DNC/HNC RATIO OF MASSIVE CLUMPS IN EARLY EVOLUTIONARY STAGES OF HIGH-MASS STAR FORMATION

As mentioned in the Introduction, the equilibrium deuterium fractionation ratios would be affected by the gas kinetic temperature. To examine this, we estimate the kinetic temperature from the NH₃ rotation temperature by using the Equation (2) in Walmsley & Ungerechts (1983). For discussion, we only use the NH₃ data obtained by Sakai et al. (2008) in order to minimize the systematic errors caused by the difference in angular resolution. We exclude I18089−1732 MM1 and I18264−1152 MM1 in the following discussion because we do not have the NH₃ data observed with the NRO 45 m telescope. Although the NH₃ lines were observed toward these objects by Sridharan et al. (2002) using the Effelsberg 100 m telescope, the beam size (40'') is smaller than that of our NRO 45 m observations by a factor of two. The kinetic temperature of I18089−1732 MM1 is much higher than the other sources. This may be partly related to the difference in the angular resolution.

In Figure 3, we plot the N(DNC)/N(HNC) ratio against the gas kinetic temperature for the observed sources. For comparison, we also plot the data of low-mass cores, which are reported by Hirota et al. (2001). We only use the data of the low-mass cores toward which the gas kinetic temperature is reported (Jijina et al. 1999 and references therein). The temperature is systematically higher in the high-mass sources than in the low-mass sources. In Figure 3, we can clearly see the difference in the DNC/HNC ratio between low- and high-mass star-forming regions. The average value of the DNC/HNC ratio is 0.009 (±0.005) for the observed high-mass sources, while it is 0.06 (±0.03) for the low-mass sources.

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Since the high-mass sources are generally more distant than the low-mass sources, the lower DNC/HNC ratio might be due to the lower spatial resolution for the high-mass sources. However, Hirota et al. (2003) revealed the distribution of the DNC/HNC ratio toward the low-mass cores, and found that the DNC/HNC ratio is quite uniform within the cores with a scale of about 3' from the edge to the center. Even if the low-mass cores would be located at a distance of a few kiloparsecs, which is more distant than the low-mass cores typically by a factor of 10, the high DNC/HNC ratio would be observed with our 20''. We therefore think that the lower DNC/HNC ratios of the high-mass sources are not due to the distance effect. Indeed, there is no correlation between the distance and the DNC/HNC ratio.

In addition, we can see a trend that the N(DNC)/N(HNC) ratios of the Spitzer-dark sources are slightly higher than those of the other sources. The average value for the Spitzer-dark sources is also higher than that for the other sources (see Table 5). This trend is similar to that reported by Fontani et al. (2011), where the N(N₂D⁺)/N(N₂H⁺) ratios of high-mass starless cores tend to be higher than that of the HMPOs and UC H ii regions. However, our observed Spitzer-dark sources have lower N(DNC)/N(HNC) ratios than the low-mass cores. This is different from that found by Fontani et al. (2011), where the N(N₂D⁺)/N(N₂H⁺) ratio of several high-mass starless cores is comparable to that of low-mass starless cores. This difference may partly be due to a diversity of the deuterium fractionation in the high-mass starless-core phase. Indeed, the N(N₂D⁺)/N(N₂H⁺) ratios of some high-mass starless cores are as low as those of the HMPOs and the UC H ii regions even in the sample of Fontani et al. (2011). In addition, Tatematsu et al. (2010) found a starless core that has the low DNC/HNC ratio (∼0.008) toward the Orion A giant molecular cloud. On the other hand, the difference may be attributed to chemical reasons. If N₂D⁺ and DNC is formed mainly from H₂D⁺ and CH₂D⁺, respectively (Roueff et al. 2007), for instance, the deuterium fractionation ratio is thought to be different between N₂D⁺ and DNC. We need to observe all sources with the same molecular lines in order to confirm the diversity of the deuterium fractionation ratio in the starless phase.

In the present stage, it is still controversial whether the Spitzer-dark sources are really in the starless phase of high-mass stars. The HN¹³C column density of our observed Spitzer-dark sources is smaller than that of the other sources (Table 5), and is comparable to that of the low-mass cores (Hirota et al. 2001). In addition, the 1.2 mm peak flux of the Spitzer-dark sources (37–115 mJy) is lower than that of the Spitzer-bright sources (110–424 mJy; Beuther et al. 2002; Rathborne et al. 2006). It may be possible that the lower HNC abundance is due to the depletion onto dust grains, and that the lower millimeter-continuum emission is due to the low temperature. Nevertheless, we cannot rule out a possibility that the observed Spitzer-dark sources are smaller than the other sources and they are just low-mass star-forming regions. On the other hand, the HNC column density is comparable between the Spitzer-bright IRDCs and HMPOs, and hence, we may say that their masses are similar. Thus, we think that comparison of the DNC/HNC ratio between the Spitzer-bright IRDCs and the HMPOs is much more secure to investigate the evolution of the DNC/HNC ratio.

To investigate whether the lower DNC/HNC ratio of the high-mass sources is explained only by the difference of the gas kinetic temperature, we performed chemical model calculations. The chemical network used is the same as that reported by Aikawa et al. (2005). This model includes the gas-phase reactions, grain-surface reactions, depletion onto dust grains, and desorption from dust grains. We assume a static geometry with a constant H₂ density of 10⁵ cm⁻² for simplicity, and calculated the temporal variation of the molecular abundances for 10 K, 20 K, and 30 K. We assume the so-called low-metal values (see Table 1 of Aikawa et al. 2001) as the elemental abundances. All the heavy elements are assumed to be initially in the atomic form and the hydrogen in the molecular form. The deuterium is assumed to be in the form of HD, with the fractional abundance of 3.0 × 10⁻⁵ relative to H₂. We adopt the binding energy of CO on the dust to be 1180 K. Therefore, CO still remains on the dust at the temperature of 20 K, and the sublimation temperature of CO is about 21 K in this model. The results at 10⁵ yr and 10⁶ yr after starting chemical reactions from the initial condition are plotted in Figure 3.

According to the model calculation, the DNC/HNC ratio does not change very much between 10 K and 20 K, while it considerably decreases at 30 K. Roueff et al. (2007) also reported a similar result for DNC/HNC. In Figure 3, the observed DNC/HNC ratios for the low-mass sources are consistent with the model calculation. On the other hand, the ratios observed for the massive clumps are lower than the model prediction. The discrepancy is particularly significant for the sources with the gas kinetic temperature around 20 K.

Roueff et al. (2007) predicted that the D/H ratio for some molecules such as C₂H⁺₂ could become, in general, higher in denser regions. However, they suggest from their model calculation that the equilibrium DNC/HNC ratio does not depend on the density in the low-metal abundance case. Therefore, the differences of the H₂ density would not explain the trend seen in Figure 3. Indeed, it is unlikely that the high-mass star-forming regions are less dense than the low-mass star-forming regions.

It is known that the existence of the ortho-H₂ molecule enhances the backward reaction of (1) because the ortho-H₂ molecule in its lowest rotational state (J = 1) has a rotational energy of about 170 K (Gerlich et al. 2002; Flower et al. 2006). Hence, it decreases the deuterium fractionation ratio of H₂D⁺ and those of various molecules. We ignored this effect in the chemical model calculation because the ortho-to-para ratio of H₂ is reported to be close to 0 for low-mass protostar sources (Flower et al. 2006; Caselli et al. 2008; Pagani et al. 2009; Troscompt et al. 2009). If the ortho-to-para ratio of H₂ is significantly higher in the massive clumps, the lower deuterium fractionation at 20 K could be explained. However, the fractionation ratio at higher temperatures would also have to decrease in this case, which contradicts with the ratios in HMPOs (Figure 3). Although the ortho-to-para ratio of H₂ may affect the deuterium fractionation ratio to some extent, we do not consider it in the following discussion for simplicity.

Another possibility for the discrepancy between the model and observational results is that the DNC and HN¹³C emissions would come from warmer regions than the NH₃ (1, 1) and (2, 2) emissions. Since the critical density of the DNC and HN¹³C lines (∼10⁶ cm⁻³) is higher than that of the NH₃ lines (∼10⁴ cm⁻³), the DNC and HN¹³C emissions trace denser regions. In the objects associated with the Spitzer sources, the inner dense part is likely to be warmer due to various activities of newly born stars, and hence, the DNC and HNC emissions tend to trace such regions. The smaller beams size of the DNC and HNC observations in comparison with the NH₃ observations may also contribute to this effect. If this is the case, the temperature estimated from the NH₃ observation may be underestimated, and the data points around 20 K may have to be shifted to the higher temperature, giving a better agreement with the chemical model calculation.

However, some massive clumps have relatively lower DNC/HNC ratio than the HMPOs, although the gas kinetic temperature of the massive clumps is lower than that of the HMPOs (Figure 3). For example, the DNC/HNC ratio of G034.43+00.24 MM3 (0.0029) is lower than that of I18151−1208 MM1 (0.0088), while the kinetic temperature of G034.43+00.24 MM3 (19 K) is lower than that of I18151−1208 MM1 (31 K). This trend is not explained only with the difference in the gas kinetic temperature.

In Figure 3, the model results at 10⁵ and 10⁶ yr are shown. At 10⁵ yr, the deuterium fractionation ratio does not reach its steady state value, as seen in the difference of the ratio between 10⁵ and 10⁶ yr. This means that the deuterium fractionation ratio depends not only on the current temperature but also on the past physical history of the clump. Hence, the time dependence effect has to be considered for the DNC/HNC ratio, as discussed in the next section.

When we consider the evolution of molecular clouds from diffuse clouds into dense cores, the deuterium fractionation ratio of molecules gradually increases with time from the cosmic D/H ratio (∼10⁻⁵); the deuterium fractionation is expected to be low in the early stage of molecular cloud evolution. In fact, Hirota et al. (2001) found the low deuterium fractionation in a few young low-mass starless cores. In addition, Crapsi et al. (2005) found that the deuterium fractionation ratio is higher in the cores closest to the onset of gravitational collapse among the sample of low-mass starless cores, and they suggest that the deuterium fractionation increases with the core evolution.

The birth of protostars raises the temperature around them. The deuterium fractionation ratio then starts to decrease toward the equilibrium value at the new temperature. The timescale of this change is different from species to species, depending on the destruction timescale of each species. First, we consider the timescale for DNC/HNC. The main destruction pathways of DNC are as follows:

$$\begin{equation} {\rm DNC} + {\rm HCO^+} \rightarrow {\rm DNCH^+} + {\rm CO}, \end{equation} \tag{ 7 }$$

$$\begin{equation} {\rm DNC} + {\rm H_3^+} \rightarrow {\rm DNCH^+} + {\rm H_2}. \end{equation} \tag{ 8 }$$

Although the dissociative recombination of DNCH⁺ can reproduce DNC, it competes with HCN + D and CN + D + H. Thus, the abundance of DNC could decrease with the above reactions. The timescale of the above reactions (7) and (8) is comparable to each other, and depends on the abundances of HCO⁺ and H⁺₃. For instance, the timescale of the reaction with HCO⁺ is represented as

$$\begin{equation} \tau \sim \frac{1}{k[{\rm HCO^+}]} \sim 4 \times 10^{12} \; {\rm s} \sim 10^5 \; {\rm yr}, \end{equation} \tag{ 9 }$$

in the case of the density of 10⁵ cm⁻². Since the HCO⁺ abundance depends on the H₂ density (Umebayashi & Nakano 1980), the above timescale would have the weak power-law dependence on the density as τ∝n^0.3–0.5. Therefore, the DNC/HNC ratio can be preserved after the temperature rise.

On the other hand, we note that the destruction timescale of molecular ions is much shorter than that of neutral molecules because they can react with CO and/or electron. For example, the main destruction pathway of N₂D⁺ is the following reaction:

$$\begin{equation} {\rm N}_2{\rm D}^+ + {\rm CO} \rightarrow {\rm N_2} + {\rm DCO}^+. \end{equation} \tag{ 10 }$$

The destruction timescale of N₂D⁺ is therefore given as

$$\begin{equation} \tau \sim \frac{1}{k[{\rm CO}]} \sim 10^{8} \; {\rm s} \sim 4 \; {\rm yr}. \end{equation} \tag{ 11 }$$

The deuterium fractionation ratio of molecular ions immediately decreases after the onset of star formation, and reaches the equilibrium value at the new temperature.

To investigate how the deuterium fractionation ratio changes after the temperature rise, we performed the following chemical model calculations. We simply assume a sudden temperature rise from 10 to 30 K at a given age, 1 × 10⁵ yr or 3 × 10⁵ yr, and calculate the temporal variation of chemical compositions after that. We plot the calculated DNC/HNC and N₂D⁺/N₂H⁺ ratios in Figure 4(a). We also plot the DNC/HNC and N₂D⁺/N₂H⁺ ratios for the cases without the temperature rise.

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As seen in Figure 4(a), the DNC/HNC and N₂D⁺/N₂H⁺ ratios slowly increase with time until the temperature rise, and they decrease after that. The decrease of the deuterium fractionation ratios originates from the above gas-phase processes. Although molecules are evaporated from dust grains after the temperature rise, the DNC/HNC ratio in the gas phase is not affected by this effect. HNC is not efficiently formed by grain-surface reactions, so that the DNC/HNC ratio in ice mantle is not significantly different from the ratio in the gas phase.

For clarity, we plot the DNC/HNC ratio after the temperature rise in Figure 4(b). In Figure 4(b), we can see that the DNC/HNC ratio gradually decreases with a timescale of several times 10⁴ yr, while the N₂H⁺ ratio rapidly decreases with a timescale of several tens of years. This is consistent with the rough estimate of the timescales mentioned before. More importantly, the DNC/HNC ratio after the temperature rise depends on the time when the temperature is raised. In other words, the DNC/HNC ratio in the star-forming clumps depends on the initial DNC/HNC ratio before the onset of star formation. Since the dynamical age of outflows of the HMPOs is estimated to be several times 10⁴–10⁵ yr (Beuther et al. 2002b), the initial DNC/HNC ratio is conserved in the massive clumps and HMPOs to some extent. As mentioned in Section 4.1, some massive clumps with the Spitzer sources have a lower DNC/HNC ratio than the HMPOs. This difference would reflect the difference of the deuterium fractionation ratio at the onset of star formation.

For comparison, we plot the average value of all of our observed sources in Figure 4. The observed value is comparable to the constant temperature case of 30 K. On the other hand, the cases that the temperature rise from 10 K to 30 K at 10⁵ yr and 3 × 10⁵ yr cannot reproduce the observed value because the DNC/HNC ratio just before the temperature rise is preserved after the temperature rise. This indicates that the DNC/HNC ratio just before the onset of star formation should have been low for these sources. Thus, we speculate that the DNC/HNC ratio just before the onset of star formation would be lower for the observed high-mass sources than for the low-mass cores. The lower DNC/HNC ratio implies that the cold starless phase of the observed sources is shorter than that of the low-mass cores, or that the initial temperature is warmer (>20 K) than that of the low-mass cores (∼10 K).

The timescale of high-mass starless phase is still controversial. From the statistical study, Chambers et al. (2009) estimated the timescale of starless phase to be 3.7 × 10⁵ yr, while Parsons et al. (2009) estimated it to be a few 10³–10⁴ yr. Although our observed results seem to support the short timescale of the starless phase, we need more careful considerations. In fact, Sakai et al. (2008) measured the CCS/N₂H⁺ ratio toward the IRDCs and HMPOs, and obtained only the upper limits of the CCS/N₂H⁺ ratio. From these results, they suggest that massive clumps in IRDCs and HMPOs are chemically more evolved than young low-mass dense cores. However, this argument is based on the single-dish observations, which may be affected by the limited angular resolution and sensitivity. If the DNC/HNC ratio reflects the timescale of starless-core phase, we should see a correlation between the DNC/HNC ratio and the CCS/N₂H⁺ ratio with high-sensitivity and high-angular resolution observations. In this relation, Devine et al. (2011) have recently found the chemically young envelope toward the IRDC G19.30+00.07 with the Very Large Array (VLA) observations. Existence of such a chemically young envelope may be related to the chemical youth of the clump.

The initial temperature of high-mass star formation has not been established well either. The theoretical models of high-mass star formation generally assume the initial temperature from 10 to 30 K (e.g., Krumholz et al. 2009; Peters et al. 2011). However, this assumption is not based on the observational results. If the deuterium fractionation ratio would reflect the initial temperature, it will provide us with novel information for understanding the high-mass star formation because the initial temperature affects the accretion rate and the gravitational instability causing clump fragmentation.

Discrimination of these two possibilities is not an easy task. A systematic observation of N₂D⁺/N₂H⁺ toward the same sources would be an important clue to this, as shown in Figure 4(a). The N₂D⁺/N₂H⁺ ratio is expected to be higher than the DNC/HNC ratio if the clump temperature is 30 K from the starless-core phase (see the curves for the constant temperature of 30 K).

In a future work, we are going to observe the DNC/HNC and N₂D⁺/N₂H⁺ ratios toward an IRDC clump with high angular resolution by using ALMA. From this observation, we will obtain important information about the behavior of the deuterium fractionation in the high-mass star-forming regions in more detail.