Transcript Les Houches 1996 Winter School

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
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)
2
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
-16
-17
\ t  100 at 1 mm
AV  300
nFn
-19
-20
Observed AV ~ 3
Excess emission
over photosphere
-18
n3 blackbody
XX Cha
1
\ clear line of sight
to star and dust.
10
100
Wavelength (mm)
1000
3
Why does a disk dominate the infrared
emission?
Spectral Energy Distributions
(SEDs)
Thin, black disk: "standard theory"
Lynden-Bell & Pringle 1974, MNRAS, 168, 603.
Adams, Lada, & Shu 1988, Ap. J., 326, 865.
Star luminosity, L*
D
L*
angle q
flat, black disk
r
Power/area absorbed ~
L* sin q
4pr2
L* D
~
4pr 2 r
Power/area emitted =
sT4
~
~
L*
r3
L*
r3
(r >> D)
T(r) ~ r
Also true for accretion energy.
-3/4
5
Spectral Energy Distribution (SED)
Bn(T)
10
1
p nBn[T(r)] 2pr dr
T(r) ~ r-3/4
nFn = C
1000
nFn

r
min
L*
100
nFn =
rmax
Thin disk
n4/3
T08/3
n4/3
area
element
surface
emission

x
xmax
X
exp(x-3/4)
-1
min
 nFn ~ n4/3
Planck n3
1
10
100
Wavelength (mm)
6
dx
Thin disk SED: observations
Adams, Lada, & Shu 1988, Ap. J., 326, 865.
Beckwith et al. 1990, AJ, 99, 924
Thin disk nFn ~ n4/3
1000
XX Cha
100
nFn
10
n4/3
1
Planck n3
1
10
The SED from a theoretically thin
black disk almost never fits the
observations of young stars with
excess infrared emission!
• most SEDs flatter than n4/3
• some SEDs very flat, nFn ~ n0
100
Wavelength (mm)
7
Power law nFn  power law T(r)
Lynden-Bell & Pringle 1974, MNRAS, 168, 603.
Adams, Lada, & Shu 1988, Ap. J., 326, 865.
rmax
T(r) = T0(r/r0)
1000
-q
XX Cha
r
10
na
xmax
min
nFn = C T0
100
nFn
nFn =  pnBn[T(r)] 2pr dr
2/q
a = 4-2/q
na
 X
x exp(x ) - 1
q
dx
min
 nFn ~ na ~ n4-2/q
1
n3
1
10
Wavelength (mm)
q = 1/2 for a flat SED
100
• we can derive q from a
• T(r) uniquely follows from a
8
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.
9
Geometrical changes: Flaring
Kenyon & Hartmann 1987, Ap. J., 323, 714.
Star luminosity, L*
angle q'
r
•
•
•
gravity  (z/r)(GM/r2) ~ r-3
absorbed radiation ~ sinq' >> sinq
Tflare(r) > Tflat(r), especially at large r
h
Flared,
black disk
h
~ r2/7
r
Ti(r) ~ r-6/15
BUT
 cannot account for flat SEDs (6/15 < 1/2)
 still assumes “black” disk (no radiative transfer)
10
Radiative transfer
Chiang & Goldreich 1997, Ap. J., 490, 368.
Star luminosity, L*
Surface t~ 1
in optical
angle q'
D
Interior t> 1
in infrared
r
optical light absorbed tV ~ 1, tIR << 1
 small grains "bare" => Tgrain > Tblackbody
 disk emission tIR < 1 (5 - 100 mm)

Still cannot account for very flat
SEDs but does fit majority.
h
r

0.9
r
209 AU
Ti(r)  21 K
(
(
r
209 AU
Prediction: disk surface emission is optically thin
)
)
13
45
19
45
11
Radiative heating: isolated particle
Distance r
Particle radius a (spherical; rapidly spinning)
Temperature T
Absorbed radiative power: pa 2
L
4pr 2
Emitted radiative power: 4pa 2 sT 4
Luminosity L
T=(
L
)
16ps
1/4
r -1/2
Using en for small particles: T ~ r -2/5
cf L. Spitzer, Jr., Physical Processes in the Interstellar Medium, ch. 9.1
12
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 (T~r-1/2, T~r-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
13
Physical Modification: Holes
L*
“hole”
rmin ~ R*
rmin
Disk
rmax
nFn = 2pn Bn[T(r)] r dr
rmin ~ 5 R*
r
SED from continuous
“flat-spectrum” disk
100
min
5 R* hole in center
nFn
Star SED
rmin ~ 50 R* (0.5 AU)
hole in center (large)
10
To produce an observable flux
deficit, the hole must be large,
~10x larger than the star
1
10
Wavelength (mm)
100
14
Inner holes produce flux deficits
34
Superheated surface
layer with small grains
produces infrared light.
32
31
30
“Black” interior produces
mm-wave emission.
GM Aur
Flux deficit from interior hole
33
Log nFn (erg s-1)
Interior
hole
Flared equilibrium disk
Stellar
blackbody
Disk
surface
t<1
Disk
interior
t>1
29
1
100
10
Wavelength (mm)
1000
15
n Fn(Jy)x10 11
Evolution of
structure
LKHa332-20
1000
PIA 7.2
100
10
As disks age,
the hole sizes
should increase
1
0.1
1
10
100
(mm)
CS Cha
1000
PIA 7.2
HR4796
n Fn (Jy)x10
11
100
10
1
Weinberger et al. 1999, ApJ Let, 525, L53
0.1
0.1
1
10
 (m m)
16
100
Fomalhaut: Ring Emission
Holland et al. 2003, ApJ, 582, 1141
17
Kalas et al. 2005, Nature, 435, 1067
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
“Ring”
rmin = 100 AU
rmax = 140 AU
Mgrains = 1.4Mmoon
Figure 1: Best fit
10 µm
 = 1.1
These results indicate
a typical grain is ~100
µm in size. The models
assume fixed total
grain mass.
Figure 6: varying grain size
18
HD 4796
Modification 2: Gaps & Rings
Weinberger et al. 1999
Gaps must be large to
cause observable
changes to the SEDs
Fomalhaut
rring ~ 130 AU
∆ring~ 25 AU
100
nFn
r1 = 67, r2 = 150, Log(∆) = 0.35
Kalas, Graham, Clampin 2005
r1 = 50, r2 = 200, Log(∆) = 0.60
10
r2
∆= r
1
1
r1 = 25, r2 = 400, Log(∆) = 1.20
10
Wavelength (mm)
100
19
Optically thin, dT/dr > 0  Emission features
Chiang & Goldreich 1997, Ap. J., 490, 368.
Superheated surface
layer with small grains.
Surface layer t1:
dust emission
features
(face-on orientation).
33
log Ln (erg s-1)
Optically
thick interior
cf Cohen & Witteborn 1985, Ap. J.
32
Stellar
31
Surface
30
29
Interior
1
10
100
Wavelength (mm)
1000
20
Silicate emission confirms t<1 atmospheres
Fits: 1.2 µm pyroxene grains, CG97 model
Top of atmosphere
t11µm~1
t9µm~1
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
21
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 s10/smix
DL silicates
e= 0.84-2.2
1 mm 0.5:0.5 olivine/pyroxene
0.1 mm 0.3:0.7 olivine/pyrox.
e= 10-21
e= 0.6-1.2
1.2 mm pyroxene
0.1 mm pyroxene
1.2 mm olivine
0.1 mm olivine
Waelkens et al. 1996, A&A, 315, L245.
200
Comet Hale-Bopp
6 Oct 1996
Fn(Jy)
100
0
Foresterite is a "primordial"
constituent of Solar dust
HD 100546
200
Fn(Jy)
Foresterite Mg2SiO4
100
PAH
0
10
20
30
Wavelength (mm)
40
24
HD 100546 - SWS and LWS : all components
PAH
PAH (7.8 µm)
PAH (8.6 µm)
PAH (6.2 µm)
PAH
(11.3 µm)
8
Hot & cold continuum
Total
0
Crystalline forsterite
Amorphous olivine
-50
10
Malfait et al. 1998, A&A, 332, L25
[ OII ] (157.7 µm)
Pf g
Br a
6
4
Wavelength (µm)
[ OI ] (63.2 µm)
2
H2O - ice (43.8 µm)
PAH
Crystalline pyroxene (40 µm)
HD 100546
Stellar photosphere
Hot continuum
Cold continuum
Total
PAH
5
0
PAH (3.3-3.4-3.5 µm)
Flux (Jy)
50
H2O - ice
10
150
100
Short wavelength part - SWS
Br d
FLUX (Jy)
200
15
Pf d
250
FeO
Wavelength (µm)
100
25
Near- IR Disk Lifetimes
Haisch, Lada, Lada 2001, ApJL, 553, L153.
– 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?
100
Systematic
NGC 2024
Trapezium
80
Fraction of JHKL Excess (%)
• L-band (3.4 µm) light
used as disk proxy
Taurus
IC 348
60
Cham I
40
tdisk ~ 6 Myr
20
0
NGC 2264
NGC 2362
0
2
4
6
Age (Myr)
8
10
26
How do we observe disk mass?
Beckwith et al. 1990, AJ, 99, 924
Beckwith 1999, “OSPS”, p. 579.
Fn ~ k0n2+ Td Md
We want to observe where
the disk is transparent
(to see all the material)
For long enough wavelengths
( > 200 mm), the dust t < 1.
Fn ~ (Ad/D2) Bn(Td) (1 - e-t)
Ad  disk projected area
D  distance to source
Td  disk particle temperature
tn  optical depth at n
Md mass of disk
kn  mass opacity (cm2 g-1)
~ (Ad/D2) kTdn2 tn
~ (Ad/D2) Tdn2 kn (Md/Ad)
~ D-2 Td n2 kn Md
kn ~ k0 (n/n0)
Md = 0.03 Msun
Fn
1 Jy
(
2
D
100 pc
) (
3
50 K

1.3 mm
T
)
0.02 cm2 gm-1
k1.3mm
27
mm-wave continuum is easily seen
13CO
2-1
4.4-5.8 km s-1
HL Tau
1.3mm Continuum
SII
“ FWHM
1.4
Mundt et al. 1990, A&A, 232, 37.
Koerner & Sargent 1995,
Ap.SS., 223, 169
and unpublished data.
28
T(r) & S(r) govern where Fn originates
Temperature:
T(r) r
rout
rout
Fn ~ D-2 Bn[T(r)] (1-e-t(r)) 2pr dr
r
in
rin
Fn ~ D-2
{
Surface density:
S(r)
rout
tn(r)
 k T(r) n2 knS(r) 2pr dr
r
in
T(r) ~ r-q
3/4 < q < 1/2
S(r) ~ r-p
0<p<2
kn ~
~2
n
p = 3/2, q = 3/4
p = 1, q = 1/2
rout
Fn ~ n2+k
r1-q-p dr
r
~ k0n2+r2-q-p
in
Fn(1 mm) ~ rin-1/4
Fn(1 mm) ~ rout1/2
29
Inner Parts May Have t >> 1
rout
r1
rout
Fn ~
 Bn[T(r)] (1-e-t(r)) 2pr dr
r
in
rin
r1
Fn ~
 k T(r) n2 2pr dr
r
(t > 1)
in
The radius at which the disk appears
optically thick is a function of kn,
hence wavelength. The changing ratio
of optically thick/optically thin
regions with wavelength offsets the
changes from kn itself, thus causing a
degeneracy of parameters (makes it
difficult to derive  uniquely.)
rout
+
k T(r) n2 knS(r) 2pr dr
r
(t < 1)
1
Fn ~ T(r1) n2 pr12
+ kn S(rout)T(rout) n2 prout2
30
Optical depth effects
Andrews & Williams 2005, astro-ph 0506187 (June 2005)
1.0
0.8
Md(tn>1)
Md
450 µm
850 µm
1.3 mm
0.6
0.4
0.2
10-5
10-4
10-3
10-2
0.1
1
Md (Msun)
31
Degeneracy of Parameters: mm-waves
• Compare mm-wave spectral indices, , for opaque
(t>> 1) and transparent (t«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: S(r)~ r-p
– Find the radius, rt(), where t() = 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?
32
Disks can build planets
Limit
Solar Nebula
14
Taurus
12
Ophiuchus
10
Beckwith
& Sargent
Andre &
Montemerle
8
6
4
2
0
0.0001
assumes
gas/dust = 100
0.001
0.01
0.1
1
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)
33
Mass Evolution of Young Disks
BSCG 1990, AJ., 99, 924.
1
0.1
MD
M
"Minimum"
Solar nebula
0.01
0.001
Solar System planets
0.1
1
Age (Myr)
10
34
Disk Mass
Andrews & Williams 2005, astro-ph 0506187
35
Distribution of Disk Radii: Orion
Vicente & Alves 2005, astro-ph 0506585 (2005)
150
135 bright proplyds
14 pure silhouettes
100
a = -1.9 +/- 0.3
50
100
N
N
20
50
10
5
0
218-354
0
400
800
Diameter (AU)
114-426
1200
100
200
400
Diameter (AU)
36
MM-waves interact with all atoms
Particle size << wavelength
 coupling ~ -
1st order: size independent,
wave sees every atom
Conductors: “antenna” growth,
absorption by free electrons
Insulators: absorption by
lattice resonances
kn ~ n2 ~ -2 Lorentz “tail”
kn ~ n2 ~ -2 plasma
skin depth
Fe, graphite
Olivines (silicates):
Mg2SiO4, [Mg,Fe]Si2O5
37
Absorption in Insulators
Lattice resonances
np2 g n
e” = (n 2 - n2)2 + g2n2
0
log(e”)
0
Vibrational modes
~ 1 – 30 mm
-2
s~
-4
8pa
Im(e'') ~ n2

kn ~ s(n) / mp
~ n2
-6
2
1
0
log (n)
-1
-2
long wavelengths
38
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
10-16
0.01
nFn ~ n3
nFn ~ n5
Interstellar Dust
0.1
1.0
Wavelength (mm)
Pebbles
10
39
Spectral Index: 
Fn ~ kn (Mdust/A) Bn(T)
kn = k0 (n/n0)
 = -0.5
RY Tau
=0
1
0.1
GW Ori
= 1.8
0.01
HK Tau
 =2
"Galactic"
10-3
 =1
Planck  = 0
0.5
10
DG Tau
= 1
– Interstellar dust:  = 2
– Planetesimals:  = 0
– Observed: -0.5 <  < 2
Later work by:
Lay et al. 1994 (0.85 mm CSO-JCMT)
Wilner et al. 2000, 2005
DL Tau
 = -0.2
• Opacity index 
Adams et al. 1990
Beckwith & Sargent 1991
Mannings & Emerson 1994
(Fn/ n2) x C
1
2
Wavelength (mm)
40
Radio Wavelength Emissivity
Natta et al. 2004, AA, 416, 179
See also: Andrews & Williams 2005, astro-ph 0506187
41
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
42
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 (>1
µm) scattering
particles
43
Numerical Models: TW Hydra
star
inner disk
outer disk edge
outer disk
Calvet et al. 2002, ApJ, 568, 1008
44
Grain size does alter opacity
Miyake & Nakagawa 1993, Icarus, 106, 20.
amax
n(a) ~ a-p
kn (cm2 g-1)
kn (cm2 g-1)
p=4
1
p=3.5
p=3
p=2.5
p=2
100 mm
Wavelength
10-2
10-4
compact spheres
n(a) ~ a-3.5
1 mm
102
compact sphere
amax = 1 cm
1 cm
1 mm
100 mm
10-6
1 cm
Wavelength
45
Interstellar opacities are uncertain
Henning, Michel, & Stognienko 1995, Plan. & Sp. Sci.
100
kn (cm2 g-1)
10
=1
1
0.1
Draine & Lee (1984)
dense regions
=2
diffuse regions
circumstellar
0.05 0.1
0.2
0.5
1
2
Wavelength (mm)
46
Particles grow quickly
Coagulation times (yr)
Weidenschilling, S. J. 1988, Meteorites & Early Solar Sys.
Chokshi et al. 1993, Ap. J., 407, 806,
Blum et al. 1999, EM&P, 80, 285 (lab experiments)
105
z/z•
Turbulence M=0.01
104
Radial Drift z=0
103
Settling
d=fr
z=c/W d=fr
102
10
a/a•
Turbulence
M=1/3
Radial Drift
z=0
1
ISM grain
sizes
YSO ages
10-4
10-2
1
102
Particle size (cm)
Calculations for
1 AU orbits
104
106
47
Disk dynamics: what is the velocity field?
Keplerian velocity field is clear signature.
Velocity gradients & gravity
r
Pure Keplerian rotation
q
Circular disk viewed at
high inclination angle
v(r)
Pure radial infall
v f(r) = GM r -1/2
vr(r) =2GM r -1/2
vr(r) = 0
Major axis Dx
vf(r) = 0
Minor axis Dx
v(r)
velocity gradient
Dutrey et al. 1994, A&A, 286, 149.
Saito et al. 1995, Ap. J., 453, 384
velocity gradient
Hayashi et al. 1993, Ap. J. Lett., 418, L71.
49
Gas Dynamics in HL Tau: mostly infall
4.4 – 5.8 km s-1
HL Tau
HL Tau shows an
infalling disk.
Hayashi et al. 1993,
Ap. J. Lett., 418, L71.
Koerner & Sargent 1995,
Ap.SS., 223, 169
and unpublished data.
6.2 – 7.6 km s-1
13CO
8.0 – 9.4 km s-1
2-1
HST image
64"
1.4” FWHM
2000 AU
50
GG Tau system: a rotating disk
Dutrey et al. 1994, A&A, 286, 149
13CO
J=1-0
6.5
6.93
6.29
6.07
7.14
6.71
5.86
5.44
5.22
7.35
5.65
7.56
5.01
4.8
8.20
7.78
7.99
Model calculation
7.19
6.77
6.55
6.34
6.13
4.85
5.49
6.98
5.07
5.70
5.28
5.92
7.40
7.83
8.25
8.04
7.62
Observed velocity map
51
To see real* disks, need high resolution
HL Tau
13CO
Koerner & Sargent 1998
McCaughrean
& O’Dell 1996
183-405
Solar System
114-426: "Largest disk"
400 AU
*according to Shu
(1998, ASI, public
communication)
HH 30
Burrows et al. 1996
52
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
53
van den Ancker 2000, astro-ph 0005060
H2 0-0 S(5)
H2 0-0 S(3)
H2 0-0 S(4)
Ground-based spectroscopy call some of these
detections into question (envelope/ISM emission?)
54
H2 in the GG Tau Disk
Thi et al. 1999, Ap.J.Lett., 521, L63
55
Disk boundaries appear to be sharp
O’Dell & 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"
1.60 µm
2.0 µm POL
McCaughrean et al. 1998, ApJL, 492, L157.
56
114-426
Achromatic
extinction
114-426
Interpretation: the particles
have grown to pebbles or rocks.
Throop et al., Science, April, 2001
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
59
stars in addition to more massive objects.
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
60