Chemical model
We describe in detail all considered chemical processes adopted in our benchmarking study in the main paper and refrain from repeating it here. Our chemical network (for both models) is based on the original gas-phase osu_03_2008 ratefile and includes gas-grain interactions and a set of surface reactions for the H-, O-, C-, S-, and N-bearing molecules. The utilized ratefile is available here.
The first-order and second-order kinetics, without three-body reactions, is considered. The chemistry includes both gas phase, gas-grain, and surface reactions. The considered gas-phase processes are ion-molecule, neutral-neutral, charge exchange, radiative association, radiative recombination, dissociative recombination, CRP and FUV ionization and dissociation, and other reactions. Gas-grain interactions include accretion of neutral molecules and electrons onto the surfaces of 0.1μm amorphous silicate spherical grains, dissociative recombinations of molecular ions and radiative recombinations of atomic ions on negatively charged grains, as well as thermal, CRP-driven and UV-desorption (with the UV yield of 0.001). Surface reaction rates are calculated assuming no H/H2 tunneling through potential wells of the surface sites and reaction barriers, in the Langmuir-Hinshelwood approximation using the standard rate equation approach. All model parameters and constants used in our comparison of chemical codes are listed below:
Boltzmann's constant |
kB |
1.38054×10-16 erg K-1 |
Planck's constant |
ℏ |
1.05459×10-27 erg s-1 |
Proton's mass |
1.66054×10-24 g |
|
CR ionization rate |
ζCR |
1.3×10-17 s-1 |
Dust radius |
ag |
0.1μm |
Dust density (olivine) |
ρg |
3 g cm-3 |
Dust-to-gas mass ratio |
md/g |
0.01 |
Surface density of sites |
Ns |
1.5×1015 sites cm-1 |
Number of surface sites per grain |
S |
1.885×106 sites |
Gas molecular weight |
μ |
1.43 |
Peak grain temperature after a CRP hit |
TCR |
70 K |
Grain cooling time / Time between 2 CR hits |
f |
3×10-19 |
Diffusion / desorption ratio for surface species |
Tdiff/Tdes |
0.77 |
Initial abundances
We use an up-to-date set of elemental abundances from Wakelam et al. (2008). The 12 elemental species include H, He, N, O, C, S, Si, Na, Mg, Fe, P and Cl. Except for hydrogen, which is assumed to be entirely locked in molecular form, all elements are initially atomic. They are also ionized except for He, N and O. All heavy elements are heavily depleted from the gas phase similar to the "low metals" abundances of Lee et al. (1998). All grains are initially neutral. The input file with these initial abundances is available for download. Since large-scale chemical models with an extended set of surface reactions rarely reach a chemical steady state, all benchmarking tests run over a long evolutionary time span of 109 years (with 60 logarithmic time steps, starting from 1 year). Both chemical codes use the same absolute and relative accuracy parameters for the solution, 10-20 and 10-6, respectively.
Physical models
The physical conditions of the five benchmarking cases are chosen to represent realistic astrophysical object yet to be relatively simple. We decided to focus first on physical models representative of less complex and a hot corino ("HOT CORE"). The "TMC1" model has a temperature of 10 K, a hydrogen nucleus density of 2×104 cm-3, and a visual extinction of 10 mag. The corresponding input file is provided. The "HOT CORE" model has a temperature of 100 K, a hydrogen nucleus density of 2×107 cm-3, and a visual extinction of 10 mag. Both models have FUV IS RF adopted from Draine (1978). The cosmic ray (CR) ionization rate is ζCR=1.3×10-17 s-1. The input file for the "HOT CORE" model can be downloaded here.
Protoplanetary disks are more complex objects from chemical point of view as they have strong gradients of temperature, density, and ionizing radiation flux. Thus we decided to focus on a few representative disk regions with highly distinct physical conditions. We take physical conditions similar to those encountered in the DM Tau disk, for which a lot of high-resolution molecular data are available. The "DISK1" model is located at 6.768 AU above the midplane, has a temperature of 11.4 K, a hydrogen nucleus density of 5.413×108 cm-3, a visual extinction toward the star of 40.35 mag., extinction of 37.07 mag. in the vertical direction, and the FUV RF intensity of χ=428.3χ0. The "DISK2" model is located at 29.97 AU above the midplane, has a temperature of 45.9 K, a hydrogen nucleus density of 2.588×107 cm-3, a visual extinction toward the star of 23.23 mag. and the vertical extinction of 1.939 mag., and the FUV RF intensity of χ=393.2χ0. Finally, the "DISK3" cell is located at 45.44 AU above the midplane, has a temperature of 55.2 K, a hydrogen nucleus density of 3.669×106 cm-3, a visual extinction toward the star of 1.608 mag. and the vertical extinction of 0.217 mag., and the FUV RF intensity of χ=353.5χ0. The corresponding input data are available for download. All physical model parameters are summarized in Table below:
Model |
T [K] |
n(H+2H2) [cm-3] |
Av [mag] |
χ |
TMC1 |
10 |
2×104 |
10 |
1 |
HOT CORE |
100 |
2×107 |
10 |
1 |
DISK1 |
11.4 |
5.41×108 |
37.1 |
428.3 |
DISK2 |
45.9 |
2.59×107 |
1.94 |
393.2 |
DISK3 |
55.2 |
3.67×106 |
0.22 |
353.5 |
Last update by Dmitry Semenov (MPIA): July 7, 2010