Radiative Transfer in Protoplanetary Disks

Radiative Transfer in
Protoplanetary Disks
Christophe Pinte

Outline
•Context: Circumstellar Disks around Young Stars
•Elements of continuum radiative transfer
•Constraints from various techniques:
- thermal emission & spectroscopy,
- light scattering,
- polarization,
- infrared interferometry
•Multi-technique modelling
•Observation & modelling of Gas in disks

Text
From clouds
to envelopes,
to disks,
to planets

- Timescale for gas dispersal
and planet formation?
- Grain growth and settling ?
- Relative evolution of dust
and gas ?
Text
From clouds
to envelopes,
to disks,
to planets
?

Processes in Protoplanetary disks
Processes in Protoplanetary Disks
© Peter Woitke

Dust in Protoplanetary disks
•Dust grains are expected to grow by
coagulation and to settle by gravity
•Disks should have a stratified structure
•Physical models predict extremely short
timescales (

Why the need for Monte Carlo?
• multiple-scattering
• anisotropic scattering (+ polarisation)
• complex 3D structure
• benchmark: tested up to very high optical depths (106 42
)
• Fast: variance reduction techniques, MC + diffusion
approx., MC + ray-tracing
Lefevre et al 1982, 1983
Bjorkman & Wood, 2001
Wolf, 2003
Niccolini, 2003
Juvela, 2005
Pinte et al, 2006, 2009
marche
au hasard
environnement
circumstellaire
x
z
étoile
photon
stellaire
y
photon thermique
émis par le disque
limite
du modèle

© P. Woitke

Small grains
IR spectroscopy with Spitzer
Grains grow to μm sizes in the
surface
Evidence for grain growth
Grains grow to micron sizes …
Large grains
v. Boekel et al. 2003
v. Boekel et al 2003

Tau
First evidence of differential grain growth ?
β might be larger in
central parts of the disk
→ ALMA
See also Guilloteau et
al 2010
ISM dust
0 30 40 50 60 70 80 90 100
R (AU)
!
2.5
2
1.5
1
0.5
DG Tau
ISM dust
0
10 20 30 40 50 60 70 80 90 100
R (AU)
lope of the millimeter dust opacity β as a function of the radius for RY Tau (left panel) and
t panel). Values of β outside the colored Isella regionet are al excluded 2010
by our observations at more
vel. The dashed lines show the mean value of β derived in Paper I as discussed in Section 4.
0
2.5
2
1.5
1
0.5
RY Tau
I

Light scattering: anisotropy
56 2.6.4 Quelques remarques sur la distribution angulaire de rayonnement
Polarisability depends on grain size
S11
S11
0.012
0.010
0.008
10 +0
10 −2
10 −4
2πa
λ 0.012
=0.01 2πa
λ =0.1
0 90 180
0.010
0.008
10 −2
10 −4
0 90 180
1.5
10 −2
8.0
6.0
10 +0
10 +0
2πa
λ = 10 2πa
λ = 100 2πa
λ
angle de diffusion ( ◦ )
angle de diffusion ( ◦ )
10 −2
2πa
λ =1
= 1000
10
0 90 180
−4
angle de diffusion ( ◦ )
Figure 2.8 – Comparaison entre la fonction de phase calculée par la théorie de Mie (ligne pleine)
Mie theory grain size distribution dn(a) α a et la fonction de Henyey-Greenstein (ligne en tirets) de même premier moment g = 〈cos θ〉
-3.5 da

The case of GG Tau
•A 0.13M, 180AU-radius circumbinary ring
•Clear detection of the ring in scattered light
•Morphology extremely similar to visible
image
ISM dust models
match the visible
Image with i ! 40 o
HST (0.8µm)
Krist et al. (2002)
Keck AO (3.8µm)
Duchêne et al. (2004)
1”

A first direct evidence
Scattered light at Lʼ comes from 25AU above the
midplane; I band, 50AU above
•Arguably the most direct evidence of dust
stratification to date
Settling and/or growth?

atified model can reproduce all observations at once
GG Tau: models with dust stratification
ts
Models with
Observations Models without dust settling
Observations Models without dust settling with dust dust settling
> 5µm
Pinte et al. (2007)
Christophe Pinte An in-depth look at protoplanetary disks

G Tau : un anneau stratifié
Tau : un anneau stratifié
Pinte et al, 2007,
Pinte et al, 2007, A&A
G Tau : un anneau stratifié Pinte et al, 2007, A&A
GG Tau: a stratified ring
Images en lumière diffusée entre 0.5 et 3.8 µm
mages en lumière diffusée entre 0.5 et 3.8 µm
Images Stratification en lumière permet diffusée de entre les reproduire 0.5 et 3.8 µm simultanément
Model with stratification reproduces images from 0.5 to 3.8μm
Stratification permet de les reproduire simultanément
Obs Models Modèles
tratification permet de les reproduire simultanément
Obs Modèles
Obs Modèles
paramétrique
paramétrique
paramétrique
Lyon (Gonzalez) &
Lyon Lyon (Gonzalez) (Gonzalez) & &
Berne (Fouchet)
Berne Berne (Fouchet) (Fouchet)
hydro
modélisation hydrodynamique
hydr
hydro
modélisation modélisation hydrodynamique
hydrodynamique
+transfertradiatif
+transfertradiatif
+transfertradiatif
SPH simulations (Fouchet, Gonzalez, Lyon) + radiative transfer
Pinte et al 2007
Christophe Pinte Formation et évolution des systèmes planétaires 8/14
Christophe Pinte Formation et évolution des systèmes planétaires
Christophe Pinte Formation et évolution des systèmes planétaires 8/1

Dust grains properties
!"#$"%&'&()#$'%*+,()-,()."/%0(
!"#$%&'%()%*)+,-).//0
! !"#$%$&'(
! ")*+,-#' ./ 0-.-123)4.
HD 181327 (debris
56477-#8-32#9)6:
disk).
The dust is more
;-*##*4.3#
generation)

Evidence of non spherical grains

S11 S11 S11 S11
Signatures of agregates ?
0 50 100 150
sph1x.5x150#1(cmpt)
sph1x.5x150#7(fl 100)
sph1x.5x150 Average of #3,4,5
0 50 100 150
Angle de diffusion ( ◦ Angle de diffusion ( ) ◦ Angle de diffusion ( ) ◦ Angle de diffusion ( ) ◦ )
Mie sphere

Polarisability of dust grains
Unresolved polarisation Scattering & polarisation Dust properties
Effect Polarisability of particle depends size : polarisability on grain size
Grain size distribution: dn(a) ∝ a −3.5 da
S12/S11
S12/S11
1.0
0.5
0.0
1.0
0.5
0.0
2πamax
λ
2πamax
λ
0 90 180
angle
= 0.1
= 5
1.0
0.5
0.0
1.0
0.5
0.0
2πamax
λ
2πamax
λ
0 90 180
angle
= 1
= 10
1.0
0.5
0.0
1.0
0.5
0.0
2πamax
λ
2πamax
λ
0 90 180
angle
= 2
= 100
Mie theory Marshall Perrin &grain Christophesize Pinte distribution Polarimetry of Circumstellar dn(a) Disks around α aYoung Stars 6/13 -3.5 da

Polarisability of dust grains
Unresolved polarisation Scattering & polarisation Dust properties
Effect Polarisability of particle depends size : polarisability on grain size
& composition/porosity (real part of refractive index)
Grain size distribution: dn(a) ∝ a−3.5 Grain size distribution: dn(a) ∝ a da −3.5 da
S12/S11
S12/S11
1.0
0.5
0.0
1.0
0.5
0.0
2πamax 2πamax 2πamax
λ
2πamax 2πamax 2πamax
λ
0 90 180 180
angle
= 0.1
= 5
1.0
0.5
0.0
1.0
0.5
0.0
2πamax 2πamax
λ
2πamax 2πamax 2πamax
λ
0 90 180
angle
= 1
= 10
1.0
0.5
0.0
1.0
0.5
0.0
2πamax 2πamax 2πamax
λ
2πamax 2πamax 2πamax
λ
0 90 180
angle
= 2
= 100
Mie theory grain size distribution dn(a) α a -3.5 da
Marshall Perrin & Christophe Pinte Polarimetry of Circumstellar Disks around Young Stars 6/13

ect of chemical composition / porosity
Effect of chemical composition/porosity
Scattering phase function &
attering phase function &
polarisability both depend on
larisability also depend on
grain composition & porosity
ain composition & porosity
Porous grains produce larger
rous grains produce larger
polarization for same
larisation for same assymetry
asymmetry parameter
rameter g
need to constrain g
need to constrain g:
Polarisability
0.0
→ multi-technique analysis
lti-technique analyses 0.0 0.5 1.0
1.0
0.5
Porous grains (Mathis & Whieffen)
Compacts grains (Draine)
g

Introduction Scattering & polarisation Unresolved polarisation Resolved polarimetry Final remar
Solution is not unique !!!
GG Tau : models with stratification . . .
Models with well-mixed
A parametrized
stratification of dust
grains :
dust population can also
reproduce but this
requires an “exotic” dust
size distribution
h0(a) = h0(amin)
amin
a
dn(a) α a -5.5 da
A single model reproduce
all observations
ξ
ξ = 0.15 amax > 5 µm

odeling of disks
. polarisation can canhelp!!! help!!!
... polarization can help !!!
Gaspard Duchêne
Using polarimetry to refine the model
Using Usingpolarimetry polarimetryto torefine refine the the model model
Observations With Withstratification stratification
60%
15%
100
50
100
100
50
65%
15%
Without Without stratification
0
0 0 50 100
0 0
50 100 0
0 50 100 0 0
50 100
0 50 10
Observations Warning Warning : noteModel : note the the different with strat
different orientation! without strat
orientation!
Marshall
Marshall
Perrin
Perrin
& Christophe
& Christophe
Pinte
Pinte
Polarimetry
Polarimetry
of Circumstellar
of Circumstellar
Disks
Disks
around
around
Young
Young
Stars
Stars
12/14
12/14
100
50
100
50
80%
10%

Another example: AU Mic
HST 0.606 µm +pola
10−10 e débris autour d’une d’uneM0 M0
brillance
re revers vers35 35AU AU
ur r bleue bleue
mple ple à àdeux deuxzones zones
SED and images can be
SED SED + profils profils
la la and polarisation porous dust grains pour pour
re e les les propriétés propriétésdes desgrains grains
reproduced both with compact
Large polarisation → porous
Schneider grains (ices) et et al, al, 2006 2006
étude tude sur surHD HD181327 181327
ation des disques protoplanétaires 37/39
Fitzgerald et al 2007
Grains Grains poreux, Mathis &
Whieffen
λFλ (W/m2 )
λFλ (W/m2 )
m − m∗ (mag/arcsec2 )
m − m∗ (mag/arcsec2 )
10 −10
10−11 10−11 10−12 10−12 10−13 10−13 10−14 10−14 10−15 10−15 10−16 10−16 10−17 10−17 6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
100 101 102 103 100 101 102 103 λ (µm)
λ (µm)
H
H
V (F606W)
V (F606W)
2MASS
2MASS Spitzer
Spitzer IRAS
IRAS CSO
CSO JCMT
JCMT total
total inner
inner outer
outer stellar
stellar
10 20 30 40 50 60 80 100
10 20 30 40 50 60 80 100
projected distance (AU)
projected distance (AU)

Another example: AU Mic
HST 0.606 µm +pola
10−10 e débris autour d’une d’uneM0 M0
brillance
re revers vers35 35AU AU
ur r bleue bleue
mple ple à àdeux deuxzones zones
SED and images can be
SED ébris SED + autour profils profils d’une M0
la la and polarisation porous dust grains pour pour
illance
re e les les propriétés propriétésdes desgrains grains
vers 35 AU
reproduced both with compact
Large polarisation → porous
bleue
Schneider grains (ices) et et al, al, 2006 2006
étude tude sur surHD HD181327 181327
le à deux zones
ation des disques protoplanétaires 37/39
Grains Grains poreux, Mathis &
Whieffen
λFλ (W/m2 )
λFλ (W/m2 )
m − m∗ (mag/arcsec2 )
m − m∗ (mag/arcsec2 )
10 −10
10−11 10−11 10−12 10−12 10−13 10−13 10−14 10−14 10−15 10−15 10−16 10−16 10−17 10−17 0.456
6
0.407
7
0.35
8
8
0.30
9
0.25 9
10
0.20 10
11
0.15 11
12
0.10 12
0.05 13
13
0.00 14
14
100 101 102 103 10
λ (µm)
0 101 102 103 Grains poreux
λ (µm)
H
H
V (F606W)
V (F606W)
2MASS
2MASS Spitzer
Spitzer IRAS
IRAS CSO
CSO JCMT
JCMT total
total inner
inner outer
outer stellar
stellar
tion Études multi-tech. Sédimentation Naines brunes et * Herbig Disques évolués Concl
le : AU Mic
Fitzgerald et al 2007
Q 2 + U 2 /I
model
NW
SE
Porous grains
20 10 30 40 20 50 30 60 40 70 50 60 80 80 100 90
10 20 30 40 50 60 80 100
projected distance (AU)
projected distance (AU)

Another example: AU Mic
HST 0.606 µm +pola
10−10 e débris autour d’une d’uneM0 M0
brillance
re revers vers35 35AU AU
ur r bleue bleue
mple ple à àdeux deuxzones zones
SED and images can be
SED ébris SED + autour profils profils d’une M0
la la and polarisation porous dust grains pour pour
illance
re e les les propriétés propriétésdes desgrains grains
vers 35 AU
reproduced both with compact
Large polarisation → porous
bleue
Schneider grains (ices) et et al, al, 2006 2006
étude tude sur surHD HD181327 181327
le à deux zones
ation des disques protoplanétaires 37/39
Grains Grains poreux, Mathis &
Whieffen
λFλ (W/m2 )
λFλ (W/m2 )
m − m∗ (mag/arcsec2 )
m − m∗ (mag/arcsec2 )
10 −10
10−11 10−11 10−12 10−12 10−13 10−13 10−14 10−14 10−15 10−15 10−16 10−16 10−17 10−17 0.456
6
0.407
7
0.35
8
8
0.30
9
0.25 9
10
0.20 10
11
0.15 11
12
0.10 12
0.05 13
13
0.00 14
14
100 101 102 103 10
λ (µm)
0 101 102 103 Grains poreux
λ (µm)
H
H
V (F606W)
V (F606W)
2MASS
2MASS Spitzer
Spitzer IRAS
IRAS CSO
CSO JCMT
JCMT total
total inner
inner outer
outer stellar
stellar
tion Études multi-tech. Sédimentation Naines brunes et * Herbig Disques évolués Concl
le : AU Mic
Fitzgerald et al 2007
Q 2 + U 2 /I
model
NW
SE
Porous grains
Compact grains
20 10 30 40 20 50 30 60 40 70 50 60 80 80 100 90
10 20 30 40 50 60 80 100
projected distance (AU)
projected distance (AU)

Unresolved polarimetry: tomography of inner
The magnetospheric
accretion predicts
formation of warp at
the inner edge
disk
Tool to probe the disk-star interface
No. 2, 2004
of TeA is important for understanding the variability in different
spectral bands. The spots are expected to be smaller at
higher TeA and larger at lower TeA. An indication of such a
distribution may have been observed in the CTTS object BP
Tauri, where the estimated area of the hot spots was different
when different methods were used. Errico et al. (2001) esti-
mated the area to be 20% of the surface of the star. They used
spectral lines that are thought to originate in the external
regions of the funnel flow. Ardila & Basri (2000) estimated the
area to be much smaller, 0.3%. However, they modeled the UV
continuum, which originates in the hottest region of the spots.
DISK ACCRETION TO INCLINED DIPOLE. II. 925
Fig. 4.—X -Z slice through the middle of the funnel stream at ¼ 15 . The contour lines show the plane cross section of the density distribution inside the funnel
stream. The density changes exponentially from ¼ 0:2 (blue) to ¼ 2:0 (red). The density in the corona above the disk is ¼ 0:01 0:02. Red lines with arrows
show selected magnetic field lines. The magnetic moment, m, and the rotation axis, 6, are shown.
≈ 0.025 AU
4. INTENSITY OF RADIATION AND LIGHT CURVES
To calculate the radiation intensity from the hot spots,
we suppose that all the kinetic energy flux Fe(R) goes
into radiation. The energy radiated from a unit area of the
spot is
Figure from Romanova et al 2004
Z
Fe(R) ¼
cos >0
d f (R; m); ð5Þ
where f (R; m) is the intensity of the radiation from a unit area

i
mary:
Tomography of the inner disk
variable achromatic
ction
ltation by a
prehensive monitoring
ormed” AA Taudisk
y rotation periods
Interaction with
magnetosphere
mary:
See Terquem &
Quick summary:
Papaloizou 2000
variable achromatic
ction
ltation by a
ormed” disk
synoptic monitoring
Many rotation periods
Need variable achromatic
extinction → occultation
Interaction with
magnetosphere
Wood et al 1996
Ménard et al 2003
O’Sullivan et al 2005
Bouvier et al, 1999
Marshall Perrin & Christophe Pinte Polarimetry of Circumstellar Disks around Young Stars 2/1
by a “deformed” disk

i
mary:
Tomography of the inner disk
variable achromatic
ction
ltation by a
prehensive monitoring
ormed” AA Taudisk
y rotation periods
Interaction with
magnetosphere
mary:
See Terquem &
Quick summary:
Papaloizou 2000
variable achromatic
ction
ltation by a
ormed” disk
synoptic monitoring
Many rotation periods
Need variable achromatic
extinction → occultation
Interaction with
magnetosphere
Unresolved polarisation Scattering & polarisation D
Inner region model
Bouvier et al, 1999
Marshall Perrin & Christophe Pinte Polarimetry of Circumstellar Disks around Young Stars 2/1
by a “deformed” disk
2%
Pola
Photo-polarimetric variation 0%
Wood et al 1996
Ménard et al 2003
O’Sullivan et al 2005

ng the inner radius of circumstellar disks
Measuring the inner radius of disks
teristic NIR size measured by interferometers
Characteristic NIR size measured by interferometers < 1 AU:
:comparabletothelocationofterrestrialplanetsin
comparable to the location of terrestrial planets in more
volved systems
odel
evolved systems
ple emission model :
Ring model:
resolved central star + narrow
g
simple emission model:
unresolved central star + narrow
ative contribution from the
ring
r and the disk estimated from
relative contribution from star &
uxdecompositionofthe
disk estimated from SED
ad-band SED (Millan-Gabet
01)

Ring Radius (AU)
100.00
10.00
1.00
0.10
0.01
Inner radius ot T Tauri stars
Radii inferred from interferometry larger than predicted
HAe Objects
HBe Objects
TTS Objects
Sublimation radius: direct dust heating, backwarming
Sublimation radius: direct dust heating, no backwarming
Sublimation radius: standard model
10 0
10 0
10 0
Herbig Ae
10 2
10 2
10 2
Lstar + Laccretion (Lsolar)
10 4
10 4
10 4
1000K 1000K 1000K
1000K 1000K
1500K 1500K 1500K
1500K 1500K 1500K
1000K 1000K 1000K
1500K 1500K 1500K
10 6
10 6
10 6
Direct heating of inner dust disk
Star
(magnetospheric
accretion?)
optically!thin gas
(puffed!up
inner wall?)
Dust Sublimation
Radius R s
"Standard" Disk Model ! oblique disk heating
Star
(magnetospheric
accretion?)
optically!thick
gas
Dust Sublimation
Radius R s
Fig. 2.— Measured sizes of HAeBe and T Tauri objects vs. central luminosity (stellar + accretion shock); and com
sublimation Millan-Gabet radii for dust directly et heated heatedal by by2006 the central luminosity (solid and dashed lines) and for the oblique heating i
classical models (dotted line). A schematic representation ofthekeyfeaturesofinnerdiskstructureinthesetwoclasses
f
flared flared flared disk disk disk

Ring Radius (AU)
100.00
10.00
1.00
0.10
0.01
Inner radius ot T Tauri stars
Radii inferred from interferometry larger than predicted
HAe Objects
HBe Objects
TTS Objects
Sublimation radius: direct dust heating, backwarming
Sublimation radius: direct dust heating, no backwarming
Sublimation radius: standard model
10 0
10 0
10 0
Sublimation radius
Herbig Ae
10 2
10 2
10 2
Lstar + Laccretion (Lsolar)
10 4
10 4
10 4
1000K 1000K 1000K
1000K 1000K
1500K 1500K 1500K
1500K 1500K 1500K
1000K 1000K 1000K
1500K 1500K 1500K
10 6
10 6
10 6
Direct heating of inner dust disk
Star
(magnetospheric
accretion?)
optically!thin gas
(puffed!up
inner wall?)
Dust Sublimation
Radius R s
"Standard" Disk Model ! oblique disk heating
Star
(magnetospheric
accretion?)
optically!thick
gas
Dust Sublimation
Radius R s
Fig. 2.— Measured sizes of HAeBe and T Tauri objects vs. central luminosity (stellar + accretion shock); and com
sublimation Millan-Gabet radii for dust directly et heated heatedal by by2006 the central luminosity (solid and dashed lines) and for the oblique heating i
classical models (dotted line). A schematic representation ofthekeyfeaturesofinnerdiskstructureinthesetwoclasses
f
flared flared flared disk disk disk

Ring Radius (AU)
100.00
10.00
1.00
0.10
0.01
Inner radius ot T Tauri stars
Radii inferred from interferometry larger than predicted
HAe Objects
HBe Objects
TTS Objects
Sublimation radius: direct dust heating, backwarming
Sublimation radius: direct dust heating, no backwarming
Sublimation radius: standard model
CTTS
10 0
10 0
10 0
Sublimation radius
Herbig Ae
10 2
10 2
10 2
Lstar + Laccretion (Lsolar)
10 4
10 4
10 4
1000K 1000K 1000K
1000K 1000K
1500K 1500K 1500K
1500K 1500K 1500K
1000K 1000K 1000K
1500K 1500K 1500K
10 6
10 6
10 6
Direct heating of inner dust disk
Star
(magnetospheric
accretion?)
optically!thin gas
(puffed!up
inner wall?)
Dust Sublimation
Radius R s
"Standard" Disk Model ! oblique disk heating
Star
(magnetospheric
accretion?)
optically!thick
gas
Dust Sublimation
Radius R s
Fig. 2.— Measured sizes of HAeBe and T Tauri objects vs. central luminosity (stellar + accretion shock); and com
sublimation Millan-Gabet radii for dust directly et heated heatedal by by2006 the central luminosity (solid and dashed lines) and for the oblique heating i
classical models (dotted line). A schematic representation ofthekeyfeaturesofinnerdiskstructureinthesetwoclasses
f
flared flared flared disk disk disk

Ring Radius (AU)
100.00
10.00
1.00
0.10
0.01
Inner radius ot T Tauri stars
Radii inferred from interferometry larger than predicted
HAe Objects
HBe Objects
TTS Objects
Sublimation radius: direct dust heating, backwarming
Sublimation radius: direct dust heating, no backwarming
Sublimation radius: standard model
CTTS
10 0
10 0
10 0
Sublimation radius
Herbig Ae
10 2
10 2
10 2
Lstar + Laccretion (Lsolar)
10 4
10 4
10 4
1000K 1000K 1000K
1000K 1000K
1500K 1500K 1500K
1500K 1500K 1500K
1000K 1000K 1000K
1500K 1500K 1500K
10 6
10 6
10 6
Star
accretional
Direct heating of inner dust disk
heating? lower
sublimation
optically!thin gas
temperature?
(magnetospheric
accretion?)
smaller dust
grains?
photoevaporation?
optically!thick
gas
magnetospheric
Dust Sublimation
truncation?
(puffed!up
inner wall?)
Dust Sublimation
Radius R s
"Standard" Disk Model ! oblique disk heating
Star
(magnetospheric
accretion?)
Radius R s
scattered light?
Fig. 2.— Measured sizes of HAeBe and T Tauri objects vs. central luminosity (stellar + accretion shock); and com
sublimation Millan-Gabet radii for dust directly et heated heatedal by by2006 the central luminosity (solid and dashed lines) and for the oblique heating i
classical models (dotted line). A schematic representation ofthekeyfeaturesofinnerdiskstructureinthesetwoclasses
f
flared flared flared disk disk disk

!.F! (W.m )
hy should should we we care care about about scattered light light ? ?
Why should we care about scattered light?
ak Peak of the of the photosphere moving moving towards towards longer longer λ λ
Peak of the photosphere moving towards longer λ
action Fraction of stellar of stellar (and (and then then also also scattered) light light is larger is larger
Fraction of stellar (and then also scattered) light is larger
bedo Albedo can can be large be large in the in the NIR NIR ! !
10 −12
10 −14
10 −16
Albedo can be large in the NIR ! between 0.4 and 0.9 at 2.2
albedo albedo between between 0.4 0.4 and and 0.9 0.9 at 2.2 at 2.2 µm, µm, dependingon
μm, depending on grain sizes and dust composition
grain grain sizes sizes and and dust dust composition
!.F! (W.m −2 )
10 −12
10 −14
10 −16
Herbig Herbig Ae star Ae star
0.1 0.1 1.0 1.010.0 10.0 100.0 100.0 1000. 1000.
! (µm) ! (µm)
!.F! (W.m −2 )
10 −12
10 −14
10 −16
!.F! (W.m −2 )
10 −12
10 −14
10 −16
TTauristar
0.1 0.1 1.0 1.010.0 10.0100.0 100.0 1000. 1000.
! (µm) ! (µm)

But models were neglecting
scattered light, which is the
dominant contribution
→ over-estimation by factor 2
Inner radius of T Tauri stars
Inner radius measured by IR interferometry apparently larger
than sublimation radius for T Tauri stars
Need for detailed RT codes like
MCFOST
Interpretation of AMBER data:
Tatulli et al 2008
Benisty et al 2010
Olofsson et al 2010
Tatulli et al 2010
1 AU
Total Thermal emission
Scattered light Scat. thermal em.
FOV VLTI
Pinte et al 2008

Introduction MCFOST IM Lup GG Tau IRAS 04158 Inner dust disk Summary
Introduction MCFOST IM Lup GG Tau IRAS 04158 Inner dust disk Summary
What radius would have been measured ?
What What radius radius would would
What radius would have have have
been been been
measured measured
?
?
Synthetic Disk model image
Synthetic image
Fitted ring
Fitted ring
Fitted ring
Scattered light can be a sufficient explanation
Scattered light can be a sufficient explanation
Scattered The location light can of fitted be ainner sufficient radii explanation mimics very
The location of fitted inner radii mimics very
The well location the distribution of fitted inner of data radii points mimics very
d=140 pc, B = 80 mwell
the distribution of data points
d=140 pc, B = 80 m well the distribution of data points
d=140 pc, B = 80 m
Teff =4000K,
Teff =4000K,
Teff =4000K,
Rin Rin (AU) (AU)
Rin (AU)
0.5
0.5
0.5
0.2
0.2
0.2
0.1
0.1
0.1
0.05
0.05
0.05
0.02
0.02
0.02
1.0 10.0
1.0 L (Lsun) 10.0
1.0 L (Lsun) 10.0
L (Lsun)
Scattered light is a sufficient explanation
The location of fitted inner radii mimics very
Christophe Pinte An in-depth look at protoplanetary disks 29/31
Christophe Pinte An in-depth look at protoplanetary disks 29/31
Christophe Pinte An in-depth look at protoplanetary disks 29/31
well the distribution of data points

Introduction Activités Activités de de recherche recherche Projet Projet de de recherche recherche Résumé Résumé
Un Un exemple exemple : IM : IMLup, Lup, une une CTTS CTTStypique typique
Multi-λ modelling of IM Lupi
Modélisation du dudisque disque d’IM Lup Pinte et etal, al, 2008b, A&A
!.F! (W.m−2 !.F! (W.m
)
−2 )
A single model with mild stratification remarkably reproduces
all Un Un observations: unique modèle H(1mm) avec une une ≈ 0.5 faible H(1μm) stratification
reproduit remarquablement bien l’ensemble des données
WFPC2 bien l’ensemble 0.6 μm des données
1’’
E
N
1.0
WFPC2 0.6 0.6 µm µm
SMA SMA1.3 1.3mm mm
10−12 10−12 10−14 10−14 2
2
10−16 10−13 10−16 10−13 5.
5.
10.0
10.0
20.
20.
1.0
1.0
10.0
10.0
100.0
100.0
1000.
1000.
! (µm) ! (µm)
⇓⇓
Mdisque, croissanceet
Mdust,
croissanceet
grain growth
sédimentation
& settling
➜
10 C. Pinte et al.: Probing dust grain evolution in IM
1’’
1’’
E
E
N
Nicmos
Nicmos 1.6
1.6
Nicmos 1.6 µm µm
μm
Obs Modèles
Model
⇓
F" (Jy)
F" (Jy)
F" (Jy)
F" (Jy)
0.2
0.2
0.1
0.1
0.05
0.05
0.02
0.02
0.01
0.01
0.005
0.005
p=0 p=0 p=1 p=1
ATCA 3.3 3.3 mm mm
p=2 p=2
p=0 p=0
0 50 100
0 50 100
Baseline
Baseline
(k!)
(k!)
p=2 p=2
p=1 p=1
⇓
Densité de surface
Σ(r) ∝ r −p
⇓
Densité de surface
Σ(r) ∝ r −p
Surface density
Σ(r) α r-p Coll. Coll. Grenoble (Ménard, Augereau, Duchêne), JPL/Caltech (Padgett,Stapelfeldt),
Pinte et al 2008
Arizona (Schneider), Leiden Leiden (Panić, van vanDishoeck), Dishoeck), Spitzer Legacy Team Teamc2d c2d
N
Brightness profile
0.5
0.0
0 90 180 270
Azimuthal angle ( o )
Fig. 8. Scattered light images of the best models compared to observations. L
at 0.606 µm andthelowerrowtothoseat1.6µm. Synthetic maps (right) w
from theRext, peak). Rext, Central i, i, H0
H0panel:
0.6 µm azimuthalbrightnessprofile.Right
central Rout, and right i, Ho, panels, grain the red dashed line correspond to the best fit of the
of all observations simultaneously and the blue dotted to the scatteredlight
in the front side of the disc, i.e. towards bottom in the first panel.
➜
size, composition
➜

≈ 400 000 models
Some parameters
fixed from data
(amax, Mdust, Rout)
→Fitting for 6
parameters
IM Lupi: quantitative constraints
Bayesian method to estimate model parameters:
for SED
Pinte et al 2008
Probability
Probability Probability Probability Probability Probability
1.0
0.5
0.0
1.0
0.6
0.4
0.2
0.5
cos(i)
0.0
0.05 0.1 0.2 0.5 1.0
rin
1.0
0.5
0.0
0.0
1.0
0.5
0.0
0
−1
−2
5 10 15
1.0
0.5
0.0
0.6
0.4
0.2
1.0 1.1 1.2
surface density flaring
0.0
0.00 0.05 0.10 0.15 0.20
H stratification
See also Glauser et al 2008, Bouy et al 2008, Duchêne et al 2010

≈ 400 000 models
Some parameters
fixed from data
(amax, Mdust, Rout)
→Fitting for 6
parameters
IM Lupi: quantitative constraints
Bayesian method to estimate model parameters:
for SED + mm visibilities
Pinte et al 2008
Probability
Probability Probability Probability Probability Probability
1.0
0.5
0.0
1.0
0.6
0.4
0.2
0.5
cos(i)
0.0
0.05 0.1 0.2 0.5 1.0
rin
1.0
0.5
0.0
0.0
1.0
0.5
0.0
0
−1
−2
5 10 15
1.0
0.5
0.0
0.6
0.4
0.2
1.0 1.1 1.2
surface density flaring
0.0
0.00 0.05 0.10 0.15 0.20
H stratification
See also Glauser et al 2008, Bouy et al 2008, Duchêne et al 2010

≈ 400 000 models
Some parameters
fixed from data
(amax, Mdust, Rout)
→Fitting for 6
parameters
IM Lupi: quantitative constraints
Bayesian method to estimate model parameters:
for SED + mm visibilities + scattered light images
Pinte et al 2008
Probability
Probability Probability Probability Probability Probability
1.0
0.5
0.0
1.0
0.6
0.4
0.2
0.5
cos(i)
0.0
0.05 0.1 0.2 0.5 1.0
rin
1.0
0.5
0.0
0.0
1.0
0.5
0.0
0
−1
−2
5 10 15
1.0
0.5
0.0
0.6
0.4
0.2
1.0 1.1 1.2
surface density flaring
0.0
0.00 0.05 0.10 0.15 0.20
H stratification
See also Glauser et al 2008, Bouy et al 2008, Duchêne et al 2010

≈ 400 000 models
Some parameters
fixed from data
(amax, Mdust, Rout)
→Fitting for 6
parameters
IM Lupi: quantitative constraints
Bayesian method to estimate model parameters:
for SED + mm visibilities + scattered light images
Pinte et al 2008
Probability
Probability Probability Probability Probability Probability
1.0
0.5
0.0
1.0
0.6
0.4
0.2
0.5
cos(i)
0.0
0.05 0.1 0.2 0.5 1.0
rin
1.0
0.5
0.0
0.0
1.0
0.5
0.0
0
−1
−2
5 10 15
1.0
0.5
0.0
0.6
0.4
0.2
1.0 1.1 1.2
surface density flaring
0.0
0.00 0.05 0.10 0.15 0.20
H stratification
See also Glauser et al 2008, Bouy et al 2008, Duchêne et al 2010

• Gas represents 99% of
the disk mass
• Difficult to observe but
Herschel is opening the
far-IR window
• Gas & dust evolution
strongly coupled
Gas and Dust Evolution
Gas & Dust evolution
VIMOS Multi-object Spectroscopy and Spitzer/IRA
Fedele et al. 2009
Fedele et al. (2009, Poster A 31)

IR excesses, we can measure a truly independent gas depletion timescale and examine the possibility of gas rich,
dust poor systems. These objects are (initially) only observed in [CII]158µm and [OI]63µm and account for
Gas in Protoplanetary Systems
14% of the Phase I time. A significant fraction of the targets are multiple stars (25%, separations 5-1000 AU),
enabling the survey to be used to study the effect of companions on gas disks. These have not been excluded
to avoid selection bias. Finally the target list has a wide range of X-ray luminosity (10 28 − 10 31 erg s −1 ) and
Hα line strength (W (Hα) =1− 150 ˚A). This allows multivariate analysis of line strengths and ratios, which
is only possible with such a large and unbiased sample, and increases the legacy value. An estimate of the
Statistical survey (≈ 250 disks) : evolution of gas
required number of targets is given by the number of bins of primary parameters (mass, spectral type and age):
Ntargets = Nmass.Nsp.t.Nage.N, whereN is the number in each bin. To investigate effects of other parameters
and dust from young gas-rich protoplanetary disks,
and give a statistically-robust result, we have set Nb = 10. A minimum of 3 logarithmically-spaced bins of
each parameter means we need ∼270 targets. Figure 4 shows the distribution over the primary parameters, and
Table 4 summarises the sample clusters.
to old “dry” debris disks:
Table 4. Target clusters
•Ages 1 – 30Myr, M to A stars, disk dust mass (10-2 - 10-5 Distance Age Total Number Mo)
Group (pc) (Myr) number Phase I
Taurus 140 0.3 − 4 109 48
Upper Sco 145 5 48 2
η Cha 112 5 − 9 17 1
TW Hya 50 8 − 10 13 0
β Pic 30 10 − 20 19 0
Tuc Hor 46 30 18 0
Ae/Be stars 50 − 200 0.5 − 30 50 26
•Well-known star-forming regions (Taurus, TW Hydra, η Cha,
β Pic, Tuc Hor, Upper Sco, Herbig Ae/Be)
•Key far-IR tracers: [OI], [CII], H2O, CO + Phot. at 70 & 160μm

Modelling tools: MCFOST + ProDiMo
Interpretation of line observations is complex !
→ need for detailed modelling.
MCFOST: 3D continuum & line radiative transfer (Pinte et al
2006, 2009)
+ ProDiMo: thermal balance & chemistry (Woitke et 2009,
Kamp et al 2010)

Modelling tools: MCFOST + ProDiMo
Interpretation of line observations is complex !
→ need for detailed modelling.
MCFOST: 3D continuum & line radiative transfer (Pinte et al
2006, 2009)
+ ProDiMo: thermal balance & chemistry (Woitke et 2009,
Kamp et al 2010)

Modelling tools: the DENT grid
Grid of ≈ 300 000 disk
models:
•sample the disk parameters
observed by GASPS
•thermo-chemical structure:
Tdust, Tgas, abundances
•SEDs
•29 line fluxes and profiles:
[OI], [CII], 12 CO, o-H2O,
p-H2O
→ Statistical tool
78.74 423 423 423 → 312 312 312 0.484 LAMBDA
p-H2O 303.46
269.27
144.52
138.53
100.98
89.99
202 202 202 → 111 111 111
111 111 111 → 000 000 000
413 413 413 → 322 322 322
313 313 313 → 202 202 202
220 220 220 → 111 111 111
322 322 322 → 211 211 211
0.0058
0.0184
0.0332
0.125
0.260
0.352
LAMBDA
LAMBDA
LAMBDA
LAMBDA
LAMBDA
LAMBDA
Table 2. Parameters for the model grid and values assumed. Constant
scale height H0 H0 H0 = 10 AU is assumed at r0 r0 r0 = 100 AU and a constant
maximum grain Ménard size of et amax amax amax =1mm. al, in prep.
stellar parameter
Woitke et al 2010
Kamp et al, in prep.
M⋆ M⋆ M⋆
age
stellar mass [M⊙]
age [Myr]
0.5, 1.0, 1.5, 2.0,2.5
1, 3, 10, 100
fUV fUV fUV excess UV fUV fUV fUV = LUV/L⋆ LUV/L⋆ LUV/L⋆ 0.001, 0.1
disc parameter
Md disc dust mass [M⊙] 10−7 ,10−6 ,10−5 ,10−4 ,10−3 Md disc dust mass [M⊙] 10−7 ,10−6 ,10−5 ,10−4 ,10−3 Md disc dust mass [M⊙] 10−7 ,10−6 ,10−5 ,10−4 ,10−3 δ = ρd/ρg ρd/ρg ρd/ρg dust/gas mass ratio 0.001, 0.01, 0.1, 1, 10
Rin Rin Rin inner disc radius [Rsubli] 1, 10, 100
Rout outer disc radius [AU] 100, 300, 500
ɛ column density NH(r) ∝ r−ɛ Rout outer disc radius [AU] 100, 300, 500
ɛ column density NH(r) ∝ r 0.5, 1.0, 1.5
−ɛ Rout outer disc radius [AU] 100, 300, 500
ɛ column density NH(r) ∝ r 0.5, 1.0, 1.5
−ɛ 0.5, 1.0, 1.5
β
r
β flaring H(r) = H0
dust parameter
r0
0.8, 1.0, 1.2
s settling H(r, a) ∝ H(r) a−s/2 0, 0.5
amin minimum grain size [µm] 0.05, 1
radiative transfer parameter
i inclination 0o , 41.41o , 60o , 75.52o , 90o β flaring H(r) = H0
dust parameter
r0
0.8, 1.0, 1.2
s settling H(r, a) ∝ H(r) a
(edge-on)
−s/2 0, 0.5
amin minimum grain size [µm] 0.05, 1
radiative transfer parameter
i inclination 0o , 41.41o , 60o , 75.52o , 90o β flaring H(r) = H0
dust parameter
r0
0.8, 1.0, 1.2
s settling H(r, a) ∝ H(r) a
(edge-on)
−s/2 0, 0.5
amin minimum grain size [µm] 0.05, 1
radiative transfer parameter
i inclination 0o , 41.41o , 60o , 75.52o , 90o (edge-on)
3. Gas physics and chemistry
200 000 cpu-hours (ANR “Dusty
The large number of disk models makes it impossible to carry
out an individual study of their chemical and thermal structure.
Hence in the following, we study the statistics of species gas
temperatures and masses and how they depend on certain grid
Disk” supercomputer, PI: F. Ménard)

HD169142 in PAHs
Imaging in Mid-IR
VISIR observations
→ disk resolved in continuum
and PAHs bands
Model consistent with
observations
→ confirms amount of PAHs
and geometry of the disk
surface
See also Lagage et al, 2006
and Doucet et al, 2007
J. Ibanez et al.: Extended PAH
Fig. 3. Image of the disk of HD 169142 in the continuum centered at
12.81µm. The image has been PSF subtracted. North is up and East
to the left (VERFIER, Justine, tu confirmes? A distance of 145pc is
assumed.

Spatial origin
of the lines
HD 169142
z/r
z/r
z/r
z/r
z/r
0.6
0.4
0.2
0.6
0.4
0.2
0.6
0.4
0.2
0.6
0.4
0.2
0.6
0.4
0.2
0 2 4 6 8
log n O [cm -3 ]
0 2 4 6 8
log n O [cm -3 ]
0 2 4 6 8
log n C+ [cm -3 ]
0 2 4 6 8
log n 12CO [cm -3 ]
0 2 4 6 8
log n 13CO [cm -3 ]
[OI] 63.18µm
[OI] 145.53µm
[CII] 157.74µm
12CO 1300.40µm
13CO 1360.23µm
0.0
0.1 1.0 10.0
r [AU]
100.0

z / r
1.0
0.8
0.6
0.4
0.2
0.0
1.0 1.5 2.0 2.5 3.0 3.5 4.0
log Tg [K]
! ver
Effect of X-ray irradiation
G. Aresu et al.: X-ray impact on the protoplanetary disks around T
! rad
1 10 100
r [AU]
z / r
1.0
0.8
0.6
0.4
0.2
0.0
1.0 1.5 2.0 2.5 3.0 3.5 4.0
log Tg [K]
T gas = 8000 K
! X (1 keV) ! rad
! ver
1 10 100
r [AU]
Fig. 1. Gas temperature distribution: Model 1 (UV only) in the left panel, X-ray models wit
10 32 erg s −1 (Model 5) in the middle and right panel respectively. Contour lines are over-plo
G. Aresu et al, 2010
depth at 550 nm, dashed line), τver = 1 (vertical dust optical depth at 550 nm, dotted line)
keV
Far-IR
(dot-dashed
lines
line).
significantly
The relative position
affected
of these two
only
depth
if
depend strongly on the assum
solid line corresponds to Tgas = 8000 K.
LX ≥1031 erg/s
z / r
1.
0.
0.
0.
0.
0.

[OI] 63 µm [W.m −2 ]
Effect of X-ray irradiation
5
2
10 −16
5
2
fPAH = 0.01
fPAH = 0.001
10 +28 10 +29 10 +30 10 +31 10 +32
LX [erg/s]
G. Aresu et al, 2010
Far-IR lines significantly affected only if LX ≥10 31 erg/s

Concluding remarks
A variety of datasets = finer disk models
•Spatial differentiation is frequent in disks around T Tauri
stars
•Similar studies in Herbig Ae disks, disks around brown
dwarfs and debris disks are now possible
•Testing the physics of dust grains towards planet formation:
separate dust populations, non-spherical aggregates?
• Combining fine-structure lines, CO sub-mm lines and dust
observations + detailed modelling is a powerful diagnosis:
main gas heating mechanism, dust-to-gas ratios, ...