5 Summary

We have presented two major extensions from our previous models reported in Paper I.

Firstly, we have investigated the two-dimensional distribution of deuterated species in protoplanetary disks. The molecular D/H ratios in gaseous disks evolve in a similar way as in molecular clouds. In the vertical direction the D/H ratios are higher at lower height, where molecules are more heavily depleted onto grain surfaces.

The D/H ratios of HCO⁺, NH₃, and H₂O decrease significantly towards smaller radii at $R\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}300$ AU. These molecules are deuterated through H₂D⁺, the abundance of which is rather sensitive to the temperature, which increases at small radii. The D/H ratios of CH₄and H₂CO do not decrease inwards because these species are deuterated through CH₂D⁺, which is formed from CH₃⁺through a sufficiently exothermic reaction that it does not possess much of a temperature dependence in the range ( $T\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}40$ K) we are concerned with in this paper. The DCN/HCN ratio is higher at larger radii because DCN is formed primarily from H₂CN via the reaction with D atoms, which are more abundant at larger radii, where the density is lower.

The D/H ratios depend not only on the temperature, but also on the disk mass and the X-ray flux. In the disk with larger mass, the column-density ratios of deuterated species to normal species are generally higher because of heavier depletion of molecules onto grains. With a higher X-ray flux, the D/H ratios of HCO⁺, NH₃ and H₂O are smaller at large radial distances because the enhancement of the H₂D⁺to H₃⁺ ratio is reduced by more copious electrons.

Our results for the ratio of the column densities of DCN and HCN are in reasonable agreement with the observation of the disk around LkCa15 (Qi 2000) whether we utilize the Kyoto or the low mass model, but the absolute column densities we calculate are too low for this rather massive disk.

Secondly, we have investigated molecular column densities in disks embedded in ambient clouds using models without and with X-rays from the central T Tauri star.

In the models without X-rays, the column densities of radicals such as CN are sensitive to the attenuation of interstellar UV by ambient gas, especially in the inner radius of the disk. In the disk with direct UV irradiation, the CN column density is $3\; 10^{12}{-}3\;10^{13}$ cm^-2 in the region $50\le R \le 700$AU, while in the disk embedded in ambient gas, the column density of CN is 10¹² - 10¹³ cm^-2 in the outer region of the disk ( $R\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ }}}300$ AU), but decreases for radii $\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}300$ AU by orders of magnitude. On the other hand, in the models with X-rays, ionization and induced photolysis by X-rays enhance the abundance of CN and other radicals so that the column density of CN is as high as $\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ }}}10^{13}$ cm^-2 at $50\le R \le 700$ AU. Since the X-ray flux is higher in inner regions, radial distributions of radicals such as CN are centrally peaked. Indeed, the distributions for non-radicals tend to show a similar effect.

The molecular ion HCO⁺ is centrally peaked regardless of the X-ray luminosity, and is more abundant in the case with UV shielding via ambient clouds. Inclusion of X-rays further enhances the column density of HCO⁺.

Our calculated results, combined with the fact that CN and HCO⁺ are clearly detected in the non-embedded disks around DM Tau, GG Tau, and LkCa15, suggest that CN and HCO⁺ can be gaseous disk tracers towards embedded objects especially with high X-ray luminosity. Our results also suggest that the radial distribution of the radicals CN and C₂H and some non-radical species (HCN and H₂CO) may vary among disks depending on the X-ray luminosity of the central star.

Acknowledgements

The authors are grateful to A. Dutrey, G. Blake, C. Qi, and M. Saito for stimulating discussions on the line observation of protoplanetary disks. Y. A. is grateful for financial support from the Japan Society for Promotion of Science. The Astrochemistry Program at The Ohio State University is supported by The National Science Foundation. Numerical calculations were partly carried out at the Astronomical Data Analysis Center of the National Astronomical Observatory of Japan, and on the Cray T90 at the Ohio Supercomputer Center.