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Appendix A: On the assumed parameters

In this work, we have used a fixed set of parameters for the calculation of the thermal grain-surface reaction rates and desorption rates. Two parameters which may have a strong influence on the grain-surface abundances and subsequent gas-grain balance are the diffusion barriers between surface sites, E_b, and the probability for reactive desorption, P_rd. We assume the grain-surface diffusion barrier for each species is proportional to its binding (desorption) energy to the grain surface, E_D. Here, we assume an optimistic value, E_b/E_D = 0.3. This value allows the reasonably efficient diffusion of radicals within the grain mantle when T ≳ 15 K, which helps to build chemical complexity in the outer disk. Vasyunin & Herbst (2013) recently explored the effects of the value assumed for E_b/E_D in a macroscopic Monte Carlo model of hot core chemistry, using a “layer-by-layer” approach to calculate the grain mantle composition. They explored a range of values for E_b/E_D: 0.3 (Hasegawa et al. 1992), 0.5 (Garrod & Herbst 2006), and 0.77 (Ruffle & Herbst 2000). They concluded models using the intermediate value, E_b/E_D = 0.5, produced ice compositions in better agreement with observations; however, models with E_b/E_D = 0.3 also gave reasonable agreement for the warm-up phase.

In addition, we assume a conservative value for the probability for reactive desorption, P_rd = 0.01. This value is that constrained in investigations into the efficacy of reactive desorption in dark cloud chemical models (Garrod et al. 2007). Recently, reactive desorption has been postulated as a potential mechanism for the release of precursor COMs (e.g., H₂CO and CH₃OH) in cold, dark clouds where they eventually form larger complex organic molecules (e.g., HCOOCH₃ and CH₃OCH₃) in the gas phase via radiative association (Vasyunin & Herbst 2013). In addition, as discussed in the main body of the paper, recent experiments suggest that reactive desorption is particularly efficient for the reformation of doubly-deuterated water (D₂O) and O₂ via the surface reactions, s-D + s-OD and s-O + s-O, with efficiencies, >90% and ≈60%, respectively (Dulieu et al. 2013).

In this appendix, we present results from additional exploratory models to investigate the effects of a higher diffusion barrier and a higher probability for reactive desorption. In Table A.1, we list the parameters adopted in four models. In Model A, we assume E_b/E_D = 0.3 and P_rd = 0.01. This model corresponds to our fiducial model, the full results for which are discussed in the main section of this paper. In Model B, we adopt a higher diffusion barrier, E_b/E_D = 0.5, and in Model C we adopt a higher probability for reactive desorption, P_rd = 0.1. We present results from an additional model, Model D, in which we have adopted the higher values for both parameters.

In Figs. A.1 and A.2 we present the fractional abundances of gas-phase and grain-surface COMs, respectively, relative to the H nuclei number density, as a function of disk radius, R. We show and discuss results for the disk midplane only. This is the region where grain-surface COMs form most efficiently in our fiducial disk model. In Sects. A.1 and A.2, we discuss the effects and importance of the values adopted for the diffusion barrier and the probability for reactive desorption, respectively.

	Fig. A.1 Fractional abundance (with respect to H nuclei number density) of gas-phase molecules as a function of radius, R, along the disk midplane. The differences between Models A to D are described in the text and listed in Table A.1.
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	Fig. A.2 Same as Fig. A.1 for grain-surface species.
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Appendix A.1: Diffusion barrier

In Figs. A.1 and A.2, the red lines represent results from Model A (our fiducial model) in which we have adopted E_b/E_D = 0.3 and the green lines represent results from Model B in which we have used E_b/E_D = 0.5. There are only minor differences (less than an order of magnitude) between the gas-phase and grain-surface abundances of H₂CO, CH₃OH, HC₃N, and CH₃CCH calculated using Model A and Model B. These are species which can form either in the gas phase or which depend on hydrogenation reactions for their formation.

Lower abundances are calculated for Model B relative to Model A in the outer disk for those grain-surface species which require radical-radical association to enhance their abundance above that achieved in dark clouds. In Model B, the fractional abundances attained in the very outer disk midplane, ≈300 AU, for most species are comparable to those achieved under dark cloud conditions (see Table 1 and Fig. 4). We see an enhancement in the fractional abundances of s-C₂H₅OH, s-CH₃OCH₃, and s-HCOOCH₃ relative to their initial abundances. This is indicative that radical-radical grain-surface chemistry still operates in the outer disk midplane in Model B, albeit significantly slower relative to Model A. Moving inwards along the midplane, the temperature and density both increase and there is a corresponding increase in the fractional abundances of most COMs. This increase is mirrored in the fractional abundances attained by the analogous gas-phase species. s-CH₃CHO, s-C₂H₅OH, s-CH₃OCH₃, and s-CH₃COCH₃ exhibit an interesting behaviour between ≈50 and 150 AU. Within this region, the fractional abundances of all four species show a “dip” or minimum around 70 AU. The dust temperature within ≈150 AU in the midplane is ≳22 K allowing thermal desorption of volatile molecules, for example, s-CO (E_D = 1150 K). The species showing this minimum all form via grain-surface reactions involving the relatively volatile methyl radical, s-CH₃ (E_D = 1180 K). In Model B, the grain-surface reaction rates are not sufficiently fast to compete with the thermal desorption of s-CH₃ until the dust temperature increases to a value which allows grain-surface thermal chemistry to operate efficiently.

The mobility of grain-surface species is dependent upon exp( − E_b/T) = exp( − χE_D), where χ = (E_b/E_D)/T. In Model A, there is efficient mobility of grain-surface radicals and thus efficient grain-surface synthesis when χ ≳ 0.02. In Model B this value of χ (a measure of the degree of mobility) is attained when T ≳ 28 K which is reached within ≈70 AU in the disk midplane. In Model B, relatively high fractional abundances of grain-surface COMs are attained that are comparable with those from Model A. However, the radial range over which they reach their peak fractional abundance is restricted to regions where T ≳ 28 K and where the temperature is also lower than the desorption temperature of each molecule. Results from Model A and Model B are similar within ≈50 AU of the central star.

Appendix A.2: Reactive desorption

In Figs. A.1 and A.2, the blue lines represent results from Model C in which we have adopted a higher probability for reactive desorption, P_rd = 0.1. The increased reactive desorption has little effect on the grain-surface abundances. However, in the outer disk midplane, there is around an order of magnitude enhancement in the gas-phase fractional abundances when using the higher probability. In the inner disk, thermal desorption is the most important mechanism for releasing grain mantle material back into the gas phase so that the results from all models converge at small radii.

There is a similar effect seen when comparing results from Model B and Model D, in which the higher diffusion barrier, E_b/E_D = 0.5, has been adopted. Results for Model B and Model D are represented by the green lines and yellow lines, respectively. Again, there is little change in the grain-surface species when the probability for reactive desorption is increased to 0.1. For the gas-phase abundances, in Model D there is the familiar “order-of-magnitude” enhancement when using P_rd = 0.1. Note that for the most “optimistic” model, Model C, the gas-phase COMs reach peak fractional abundances between 10^-13 and 10^-9 in the outer disk midplane (R ≳ 10 AU). This enhancement in fractional abundance will increase the column densities of COMs; however, the main contribution to the COM gas-phase column density remains the photodesorbed material in the molecular layer.

© ESO, 2014