Observing Protoplanetary Disks at Long Wavelengths

1
Observing Protoplanetary Disks at Long Wavelengths

• Kobe International School of Planetary Sciences
• Origins of Planetary Systems
• 13 July 2005

Steven Beckwith Space Telescope Science Institute
2
Outline

• The signatures of disks in spectral energy
  distributions
• Inferring the physical properties of disks from
  the radiation signatures
• Unique degenerate parameters
• Addition of spatial information
• Disk particles
• Spectral signatures
• Size and composition dust chemistry
• Disk dynamical properties
• Orbital infall signatures
• Future observations
• Spatial information (interferometry)
• High resolution spectra (disk chemistry)

3
Spectral energy distributions
Adams, Lada, Shu 1988, Ap. J., 326, 865.
Far IR optical depth t 1 at 100 mm t
0.01 at 1 mm
\ t ³ 100 at 1 mm Þ AV ³ 300
nFn
Observed AV 3
Excess emission over photosphere
\ clear line of sight to star and dust.
n3 blackbody
XX Cha
Wavelength (mm)
4
Why does a disk dominate the infrared emission?

• Spectral Energy Distributions
• (SEDs)

5
Thin, black disk "standard theory"
Lynden-Bell Pringle 1974, MNRAS, 168, 603.
Adams, Lada, Shu 1988, Ap. J., 326, 865.
Star luminosity, L
angle q
L
D
flat, black disk
Power/area absorbed
T(r) r -3/4
Power/area emitted sT4
Also true for accretion energy.
6
Spectral Energy Distribution (SED)
B?(T)
L
area element
surface emission
T(r) r-3/4
Þ nFn n4/3
7
Thin disk SED observations
Adams, Lada, Shu 1988, Ap. J., 326,
865. Beckwith et al. 1990, AJ, 99, 924
Thin disk nFn n4/3
The SED from a theoretically thin black disk
almost never fits the observations of young stars
with excess infrared emission!
XX Cha

• most SEDs flatter than n4/3
• some SEDs very flat, ?Fn ?0

8
Power law nFn Þ power law T(r)
Lynden-Bell Pringle 1974, MNRAS, 168, 603.
Adams, Lada, Shu 1988, Ap. J., 326, 865.
T(r) T0(r/r0) -q
XX Cha
a 4-2/q
na
Þ nFn na n4-2/q
n3
q 1/2 for a flat SED

• we can derive q from a
• T(r) uniquely follows from a

9
How are disks really heated?

• "Standard" flat, black disks with accretion
• Lynden-Bell Pringle 1974, MNRAS, 168, 603.
• Adams, Lada, Shu 1987, Ap.J., 312, 788 1988,
  Ap.J., 326, 865.
• Flaring
• Kenyon Hartmann 1987, Ap.J., 323, 714.
• Calvet et al. 1994, Ap.J., 434, 330. (w/ rad.
  trans. envelope)
• Chiang Goldreich 1997, Ap.J., 490, 368. (w/
  rad. trans., disk only)
• Scattering halo
• Natta 1993, Ap.J., 412, 761.
• Wave-driven accretion heating
• Shu et al. 1990, Ap.J., 358, 495.

10
Geometrical changes Flaring
Kenyon Hartmann 1987, Ap. J., 323, 714.
Star luminosity, L
angle q'
h
Flared, black disk

• gravity (z/r)(GM/r2) r-3
• absorbed radiation sinq' gtgt sinq
• Tflare(r) gt Tflat(r), especially at large r

Ti(r) r-6/15

• BUT
• cannot account for flat SEDs (6/15 lt 1/2)
  
• still assumes black disk (no radiative
  transfer)

11
Radiative transfer
Chiang Goldreich 1997, Ap. J., 490, 368.
Surface t 1 in optical
Star luminosity, L
angle q'
D
Interior t gt 1 in infrared

• optical light absorbed tV 1, tIR ltlt 1
• small grains "bare" gt Tgrain gt Tblackbody
• disk emission tIR lt 1 (5 - 100 mm)

Still cannot account for very flat SEDs but does
fit majority.
Prediction disk surface emission is optically
thin
12
Radiative heating isolated particle
Particle radius a (spherical rapidly
spinning) Temperature T
Distance r
Emitted radiative power 4pa 2 sT 4
Luminosity L
Using en for small particles T r -2/5
cf L. Spitzer, Jr., Physical Processes in the
Interstellar Medium, ch. 9.1
13
Disk Exercises

• Calculate the typical disk radii (distance from
  the star) sampled by different wavelengths
• ?(µm) 1, 2, 4, 10, 100
• L 0.2, 1, 5 Lsun
• Vary assumptions about temperature (Tr-1/2,
  Tr-2/5, etc.)
• What areas of a disk do different search
  techniques sample?
• Set up a model calculation of an SED using the
  tools of the last few slides and show how the SED
  varies with different model parameters (rmin,
  rmax, q)
• Use MathCad, Mathematica, C, or a similar program
  to make numerical calculations easy
• Vary disk inclination to the line-of-sight

14
Physical Modification Holes
L
Disk
rmin
hole
rmin R
rmin 5 R
SED from continuous flat-spectrum disk
100
5 R hole in center
nFn
rmin 50 R (0.5 AU) hole in center (large)
Star SED
10
To produce an observable flux deficit, the hole
must be large, 10x larger than the star
1
10
100
Wavelength (mm)
15
Inner holes produce flux deficits
34
Flared equilibrium disk
GM Aur
Superheated surface layer with small
grains produces infrared light.
Flux deficit from interior hole
33
32
Stellar blackbody
Log nFn (erg s-1)
31
Interior hole
Disk interior t gt 1
Disk surface t lt 1
30
29
100
1000
1
10
Wavelength (mm)
16
Evolution of structure
L
K
H
a
3
3
2
-
2
0
P
I
A

7
.
2
1
0
0
0
11
1
0
0
(Jy)x10
n
F
1
0
n
As disks age, the hole sizes should increase
1
0
.
1
1
1
0
1
0
0
l
m
(
m
)
C
S

C
h
a
P
I
A

7
.
2
1
0
0
0
1
0
0
11
HR4796
(Jy)x10
1
0
n
F
n
1
0
.
1
Weinberger et al. 1999, ApJ Let, 525, L53
0
.
1
1
1
0
1
0
0
l
m
(
m
)
17
Fomalhaut Ring Emission
Kalas et al. 2005, Nature, 435, 1067
Holland et al. 2003, ApJ, 582, 1141
18
Vega-type stars Fomalhaut
Dent et al. 2000, MNRAS, 314, 702
1000 µm grain radius
Note inner hole
300
100
30
T 40 K BB
10 µm
? 1.1
These results indicate a typical grain is 100 µm
in size. The models assume fixed total grain mass.
Ring rmin 100 AU rmax 140 AU
Mgrains 1.4Mmoon
Figure 6 varying grain size
Figure 1 Best fit
19
Modification 2 Gaps Rings
HD 4796
Fomalhaut
Gaps must be large to cause observable changes to
the SEDs
rring 130 AU ?ring 25 AU
Weinberger et al. 1999
100
nFn
r1 67, r2 150, Log(?) 0.35
Kalas, Graham, Clampin 2005
r1 50, r2 200, Log(?) 0.60
10
r1 25, r2 400, Log(?) 1.20
1
10
100
Wavelength (mm)
20
Optically thin, dT/dr gt 0 Þ Emission features
Chiang Goldreich 1997, Ap. J., 490, 368.
Superheated surface layer with small grains.
cf Cohen Witteborn 1985, Ap. J.
33
Stellar
32
31
Surface
log Ln (erg s-1)
30
Optically thick interior
29
Surface layer t1 dust emission
features (face-on orientation).
Interior
1
10
100
1000
Wavelength (mm)
21
Silicate emission confirms ?lt1 atmospheres
Top of atmosphere
Fits 1.2 µm pyroxene grains, CG97 model
?11µm1
?9µm1
r, T(r) increasing
Emission features indicate optically thin
emission from in an atmosphere with vertically
increasing temperature gradients
Natta, Meyer, Beckwith 2000, ApJ, 534, 838
22
10 mm emission Mineralogy
Natta, Meyer, Beckwith 2000, ApJ, 534, 828.
Grain sizes 1 mm (from e) Some evidence for
features at 8.5 and 11.3 mm
crystalline silicates
e º s10/smix
DL silicates
e 0.84-2.2
1 mm 0.50.5 olivine/pyroxene 0.1 mm 0.30.7
olivine/pyrox.
e 10-21
1.2 mm pyroxene 0.1 mm pyroxene
1.2 mm olivine 0.1 mm olivine
e 0.6-1.2
23
Silicate emission confirms ?lt1 atmospheres
Top of atmosphere
3
1.5
LkHa 332
CT Cha
1.0
2
?11µm1
?9µm1
0.5
1
0.0
0
r, T(r) increasing
1.5
15
SX Cha
Glass Ia
Emission features indicate optically thin
emission from in an atmosphere with vertically
increasing temperature gradients
Flux (Jy)
1.0
10
5x
0.5
5
0.0
0
0
5
10
15
0
5
10
15
0.5
10
XX Cha
WW Cha
5
Natta, Meyer, Beckwith 2000, ApJ, 534, 838
0.0
0
0
5
10
15
0
5
10
15
Wavelength (mm)
Wavelength (mm)
24
Waelkens et al. 1996, AA, 315, L245.
Comet Hale-Bopp
6 Oct 1996
Fn(Jy)
Foresterite is a "primordial" constituent of
Solar dust
HD 100546
200
Fn(Jy)
Foresterite Mg2SiO4
100
PAH
0
10
30
40
20
Wavelength (mm)
25
HD 100546 - SWS and LWS all components
250
Short wavelength part - SWS
15
HD 100546
H2O - ice (50-80 µm)
PAH
Stellar photosphere
PAH
Hot continuum
Cold continuum
Total
10
PAH
200
H2O - ice
FLUX (Jy)
5
Pf d
Br d
Br a
Pf g
150
H2O - ice (43.8 µm)
0
2
6
8
4
OI (63.2 µm)
Crystalline pyroxene (40 µm)
Wavelength (µm)
PAH (11.3 µm)
OII (157.7 µm)
100
Flux (Jy)
PAH (8.6 µm)
PAH (7.8 µm)
Hot cold continuum
PAH (3.3-3.4-3.5 µm)
50
PAH (6.2 µm)
Total
0
Crystalline forsterite
Amorphous olivine
-50
FeO
10
100
Wavelength (µm)
Malfait et al. 1998, AA, 332, L25
26
Near- IR Disk Lifetimes
Haisch, Lada, Lada 2001, ApJL, 553, L153.

• L-band (3.4 µm) light used as disk proxy
• 900 K
• 1020 gm of dust
• Inner disk (TBD)
• Disk lifetime 6 Myr
• Principal uncertainty driven by NGC 2362
• Are outer and inner disk lifetimes the same?

Fraction of JHKL Excess ()
27
How do we observe disk mass?
Beckwith et al. 1990, AJ, 99, 924 Beckwith 1999,
OSPS, p. 579.
Fn k0n2b Td Md
We want to observe where the disk is
transparent (to see all the material)
For long enough wavelengths (l gt 200 mm), the
dust t lt 1.
Fn (Ad/D2) Bn(Td) (1 - e-t) (Ad/D2)
kTdn2 tn (Ad/D2) Tdn2 kn (Md/Ad)
D-2 Td n2 kn Md kn k0 (n/n0)b
Ad º disk projected area D º distance to
source Td º disk particle temperature tn º
optical depth at n Mdº mass of disk kn º mass
opacity (cm2 g-1)
28
mm-wave continuum is easily seen
HL Tau
13CO 2-1 4.4-5.8 km s-1
1.3mm Continuum
SII
Koerner Sargent 1995, Ap.SS., 223, 169 and
unpublished data.
Mundt et al. 1990, AA, 232, 37.
29
T(r) S(r) govern where Fn originates
rout
Temperature T(r)
r
Fn D-2 ? BnT(r) (1-e-t(r)) 2pr dr
rin
tn(r)

Surface density S(r)
T(r) r-q 3/4 lt q lt 1/2
S(r) r-p 0 lt p lt 2
?0?2??r2-q-p
?? ??????????? 2
p 3/2, q 3/4 Fn(1 mm) rin-1/4
p 1, q 1/2 Fn(1 mm) rout1/2
30
Inner Parts May Have ? gtgt 1
rout
Fn ? BnT(r) (1-e-t(r)) 2pr dr
r1
rin
The radius at which the disk appears optically
thick is a function of ??, hence wavelength. The
changing ratio of optically thick/optically thin
regions with wavelength offsets the changes from
?? itself, thus causing a degeneracy of
parameters (makes it difficult to derive ?
uniquely.)
Fn T(r1) n2 pr12 ?? ?(rout)T(rout) ?2
?rout2
31
Optical depth effects
Andrews Williams 2005, astro-ph 0506187 (June
2005)
450 µm
850 µm
1.3 mm
Md (Msun)
32
Degeneracy of Parameters mm-waves

• Compare mm-wave spectral indices, ?, for opaque
  (??gtgt 1) and transparent (?1) disks at ? 1 mm
• What are the limiting cases?
• Estimate the relative contributions of optically
  thick and optically thin parts of a disk to
  mm-wave light
• Assume a surface density law ?(r) r-p
• Find the radius, r???(?), where ?(?) 1
• What happens to relative contributions of
  thick/thin emission as wavelength varies?
• Show how this degeneracy makes it impossible to
  derive the dust spectral index, ?, uniquely from
  an SED
• How can one use spatial resolution to overcome
  this problem?

33
Disks can build planets
Limit
Beckwith Sargent
14
12
Andre Montemerle
10
8
6
4
2
0
1
0.0001
0.001
0.01
0.1
assumes gas/dust 100
Mdisk (M)
similar mass distribution for NGC 2071 by E. Lada
1998 but not Orion HST disks (E. Lada et al.,
Bally et al., unpublished)
34
Mass Evolution of Young Disks
BSCG 1990, AJ., 99, 924.
1
0.1
"Minimum" Solar nebula
0.01
0.001
Solar System planets
0.1
1
10
Age (Myr)
35
Disk Mass
Andrews Williams 2005, astro-ph 0506187
36
Distribution of Disk Radii Orion
Vicente Alves 2005, astro-ph 0506585 (2005)
100
? -1.9 /- 0.3
50
N
20
10
5
100
200
400
Diameter (AU)
37
MM-waves interact with all atoms
Particle size ltlt wavelength Þ coupling l-b
1st order size independent, wave sees
every atom
Insulators absorption by lattice resonances
Conductors antenna growth, absorption by
free electrons
kn n2 l-2 Lorentz tail
kn n2 l-2 plasma skin depth
Olivines (silicates) Mg2SiO4, Mg,FeSi2O5
Fe, graphite
38
Absorption in Insulators
Lattice resonances
log(e)
0
Vibrational modes 1 30 mm
-2
-4
kn s(n) / mp n2
-6
-2
-1
0
1
2
log (n)
long wavelengths
39
Particle Emissivity in Disks
Beckwith Sargent 1991, Ap. J., 381,
250. Mannings Emerson 1994, MNRAS, 267, 361

DG Tau
10-12
nFn (W/m2)
10-14
nFn n3
nFn n5
10-16
Interstellar Dust
Pebbles
0.1
0.01
10
1.0
Wavelength (mm)
40
Spectral Index b
(Fn/ n2) x C
10
Fn kn (Mdust/A) Bn(T) kn k0 (n/n0)b
1

• Opacity index b
• Interstellar dust b 2
• Planetesimals b 0
• Observed -0.5 lt b lt 2

0.1
0.01
Adams et al. 1990 Beckwith Sargent
1991 Mannings Emerson 1994
b 2
"Galactic"
10-3
b 1
Planck b 0
Later work by Lay et al. 1994 (0.85 mm
CSO-JCMT) Wilner et al. 2000, 2005
2
0.5
1
Wavelength (mm)
41
Radio Wavelength Emissivity
Natta et al. 2004, AA, 416, 179
See also Andrews Williams 2005, astro-ph
0506187
42
TW Hydra 3.5cm dust emission

• Very long wavelengths sensitive to
  centimeter-size grains
• Must rule out synchrotron free-free (plasma)
  emission
• Large grains out to tens of AU
• Assumed disk mass 0.1Msun

Wilner et al. 2005, ApJL, 626, L109
43
Spatially Resolved Spectra TW Hydra
Roberge et al. 2005, ApJ, 622, 1121
The scattered light from the disk is essentially
gray from 50 AU to 150 AU. This result argues
for relatively large (gt1 µm) scattering particles
44
Numerical Models TW Hydra
inner disk
outer disk edge
outer disk
star
Calvet et al. 2002, ApJ, 568, 1008
45
Grain size does alter opacity
Miyake Nakagawa 1993, Icarus, 106, 20.
amax
n(a) a-p
102
kn (cm2 g-1)
kn (cm2 g-1)
p4
1
p3.5
p3
p2.5
10-2
p2
10-4
compact spheres n(a) a-3.5
compact sphere amax 1 cm
10-6
1 mm
100 mm
1 cm
1 mm
100 mm
1 cm
Wavelength
Wavelength
46
Interstellar opacities are uncertain
47
Particles grow quickly
Weidenschilling, S. J. 1988, Meteorites Early
Solar Sys. Chokshi et al. 1993, Ap. J., 407,
806, Blum et al. 1999, EMP, 80, 285 (lab
experiments)
YSO ages
105
Turbulence M0.01
Transverse
104
Gravitational
Radial Drift z0
S 3 g cm-2
dfr
103
Coagulation times (yr)
Settling
zc/W dfr
102
Transverse
Radial Drift
d r
Turbulence
10
z0
M1/3
Calculations for 1 AU orbits
1
10-4
10-2
1
102
104
106
ISM grain sizes
Particle size (cm)
48
Disk dynamics what is the velocity field?

• Keplerian velocity field is clear signature.

49
Velocity gradients gravity
r
Circular disk viewed at high inclination angle
q
Pure Keplerian rotation
v(r)
Pure radial infall
vr(r) Ö2GM r -1/2
vr(r) 0
vf(r) 0
Major axis Dx
Minor axis Dx
v(r)
velocity gradient
velocity gradient
Dutrey et al. 1994, AA, 286, 149. Saito et al.
1995, Ap. J., 453, 384
Hayashi et al. 1993, Ap. J. Lett., 418, L71.
50
Gas Dynamics in HL Tau mostly infall
4.4 5.8 km s-1
8.0 9.4 km s-1
6.2 7.6 km s-1
HL Tau 13CO 2-1
HL Tau shows an infalling disk.
Velocity gradient
HST image
64"
Hayashi et al. 1993, Ap. J. Lett., 418,
L71. Koerner Sargent 1995, Ap.SS.,
223, 169 and unpublished data.
2000 AU
1.4 FWHM
51
GG Tau system a rotating disk
Dutrey et al. 1994, AA, 286, 149
13CO J1-0
Model calculation
Observed velocity map
52
To see real disks, need high resolution
McCaughrean ODell 1996
Koerner Sargent 1998
HL Tau 13CO
Solar System
according to Shu (1998, ASI, public
communication)
Burrows et al. 1996
400 AU
53
Future Observations

• Use high spatial resolution to break degeneracies
• ALMA resolution of mm-wave emission to tens of
  AU
• VLT/Keck/LBTI resolution of thermal IR emission
  to 1 AU
• Use spectral resolution to analyze disk
  atmospheres and grain/gas composition
• Spitzer spectra of disks
• SOFIA spectra in far infrared
• ALMA for molecular abundances in disk interiors
  on few x 10 AU scales

54
van den Ancker 2000, astro-ph 0005060
Ground-based spectroscopy call some of these
detections into question (envelope/ISM emission?)
55
H2 in the GG Tau Disk
Thi et al. 1999, Ap.J.Lett., 521, L63
56
Disk boundaries appear to be sharp
ODell Wen 1992, Ap.J., 387, 229.
0.55 µm
1.10 µm
1.7"
Inner S(r) flat (r-1) Sharp outer boundary
2.9"
2.0 µm POL
1.60 µm
McCaughrean et al. 1998, ApJL, 492, L157.
57
Achromatic extinction
114-426
114-426
Interpretation the particles have grown to
pebbles or rocks.
Throop et al., Science, April, 2001
58
HST 16
114-426
HST 10
Grain size gt Wavelength
Throop et al., Astro-ph 0104445
59
Keck interferometer observations at 2 µm
Eisner et al. 2005, ApJ, 623, 952
For AS 207A, V2508 Oph, and PX Vul, simple flat
accretion disk models suggest much smaller sizes
(when fitted to SEDs) than those determined
interferometrically. Models incorporating
puffed-up inner walls and flared outer disks
provide better fits to our V2 and SED data than
the simple flat disk models. This is consistent
with previous studies of more massive Herbig Ae
stars (Eisner et al. 2004 Leinert et al. 2004)
and suggests that truncated disks with puffed-up
inner walls describe lower mass T Tauri stars in
addition to more massive objects.
60
Summary Lessons

• Our understanding of disk atmospheres is
  compatible with observed SEDs
• We can measure sizes, temperature distributions,
  masses, and some features (holes, gaps) with
  reasonable certainty
• Parameter degeneracies that affect
  interpretations may be resolved with high angular
  resolution
• ALMA for mm-wave disk interiors
• IR-interferometry for inner disks, holes, and
  surfaces
• Spectra and SEDs show good evidence for
• Grain growth leading to small rocks
• Constituents similar to proto-Solar nebula
• Gas entrained with dust
• Disks bound to stars