1 Introduction

Protoplanetary disks are formed around young stellar objects as the stars are created, and are birthplaces of planetary systems. Molecular evolution in protoplanetary disks is important because it can reveal the chemical connection between planetary and interstellar matter. Since chemical abundances are determined by physical parameters such as temperature and density, studies of molecular evolution in protoplanetary disks can also be of help in determining the structure and physical evolution of the disks from the molecular line observations.

In recent years it has become possible to detect molecular lines in protoplanetary disks by radio astronomy. Aperture-synthesis images have directly revealed gaseous CO disks, which are in Keplerian rotation (Kawabe et al. 1993; Koerner et al. 1993; Dutrey et al. 1994; Koerner & Sargent 1995; Saito et al. 1995; Guilloteau & Dutrey 1998). In addition to the CO studies, Dutrey et al. (1997) surveyed other molecular lines in the disks around DM Tau and GG Tau using the IRAM 30 m telescope. These stars, with ages $1\; 10^6$ yr and $3\; 10^5$ yr respectively (Beckwith et al. 1990; Handa et al. 1995), have large gaseous disks with radii $\sim$800 AU. The molecular line spectra detected towards the two stars are similar despite the fact that the disk around GG tau is circumbinary. The averaged fractional abundances of gaseous CO, CN, CS, HCN, HNC, H₂CO, C₂H, and HCO⁺ were reported by Dutrey et al. (1997), who found that the abundances of heavy-element-containing molecules relative to hydrogen are lower than those in molecular clouds by factors of 10-100, and relative abundances among heavy molecules are also different. Specifically, the abundance ratio of CN to HCN is much higher in disks than in molecular clouds.

In order to reveal the chemical and physical causes for these differences, Aikawa & Herbst (1999a) (hereinafter Paper I) investigated the two-dimensional distribution of molecules in a disk by calculating molecular concentrations from a network of chemical reactions. They found molecular abundances to vary with height Zfrom the midplane. At larger radii ( $R\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ }}}100$ AU), which contribute most to the molecular emission lines because of the large area, the temperature is so low ($T\sim 10$ K), that most molecules, except for H₂ and He, are partially adsorbed onto grains to form ice mantles. In the midplane region ( $Z \approx 0$) molecular depletion is the most effective because disks are in hydrostatic equilibrium in the vertical direction, and the density is the highest in the midplane region.

In regions above and below the midplane, significant amounts of molecules remain in the gas phase because of lower densities, and because of non-thermal desorption, which is caused by cosmic rays and/or radiation (ex. X-rays) from the interstellar field and the central star. Aikawa & Herbst (1999a) suggested that the observed molecular lines come mostly from this region. There is a height distinction between stable molecules and radicals, however. In the surface (uppermost) region of a disk, radicals such as CN are very abundant because of photodissociation via UV radiation. The molecular column densities obtained in Paper I by integrating over height are in reasonable agreement with observation; molecular depletion in the midplane explains the low average abundance of heavy-element-containing species relative to hydrogen, and the high abundance ratio of CN to HCN is caused by photochemistry in the surface region. It is clear that consideration of the 2-D distribution of molecules is essential in order to interpret the observed molecular line intensities.

In this paper we present two extensions of the work in Paper I. Firstly, we include deuterium chemistry in the 2-D disk model. Since the line survey by Dutrey et al. (1997), further searches for molecular lines in protoplanetary disks have been conducted by several groups of observers. One of the most interesting results is the detection of deuterated species in the disk of LkCa15 (Qi et al. 1999; Qi 2000). The average DCN/HCN ratio is estimated to be about 0.01, which is much higher than the D/H elemental abundance ratio of $1.5\; 10^{-5}$. Aikawa & Herbst (1999b) showed that a high D/H ratio in a disk is a natural outcome of the incorporation of interstellar material to the protoplanetary disk and a low temperature disk chemistry, which is similar to cloud chemistry. They were concerned, however, only with icy material in the midplane region, and did not predict column densities for deuterated gaseous molecules. A two-dimensional disk model with deuterium chemistry and comparison with observation should be helpful in constraining the physical properties of the disk, such as temperature. Such a theoretical model should also be useful in guiding searches for other deuterated molecules. The results presented here fulfill these expectations, at least partially.

Secondly, we consider disks that are embedded in molecular clouds or circumstellar envelopes. Up to now, molecular line observations of disks have been successful only in cases where a disk is removed from molecular clouds or where the system velocity is quite different from the cloud velocity. Most disks, which presumably are embedded in cloud gas or circumstellar envelopes, are hard to observe via molecular lines because of contamination with ambient gas. If we were able to predict which molecules could selectively trace disk gas, the species could be used to search for embedded gaseous disks, and so permit more statistically reliable arguments on disk properties, such as their size and time scales of gaseous dissipation.

The rest of the paper is organized as follows. In Sect. 2 we describe our model of protoplanetary disks and the chemical reaction network we utilize. Numerical results on the distribution of molecular abundances, the column density ratio of deuterated and normal species, and the dependence of D/H ratios on selected physical properties of disks are discussed in Sect. 3. In Sect. 4, we report our investigation of molecular abundances in disks that are embedded in ambient gas, and discuss which, if any, molecular lines can be used as disk tracers. We summarize our results in Sect. 5.