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Astron. Astrophys. 342, 542-550 (1999)

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3. Results

We adopt physical conditions believed to be appropriate to the Orion Bar and compare the column densities derived from the model with those observed. Thus, we assume the incident radiation field to be a factor of [FORMULA] times the Draine (1978) interstellar UV field, and the hydrogen density nH to be [FORMULA] [FORMULA] (see Jansen et al. 1995, Hollenbach and Tielens 1997, Wyrowski et al. 1997, and Marconi et al. 1998 for estimates of these parameters). It is also important to realize that the Orion Bar is not seen face-on, whereas we shall report column densities integrated along the normal to the face of the PDR. As the Bar inclination angle is poorly known (see the discussion of Marconi et al. 1998), it is difficult to correct for this projection effect, which may lead to the absolute column densities being underestimated by an order of magnitude.

The assumed fractional elemental abundances are consistent with the available Orion Bar observations. Thus [C]/[H] [FORMULA] and [O]/[H] = [FORMULA], whereas Si in various initial forms is assumed to have an abundance of 10 percent of the solar value (which gives [Si]/[H] = [FORMULA]), in accordance with the results of Haas et al. (1986, 1991; see also Stacey et al. 1995). Thus, 90 percent of Si is assumed to be in a highly refractory grain core.

We consider various possible forms in which Si might be "hidden" at large depth in the molecular cloud associated with a PDR and use the model to predict the evolution of chemical abundances as the gas and dust are advected towards the ionization front. Our first model considers purely gas phase processes and is intended to demonstrate that it is not possible to "hide" silicon without recourse to processes converting from solid to gas phase. Here, we suppose that the available silicon (i.e. that which is not in refractory form) is present as gas phase [FORMULA] at [FORMULA] mag. and follow the chemistry for the case of [FORMULA] = 1 [FORMULA]. In models 2-4, we suppose that the available silicon is initially present as a "contaminant" in an ice mantle of binding energy [FORMULA]. This mantle is allowed to evaporate according to the prescription in the previous section. In model 5, we also suppose silicon to be initially present in the ice mantle but allow transfer into the gas phase only by photodesorption (Eq. 4, using the Westley et al. data for the photodesorption of ice). Finally, in models 6-8, we consider a constant photodesorption yield of [FORMULA] with various assumptions about the gas temperature and the form in which silicon enters the gas phase.

In all these models, initial abundances for other than Si-bearing species have been obtained by solving the steady state equations. This procedure has the consequence that C, for example, is initially in the form of CO, whereas oxygen is divided between CO, O and O2. For models 5-8 moreover, oxygen is initially also in the form of water ice which can be photodesorbed. In models 2-5, SiO is considered to be mixed with the evaporating (or photodesorbing) ice mantle. Otherwise, we do not consider possible "contaminants" in the solid phase.

Input parameters for the eight models are given in Table 1 where we also give the total column densities predicted by the models, as well as the SiO and Si+ column densities measured towards the Orion Bar. The latter is an estimate which we have made based upon the results of Haas et al. (1986) and has a factor of 2 uncertainty. Table 1 also gives information on the assumptions made concerning the initial form of Si in different models.


Table 1. Parameters and predicted column densities for models discussed in the text. All models assume a homogeneous PDR of nucleon density [FORMULA] [FORMULA] and incident radiation field [FORMULA] (in units of the interstellar field) [FORMULA]. Models are distinguished (see Comment and Init. columns) by the initial form of Si and the form in which Si initially in the mantle reaches the gas phase. Thus in the Init. column, SiO(Ice) refers to models where SiO comes directly into the gas phase due to evaporation of the ice mantle and Si(sol) refers to models where Si from refractory material is photo-desorbed in atomic form. In the comment column, PE stands for models where thermal evaporation of ice mantles with a given binding energy [FORMULA] in K (in parentheses) is considered and PD stands for models where direct photodesorption is considered. Models are also distinguished by the assumption made about the gas temperature variation and photodesorption yield (Y). In model 7, we assume a constant gas temperature of 500 K but in all other models we take the temperature to vary as T = 1000/(1+2 Av). For the photodesorption yield, a W in parentheses in the comments column implies use of the Westley et al. (1995) form for the photodesorption yield, whereas a C in parentheses means that a constant value of Y=[FORMULA] was used. The last line of the table (Obs.) gives observed column densities of SiO and Si+ towards the Orion Bar based on the results of Schilke et al. (1998) and Haas et al. (1986)

In Fig. 1, we show the abundances predicted in model 1 as a function of depth (parametrized in terms of the visual extinction [FORMULA]). One sees that, as the ionization front is approached, [FORMULA] is photodissociated, yielding SiO. This species is, in turn, photodissociated on a rather similar timescale to Si, and finally Si is photoionized to Si+. We note that the SiO abundance is non-negligible in this model, as in the steady-state models of Sternberg and Dalgarno (1995) and Jansen et al. (1995). Also, Si+ becomes the main Si carrier at an extinction of [FORMULA] 6 mag. from the surface. It is very difficult, in this type of model, to produce SiO column densities which are orders of magnitude smaller than that of Si+. We find that the same conclusion holds when other choices are made (e.g. [FORMULA]) for the initial (gas phase) form of Si. One of the reasons for this is that atomic silicon can react with either [FORMULA] or with OH to produce SiO (see discussion in the previous section):



Thus, if either [FORMULA] or OH is abundant in the layers of the PDR where atomic Si is produced by photodissociation of Si-containing species, SiO can form rapidly. A consequence of this is that our results are not very sensitive to the initial form assumed for gas phase silicon. Our calculations show that, whilst [FORMULA] is photodissociated at depths beyond those at which atomic Si becomes important, OH is abundant at the high temperatures which occur close to the ionization front (see e.g. Sternberg and Dalgarno 1995) and plays an important role in the Si chemistry.

[FIGURE] Fig. 1. Fractional abundances (relative to nH) of Si bearing species plotted against visual extinction for model 1, where Si is initially in the form of gaseous [FORMULA]. The radiation field is incident on the left hand side and we begin the integration at a depth of A[FORMULA]. The full curves show the variation of gaseous [FORMULA] at high extinction and Si+ at low extinction. SiO is shown as the dotted curve and atomic Si as dashes.

Let us now consider the models (2-4) where Si is initially in an ice mantle which is subsequently evaporated. We assume that the silicon is released as SiO but, again, our results are relatively insensitive to this assumption. In Fig. 2 (see also models 2-4 of Table 1), we show the computed abundances as functions of depth (visual extinction) in the PDR. Fig. 2 shows the sensitivity of our results to the binding energy ([FORMULA]) of the grain mantle. In all three models, Si is supposed to be initially present (at [FORMULA] = 10 mag.) in the ice mixture in the form of SiO. In the upper panel (Fig. 2a), where [FORMULA] K, we see that solid SiO is instantaneously evaporated from the mantles, at a grain temperature of approximately 44 K. SiO is then photodissociated at [FORMULA] = 6 magnitudes, leading to an abundance profile similar to those found by Sternberg and Dalgarno (1995) and Jansen et al. (1995). In the middle panel (Fig. 2b), where [FORMULA] K, silicon remains in solid form to an extinction of 2.5 magnitudes, corresponding to a grain temperature of 48 K. At this point, it is suddenly transformed into Si+. This transformation occurs irrespective of the form of Si in the ice mixture. We see also that the SiO abundance reaches 10 percent of the "available" silicon at [FORMULA] = 8 magnitudes but rapidly decreases at lower values of [FORMULA] due to photodissociation. In contrast, for [FORMULA] K (model 3), SiO reaches an abundance of only [FORMULA] of the available silicon prior to the onset of photodissociation. For a grain temperature of 45 K, at [FORMULA] 6 mag., the evaporation rate (see Eq. 2) is very sensitive to [FORMULA]. Thus, Fig. 2 demonstrates that, in this type of model, a situation can obtain in which Si+ is the only gas phase form of Si with appreciable abundance.

[FIGURE] Fig. 2a-c. Fractional abundances (relative to nH) of Si-bearing species as functions of depth for Models 2, 3 and 4. Si is supposed initially ([FORMULA]) in solid form, immersed in an ice layer having binding energy [FORMULA] = 2500 K a , 2800 K b and 3000 K c . The variation of grain temperature is shown as the dashed line on the three plots (see scale on right hand axis). The full curves on all three panels show SiO, the thin full curves Si and the light dots Si+. SiO in solid (ice) form is shown as the bold dots in the bottom two panels; it disappears immediately for [FORMULA] = 2500 K.

One can attempt to determine a value of [FORMULA] compatible with the current perception of the characteristics of the Orion Bar. For low values of [FORMULA], the Si-containing mantle is evaporated deep in the cloud, and an appreciable column density of SiO (comparable with that observed in Si+) is to be expected. For high values of [FORMULA] (6000 K, as expected for water ice), the ice survives its traversal of the PDR and is presumably destroyed in the ionized gas. In this case, the Si+ emission does not arise in the neutral PDR layer, and, furthermore, it is likely that silicon will be rapidly transformed into Si[FORMULA] within the HII region. For intermediate values of [FORMULA], of order 3000-3500 K, there is an appreciable ([FORMULA] [FORMULA]) column density of Si+ but small amounts of Si-containing molecules such as SiO. We have examined the sensitivity of these results to the form (SiO or other) in which Si is ejected from the surface and find that this is of minor importance in general. We note also that comparison with observed FIR color temperatures towards the bar ([FORMULA] 75 K, see Werner et al. 1976) suggests that our grain temperatures may be underestimates and hence that our estimate for [FORMULA] is also too low. In fact, if the temperature is really so high, water ice evaporation would become possible. However, the Werner et al. observations were carried out with a [FORMULA] beam which is not sufficient to resolve the bar and hence the observed color temperature is probably "contaminated" by hot dust within the ionized region. Moreover, as discussed below, we believe that direct photo-desorption is the dominant process causing the ejection of the water ice mantle into the gas phase.

We now consider the possibility (Models 5-8) that the photodesorption yield Y of Si-containing species is non-negligible and that this process rather than mantle evaporation accounts for the appearance of Si in the gas phase. We distinguish between Si mixed into the ice mantle and Si in a more refractory layer containing 10 percent of the cosmic Si abundance. In the former case (model 5), we use the Westley et al. (1995) data for the photodesorption yield and thus assume that the probabilities of photodesorption of water and SiO are the same. We also assume that the SiO molecule is not dissociated during the photodesorption process. In the case where we take Si to be in a more refractory layer, we adopt a yield of [FORMULA] and assume that Si enters the gas phase in atomic form.

Fig. 3 shows that, for the conditions of model 5 (essentially the conditions of the Orion Bar), the ice mantles are photodesorbed at [FORMULA]= 6 mag. and SiO attains an abundance relative to H of [FORMULA]. The column densities (Table 1) are such that one would expect to observe both SiO and Si+ in a region such as the Orion Bar. Thus, the observations exclude SiO as an important component of the water ice mantle. Moreover, photodesorption of water ice mantles is rapid starting at a depth corresponding to 7 magnitudes of extinction (Fig. 3b) and is is more important than thermal evaporation of [FORMULA] ice under the conditions of the Orion Bar (the photodesorption occurs at a depth where the grain temperature is too low for evaporation as one sees in Fig. 2). Again we stress that ejecting silicon in a form other than SiO would not change our qualitative conclusions.

[FIGURE] Fig. 3a and b. a  The top panel shows the abundances of Si-containing species as function of depth for Model 5, where we allow photodesorption of the water ice mantle (containing SiO) using the yield of Westley et al. (1995). The bold dotted line shows the variation of the abundance of SiO in solid form whereas the dashed line shows the variation of gaseous SiO. The full curve and light dots show ionized and neutral Si, respectively b  The bottom panel shows the corresponding behaviour of water ice (bold dots) and gas phase water (dashes). The full curves give the results for atomic oxygen, molecular oxygen, and the hydroxyl radical.

The situation is somewhat different in models 6-8, where we have adopted a considerably lower photodesorption yield for silicon. Moreover, in models 7 and 8, we assume that Si is ejected into the gas phase in atomic form. We show the dependence of abundance on depth in Fig. 4, where the top panel (model 8) shows results for our standard temperature profile, whereas the bottom panel shows results for a constant temperature of 500 K (model 7). One sees that, in models in which Si is photodesorbed in atomic form, the SiO abundance is sensitive to the presence of OH and hence to the gas temperature. Comparison of models 6 and 8 of Table 1 shows that, in this case, the SiO abundance is sensitive to the form in which Si enters the gas phase. We conclude that Si is most effectively "hidden" if it is ejected into the gas phase in atomic form and if, in addition, the temperature in the layer of Si ejection is sufficiently low that OH cannot form rapidly.

[FIGURE] Fig. 4a and b. Abundances of Si-containing species as functions of depth for model 8 (top panel ) and model 7 (bottom panel ). Calculations were carried out for a constant photodesorption yield of [FORMULA]. The top panel shows results for our "standard" temperature profile ([FORMULA])), whereas the bottom panel shows results for a constant temperature of 500 K. Bold dots show the variation of the abundance of Si in "refractory form", whereas the dashed lines and the full curve show the variation of gaseous SiO and Si+, respectively; the light dots indicate atomic silicon.

The most satisfactory model, from the viewpoint of consistency with the observations, is model 8 (top panel of Fig. 4), where we allow for the decrease of gas temperature with depth. In this case, the region where OH is abundant [FORMULA] is sufficiently close to the ionization front [FORMULA] that Si photoionization is a competitive process. The SiO abundance is of the order of [FORMULA] and is thus similar to the limit of Jansen et al. (1995) and a factor of a few larger than the recent measured value of Schilke et al. (1998). We conclude that photodesorption, with parameters similar to those adopted in model 8 (or with a smaller photodesorption yield), is a possible explanation of the "paradox" discussed earlier. Put in other words, a photodesorption yield consistent with the observations of Turner (1998) can explain the observations of Si-containing species towards the Bar.

Finally, we note that the atomic Si column densities given in Table 1 are small in almost all circumstances, suggesting that it will be difficult to detect the [Si I] FIR fine structure lines in a PDR. In model 8 for example, the atomic Si column density is [FORMULA] that of Si+. Atomic Si is rapidly destroyed, either by photoionization or in its reactions with OH and [FORMULA].

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© European Southern Observatory (ESO) 1999

Online publication: February 22, 1999