectrum
image
Courtesy Brandeker, Liseau & Ilyn 2002
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2 Categories of Disks
T Tauri Disks: around young stars
(0.1 - 10 Myr)
of half a solar mass
(0.1 - 1 Msun)
at 150 pc distance
(50 - 450 pc)
in and/or near molecular clouds
gas rich
Accretion Disks
Debris Disks: around young ms-stars (10 - 400 Myr)
of about a solar mass
(1 - 2 Msun)
at 20 pc distance
(3 - 70 pc)
in the general field
gas poor
Vega-excess stellar disks
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L6 - Stellar Evolution II: August-September, 2004
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Frequency of Disks
High Rate of occurence around young stars
NGC 2024
Trapezium cluster
IC 348
86%
80%
65%
Haisch et al. 2001
65%
Muench et al. 2001
and around
BDs in Trapezium cluster
see also G. Gahm’s lecture
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Gas Disks - Sizes
Fridlund et al. 2002
for
One Object
Size scale (AU)
Tracer (mode)*
Reference
20000
5000 - 10000
1400
<500
45 + 1600
200
7000
5000
4000 - 6000
1200
4000
5000
2500
CS (1- 0) (S)
13CO (1- 0) (S)
C18O (1- 0) (I)
1.4 mm (I)
mm, cm (I)
0.8 mm (I)
H13CO+ (1- 0) (S)
0.7 - 1 mm (S)
C18, 17O (2- 1) (S)
13CO (1- 0) (I)
H13CO+ (1- 0) (I)
H12, 13CO+ (1- 0) (S, I)
C18O+ (1- 0) (I)
Kaifu et al. 1984
Fridlund et al. 1989
Sargent et al. 1988
Woody et al. 1989
Keene & Masson 1990
Lay et al. 1994
Mizuno et al. 1994
Ladd et al. 1995
Fuller et al. 1995
Ohashi et al. 1996
Saito et al. 1996
Hogerheijde et al.1997, 98
Momose et al. 1998
*S=single dish, I=Interferometer
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Size depends on frequency/mode of observation
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Gas Disks - Sizes
generally
T Tauri/HABE disks
50 - 100 AU
Dust: mm-continuum interferometry
100 - 300 AU
Dust: scattered stellar light
300 AU
Gas: CO lines (evidence for Kepler rotation)
Silhouettte disks (``proplyds´´)
up to 1000 AU
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Dust: scattered stellar light
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Gas Disks - Masses
H2
Gas
Directly
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CO
and
Dust
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? Why ?
Gas Disks - Masses
Lower limit: 0.001 to 1 MSun
gas
(based on mm / submm continuum)
dust
+dust
How good are these numbers ?
Do we understand disks ?
Solar Minimum Mass Nebula = 0.002 MSun
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L6 - Stellar Evolution II: August-September, 2004
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Gas Disks - Make up
gas disks consist of gas and dust
what components?
what proportions?
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2 T Tauri Disks - Make up
13CO
CO (200)
(1)*
HCO+
HCO+ (200)
(5)
HCN (200)
HCN (5)
*(N) = depletion factor
LkCa 15
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TW Hya
van Zadelhoff 2002
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2 T Tauri Disks - Chemistry
Molecular abundances (rel. H2)
Species
LkCa 15
TW Hya
CO
HCO+
H13CO+
DCO+
CN
HCN
H13CN
HNC
DCN
CS
H2CO
CH3OH
N 2H +
H 2D +
3.4 ( - 7)
5.6 (-12)
< 2.6(-12)
….
2.4 (-10)
3.1 (-11)
….
….
….
8.5 (-11)
4.1 (-11)
< 3.7(-10)
< 2.3(-11)
< 1.5(-11)
5.7 ( - 8)
2.2 (-11)
3.6 (-13)
7.8 (-13)
1.2 (-10)
1.6 (-11)
< 8.4(-13)
< 2.6(-12)
< 7.1(-14)
….
< 7.1(-13)
< 1.9(-11)
< 1.8(-11)
< 7.8(-12)
Thi 2002
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Gas Disks - Evolution
Time scales (viscous accretion disk)
tdyn ~ a ttherm ~ a (H/R)2 tvisc
tdyn ~ 1/WKepler
a ~ 10-3 - 10-2
H/R << 1
if T ~ R-1/2
, tvisc ~ R
tvisc ~ 105 yr (a/0.01)-1 (R/10 AU)
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Gas Disks - Evolution
Disk dispersal and disk lifetimes
SE = Stellar Encounter
(tidal stripping)
WS = Stellar wind
stripping
evap E = photoevaporation
external star
evap c = photoevaporation
central star
All for Trapezium conditions
Physical Mechanisms
Hollenbach et al. 2000 PPIV
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Gas (T Tauri) Disks - Evolution
Disk dispersal and disk lifetimes
Average Error Bar
Mass accretion evolution
Calvet et al. 2000 PPIV
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Gas Disks to Debris Disks – Evolution ?
How ?
fdust = DLIR/L
vs
stellar age
See also lecture by G. Gahm
(F)IR - excess
Stellar luminosity
(bolometric)
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Gas Disks to Debris Disks – Evolution ?
Clusters
Individual stars
(= 1 zodi)
Spangler et al. 2001
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Debris Disks - Properties
debris (collision products) or particulate (gas free)
percentage of Main Sequence stars (15%?)
(observationally) biased towards Spectral Type A
for (detectable) ages <400 Myr Habing et al. 1999, 2001
disk sizes
100 to 2000 AU
disk masses
>1 to 100 MMoon (small grains)
Pre-IRAS
Solar system Zodi
Vega
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US Navy Chaplain G. Jones 1855 AJ 4, 94
Blackwell et al. 1983
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http://www.hep.upenn.edu/~davidk/bpic.html
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How much Gas in Dusty Debris Disks ?
Disk evolution hypothesis: gas rich to gas poor
Census of material (mgas/mdust): planet formation
planet formation:
enough gas for GPs ?
planet formation:
time scales ?
planet formation:
seeds of Life ?
See review
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L 6: conclusions
• circumstellar disks are a consequence of star
formation
• disks and bipolar outflows/jets are connected
• disks form potentially planetray systems
L 6: open questions
• what are the physics of disks and their outflows ?
• how do disks evolve ?
• what fraction forms planetary systems ?
• when and how ?
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