Models of Disk Structure, Spectra and Models of Disk Structure, Spectra and EvaporationEvaporation

Kees Dullemond, David Hollenbach, Kees Dullemond, David Hollenbach, Inga KampInga Kamp, Paola D’Alessio, 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 Why study the structure of protoplanetary disks?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 formationdepend on gas-dust dynamics

OverviewOverview• Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10-8 M/yr ~ R-1

Accretion and radial disk structureAccretion and radial disk structure

Formation of the disk...

Accretion and radial disk structureAccretion and radial disk structure

Mass accretion

Accretion and radial disk structureAccretion and radial disk structure

Angular Momentum transport

Accretion and radial disk structureAccretion and radial disk structure

Viscous spreading of the disk...

... while disk loses mass by accretion

Accretion and radial disk structureAccretion and radial disk structure

Viscous spreading of the disk...

... while disk loses mass by accretion

Accretion and radial disk structureAccretion 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 structureAccretion 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 diskBrief history of a star and a disk

After: Hueso & Guillot 2005(Lynden-Bell & Pringle; Hartmann et al. ; Nakamoto & Nakagawa)

Actively accreting irradiated Actively accreting irradiated disksdisks

Solid line: Hueso & Guillot (2005)

Dashed line: D’Alessio et al. (2001)

-profile clearly shallower than ‘Minimum mass solar nebula’• Very young disk (accretion-heating dominated): ~R-0.5.• T Tauri disk (irradiative heating dominates outer disk): ~R-1

~ R-1~ R-1.5 (MMSS)

OverviewOverview• Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10-8 M/yr ~ R-1

• Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius)

SEDs of intermediate-mass starsSEDs of intermediate-mass stars

Classification of Meeus et al. 2001

Group I Group II

(Note: not to be confused with class 0,I,II,III of the Lada et al classification!)

AB Aurigae (Group I) HD104237 (Group II)

SEDs of intermediate-mass starsSEDs of intermediate-mass stars

Group I Group II

Fitting pure accretion disk models...Fitting pure accretion disk models...

€

need ˙ M = 7 ×10−7 Msun /yr

AB Aurigae (Group I) HD104237 (Group II)

€

need ˙ M = 2 ×10−7 Msun /yr

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...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...Dust evaporation: (puffed-up) inner rim...

AB Aurigae (Group I) HD104237 (Group II)

All sources: Dust inner rim might solve the NIR problemGroup 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...Reducing somehow the far-IR flux...

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)

AB Aurigae (Group I) HD104237 (Group II)

Irradiated surface & visc. heated midplaneIrradiated 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

z [AU]0.1 0.2

D’Alessio et al. model

SED of disk with hot surface layerSED of disk with hot surface layer

After: Chiang & Goldreich 1997Calvet et al. 1991; Malbet & Bertout 1991; Many 2D/3D RT papers

OverviewOverview• Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10-8 M/yr ~ R-1

• Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius)

• Tgas > Tdust in disk surface layers (ross <~ 1.0): gas and dust are not well coupled molecules can form

Disk surface layersDisk surface layers

ross=1

no PAHswith PAHs

ross=1

(Kamp & Dullemond 2004; Jonkheid et al. 2004; Nomura & Millar 2005;Kamp et al. 2005)

CTTS

HAe

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*mp/kr

Vertical cut at R = 9 AUVertical cut at R = 9 AU

Tgas

Tdust

Tevap

Molecules like H2, CO, OH etc. exist in these hot surface layers.

Vertical cut at R = 9 AUVertical cut at R = 9 AU

Tgas

Tdust

Tevaporation

H2/H

Vertical cut at R = 9 AUVertical cut at R = 9 AU

Tgas

Tdust

Tevaporation

H2/H CO/C/C+Molecules like H2, CO, OH etc. exist in these hot surface layers.

Gas temperature is set by the balance of photoelectric heating, H2 formation heating and OI, H2 line cooling.

Below ross~1, gas-grain collisions thermalize the gas and dust.

Vertical cut at R = 9 AUVertical cut at R = 9 AU

Tgas

Tdust

Tevaporation

PE heatingH2 formation

gas-graincollisions

CO/C/C+H2/H

Vertical cut at R = 9 AUVertical cut at R = 9 AU

Tgas

Tdust

Tevaporation

PE heatingH2 formation

gas-graincollisions

OI cooling Ly cooling

H2 lines

gas-graincollisions

Gas temperature is set by the balance of photoelectric heating, H2 formation heating and OI, H2 line cooling.

Below ross~1, gas-grain collisions thermalize the gas and dust.

CO/C/C +H2/H

Vertical cut at R = 9 AUVertical cut at R = 9 AU

Tgas

Tdust

Tevaporation

CO/C/C +H2/H

Vertical cut at R = 9 AUVertical cut at R = 9 AU

Tgas

Tdust

Tevaporation

Photoevaporation flow starts well below Tgas=Tevaporation

(Adams et al. 2004)

CO/C/C +H2/H

origin of theflow

OverviewOverview• Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10-8 M/yr ~ R-1

• Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius)

• Tgas > Tdust in disk surface layers (ross <~ 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 FUVStellar EUV and FUV

EUV FUV

Photoevaporation by the central star Photoevaporation by the central star

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)

rcritrcrit

viscous accretion

Disk evaporation by FUV photonsDisk evaporation by FUV photons

T Tauri star: Mgas = 0.03 M*, ~ 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

times

cale

Additional Applications of Additional Applications of Evaporation 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 Additional Applications of Evaporation 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

SummarySummary• Accretion determines the surface density as a function of radius: typical accretion rates are dM/dt~10-8 M/yr ~ R-1

• Vertical structure models predict SEDs: disks are flared disks possess an inner rim (dust evaporation radius)

• Tgas > Tdust in disk surface layers (ross <~ 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 disksSchematic view of protoplanetary disks

Dust

Schematic view of protoplanetary disksSchematic view of protoplanetary disks

Gas