DEUTERIUM FRACTIONATION AS AN EVOLUTIONARY PROBE IN THE INFRARED DARK CLOUD G28.34+0.06

Single-dish observations of N₂H⁺(3-2) and N₂D⁺(3-2) toward G28-MM1, MM4, and MM9 were carried out on 2008 April 13 with the 10 m SMT at Mount Graham, Arizona. The observations were performed in the beam-switching mode. The pointing centers followed the peak positions given by Rathborne et al. (2006): (α, δ)(J2000) = (18^h42^m5210, − 3°59'450) for MM1, (α, δ)(J2000) = (18^h42^m5070, − 4°3'150) for MM4, and (α, δ)(J2000) = (18^h42^m4670, − 4°4'80) for MM9. The primary beam is about 26'' for N₂H⁺ and 32'' for N₂D⁺. The spectral resolution is 1 MHz, corresponding to a velocity resolution of 1.07 km s^-1 for N₂H⁺ and 1.30 km s^-1 for N₂D⁺. The temperature scale T*_A was obtained using standard vane calibration, and the main beam temperature, T_mb, was derived through T_mb = T*_A/η_mb with a main beam efficiency η_mb = 0.75. The respective rms noise level is about T_mb = 20 and 10 mK for the N₂H⁺ and N₂D⁺ data, respectively. Data reduction was done with the CLASS package.

Observations with the SMA were carried out with seven antennas in the compact configuration on 2008 June 17 for N₂H⁺ and 2008 September 30 for N₂D⁺. The system temperature varied from 150 to 350 K during the N₂H⁺ observation and from 100 to 180 K during the N₂D⁺ observation. The correlator was set to have a spectral resolution of 410 kHz, equivalent to 0.44 and 0.53 km s^-1 for N₂H⁺ and N₂D⁺, respectively. The projected baselines ranged from 11 to 118 kλ and 11 to 59 kλ, which are insensitive to structures larger than 8'' (Wilner & Welch 1994). The full width at half-power (FWHP) of the primary beam is roughly 44'' for N₂H⁺ and 53'' for N₂D⁺.

The observing cycle comprised scans of 1751+096, MM1, MM4, MM9, and 1911 − 201, and was repeated every 27 minutes. The phase centers of the first observation run were the same as those of the SMT observations. Based on the results of the first observation run, we adjusted the phase center for the second observation run on the continuum peak in MM1 to (α, δ)(J2000) = (18^h42^m5200, − 3°59'5300) and in MM9 to (α, δ)(J2000) = (18^h42^m4646, − 4°4'151). Data inspection, bandpass and flux calibrations, as well as temporal gain derivation were done within the IDL superset MIR. The flux scale was derived by observations of Uranus and is estimated to be accurate within 15%.

Imaging was performed using the MIRIAD package with natural weighting. To keep comparison easy, we present all the maps with center positions consistent with the phase centers of the second observation run. For every source in each observation run, we used visibilities from both sidebands, each of a 2 GHz bandwidth, to generate a line-free continuum map. Channel maps were made with visibilities gridded into a velocity resolution of 1 km s^-1 and resulted in rms noises, σ = 0.31 and 0.20 K, equivalent to 110 and 82 mJy beam^-1, with angular resolutions of 33 × 17 and 40 × 24 for N₂H⁺ and N₂D⁺, respectively.

The J = 3 − 2 transition of N₂H⁺ and N₂D⁺ were detected in all three sources with the SMT (Figure 1). Since both transitions contain numerous hyperfine components, we fit each spectrum of every source with a model comprised of 38 hyperfine components with updated line frequencies and spontaneous emission rates (Pagani et al. 2009). For each individual source, all the hyperfine components of every J-level are assumed to be in thermal equilibrium at a single excitation temperature, T_ex, adopted from the ammonia observations with an angular resolution of 40'' (Pillai et al. 2006). The models are described by three more parameters: total column density, N, systemic velocity, υ_LSR, and FWHM as line width, Δυ. Model spectra are optimized with the minimization of the reduced χ² value, $\overline{\chi ^2}$, and the results are listed in Table 1. The N₂H⁺ spectrum toward MM1 appears to be doubly peaked, possibly affected by the presence of multiple sources (Zhang et al. 2009) and resulted in a significantly broader line width and a large $\overline{\chi ^2}$.

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Table 1. Results of SMT Spectral Fits

Parameters	MM1	MM4	MM9
Tex(K)	16.0	16.6	13.2
N2H+(3-2)
N (1012 cm-2)	10.12 ± 0.05	5.14 ± 0.04	1.86 ± 0.05
υLSR (km s-1)	77.59 ± 0.02	78.63 ± 0.02	79.82 ± 0.04
Δυ (km s-1)	6.14 ± 0.04	3.88 ± 0.04	3.42 ± 0.11
$\overline{\chi ^2}$	122.9	9.2	1.5
τmax	0.21	0.16	0.08
N2D+(3-2)
N (1011 cm-2)	1.7 ± 0.2	1.2 ± 0.3	1.0 ± 0.2
υLSR (km s-1)	78.0 ± 0.2	79.6 ± 0.4	81.1 ± 0.2
Δυ (km s-1)	2.6 ± 0.5	3.7 ± 0.9	2.2 ± 0.6
$\overline{\chi ^2}$	1.8	0.9	1.4
τmax	0.007	0.003	0.005
Dfrac	0.017 ± 0.002	0.024 ± 0.005	0.052 ± 0.011

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In cold clouds, a correction of the cosmic background temperature, T_bg = 2.7 K, is necessary when extracting the optical depth information of an observed spectrum with

$$\begin{equation} \tau (\upsilon) = -\ln \left[ 1 - \frac{T_\mathrm{mb}(\upsilon)}{J(T_\mathrm{ex}) - J(T_\mathrm{bg})} \right], \end{equation} \tag{ 1 }$$

where T_mb(υ) is the main beam temperature of the spectra and J(T) = (hν/k)(e^hν/kT − 1). All the line emissions appear to have fairly small optical depths. Meanwhile, the optimized model also provides an estimate of optical depth by integrating optical depths of all the hyperfine components. The maximum optical depth, τ_max, is less than 0.21 (Table 1). The emission of all the observed lines is optically thin. Over all, the fitted line widths, Δυ, of all the transitions are much broader than their thermal line width, $\Delta \upsilon _\mathrm{th} \equiv \sqrt{8 \ln 2 \, k T_\mathrm{ex}/m_\mathrm{N_{2}H^+}} \simeq 0.16 \; \mathrm{km \, s^{-1}}$, suggesting a significant contribution from nonthermal motions. Our N₂H⁺(3-2) spectra also have larger line widths when compared to the NH₃(1, 1) spectra observed with the Very Large Array (VLA) and the Effelsberg 100 m telescope (Pillai et al. 2007; Wang et al. 2008). Since the two transitions have similar upper state energies, E_up = 26.8 K for N₂H⁺ and 23.4 K for NH₃, but fairly different critical densities, n_crit ∼ 10⁶ cm^-3 for N₂H⁺ (Daniel et al. 2005; Pagani et al. 2009) and 10³ cm^-3 for NH₃ (Evans 1999), our N₂H⁺ observations tend to trace denser clumps possibly embedded in the inner region that is affected by star-forming activities as suggested by H₂O masers (Wang et al. 2006). Observations of lower J transitions of N₂H⁺, such as the J = 1 − 0 (E_up = 4.5 K and n_crit ∼ 10⁵ cm^-3) line, are needed to verify this interpretation.

The deuterium fractionation, D_frac, is calculated for every source (Table 1) and shows a significant enhancement of roughly 3 orders of magnitude higher than the average D/H ratio of 1.51 × 10⁻⁵ in the local interstellar medium (Oliveira et al. 2003). Such an enhancement has been observed in a large sample of high-mass star-forming cores (Fontani et al. 2006) as well as low-mass prestellar and protostellar cores (Crapsi et al. 2005; Roberts & Millar 2007; Emprechtinger et al. 2009). In particular, we find a decreasing trend with evolutionary stage, from D_frac = 0.051 in the younger MM9 core to D_frac = 0.016 in the more evolved MM1 core, a change over a factor of roughly 3. Although a decreasing trend over a factor of roughly 8 has been identified in low-mass protostellar cores (Emprechtinger et al. 2009), there was no evidence for such trend in a sample of massive star-forming cores associated with different molecular clouds (Fontani et al. 2006). Variations in thermal history, external environment, and initial chemical abundances across different molecular clouds may cause undesired confusion. Although our sample contains only three sources, the association in one single IRDC helps to minimize the environmental variations among the sources and to reveal the gentle drop in deuterium fractionation as the dusty envelope warms up.

Using the SMA, we further imaged the N₂H⁺ and N₂D⁺ emission to study more centrally concentrated structures. The N₂H⁺ emission shows clear detections in MM1 and MM4 as well as a marginal detection in MM9 (Figure 2). Since an interferometer is insensitive to structures larger than the scale corresponding to its shortest projected baseline, our SMA observations serve as a spatial filter to probe the fractional flux contained in clumps smaller than 8'' (Wilner & Welch 1994). A comparison of the integrated intensity observed with the SMA, W_SMA, to that with the SMT, W_SMT, can be made by convolving the SMA maps with the SMT beam after masking out regions below −3σ, which are believed to be artifacts induced by the lack of short baselines. For every source, we compare the N₂H⁺ integrated intensity observed with the SMA to that with the SMT (Figure 1) and estimate the fraction of the SMA integrated intensity, W_SMA/W_SMT, which indicates the state of a mass concentration process (Table 2). The small values of W_SMA/W_SMT suggest that most of the N₂H⁺ emission is in structures larger than 8''. An increasing trend from MM9 to MM1 is found and agrees with the presumed evolutionary stage of the central sources. On the other hand, N₂D⁺ is not detected in all regions at a level of 4σ ≃ 2.3 K km s^-1, translating to an upper limit of N(N₂D⁺) = 2.0 × 10¹² cm^-2 at T_ex = 13 K. Compared to the SMT integrated intensity in MM9, this detection limit sets a maximum fraction of 19% for emission coming from compact structures. Given the high critical density of n_crit ∼ 10⁶ cm^-3, the large fraction of the N₂H⁺(3 − 2) emission missed by the SMA observations strongly suggests the presence of cold and dense gas in scales larger than 8'' (∼0.2 pc). Similar to N₂H⁺, most of the N₂D⁺ emission is in extended structures.

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Continuum emissions at 284.2 and 236.5 GHz are detected in all sources with similar morphology. For the first time, a compact continuum source is detected in MM9 (Figure 2). Since the visibility coverages of the two observation runs were quite different, we made continuum maps with visibilities of projected baselines within 13–57 kλ, the range that all sources have in common at the two frequencies. If the dust emission is optically thin, the continuum flux density F_ν ∝ κ_ν B_ν(T_d), where κ_ν = 0.006(ν/245 GHz)^β cm² g^-1 (Shepherd & Watson 2002) is the dust opacity at the observing frequency ν and B_ν(T_d) is the Planck function at a dust temperature T_d. The opacity spectral index, β ≡ Δlog κ_ν/Δlog ν, can be measured by comparing flux densities at two observing frequencies. In cold clouds, the condition hν ∼ kT_d makes the Rayleigh–Jeans approximation inappropriate. We estimate the opacity spectral index in the selected regions with

$$\begin{equation} \beta = \frac{\log (F_{\nu _2}/F_{\nu _1}) + \log [(e^{h\nu _2/kT_d}-1)/(e^{h\nu _1/kT_d}-1)]}{\log (\nu _2/\nu _1)} - 3, \end{equation} \tag{ 2 }$$

and the core mass with M_core = F_νD²/κ_νB_ν(T_d), where D is the distance of the source. Assuming thermal equilibrium between gas and dust over similar spatial scales in the calculations of β and M_core, we adopt the gas temperature derived from the VLA ammonia observations with a comparable angular resolution of 5'' × 3'' (Zhang et al. 2009) to be the dust temperature, T_d. The results are listed in Table 2. Because of the limited frequency span of 48 GHz, we note that a systematic uncertainty of 15% in flux density measurements will produce a fairly large uncertainty of Δβ ≃ 1.2 in our calculations.

The dust opacity spectral index shows an increasing trend from MM9 to MM1 as the central sources evolve although the multiplicity in MM4 may complicate the interpretation of its averaged β. Nevertheless, a smaller value of β is observed in MM9 with respect to MM1. At millimeter wavelengths, the value of β is a good probe for the size distribution of dust grains (Miyake & Nakagawa 1993), and a smaller β suggests that MM9 is surrounded by larger dust grains as a result of grain growth in high-density environment. On the other hand, the larger β in the more evolved region MM1 may be attributed to possible changes in the size distribution and chemical composition of the surrounding dust grains, which have been exposed to strong radiation fields generated by the associated massive young stellar objects (YSOs).

In cold, dense environment, CO tends to freeze out onto dust grains while N₂H⁺ and NH₃ suffer less from depletion (Bergin et al. 2002; Tafalla et al. 2004). Since CO is the major destroyer of molecular ions, its removal from the gas phase results in a subsequent enrichment of N₂H⁺ (Aikawa et al. 2005). In later evolutionary stages when the internal heating of YSOs becomes important, the temperature will rise up and lead to sublimation of ice mantle, which returns volatile species such as CO back to the gas phase. The warmer temperature together with the reappearance of gas-phase CO can alter the competition among chemical reaction routes and destroy N₂H⁺ that has been produced during the cold early phase (Roueff et al. 2005; Aikawa et al. 2005).

In MM1, a deficiency of N₂H⁺ is observed in the location of the dust continuum emission as well as the ¹³CO(2 − 1) emission (Figure 3) in a previous study (Zhang et al. 2009). Observationally, a centrally heated temperature structure from 16 to 30 K is derived in MM1 over spatial scales of roughly 1–0.1 pc (Pillai et al. 2006; Zhang et al. 2009). Theoretically, a significant drop in D_frac is predicted across this temperature range (Roueff et al. 2005), and an instant release of CO is expected due to a significant drop of the CO sublimation timescale from 10⁸ yr at T_d ≃ 12 K to 0.1 yr at T_d ≃ 20 K (Collings et al. 2003). This hypothesized release of CO in the warm region can be traced in MM1 with the ¹³CO emission and dust continuum emission. A contrast in chemical composition can occur across the boundary between the cold, outer part and the warm, inner part that has been altered by the newly released gas-phase reactants. This chemical contrast has recently been observed in AFGL 5142 by comparing emissions of N₂H⁺ and NH₃ (Busquet et al. 2010).

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