All Figures

$\begin{figure} \par\includegraphics[width=5.75cm,clip]{9009fig1a.eps}\\ \includegraphics[width=5.75cm,clip]{9009fig1b.eps} \end{figure}$ Figure 1: ortho- ${\rm H}_{2}{\rm D}^{+}$ (1_1,0-1_1,1) spectra toward the 16 sources of our sample. The units are main beam brightness temperature in K (y-axis, assuming a unity filling factor) and velocity in ${\rm km~s}^{-1}$ (x-axis). A star in the top right indicates dense cores associated with protostellar objects. The vertical dotted line is the $V_{\rm LSR}$ velocity measured with ${\rm N}_2{\rm H}^+$ (1-0), whereas the vertical dashed line marks $V_{\rm LSR}$ as measured with the present ${\rm H}_{2}{\rm D}^{+}$ observations. Within the uncertainties, the two values are identical. Note that the strongest emission is present in the densest starless cores (L 1544, L 183, L 429, L 694-2) and in the star forming regions L 1521F, B 1, and NGC 2264G. Note also the large variation in linewidth among the various sources.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=9cm,clip]{9009fig2.eps} \end{figure}$ Figure 2: ortho- ${\rm H}_{2}{\rm D}^{+}$ fractional abundances vs. the gas volume density (n( ${\rm H}_2$ ), left panel) and gas temperature ( $T_{\rm kin}$ , right panel). Empty symbols refer to starless cores, whereas filled symbols refer to cores associated with young stellar objects. Note that upside-down triangles are upper limits. The line in the right panel is the least square fits to the x(ortho- ${\rm H}_{2}{\rm D}^{+}$ ) vs. $T_{\rm kin}$ data, the only significant correlation that has been found (see text).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=17cm,clip]{9009fig3.eps} \end{figure}$ Figure 3: [ ${\rm H}_{2}{\rm D}^{+}$ ]/[ ${\rm H}_{3}^{+}$ ], [ ${\rm D}_{2}{\rm H}^{+}$ ]/[ ${\rm H}_{3}^{+}$ ], [ ${\rm D}_{3}^{+}$ ]/[ ${\rm H}_{3}^{+}$ ] and $R_{\rm D}$ abundance ratios as a function of the gas temperature ( $T_{\rm kin}$ ) in a dense cloud with uniform volume density n( ${\rm H}_2$ ) = 10⁵ ${{\rm cm}}^{-3}$ . ( Top row) The abundance ratios are plotted against $T_{\rm kin}$ for different values of the depletion factor $f_{\rm D}$ (=1, 5, 10, 50 and 100), with fixed values of $a_{\rm min}$ = 50 Å and $\zeta$ = 3 $\times$ 10^-17 s^-1. The dotted curves are for $f_{\rm D}$ = 10 clouds with n( ${\rm H}_2$ ) = 1 $\times$ 10⁶ ${{\rm cm}}^{-3}$ (top dotted curve) and n( ${\rm H}_2$ ) = 1 $\times$ 10⁴ ${{\rm cm}}^{-3}$ (bottom dotted curve). Note the large increase of the [ ${\rm D}_{3}^{+}$ ]/[ ${\rm H}_{3}^{+}$ ] ratio for $f_{\rm D}$ = 50 and 100. ( Central panel) Abundance ratios vs. $T_{\rm kin}$ for different values of $a_{\rm min}$ and values of $f_{\rm D}$ and $\zeta$ fixed at 10 and 3 $\times$ 10^-17 s^-1, respectively. ( Bottom panel) Abundance ratios vs. $T_{\rm kin}$ for different values of the cosmic-ray ionization rate, $\zeta$ . Here, $f_{\rm D}$ = 10 and $a_{\rm min}$ = 50 Å.
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9009fig4a.eps}\vspace*{3mm} \includegraphics[width=7.5cm,clip]{9009fig4b.eps} \end{figure}$ Figure 4: ortho- ${\rm H}_{2}{\rm D}^{+}$ column density as a function of the observed deuterium-fractionation $R_{\rm D}$ (see text for details). Filled circles are protostellar cores, empty circles are starless cores. Downward arrows denote upper limits in our estimate of the column density. The names of the cores associated with each mark in the figure are shown in the top panel. The bottom panel shows the same plot, where theoretical predictions from chemical models (see text) are superposed. Solid curves are for models that use the ``standard'' rate coefficients for the proton-deuteron exchange reactions, whereas dashed curves are for models adopting the smaller GHR02 rate coefficients. Each curve has six points (filled (empty) diamonds for the models using the ``standard'' (GHR02) rate coefficients), which correspond to model cores with different central density (from 4 $\times$ 10⁴ cm^-3 to 4 $\times$ 10⁸ cm^-3, from left to right). Different curves are for different ortho/para ${\rm H}_{2}{\rm D}^{+}$ ratios, from 0.03 to 2.0. The cosmic-ray ionization rate has been fixed to 1.3 $\times$ 10^-17 s^-1.
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In the text

$\begin{figure} \par\includegraphics[width=7.15cm,clip]{9009fig5a.eps}\vspace*{3mm} \includegraphics[width=7.3cm,clip]{9009fig5b.eps} \end{figure}$ Figure 5: ( Top panel) Same models as in the bottom panel of Fig. 4 but with a fixed value o/p- ${\rm H}_{2}{\rm D}^{+}$ (=0.5), and various cosmic-ray ionization rates (from 6 to 30 $\times$ 10^-18 s^-1). The thick dashed curve connects model results using GHR02 rates, $\zeta$ = 6 $\times$ 10^-18 s^-1 and o/p- ${\rm H}_{2}{\rm D}^{+}$ = 0.3. This is an attempt to reproduce the low ortho- ${\rm H}_{2}{\rm D}^{+}$ column density values observed toward the $R_{\rm D}$ -rich protostellar cores and the two Ophiuchus pre-stellar cores Oph D and 16293E. ( Bottom panel) Plot showing predictions of models with density structures equal to the Ciolek & Basu (2000) cloud at times t_i (i = 2-5) and corresponding central densities $n_{ci} \equiv n_i$ (see text) at different stages of chemical evolution (at t = 10³, 10⁴, 10⁵, and 10⁶ yr, from bottom left to top right). The o/p- ${\rm H}_{2}{\rm D}^{+}$ ratio has been fixed at 0.5. The thick curves refer to the model of a protostellar envelope at different evolutionary times, where o/p- ${\rm H}_{2}{\rm D}^{+}$ = 0.1, to simulate a possible (slight) increase of the gas temperature due to the central heating source.
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In the text

$\begin{figure} \par\includegraphics[width=7.1cm,clip]{9009fig6a.eps}\\ \includegraphics[width=7.3cm,clip]{9009fig6b.eps} \end{figure}$ Figure 6: N(ortho- ${\rm H}_{2}{\rm D}^{+}$ ) vs. the observed CO depletion factor, $f_{\rm D}$ (CO). The same models t_i (i=1, ..., 5) described for the previous figures are used here, varying the cosmic-ray ionization rate $\zeta$ ( top panel) and the o/p- ${\rm H}_{2}{\rm D}^{+}$ ratio ( bottom panel) within the range of Fig. 4 and 5. The thick dashed curve refers to (GHR02) models with o/p- ${\rm H}_{2}{\rm D}^{+}$ ratio of 0.1 and $\zeta$ = 6 $\times$ 10^-18 s^-1. As found before, variations in the o/p- ${\rm H}_{2}{\rm D}^{+}$ ratio, plus differences in the physical structure, provide a way to reproduce the whole observed spread in the data. The labels in the top panel correspond to the source names: A $\equiv$ L 1498, B $\equiv$ TMC-2, C $\equiv$ TMC-1C, D $\equiv$ L 1517B, E $\equiv$ L 1544, F $\equiv$ L 183, G $\equiv$ Oph D, H $\equiv$ B 68, I $\equiv$ L 429, J $\equiv$ L 694-2, K $\equiv$ NGC 1333- ${\rm DCO}^+$ , L $\equiv$ B 1, M $\equiv$ IRAM 04191, N $\equiv$ L 1521F, O $\equiv$ Ori B9.
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In the text