Download Accretion and radial disk structure

Models of Disk Structure, Spectra and
Evaporation
Kees Dullemond, David Hollenbach, Inga Kamp, Paola D’Alessio
• Disk accretion and surface density profiles
• Vertical structure models and SEDs
• Gas models and disk surface layers
• Evaporation by the central star
Why study the structure of
protoplanetary disks?
Disk structure models are
the backbone of planet
formation models
• Core accretion versus
gravitational instability ?
• What is the fraction of
disks that can form planets ?
• dust settling, growth and
planetesimal formation
depend on gas-dust dynamics
Overview
• Accretion determines the surface density as a function of radius:
typical accretion rates are dM/dt~10-8 M/yr
S ~ R-1
Accretion and radial disk structure
Formation of the disk...
Accretion and radial disk structure
Mass accretion
Accretion and radial disk structure
Angular Momentum transport
Accretion and radial disk structure
Viscous spreading of the disk...
... while disk loses mass by accretion
Accretion and radial disk structure
Viscous spreading of the disk...
... while disk loses mass by accretion
Accretion and radial disk structure
Viscous spreading of the disk...
... while disk loses mass by accretion onto star
Mass reservoir of the disk, which
feeds the inner disk regions
Accretion and radial disk structure
Viscous spreading of the disk...
... while disk loses mass by accretion
Semi-stationary region, with mass
supply from outer reservoir
Brief history of a star and a disk
After: Hueso & Guillot 2005
(Lynden-Bell & Pringle; Hartmann et al. ; Nakamoto & Nakagawa)
Actively accreting irradiated disks
Solid line:
Hueso & Guillot
(2005)
Dashed line:
D’Alessio et al.
(2001)
S~ R-1.5
(MMSS)
S ~ R-1
S-profile clearly shallower than ‘Minimum mass solar nebula’
• Very young disk (accretion-heating dominated): S~R-0.5.
• T Tauri disk (irradiative heating dominates outer disk): S~R-1
Overview
• Accretion determines the surface density as a function of radius:
typical accretion rates are dM/dt~10-8 M/yr
S ~ R-1
• Vertical structure models predict SEDs:
disks are flared
disks possess an inner rim (dust evaporation radius)
SEDs of intermediate-mass stars
Group I
AB Aurigae (Group I)
Group II
HD104237 (Group II)
SEDs of intermediate-mass stars
Group I
Group II
Classification of Meeus et al. 2001
(Note: not to be confused with class 0,I,II,III of the Lada et al classification!)
Fitting pure accretion disk models...
Ý  7 107 M sun /yr
need M
Ý  2 107 M sun /yr
need M
AB Aurigae (Group I)

HD104237 (Group II)

Group I: Bad fit at >10 micron.
Group II: Reasonable fit (though need high accretion rate).
(Hillenbrand 1992; Rucinski 1985; Adams et al. 1988; Bertout et al. 1988; Bell et al.
1997; Lynden-Bell 1969; Lynden-Bell & Pringle 1974)
Fitting irradiated disks...
AB Aurigae (Group I)
HD104237 (Group II)
Group I: Reasonable fit for overall flat SED.
Group II: SED tends to be too flat
(Kenyon & Hartmann 1987; Chiang & Goldreich 1997; D’Alessio et al. 1998, 1999;
Lachaume et al. 2004)
Dust evaporation: (puffed-up) inner rim...
AB Aurigae (Group I)
HD104237 (Group II)
All sources: Dust inner rim might solve the NIR problem
Group II: Still not well fitted at >10 micron
(Natta et al. 2001; Tuthill et al. 2001; Dullemond et al. 2001; Muzerolle et al. 2003;
Isella & Natta 2005; Akeson et al.; Monnier et al. ; Eisner et al.; Millan-Gabet et al.)
Reducing somehow the far-IR flux...
AB Aurigae (Group I)
HD104237 (Group II)
Group II: Outer disk height can be reduced by e.g. dust settling
(D’Alessio et al. 1999; Chiang et al. 2001). Disk might be shadowed (Dullemond &
Dominik 2004b), but this is still under debate (Walker et al. 2006)
Irradiated surface & visc. heated midplane
Vertical structure of disk at 1AU:
Viscous accretion heating
dominates the disk midplane,
while the surface layer
temperatures are set by
irradiation only
0.1
z [AU]
D’Alessio et al. model
0.2
SED of disk with hot surface layer
After: Chiang & Goldreich 1997
Calvet et al. 1991; Malbet & Bertout 1991; Many 2D/3D RT papers
Overview
• Accretion determines the surface density as a function of radius:
typical accretion rates are dM/dt~10-8 M/yr
S ~ R-1
• Vertical structure models predict SEDs:
disks are flared
disks possess an inner rim (dust evaporation radius)
• Tgas > Tdust in disk surface layers (tross <~ 1.0):
gas and dust are not well coupled
molecules can form
Disk surface layers
with PAHs
CTTS
no PAHs
tross=1
HAe
tross=1
Tgas = Tdust
(Kamp & Dullemond 2004; Jonkheid et al. 2004; Nomura & Millar 2005;
Kamp et al. 2005)
Vertical cut at R = 9 AU
Tevap
Tgas
Tdust
Gas temperature is
higher than dust
temperature in the
surface layers
(Jonkheid et al.
2004, Kamp et al.
2004, Nomura &
Millar 2005)
Tevap:= GM*mmp/kr
Vertical cut at R = 9 AU
H2/H
Tevaporation
Tgas
Tdust
Molecules like H2,
CO, OH etc. exist in
these hot surface
layers.
Vertical cut at R = 9 AU
H2/H CO/C/C+
Tevaporation
Tgas
Tdust
Molecules like H2,
CO, OH etc. exist in
these hot surface
layers.
Vertical cut at R = 9 AU
H2/H CO/C/C+
Tgas
Tevaporation
gas-grain
collisions
H2
formation
PE heating
Tdust
Gas temperature is
set by the balance of
photoelectric
heating, H2 formation
heating and OI, H2
line cooling.
Below tross~1,
gas-grain collisions
thermalize the gas
and dust.
Vertical cut at R = 9 AU
H2/H CO/C/C +
Tgas
Tevaporation
gas-grain
collisions
H2
formation
PE heating
gas-grain
collisions
Tdust
H2
lines
Lya cooling OI cooling
Gas temperature is
set by the balance of
photoelectric
heating, H2 formation
heating and OI, H2
line cooling.
Below tross~1,
gas-grain collisions
thermalize the gas
and dust.
Vertical cut at R = 9 AU
H2/H CO/C/C +
Tevaporation
Tgas
Tdust
Vertical cut at R = 9 AU
H2/H CO/C/C +
Photoevaporation
flow starts well
below Tgas=Tevaporation
Tgas
Tevaporation
origin of the
flow
Tdust
(Adams et al. 2004)
Overview
• Accretion determines the surface density as a function of radius:
typical accretion rates are dM/dt~10-8 M/yr
S ~ R-1
• Vertical structure models predict SEDs:
disks are flared
disks possess an inner rim (dust evaporation radius)
• Tgas > Tdust in disk surface layers (tross <~ 1.0):
gas and dust are not well coupled
molecules can form
• Disk dispersal can proceed via photoevaporation by the FUV/EUV
of the central star:
FUV evaporation proceeds from outside in
Stellar EUV and FUV
EUV
FUV
Photoevaporation by the central star
viscous accretion
rcrit
rcrit
rcrit = 12 (M*/1M) (103 K/Tgas) AU
Need to self-consistently calculate the chemistry, heating and cooling,
radiative transfer, vertical and radial structure, and dynamics of flow.
Approximations are made ! (Adams et al. 2004; Gorti & Hollenbach 2005)
timescale
Disk evaporation by FUV photons
T Tauri star: Mgas = 0.03 M*, S ~ R-1,
Rout = 200 AU
Disk evaporates outside in
Evaporation for various central stars:
Disk survival times peak at ~ 1 M
(Gorti & Hollenbach)  Poster 291
Additional Applications of Evaporation
• Rapid transition from classical T Tauri to weak-line T Tauri stars:
EUV photoevaporation opens a gap at rcrit at a timescale of ~ 1 Myr
 mass supply from outer disk gets cutoff
inner disk accretes onto the star on a timescale ~105 yr
(Clarke et al. 2001), (Alexander et al. 2005)  poster 292
Additional Applications of Evaporation
• Formation of planetesimals:
dust settling lowers the dust:gas ratio (Mdust/Mgas) in disk surfaces
 dust-depleted evaporation flows and dust settling leave the
midplane behind with high Mdust/Mgas (Throop & Bally 2005)
 midplane can become gravitational instable (Youdin & Shu 2002)
 spontaneous formation of km-sized planetesimals
Summary
• Accretion determines the surface density as a function of radius:
typical accretion rates are dM/dt~10-8 M/yr
S ~ R-1
• Vertical structure models predict SEDs:
disks are flared
disks possess an inner rim (dust evaporation radius)
• Tgas > Tdust in disk surface layers (tross <~ 1.0):
gas and dust are not well coupled
molecules can form
• Disk dispersal can proceed via photoevaporation by the FUV/EUV
of the central star:
FUV evaporation proceeds from outside in
Schematic view of protoplanetary disks
Dust
Schematic view of protoplanetary disks
Gas