4 Discussion of results

Our values for [HDCO]/[H₂CO] and [DCN]/[HCN] are summarised in Fig. 3.

Figure 3: A summary of our observed a) [HDCO]/[H2CO] ratios (using N(H212CO)) and b) [DCN]/[HCN] ratios (using N(H13CN) (solid error bars) and N(H12CN) (dashed error bars)), plotted against the bolometric temperature of the source, along with least-squares fits to the data (see text), arrows indicate upper limits.

The ratios for each source have been plotted against its bolometric temperature, which provides one way of measuring its evolutionary stage (Myers & Ladd 1993).

To determine the average fractionation, and test if fractionation is a function of evolutionary stage, we have calculated the least squares fits of a straight line to the data in Fig. 3. For the [HDCO]/[H₂CO] ratios a good fit could not be found to all the data points, however, when we left out the source HH211, which has a significantly lower HDCO fractionation, we obtained the fit shown as a solid line in Fig. 3a, with uncertainties on this fit shown as dashed lines. This suggests that, with the exception of HH211 and HH111, where [HDCO]/[H₂CO] ratios are $0.018 \pm 0.003$ and $0.029 \pm 0.014$, respectively, the observed [HDCO]/[H₂CO] ratios are all consistent with a value of 0.05-0.07.

Figure 3b shows the line of best fit to the observed [DCN]/[HCN] ratios (solid line), along with its associated uncertainty (dotted lines). With the exception of HH111, where [DCN]/[HCN] < 0.015, the best fit to our observed ratios is [DCN]/[HCN $] \sim 0.04$, which remains flat as $T_{\rm bol}$ varies. Figure 4a compares the linewidths of H¹³CN to DCN emission,

Figure 4: A comparison of the linewidths of the molecules surveyed, the dotted line on each plot indicates equal widths; a) $\Delta v$ for the 13C-substituted isotopomers of H2CO and HCN vs. $\Delta v$ for the analogue deuterium-substituted molecules; b) $\Delta v$ for the main isotopomers vs. $\Delta v$ for the deuterium-substituted molecules.

and of H₂¹³CO to HDCO emission for each source, these being the lines we assumed to be optically thin. The linewidths are fairly similar, indicating that the emission from these molecules probably arose in the same region of the cloud, and so we are justified in taking ratios of the column densities. Figure 4b compares linewidths from H₂CO to HDCO and HCN to DCN in each source. HCN linewidths are fairly similar to DCN linewidths, however, the agreement between $\Delta v$ for H₂CO and HDCO is not so good. This broadening is likely to be due to the optical depth in the H₂CO lines, since, for an opacity of 5, the line width is expected to increase by a factor of 1.7 (Phillips et al. 1979), which is close to the observed H₂CO vs. HDCO linewidth ratio for most sources.