1. Chemistry and Dynamics in Protoplanetary Disks
Thomas Henning and Dima Semenov
Max-Planck-Institut für Astronomie, Heidelberg
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Chemistry and Dynamics in Protoplanetary Disks
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Courtesy of David E. Trilling

2. Motivation Initial conditions for planet formation
Chemical composition of primitive bodies in the solar system
Gas depletion and dissipation in disks – Molecules as tracers of disk history
Chemistry – Physical state of the disk (temperature, density, radiation, ionization, transport)
General note
Observational fatcs and data:
solid bodies from early Solar System
young disks around young stars
Chemistry-Physics connections in disks

3. Any Hot Topics? Coupling between dynamics and chemistry
Complete evolutionary track from cold cores to disks (e.g. deuteration sequence)
Coupling between solid-phase and gas-phase disk components (grain evolution and settling)
Early stellar activity (winds, X-rays, UV, …)
Coupling Chem with Dyn: timescales! (e.g., freeze-out ~10^3-4 yrs, mixing = H2/D ~ 10^4-5, but surface chemistry ~ 10^6)
Imprint of core properties & composition in young disks
Accretin/desorption, grain growth & settling, rocessing of ices, etc.
X-ray, UV non-thermal rádiation fields (variability), stellar winds

4. Disk Structure ~500 AU 100 AU 1 AU ~1000 AU
Observable region with interferometers
wind
photon-dominated layer
cold midplane
warm mol. layer
accretion (magneto-
rotational instability)
hν, UV,
X-rays
turbulent mixing
IS UV, cosmic rays
snowline
Only region r> AU is accessible with (sub)mm-interferometers
“Sandwich”-like 3-layered structure: cold midplane (freeze-out), warm inermediate layer (mild UV, X-ray, rich chemistry, lines!), surface (only simle species/atoms)
Accretion is thought to be driven by the so-called magnetorotational instability (next slide)

5. Highly Dynamical Environment
Disk Physics
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Highly Dynamical Environment
Klahr, Henning, and Kley (1999)
-7 ° - 7 ° (#20)
ΩK = 12
Flux limited RT
AU (#51)
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6. MRI Overview __________ __________ Rotational axis
Magnetic field geometry
faster rotation
slower rotation
centrifugal force & magnetic tension  loop generation
(turbulence)
How MRI works?
Imagine a rotating disk with a radial velocity gradient (a natural consequence of angular momentum transport) and magnetic field oriented vertically. Simple 2D picture: if there is a tiny dispatch of the material in outward direction, then disbalanced centrifugal force coupled to magnetic tension will tend to increase the dispatch and create a loop configuration with disturbed velocities. Eventually, it leads to turbulence generation. The MRI is a robust mechanism that works even if weak plazmas with ionization fracion > 10^-10-10^-8.
N. Dziourkevitch & H. Klahr (2006), ApJ, in prep.
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7. Ionization Structure of a Disk: Effect of Grain Evolution
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Shown here are two identical models of a young disk around a Sun-like star.
Upper panel depicts the final ionization degree in the disk at 5 Myr computed with extended chemistry and tiny dust grains (0.1 mum). A „dead“ zone for MRI in the midplane with very low ionization degree is clearly visible. Lower panel shows the same model but computed in assumption that dust grains are large, cm-sized, and setteld toward the midlane. In this case there is no low ionized region in the disk, so MRI operates everywhere and accretion is more efficient.
Time evolution is presented on the next slide.
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8. Ionization Structure of a Disk: Effect of Grain Evolution
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„Layered“ vertical structure
Semenov, Wiebe, Henning (2004)
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9. N2H+ in disks: CID Collaboration
(Bordeaux – Heidelberg – Jena – Grenoble - Paris)
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N2H+/HCO+ ~ 0.03
HCO+ is dominant ion
N2H+ is not a good tracer of ionization
1012
We observed N2H+ in two disk around Sun-like stars (DM Tau, LkCa15) and around a more massive star (MWC 480). Surprisingly, detected N2H+ column density is 100 times lower that was previously observed (Lkca 15, Qi et al. 2003?). We also obtained HCO+ column density and estimated N2H+/HCO+ ration ~ , similar to the value measured in cold cores.
Using a realistic disk physical structure & extended gas-grain chemical model with surface reactions, we predicted HCO+ & N2H+ abundance distributions & column densities. Our model is fairly good in comparison with observational data (but radial dependence is not well constrained). Important conclusion is that due to much lower abundance and the fact that it is locally peaked at lower part of warm molecular layer, N2H+ is not a reliable tracer of the ionization degree. In this respect, HCO+, being the dominant ion, looks more promising ionization degree tracer in disks. 10
1010
Dutrey, Henning et al. (2006), A&A, submitted
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10. CID I: N2H+ in three disks
Main results:
HCO+ remains the more abundant molecular ion in disk
[N2H+]/[HCO+] ~ , similar to dense cores
A lower limit on the ionization fraction can be obtained from HCO+ column density (and 13CO abundance)
[e] > 10-10
HCO+ and N2H+
Comparison observations / model
(chemical model by Semenov et al., 2005)
Good agreement (even if the slope p
Is not yet properly reproduced) !

11. Dynamics and Chemistry
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Chemically reacting flow system
„Well-mixed reactor system“
Flow along predominant direction including mixing
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12. __________ Theoretical Milestones
Anomalous viscosity (von Weizsäcker, early 40s)
α model of disk viscosity (Shakura & Sunyaev 1973)
Magneto-rotational instability (Balbus & Hawley 1991)
Observational Evidence
Non-thermal line broadening (~100 m/s)
Crystalline silicates in comets and disks (van Boekel et al. 2005, Crovisier et al. 1997, Wooden et al. 2005)
Chondritic refractory inclusions in meteorites (MacPherson et al. 1988)
Gas-phase CO at T<25K in DM Tau (Dartois et al. 2003)
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13. __________ Observational Evidence
Non-thermal line broadening (~100 m/s)
Crystalline silicates in comets and disks (van Boekel et al. 2005, Crovisier et al. 1997, Wooden et al. 2005)
Chondritic refractory inclusions in meteorites (MacPherson et al. 1988)
Gas-phase CO at T<25K in DM Tau (Dartois et al. 2003)
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14. Steady Inner Disk Model
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no vertical mixing
vertical mixing CS
Ilgner, Henning et al. (2004)
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15. Previous Studies __________ __________
Gail & Tscharnuter (>2000): 2D hydro + RT inner disk, gas-phase combustion chemistry, grain evolution  crystalline silicate distribution, carbon chains
Ilgner et al. (2004; 2006a,b): 1+1D inner disk, 1D vertical mixing & radial transport, gas-grain chemistry  molecular abundances
Lyons & Young (2005): inner solar nebula, 1D vertical mixing, photochemistry  16/18 oxygen isotopic anomalies
Willacy et al. (2006): 1+1D outer disk, 1D vertical chemistry, gas-grain + surface chemistry  molecular abundances
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16. Chemistry with Dynamics
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Evolution = Formation - Destruction Diffusion Advection
[ Chemistry ] [ Dynamics ]
Input:
Physical conditions, diffusion coefficient & flow data Initial abundances of species
A chemical network
A numerical solver
Benchmarking
Chemical evolution of species can be described using a system of ordinary differential equations that are stiff due to vastly different magnitudes of reaction rate values. If one wants to model chemistry with dynamics, one has to include also two additional terms due to turbulent diffusion and advective transport. Both these terms are characterized by diffusion coefficient, D ~ alpha x sound speed x scale height, and flow properties (U).
Thus, necessary input information for ´modeling chemistry with dynamics is T, rho, radiation field, etc., then diffusion coefficient and flow data. Also, one has to chose appropriate set of chemical reactions and efficient numerical solver. The last step is comparison with existing mixng chemical models.
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17. Surface Chemistry __________ __________ 2-body reaction Desorption
Accretion
Surface reaction
(thermal hopping)
2-body reaction
UV, CR, X-ray
heating
Mantle
Grain
Gas-phase reactions, accretion & desorption (UV, cosmic rays, collision?), surface chemistry (thermal hopping but unlikely quanum tunneling)
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18. Chemical Network __________ __________ Updated UMIST’95:
Limited deuterium chemistry
Photochemistry: Cosmic rays, UV, X-rays & radioactivity
Accretion & desorption + surface reactions (0.1 μm grains)
Molecular initial abundances
t = a few million years
Semenov et al. (2005)
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19. t ~ N3 (amount of species in the model)
Chemistry with Mixing
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2D-implicit scheme for chemistry with mixing
Fickian diffusion
Full/reduced chemical networks
1D-benchmarking with K. Willacy & D. Wiebe
t ~ N3 (amount of species in the model)
2D-implicit scheme for chemistry but not for dynamics (no operator splitting!). Fickian diffusion is approximation (dn/dt = d2/dr2(n) ).
2D code is time-consuming, time increases as 3rd power of number of species in the model -> robust reduction is needed!
Semenov , Wiebe, & Henning (2006), ApJL, submitted
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20. Disk Model __________ __________
1+1D flared disk (D‘Alessio et al. 1999)
Mdisk= 0.05M, Mdot = 10-8M/yr, M = 0.65M, R >10 AU
Mixing efficiency D ~ 0.01csH (Johansen & Klahr 2005)
Radial D = 1.5 x vertical D ~ 1015 – 1018 cm2/g
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21. Overview of Mixing Results
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10 AU AU
Deuterated chemistry is limited in our model, so the results for DCO+ and HDO should be taken with care!
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22. Disk Ionization Degree
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Stationary Vertical mix. Radial mix D-Mixing
30x65 grid, 200 species in 1600 reactions
10 AU AU
Comp. Time: 2h h h >200h
Chemical equilibrium is reached within 10^3-10^4 yrs for ionization degree. On the other hand, diffusion timescale, which is ~ H2/D, is about 10^4-10^5 yrs for this disk. Thus, chemical evolution proceeds at timescales shorther than dynamics and resulting electron concentration is not sensetive to mixing.
However, as I‘ll show later, it is not true the presence of steep abundance gradients anymore.
Unaffected by diffusion since chemical equilibrium is reached quickly
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23. Stationary Vertical mix. Radial mix. 2D-Mixing
Gas-phase CO at T<25K
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Stationary Vertical mix. Radial mix D-Mixing
10 AU AU
Dark blue color means nothing (10^-15 value for relative abundance).
From left ot right: static (non-mixing) model, model with vertical mixing, model with radial mixing, and 2D-mixing model. In static model, in cold outer midplane CO frezes out quickly, but in fact a large reservoir of CO gas at T~13 K it has been detected in DM Tau by Dartois et al. (2003). In contrast, in 2D model some of CO is transported from inner midplane region where accretion heating keeps CO in the gas phase, as well as from warm molecular layer above (these 2 effects are clearly visible on 2 & 3 plots). Moreover, it is apparent that 2D mixing can be considered as a joint aaction of radial & vertical mixing.
Abundant CO gas in cold midplane despite fast freeze-out (steep local abundance gradients)
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24. Gas-phase CO at T<25K __________ __________
N(CO) ~ 1017 cm-2 (2D-model)
optical depth is ~ 1
explains the observations of Dartois et al. (2003)
To get observed tau <~ 1 in the cold midplane, column density of CO should be around 10^17 cm^-2. We computed CO column density in the midlane and the rest of the disk, using T=25K as a limiting value. Upper panel shows N(CO) for vertical disk extend but midplane, and lower panel corresponds to the CO column density in the midplane. As clearly seen, CO is only significantly enhanced in the case of 2D-model.
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25. Diffusion-dependent H2CO enrichment due to slow surface processes
Gas-phase H2CO
100x lower
diffusion
Stationary Vertical Radial D-Mixing
10x lower
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The same slide as before but for H2CO. It shows the resuls for 4 chemical models with & without mixing included, and 3 cases of the diffusion coefficient that correspond to alpha = 10^-2 (upper panel), 10^-3, and 10^-4 (bottom panel). The chemical evolution of H2CO is governed by surface reactions: CO + H -> HCO, HCO + H -> H2CO. The first channel involves a barrier of ~1000K, and thus is not that efficient at very low T. Moreover, H2CO easily freezes out at T<~30K. Thus, in static model it appears in he gas-phase only in the shielded but warm intermediate layer and inner midplane region heated by viscous accretion heating. In contrast, vertical mixng model and 2D-mixing model show significant enhancement of the H2Co gas-phase concentration. This is due to 2 factors. First, mixing brings instanteneously frozen H2CO from cold disk part such that it can thermally desorb back to the gas phase. Second, main effect is due to slow surface hydrogenation reactions that have timescales longer that typical mixing timescale of 10^4-10^5 yrs. Thus, the chemical evolution of H2CO becomes sensitive to details of mixing process. Since the mixing is able to transport grains from very cold regions to more warmer regions, a larger fraction of surface CO is converted to surface H2CO (remeber barrier for the first reaction H + CO -> HCO!). As we lower diffusion coefficient, the increase of the H2CO abundances goes down (compare upper panel with middle and bottom panels). Thus, his molecule is sensetive to the magnitude of diffusion coefficient, i.e., mixing efficiency.
10 AU AU
Diffusion-dependent H2CO enrichment due to slow surface processes
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26. Basic Results __________ __________
“Sandwich”-like disk structure is preserved
Ionization degree is hardly affected
Abundance of photo-controlled species are not affected
Abundances of more complex (organic) species can be enhanced (grain mantle components, e.g.
H2CO)
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27. Disk Chemistry __________ __________
Large range of temperatures and densities
Importance of radiation fields
Strong coupling between chemistry and dynamics (ionization, temperature structure, …)
Chem and Dyn are connected such that Dyn is related to ionization state of a disk, which in turn depends on Chem
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28. Collaborators __________ __________
CID collaboration (A. Dutrey, S. Guilloteau, V. Pietu, A. Bacmann, R. Launhardt, Y. Pavlyuchenko, J. Pety, K. Schreyer, V. Wakelam)
D. Wiebe (Moscow): Chemistry with mixing
M. Ilgner (London): Chemistry with mixing
H. Klahr, A. Johansen (MPIA): Disk dynamics
K. Dullemond (MPIA): Grain evolution
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29. The End
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30. (broad emission lines: Hα, etc)
NIR/Mid-IR thermal dust (VLTI: Midi, Amber)
Scattered Light in Optical and NIR (opt. thick)
Domain sampled
in current images
at 150 pc
mm / submm thermal dust emission (opt. thin)
Optically thick CO lines
Accretion shock
thin lines
Accretion disk
~ Kuiper Belt
Stellar magnetosphere
Passive reprocessing disk
200
Flaring?
Approximate H(r) at 500 AU (AU)
Vertical scale near the star
Acc. Rate ~10-8M⊙/yr
Planetesimals?
Wind
Accretion columns
(broad emission lines: Hα, etc)
- 200
~ 1
~ 50
~ 100
~ 500
Approximate radius r (AU)
Adapted from A. Dutrey
Cumber03.ppt

31. Angular Momentum Machines and Chemical Factories
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Cumber01.ppt

32. Previous Models (Non-Equilibrium Thermodynamics) Markwick et al., 2002
Aikawa et al., 2002
„Molecular distributions in the inner
„Warm molecular layers in
regions of protostellar disks“
protoplanetary disks“
Willacy et al., 2000
Aikawa et al., 1999
„The importance of photoprocessing
„Evolution of molecular abundances in proto-
planetary disks with accretion flow“
in protoplanetary disks“
Finocchi et al., 1997
Willacy et al., 1998
„Gas and grain chemistry in
„Chemical reactions in protoplanetary disks“
protoplanetary disks“
Aikawa et al, 1996
Bauer et al., 1997
„Evolution of molecular abundance in
„Simulation of chemical reactions and
gaseous disks around young stars“
dust destruction in protoplanetary disks“

33. (gas phase and surface chemistry incl. vertical mixing)
Steady Disk Model
(gas phase and surface chemistry incl. vertical mixing)
accretion rate  -7 10
M / yr  yr
accretion rate  -8
510
M / yr  yr

34. (gas phase and surface chemistry incl. vertical mixing)
Steady Disk Model
(gas phase and surface chemistry incl. vertical mixing)
opacity (Henning & Stognienko) yr
opacity (Bell & Lin) yr

35. Chemistry Reduction Code “ART”
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“Automatic Reduction Technique” to reduce sizes of chemical networks:
“Important” species
Main destruction and formation reactions
Several time steps and disk regions
Remove “insignificant” reactions
Final benchmarking
Wiebe, Semenov, Henning (2003)
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36. Chemical simulations t ~ N3!
Reduced yet reliable accuracy  5X time gain
Surface chemistry  >10X loss
Old: DVODE + dense matrix formalism  slow (1 disk point ~ 5-30 min)
Now: DVODPK + sparse matrix formalism  fast >200X gain (1 disk point ~1-5 s)
t ~ N3!