Chemical models of
protoplanetary disks
What happens to water if the star‘s
luminosity suddenly increases?
Simon Bruderer (MPE Garching)
in collaboration with
Ewine van Dishoeck, Davide Fedele, Greg Herczeg, Daniel Harsono,
Andrea Banzatti, Michael Meyer, Doug Johnstone, and many others
NASA/JPL-Caltech artist‘s concept
Oort workshop 2014, 14/05/14
Outline
1.
Static models
- which basic processes are included?
(what I‘m normally doing)
2.
Time dependent models
- similar processes...
(an experiment for this workshop)
3.
Water in disks
1. Static models
Time scales
chemical time-scales
thermal time-scales
P. Woitke et al.: Radiation thermo-chemical models of protoplanetary disks
1.0
-4
-2
0
2
log τcool [yrs]
4
1.0
0
2
4
log τchem [yrs]
6
8
0.8
z/r
z/r
0.8
-2
403
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
1
10
r [AU]
100
1
10
Fig. 13. Cooling relaxation timescale τcool (l.h.s.) and chemical relaxation timescale τchem (r.h.s.).
r [AU]
100
Woitke et al. 2009
Short time scales in upper atmosphere
Table 6. Species masses in the disk and emission line
characteristics.
A models
conditions above the optically thick midplane. Due to the
➝
Static
velocity width of ∆v = 1 km s is assumed.
higher energy E required to excite the upper level, the line
D
−1
u
DALI (Dust And LInes) code
Bruderer et al. 2009-2014
Density structure
Stellar spectrum
1 Continuum RT
Tdust <Jcontinuum>
Iteration over
structure
4 Excitation
Atomic/molecular
level population
Spectra
Image cubes
5 Raytracing
u
b
A
e
c
n
a
d
n
2 Chemical
network
Tgas
3 Thermal
Balance
Calculate abundance, temperature, excitation
1 Continuum RT
Continuum
Transfer
2 Chemical
network
4 Excitation
3 Thermal
Balance
5 Raytracing
1000
Get stellar light into disk trough
absorption, scattering,
reemission
→ <Jcontinuum> and Tdust
Tdust (K)
500
Mid-plane temperature
200
100
50
20
MCFost (Pinte et al. 2006)
This work
10
20
3D Monte-Carlo code, optimized
for very high optical depths in disks
Difference (%)
15
10
5
0
−5
−10
−15
−20
Benchmark:
Pinte et al. 2009 (τ0.81 = 105)
10−6
10−4
10−2
r − rin (AU)
100
102
1 Continuum RT
Chemistry
2 Chemical
network
4 Excitation
3 Thermal
Balance
5 Raytracing
Chemical network with ~110 species (atoms/molecules) and ~1500 reactions
- Steady-state
- „pseudo time-dependent“ chemistry
(chemistry evolves, temperature constant)
- gas-phase
- FUV - grain surface
photodissociation/ionization
freeze-out, evaporation, grain surface reactions
(hydrogenation)
- PAHs - “warm“ H2 charge exchange, hydrogenation
vibrationally excited H2 to pass energy barriers
- X-rays ionization
- cosmic rays “ “
1 Continuum RT
Thermal balance
2 Chemical
network
4 Excitation
3 Thermal
Balance
5 Raytracing
Equilibrium between heating and cooling rates
- Line
cooling and (back)heating
- atoms (OI, CI, CII, SII, SiII, FeII, MgII, Lyα)
- molecules (CO,13CO,C18O,OH,H2O, CN, HCN)
- H2
line heating/cooling (UV fluorescence),
chemical heating (formation/dissociation)
- Grains, PAHs
photoelectric heating (UV), gas-grain exchange
- Cosmic/X-rays coulomb and chemical heating
1 Continuum RT
Excitation
2 Chemical
network
4 Excitation
3 Thermal
Balance
5 Raytracing
Atoms & molecules not in LTE with gas
- Collisional excitation
- Pumping by dust continuum (submm - far UV)
- Pumping by line photons
(escape probability approximation)
- Chemistry
OI(1D) pumping by OH photodissociation
H2 formation in excited level
1 Continuum RT
Iteration
2 Chemical
network
4 Excitation
3 Thermal
Balance
5 Raytracing
Coupled problem
- Gas temperature → chemistry
- Chemistry → thermal balance
- Chemistry/gas temperature → thermal balance
→ Solve chemistry
thermal balance
excitation
iteratively/self-consistently
Many connections: difficult/time-consuming to solve
➝ Static models
Example: Transitional disks
S. Bruderer: Survival of molecules in cavities of transition disks, Online Material p 2
0.8
12CO
12
δgas = 1.0
CO
12
δgas = 10−1
CO
12
12
δgas = 10−2
CO
δgas = 10−3
CO
2000
1000
0.4
∆δ (”)
500
0
200
gap
100
−0.4
50
20
−0.8
10
0.8
13CO
13
δgas = 1.0
CO
13
δgas = 10−1
CO
13
13
δgas = 10−2
CO
δgas = 10−3
CO
2000
1000
0.4
(~1/80 x 12CO)
∆δ (”)
500
0
200
gap
100
−0.4
50
20
−0.8
10
(~1/2000 x
δgas = 1.0
C O
17
δgas = 10
C O
−1
17
δgas = 10
C O
17
δgas = 10
C O
−2
−3
2000
1000
0.4
500
12CO)
∆δ (”)
C17O
0.8
17
ALMA detects
~ 1 MEarth
in cavity in just
1 hr
0
200
gap
100
−0.4
50
20
−0.8
10
0.8
(~1/50000 x
18
δgas = 1.0
C O
13
18
δgas = 10
C O
−1
13
18
δgas = 10
C O
13
−2
18
δgas = 10
C O
−3
2000
1000
Bruderer 2013
0.4
500
12CO)
∆δ (”)
13C18O
13
0
200
gap
100
−0.4
50
20
−0.8
10
Gas mass in cavity
−0.8
More: −0.4
0
∆α (”)
0.4
0.8
−0.8
0
−0.4
0.4
0.8
−0.8
∆α (”)
−1
0
−0.4
0.4
0.8
−0.8
∆α (”)
12
13
−0.4
0
0.4
0.8
∆α (”)
17
13
18
Fig. 19. Images of the integrated intensity (in K km s ) of CO isotopologues ( CO, CO, C O, and C O) from the series of representative
models (Table 1) with dusty inner disk present (δdust = 10−5 ). Models with δgas = 1, 10−1 , 10−2 and 10−3 are shown. The inclination i = 30◦ and the
black dashed lines show the size of the gap (10 < r < 45 AU). The C18 O images look similar to the C17 O images and thus not shown. 1st row:
12
CO 3 − 2. 2nd row: 13 CO 3 − 2. 3rd row: C17 O 3 − 2. 4th row: 13 C18 O 3 − 2.
Herschel DIGIT (PI Neal Evans) observations of CO ladder
(Bruderer+ 2012, Meeus+ 2013)
Fitting ALMA observations/SED/imgages of a transition disk
(Bruderer+ 2014)
2. Time dependent models
Time dependent models
• Mostly static models (computational demanding)
• But
•
Time dependent (PDR) chemistry (but temperature fixed)
(e.g.Viti, Lee+ 96, Bergin+ 97, Doty+, ..., DALI, ProDiMo, ... many others)
•
Time dependent PDR
(Störzer & Hollenbach 98, moving ionization front)
•
Chemistry along trace particles (Tgas=Tdust)
(e.g.Visser+ 11, Ilee+ 11)
•
Advection, mixing (fixed T)
(e.g. Heinzeller+ 11, Semenov+ 11)
Because: mostly focused on i.) Disk evolution time-scales
ii.) weakly irradiated gas (Tgas=Tdust)
Time dependent models
Episodic accretion: Short time-scales matter!
(few hr - years)
Here:
•
Solve the time-dependent evolution of the chemistry
and evolution of internal energy simultaneous
→ Thermo-chemical evolution
•
Similar physical processes as DALI (incl. non-LTE excitation of
atoms/molecules), but some in a simplified implementation and
only simple chemical network (still very time-consuming)
•
Test with Röllig et al. 2007 PDR-benchmark study
Temperature
H2
100
Fractional abundance
Temperature (K)
104
PDR-Test
n=105.5 cm-3
G0=105 ISRF
103
102
101
0.1
0.2
0.5
1
2
5
10
10
1
10
2
10
3
10
4
10
5
20
0.1
0.2
0.5
1
10
3
10
4
10
5
10
6
10
7
10
8
C
0.1
0.2
0.5
1
2
AV
5
10
20
2
5
10
20
AV
Fractional abundance
Fractional abundance
AV
2
5
10
20
10
3
10
4
10
5
10
6
10
7
10
8
CO
1.0e+13 s
0.1
0.2
0.5
1
AV
This is a disaster - known for a long time!
But: Relative predictions probably much more reliable/useful!
Initial: Atomic H/C
PDR-Test
n=105.5 cm-3
G0=105 ISRF
Initial: Atomic H/C
PDR-Test
n=105.5 cm-3
G0=105 ISRF
3. Water in disks
Water
•
•
Luminosity vs water abundance?
Astrophysical
780:26 (8pp), by
2014Banzatti+
January 1
Mid-IRThe
(warm
water)Journal,
observations
(13/14)
photo
gests
factor
signifi
least
neces
ducti
extrem
We
the w
durin
UV-to
Water
•
Why?
- Short (photodissociation) chemical time-scales
- Longer heating time-scales
•
Water dissociated, but abundance increases after gas
heats up (on month time-scale)
Heating (>300 K)
O Photodissociation OH
Heating (>300 K)
Photodissociation
H2O
Toy-model
•
Structure, Tdust, FUV field from typical
DALI T Tauri model (10-2 Msun)
•
Lbol increases suddenly from 1 (quiescent)
to 10 (outburst)
•
Calculate time-dependent vertical slices
at 0.5, 1, 3, and 10 AU
•
Assume Tdust increases instantaneous
(Johnstone+ 2013 → Doug‘s talk)
r = 0.5 AU
r = 0.5 AU
Column densities
H2O Column density down to depth where dust is opaque in mid-IR
H2 O Column Densit y (cm−2 )
1020
10 hr
W
M
Yr
r
r
r
r
1018
= 0.5 AU
= 1 AU
= 3 AU
= 10 AU
1016
1014
1012
104
105
106
107
108
Time after outburst (s)
109
1.) Water first drops (photodissociation) before heating kicks in!
2.) Time-scales of month needed to produce more water
3.) Drop at >= 1 AU deeper because no water down to mid-plane
Conclusions
• Thermal-chemical coupling matters for short timescale phenomena
• Model predicts heating time-scales at inner (< few AU)
upper disk of ~month leading to a slow increase of
water → Agrees to observations
• Model predicts a short period of drop of water, before
heating is efficient enough → Seems unlikely?
Observations?
Possible ways out:
- Less photodissociation: Self-shielding by water?
- We can see deeper into the disk