4 Disks embedded in ambient gas

Figure 5: Column densities of assorted molecules as a function of radius. The disk mass is assumed to be less than the Kyoto model by an order of magnitude, and the disk age is $t=9.5\; 10^5$ yr. Ionization, dissociation, and induced photolysis by X-rays are not considered. The solid lines show results for disks directly exposed to the interstellar UV field, while the dashed and dotted lines show results for disks embedded in ambient gas of $A_{\rm v}=1$ and 2, respectively

Figure 6: Same as in Fig. 5, but with X-rays from the central star included

Statistical observations of molecular emission lines in disks are important in order to determine their size, time scale of gas dissipation, and chemical abundances. Several gaseous disks have been found via surveys of CO J=2-1 and J=1-0 lines (Kawabe et al. 1993; Koerner et al. 1993; Dutrey et al. 1994; Koerner & Sargent 1995). The merit of using CO lines is that the molecule is in general much more abundant than any other molecules with heavy elements in interstellar conditions. However, the number of disks observed via molecular lines is much smaller than that via dust continuum studies. One of the difficulties in searching for gaseous disks via CO lines is contamination of the lines with ambient cloud gas. CO is abundant not only in the disk, but also in ambient clouds, and the critical densities of the excitation of its J=2-1 and J=1-0 lines are comparable to the cloud gas density. Hence it is useful if we can find molecular lines which preferentially trace the gas in disks. Such lines have to satisfy the following two conditions: (a) their critical densities should be higher than a typical density of molecular clouds ( $n_{\rm H}\sim 10^4$cm^-3) and (b) the molecule should be reasonably abundant within the disk. In fact, there are many molecular rotational lines, especially the high-J lines, the critical density of which is higher than the cloud density but lower than or comparable to the disk density. The latter condition (b) can be checked based on our model.

In our calculation of molecular column densities in disks in Paper I, however, we assumed the disks to be directly exposed to the interstellar radiation field. In order to see if there is any molecular line which can be used to trace embedded disks, we have to reconsider the problem including the UV attenuation via ambient gas. One possible tracer is CN, the rotational (N=2-1) transition of which is one of the strongest lines detected in the disks around DM Tau, GG Tau, and LkCa15 (Dutrey et al. 1997; Qi 2000). The clear detection of the line indicates that CN is relatively abundant in these disks, and the high critical densities ( $n_{\rm H}=3\;10^5$ cm^-3 for N=1-0 and 10⁶ cm^-3 for N=2-1) of the lines seem ideal in order to avoid contamination with ambient clouds at lower density. But theoretical studies show that CN exists mostly in the surface regions of disks, in which interstellar UV plays a dominant role in the chemistry (Paper I), and thus it is not clear if it is also abundant in disks shielded from interstellar radiation. In this section, we discuss the column densities of CN, together with other species, in embedded disks.

Figures 5 and 6 show calculated radial column density distributions of assorted species in the lower mass disk model at $t=9.5\; 10^5$ yr. Figure 5 contains model results in the absence of any X-ray emission from the central star, while Fig. 6 shows results when X-ray processes are included. The solid lines, dotted lines, and dashed lines are for $A_{\rm v} = 0, 1$, and 2 mag, respectively. It is easy to see that the distributions can depend on both the X-ray irradiation and the degree of extinction. In the model without X-rays, the column densities of radicals such as CN and C₂H are extremely sensitive to the existence of ambient gas above and below the disk since this gas interferes with the photodissociation that produces the radicals. The effect is especially drastic at inner ( $R\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}300$ AU) radii, where the gas density is higher and thus abundances of radical species are very low without photoprocesses. It should be noted, however, that the column density of CN in the case with $A_{\rm v}=2$ mag is still reasonably large at $R\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ }}}300$ AU. We additionally calculated molecular abundances at R=500 AU for $A_{\rm v}=4$ mag, in which the CN column density is $3.7\; 10^{12}$ cm^-2. These results suggest that CN can be a disk tracer at least in the outer regions ( $R\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$>$ }}}300$ AU) for T Tauri stars without high X-ray luminosity.

In the model with X-rays from the central star, the column densities of radicals such as CN, CH, and C₂H are high even in the inner regions. The high ionization rate and induced photolysis by X-rays significantly enhance the radical species in regions with small radius and large height. We should note that the column densities of those radicals obtained in this model are upper limits because the X-ray luminosity we assumed - $L_{\rm x}= 10^{31}$ erg s^-1 - is close to the upper limit of the temporally varying X-ray intensity from T Tauri stars. But sufficient column densities of the radicals are expected in the inner regions ( $\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}200$ AU) even if the average X-ray luminosity is lower by an order of magnitude, since their radical column densities roughly depend linearly on the X-ray luminosity there. Therefore CN can trace even the inner regions ( $R\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$ }}}\hbox{$<$ }}}200$ AU) of embedded disks when there is some X-ray luminosity.

As for other species, it is interesting to note that the column densities of HCO⁺ and NH₃ tend to be higher in disks with non-zero $A_{\rm v}$, regardless of the X-ray luminosity, which suggests that their high frequency transitions with high critical densities can also be tracers of embedded disks. The centrally peaked distribution of HCO⁺ makes it the better tracer because the line can be more sensitive to a disk with small radius.

Although the calculations reported in this section deal with the effect of embedding disks in clouds, a close observation of Figs. 5 and 6 shows that some qualitative trends are actually independent of the degree of extinction. For example, species such as CN, C₂H, and H₂CO show a central peak in the case with X-ray irradiation and a central hole in the case of no such irradiation regardless of whether or not the disk is embedded. This behavior is not universal; the HCN distribution shows a similar dependence on the X-ray luminosity only when the disks are embedded. Specifically, in the model without X-ray irradiation, HCN (in the case of $A_{\rm v}\ge 1$ mag) shows a central hole of radius $\sim$200 AU, while in all cases with X-ray irradiation it is centrally peaked. Thus, if X-ray fluxes are different from one disk to another, one can expect the radial distributions of individual molecules to be different. Interestingly, interferometric observations show that CN is centrally peaked in the disk around DM Tau (Dutrey 2000, personal communication) but exhibits a central hole in the disk around LkCa15 (Qi 2000).