the formation of stars and planets day 3, topic 3: irradiated protoplanetary disks lecture by: c.p....
TRANSCRIPT
![Page 1: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/1.jpg)
The formation of stars and planets
Day 3, Topic 3:
Irradiated protoplanetary disks
Lecture by: C.P. Dullemond
![Page 2: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/2.jpg)
Spectral Energy Distributions (SEDs)Plotting normal flux makes it look as if the source emits much more infrared radiation than optical radiation:
This is because energy is:
€
Fν dν = Fν Δν
![Page 3: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/3.jpg)
Spectral Energy Distributions (SEDs)Typically one can say: and one takes a constant (independent of ).
€
Δ = Δ(logν )
€
Δ(logν )
€
FνIn that case is the relevant quantity to denote energy per interval in log. NOTE:
€
Fν ≡ λ Fλ
![Page 4: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/4.jpg)
Calculating the SED from a flat disk
€
Iν (r) = Bν (T(r))
Assume here for simplicity that disk is vertically isothermal: the disk emits therefore locally as a black radiator.
Now take an annulus of radius r and width dr. On the sky of the observer it covers:
€
dΩ =2π rdr
d2cosi
€
Fν = Iν dΩand flux is:
Total flux observed is then:
€
Fν =2π cosi
d2Bν (T(r)) rdr
rin
rout∫
![Page 5: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/5.jpg)
Multi-color blackbody disk SED
Wien region
multi-color region
Rayleigh-Jeans region
F
![Page 6: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/6.jpg)
F
3
(4q-2)/q
Multi-color blackbody disk SEDRayleigh-Jeans region:
Slope is as Planck function:
€
Fν ∝ν 3
Multi-color region:
Suppose that temperature profile of disk is:
€
T(r)∝ r−q
Emitting surface:
€
S ∝ rdr ∝ r2
€
max(νBν )∝T 4Peak energy planck:
€
∝TLocation of peak planck:€
r∝T−1/ q
€
∝−2 / q
€
∝ 4
€
∝T−2 / q
€
Fν ∝ Smax(νBν )
€
∝−2 / qν 4 = ν (4 q−2)/ q
€
Fν ∝ν (4 q−2)/ q
![Page 7: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/7.jpg)
(4q-2)/qF
3+
Disk with finite optical depth
If disk is not very optically thick, then:
Multi-color part stays roughly the same, because of energy conservation
Rayleigh-Jeans part modified by slope of opacity. Suppose that this slope is:
€
κ ∝
€
Iν (r) = (1− eτν )Bν ≈ τ ν Bν ∝κ ν Bν
Then the observed intensity and flux become:
€
Fν ∝κ ν ν Bν ∝ν 3+β
![Page 8: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/8.jpg)
€
need ˙ M = 7 ×10−7 Msun /yr
AB Aurigae
SED of accretion disk
Remember:
€
Teff =3
8πσ˙ M ΩK
2 ⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 4
∝ r−3 / 4
According to our derived SED rule (4q-2)/q=4/3 we obtain:
€
Fν ∝ν 4 / 3
Does this fit SEDs of Herbig Ae/Be stars?
HD104237
€
need ˙ M = 2 ×10−7 Msun /yr
Bad fit
Higher than observed from
veiling (see later)
![Page 9: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/9.jpg)
Viscous heating or irradiation?
T Tauri star
![Page 10: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/10.jpg)
Viscous heating or irradiation?
Herbig Ae star
![Page 11: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/11.jpg)
Flat irradiated disks
€
≅0.4 r*
rIrradiation flux:
€
Firr = αL*
4π r2
Cooling flux:
€
Fcool = σ T 4
€
T =0.4 r* L*
4πσ r3
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 4
€
T ∝ r−3 / 4
Similar to active accretion disk, but flux is fixed.Similar problem with at least a large fraction of HAe and T Tauri star SEDs.
![Page 12: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/12.jpg)
Flared disks
flaring
irradiation
heating vs cooling
verticalstructure
● Kenyon & Hartmann 1987● Calvet et al. 1991; Malbet & Bertout 1991● Bell et al. 1997; ● D'Alessio et al. 1998, 1999● Chiang & Goldreich 1997, 1999; Lachaume et al. 2003
![Page 13: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/13.jpg)
Flared disks: Chiang & Goldreich model
The flaring angle:
€
=r∂
∂r
hs
r
⎛
⎝ ⎜
⎞
⎠ ⎟→ ξ
hs
r
Irradiation flux:
€
Firr = αL*
4πr2
Cooling flux:
€
Fcool = σ T 4
€
T 4 =ξ
σ
hs L*
4π r3
Express surface height in terms of pressure scale height:
€
hs = χ h
€
χ =1...6
![Page 14: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/14.jpg)
Flared disks: Chiang & Goldreich model
€
T 4 =ξ
σ
hs L*
4π r3
€
hs = χ h
Remember formula for pressure scale height:
€
h =k Tr3
μmpGM*
€
T 4 =ξ
σ
χ hL*
4π r3
€
h8 =k
μmpGM*
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
4
r12 T 4
We obtain
€
h8 =k
μmpGM*
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
4
r12 ξ
σ
χ hL*
4π r3
€
h8 =k
μmpGM*
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
4
r9 ξ
σ
χ hL*
4π
€
h7 =k
μmpGM*
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
4
r9 ξ
σ
χ L*
4π
![Page 15: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/15.jpg)
Flared disks: Chiang & Goldreich model
€
h7 =k
μmpGM*
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
4
r9 ξ
σ
χ L*
4π
We therefore have:
€
h = C 1/ 7r9 / 7
€
C =k
μmpGM*
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
4
ξ
σ
χ L*
4πwith
Flaring geometry:
Remark: in general χ is not a constant (it decreases with r). The flaring is typically <9/7
![Page 16: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/16.jpg)
The surface layer
A dust grain in (above) the surface of the disk sees the direct stellar light. Is therefore much hotter than the interior of the disk.
![Page 17: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/17.jpg)
Intermezzo: temperature of a dust grain
Heating:
€
Q+ = π a2 Fν εν∫ dν
a = radius of grain
= absorption efficiency (=1 for perfect black sphere)
Cooling:
€
Q− = 4π a2 π Bν (T)εν∫ dν
€
κ =π a2εν
mThermal balance:
€
4π a2 π Bν (T)εν∫ dν = π a2 Fν εν∫ dν
€
Bν (T)κ ν∫ dν =1
4πFν κ ν∫ dν
Optically thin case:
![Page 18: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/18.jpg)
€
σπ
T 4 =1
4πF
Intermezzo: temperature of a dust grain
Big grains, i.e. grey opacity:
€
Bν (T)κ ν∫ dν =1
4πFν κ ν∫ dν
€
σπ
T 4 =1
4π
L*
4π r2
€
T 4 =1
4σ
L*
4π r2
€
T 4 =1
4σ
4π r*2σT*
4
4π r2
€
T 4 =r*
2T*4
4r2
€
T =r*
2rT*
Small grains: high opacity at short wavelength, where they absorb radiation, low opacity at long wavelength where they cool.
€
T >r*
2rT*
![Page 19: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/19.jpg)
The surface layer again...
Disk therefore has a hot surface layer which absorbs all stellar radiation.
Half of it is re-emitted upward (and escapes); half of it is re-emitted downward (and heats the interior of the disk).
![Page 20: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/20.jpg)
Chiang & Goldreich: two layer model
Chiang & Goldreich (1997) ApJ 490, 368
Model has two components:
• Surface layer
• Interior
![Page 21: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/21.jpg)
Flared disks: detailed models
Global disk model...
... consists of vertical slices, each forming a 1D problem. All slices are independent fromeach other.
![Page 22: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/22.jpg)
Flared disks: detailed models
Malbet & Bertout, 1991, ApJ 383, 814D'Alessio et al. 1998, ApJ 500, 411 Dullemond, van Zadelhoff & Natta 2002, A&A 389, 464
A closer look at one slice:
![Page 23: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/23.jpg)
Dust evaporation and disk inner rim
Natta et al. (2001) Dullemond, Dominik & Natta (2001)
![Page 24: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/24.jpg)
SED of disk with inner rim
![Page 25: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/25.jpg)
Covering fraction
![Page 26: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/26.jpg)
Covering fraction
![Page 27: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/27.jpg)
Covering fraction
![Page 28: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/28.jpg)
Covering fraction
![Page 29: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/29.jpg)
Covering fraction
![Page 30: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/30.jpg)
Covering fraction
![Page 31: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/31.jpg)
Covering fraction
![Page 32: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/32.jpg)
Covering fraction
![Page 33: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/33.jpg)
Example: HD100546
Must have weak inner rim (weak near-IR flux), but must be strongly flaring (strong far-IR flux)
![Page 34: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/34.jpg)
Example: HD 144432
Must have strong inner rim (strong near-IR flux), but either small or non-flaring outer disk (weak far-IR flux)
![Page 35: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/35.jpg)
Measuring grain sizes in disks
van Boekel et al. 2003
The 10 micron silicate feature shape depends strongly on grain size. Observations show precisely these effects. Evidence of grain growth.
![Page 36: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/36.jpg)
Grain sizes in inner disk regions
R < 2 AU R > 2 AU
...infrared interferometry
Resolving inner disk
region with...
van Boekel et al. 2004
![Page 37: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/37.jpg)
Probing larger grains in disksAt (sub-)millimeter wavelength one can measure opacity slope (remember!). But first need to make sure that the disk is optically thin.
A measured flux, if F~ 3, can come from a blackbody disk surface.
Measure size of disk with (sub-)millimeter interferometry. If disk larger than that, then disk must be optically thin. A slope of F~ 3 then definitely point to large (cm) sized grains!
Evidence for large grains found in many sources. Example:CQ Tau (Testi et al.)
![Page 38: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/38.jpg)
Probinging the shape of disks
We have sources with weak mid/far-IR flux, and sources with strong mid/far-IR flux. One of the ideas is that disk can be self-shadowed to obtain weak mid/far-IR flux.
Disk starts as flaring disk: strong mid/far-IR flux. Few big grains produced.
As disk gets older: part of dust converted into big grains. Disk loses opacity, falls into own shadow. Many big grains observable at (sub-)millimeter wavelengths.
![Page 39: The formation of stars and planets Day 3, Topic 3: Irradiated protoplanetary disks Lecture by: C.P. Dullemond](https://reader035.vdocuments.us/reader035/viewer/2022062511/5517a23a5503463e368b5b62/html5/thumbnails/39.jpg)
Probinging the shape of disks
Acke et al. 2004 looked for such a correlation, and indeed found it:
Flaring disks
Self-shadowed(?) disks