INTERSTELLAR DETECTION OF c-C₃D₂^*

Investigating deuterium chemistry is useful to put constraints on the ionization fraction, temperature, density, and thermal history of dense molecular clouds (Guelin et al. 1977; Caselli et al. 2002; Cazaux et al. 2011; Taquet et al. 2012). The observations of multiply deuterated molecules in space (e.g., Ceccarelli et al. 2007 and references therein) have shown the necessity of reexamining some reaction rates in chemical networks (Roberts et al. 2002), elemental D/H ratio in cold dense gas (Roueff et al. 2007), and the density structure in sources such as L1544 and ρ Oph D (Roberts et al. 2004), as well as the effects of accretion on grains (Roberts et al. 2000), possible effects of internal dynamical motion (Aikawa et al. 2005), and the evolution of ice mantles in dense clouds and cores (Cazaux et al. 2011; Taquet et al. 2012).

The first multiply deuterated interstellar molecule detected was D₂CO, almost 20 yr ago (Turner 1990). Since then, the study of deuterated molecules in the interstellar medium has rapidly increased as they have been proven to be a unique observational probe of the early stages in low-mass star formation. Multiply deuterated species such as triply deuterated ammonia have been detected with a surprisingly high abundance ratio of 10⁻⁴ with respect to their fully hydrogenated forms (Lis et al. 2002). By comparing this ratio with the elemental D/H ratio (1.65 × 10⁻⁵; Linsky et al. 1993), it is easily seen that there is a remarkable enrichment in deuterium in this and other molecules. In IRAS 16293−2422, Ceccarelli et al. (1998) measured D₂CO/H₂CO = 5%. In the same source, Parise et al. (2004) measured CD₃OH/CH₃OH = 1.4%. This enrichment in deuterium has mainly been explained by the exothermicity of the H–D exchange reactions, and by the depletion of CO and O onto dust grains (Dalgarno & Lepp 1984; Caselli et al. 1999), which enhances the abundance of the multiply deuterated forms of H$_3^+$ and, upon dissociative recombination, the D/H ratio. Roberts et al. (2003) calculated D/H abundance ratios close to 0.3 (20,000 times the cosmic value), in regions with large amount of CO freeze-out.

Despite extensive studies of nearly 30 deuterated molecules in the interstellar gas, the processes regulating their formation are not completely understood, in particular the relative importance of gas-phase versus grain-surface chemistry. For example, simple gas-phase chemical models do not reproduce the deuterium enrichment observed in some of these species. In particular, the formation of methanol on grain mantles is presented as an explanation for its enhanced deuteration (Parise et al. 2006); for H₂CO instead, the gas-phase reaction path cannot be excluded. In fact, in the Orion Bar photodissociation region, HDCO seems to be formed solely in the gas phase (Parise et al. 2009). Deuteration of ammonia can be reproduced with gas-phase models (e.g., Roueff et al. 2005), although NH₃ and its deuterated forms are also expected to form on the surface (Tielens 1983).

The first detection of c-C₃H₂ in the laboratory (Thaddeus et al. 1985) allowed the identification of several U-lines previously detected in space (Thaddeus et al. 1981), namely, the strong lines at 85,338 and 18,343 MHz. Since then, cyclopropenylidene has been proven to be one of the most abundant and widespread molecules in our Galaxy. It has been observed in the diffuse gas, cold dark clouds, giant molecular clouds, photodissociation regions, circumstellar envelopes, and planetary nebulae (Thaddeus et al. 1985; Vrtilek et al. 1987; Cox et al. 1987; Madden et al. 1989; Lucas & Liszt 2000). Given the high abundance of the normal species, both c-C₃HD and the singly substituted ¹³C species (off-axis) have been observed with a good signal-to-noise ratio (S/N) in cold dark clouds. Furthermore cyclopropenylidene shows an enhancement in deuterium fractionation in cold dark clouds. For example, Gerin et al. (1987) measured a 1:5 ratio of the 2_{1, 2}–1_{0, 1} lines of c-C₃HD and c-C₃H₂ in TMC1. The reactions which lead to such a high deuteration are still poorly understood. Some rates of reactions which may be involved in the formation of deuterated c-C₃H₂ have been measured by Savić et al. (2005), but to our knowledge they have not been included in models thus far. Last year, the centimeter- and millimeter-wavelength spectra of doubly deuterated c-C₃H₂ were measured in the laboratory (Spezzano et al. 2012), allowing for the first time a search for c-C₃D₂ in space. Like its fully hydrogenated counterpart, c-C₃D₂ presents the spectrum of an oblate asymmetric top with b-type transitions. Furthermore c-C₃D₂ shows a deuterium quadrupole splitting resolvable at very low J. Given the presence of two equivalent off-axis bosons, it has ortho and para symmetry species with relative statistical weight of 2:1.

Unlike several of the six known multiply deuterated species observed in the radio band (D₂H⁺, CHD₂OH, NHD₂, D₂CO, D₂S, and D₂CS), c-C₃H₂ is believed to form solely by gas-phase reactions (Park et al. 2006). The interplay between the gas phase and grain surface reactions in the deuteration of interstellar molecules is not clear thus far, partially because there are not many probes available for testing the models: c-C₃H₂ is an ideal molecule for this purpose because of its easily observable transitions and because it has the possibility of double deuteration. Assuming that c-C₃D₂ is formed in the gas phase like its fully hydrogenated counterpart, cyclopropenylidene will be a unique probe for the deuteration processes happening in the gas phase. Furthermore, since c-C₃H₂ is, in terms of cloud evolution, an early-type molecule (Herbst & Leung 1989), it is a particularly useful tool to investigate early stages of a molecular cloud. This makes observations of its deuterated forms particularly important to test time-dependent chemical codes which include deuteration processes.

Here we report on the positive detection of three emission lines of c-C₃D₂ in the 3 mm band, namely, the $J_{K_a,K_c} = 3_{0,3} \hbox{--} 2_{1,2}$, 3_{1, 3}–2_{0, 2}, and 2_{2, 1}–1_{1, 0} transitions, toward TMC-1C and L1544: to our knowledge this is the first search for doubly deuterated cyclopropenylidene undertaken.¹⁰

The observations were carried out from 2012 September 28 until October 2 at the IRAM 30 m telescope, located in Pico Veleta (Spain), toward the starless cores TMC-1C and L1544. The choice of the sources was made on the basis of two simple criteria: the abundance of the normal species (c-C₃H₂) and a high deuterium fractionation. Both sources are in the Taurus molecular cloud, one of the closest dark cloud systems and low-mass star-forming regions in our Galaxy. L1544 is a perfect test bed to investigate the initial conditions of protostellar collapse: its structure is consistent with a contracting Bonnor–Ebert sphere, with central densities of about 10⁷ cm⁻³ and a peak infall velocity of ≃0.1 km s⁻¹ at about 1000 AU from the center (e.g., Keto & Caselli 2010). Its centrally concentrated structure and measured kinematics suggest that this is a prestellar core at a late stage of evolution, toward star formation. TMC-1C is a relatively young core, with evidence of accreting material toward a core and immersed in a cloud with densities higher than those surrounding the L1544 core (Schnee et al. 2007).

The coordinates that were used are α₂₀₀₀ = 04^h41^m161 δ₂₀₀₀ = +25°49'438 for TMC-1C, and α₂₀₀₀ = 05^h04^m1721 δ₂₀₀₀ = 25°10'428 for L1544. In the case of TMC-1C these are the same coordinates as reported by Bell et al. (1988) and Gerin et al. (1987), while in the case of L1544 they correspond to the coordinates of the peak of the 1.3 mm continuum dust emission from Ward-Thompson et al. (1999). In both cores, we observed two lines of c-C₃H₂, one line of c-H¹³CC₂H (off-axis), two lines of c-C₃HD, and three lines of c-C₃D₂, using three different tuning settings. A summary of the observed lines is reported in Table 1. The EMIR receivers in the E090 configuration were employed, and observations were performed in a frequency switching mode with a throw of ±4.3 MHz. All four EMIR sub-bands were connected to the Fast Fourier Transform Spectrometers set to high-resolution mode; this delivered a final spectrum with 50 kHz channel spacing (corresponding to 0.15 km s⁻¹ at 3 mm) and a total of 7.2 GHz of spectral coverage (nominal bandpass of 1.8 GHz per sub-band). Telescope pointing was checked every 2 hr on Jupiter and was found to be accurate to 3''–4''.

Lines of the isotopologues of c-C₃H₂ listed in Table 1 have been detected in both sources with very high S/N. A selection of spectra of c-C₃H₂ and isotopologues in TMC-1C and L1544 is shown in Figure 1. Table 1 lists the observed line parameters. Even the weakest line of the doubly deuterated species, 2₂₁–1₁₀ at 108 GHz, is detected at a 7.5σ level in TMC-1C (T_{mb, rms} = 2.5 mK), and at a 9σ level in L1544 (T_{mb, rms} = 4.6 mK). The GILDAS¹¹ software (Pety 2005) was employed for the data processing: high-order polynomials had to be used for baseline subtraction given the strong baseline produced by the frequency switching observing mode. The column densities and optical depths given in Table 1 were calculated using the expressions given in the Appendix. As was already pointed out by Bell et al. (1988), c-C₃H₂ shows two velocity components toward TMC-1C, one more intense at 6 km s⁻¹ and one less intense at 5.4 km s⁻¹; see Figure 1. There is a hint of detection of the component at 5.4 km s⁻¹ also in c-H¹³CC₂H, but no clear presence in the deuterated species. Assuming that all lines have the same excitation temperature in both components, we expect for the component at 5.4 km s⁻¹ a line intensity of 0.06 K for c-C₃HD (3₀₃–2₁₂) and 0.013 K for c-C₃D₂ (3₁₃–2₀₂). Comparing these estimates with the noise level in our spectra (0.007 K for c-C₃HD and 0.002 K for c-C₃D₂), we can say that the lower velocity component is absent in the deuterated species of cyclopropenylidene: this behavior may suggest that the lower velocity component traces a hotter region, where the deuterated molecules are not present in detectable amounts.

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3.1. Excitation

The observed line intensity ratios of c-C₃D₂ pose the question of whether local thermal equilibrium is a valid assumption for its excitation. Only for para-C₃D₂ is more than one optically thin line was detected. The ratios of the integrated 3_{0, 3}–2_{1, 2}/2_{2, 1}–1_{1, 0} lines should be 4.3 and 3.3 for TMC-1C (T_ex = 7 K) and L1544 (T_ex = 5 K), respectively, assuming thermalization of both lines to their assumed excitation temperature, while they are 1.5 and 1.35. To gain insight into the excitation of the lines, we performed radiative transfer calculations with RADEX (van der Tak et al. 2007). Collision rates of C₃H₂ with H₂ calculated by Chandra & Kegel (2000) and supplied by the LAMDA database (Schöier et al. 2005) were used together with molecular constants of para-C₃D₂. Calculations were done on a grid in density of molecular hydrogen, n(H₂), and column density of para-C₃D₂, N(para-C₃D₂), and the results are shown in Figure 2. It is in principle possible to read the column density of c-C₃D₂ from Figure 2, by knowing the density of molecular hydrogen. The nominal observed line ratios would, particularly for L1544, result in very high column densities. The lines would be very subthermally excited and very optically thick. However, given the fact that the observed line strengths run parallel to each other, a small change in the observed value would result in a substantial change in the ratio. The line intensities and χ² contours of both lines show that the line strengths are very close to each other along a diagonal line spanning a large range of densities and column densities (filling factors smaller than unity would move this line to the right in the plot), so that much smaller values of column densities and opacities are also in agreement with the data. The predicted excitation temperatures tend to be rather low, in the range 3–3.5 K, which introduces a considerable uncertainty in the column density determinations. Since the transitions used for the excitation calculation for c-C₃HD and c-C₃D₂ have similar upper state energy, the excitation behavior will naturally be degenerated. Therefore, in the absence of data for more transitions for c-C₃D₂, c-C₃HD, or c-H¹³CC₂H, it is difficult to derive conclusive results. Despite these uncertainties, we have assumed local thermodynamic equilibrium with T_ex values as described in the Appendix.

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In addition to the observation of two lines of c-C₃H₂, one line of c-H¹³CC₂H (with the ¹³C off of the molecular axis) and two lines of c-C₃HD, we also claim the detection of three lines of c-C₃D₂ in both TMC-1C and L1544. This first interstellar detection of c-C₃D₂ is validated for the following reasons.

• 1.  
  We detected all favorable transitions of c-C₃D₂ available in the covered frequency range.
• 2.  
  The rest frequencies employed have laboratory accuracy (Spezzano et al. 2012), and in both sources the line shapes and velocities are in agreement with each other and with those observed for more abundant isotopologues (see Figure 1).
• 3.  
  The intensities of the c-C₃D₂ lines are consistent with what is expected from the deuteration of the ring in these sources, i.e., c-C₃H₂/c-C₃HD is consistent with c-C₃HD/c-C₃D₂, as will be discussed below.

In Table 2 we present the relative abundances of the deuterated species with respect to the hydrogenated ones for cyclopropenylidene over the 27'' beam for TMC-1C and L1544 obtained from this work, and also for H₂CO, HCO⁺, N₂H⁺, and NH₃ obtained from previous work. The abundance of doubly deuterated cyclopropenylidene with respect to the normal species is 0.4%–0.8% in TMC-1C and 1.2%–2.1% in L1544. This interval has been determined considering the differences in N_tot obtained from different lines. The deuteration of c-C₃H₂ follows the same trend observed for other molecules in both sources. It is interesting to note that the ratios [c-C₃D₂]/[c-C₃HD] and [c-C₃HD]/[c-C₃H₂] are quite similar in both sources. We calculated the D/H ratio of c-C₃H₂ in prestellar cores using the network model of Aikawa et al. (2012). For the physical structure of the core, we adopt the collapsing core model of Aikawa et al. (2005; the α = 1.1 model) and also a static model of L1544 from Keto & Caselli (2010). For CO depletion factors consistent with those of the two objects, i.e., f_D = 3.8 for TMC-1C (Schnee et al. 2007) and f_D = 14 for L1544 (Crapsi et al. 2005), the calculated column density ratio of c-C₃D₂/c-C₃H₂ is ∼10⁻², consistent with the observed value of 0.6% for TMC-1C and 1.5% for L1544. There is no need for any deuterium fractionation reactions of c-C₃H₂ on grain surfaces to account for the observed D/H ratio: the deuteration of cyclopropenylidene can be explained solely by gas-phase reactions. The main route of formation of deuterated cyclopropenylidene is the successive deuteration of the main species via reaction with H₂D⁺, D₂H⁺, and D$_3^+$. An example of the reaction scheme is sketched in Figure 3, considering only H₂D⁺ as reaction partner. The depicted cycle of reactions starts with c-C₃H₂ and H₂D⁺, producing in the first step c-C₃HD and subsequently c-C₃D₂. The same reactions happen with D₂H⁺ and D$_3^+$. The overall process is a series of two reactions: the proton–deuteron transfer (slow step, red arrows) and the subsequent dissociative recombination with electrons (fast step, blue arrows). The presence of this deuteration cycle results in a time-dependent deuterium fractionation. Assuming low levels of deuteration at the start, it is expected that this level increases as a function of time, reaching a stationary level after some time. Other deuteration processes, e.g., the formation of c-C₃HD from the reaction of C₃H⁺ with HD, were found to be negligible. The D/H ratio of cyclopropenylidene is, therefore, directly related to that of H$_3^+$, the main deuterium donor in dark interstellar clouds. Recently, Huang & Lee (2011) have calculated highly accurate spectroscopic constants for ¹³C and D isotopologues of c-C₃H$_3^+$ in order to guide the laboratory and astronomical search. Since these species are intermediates in the formation of isotopic species of c-C₃H₂, their detection would be useful to put more constraints on the models.

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Doubly deuterated cyclopropenylidene appears to be a very interesting probe for the earliest stages of star formation. Its formation mechanism puts important constraints on gas-phase deuteration models, and suggests the possibility of using c-C₃D₂ as a chemical clock. Furthermore, the brightness of the $J_{K_a,K_c} = 3_{1,3} \hbox{--} 2_{0,2}$ line of c-C₃D₂ at 97 GHz in L1544 would allow us to make an on-the-fly (OTF) map of the core in a reasonable amount of time, for the first time for a doubly deuterated molecule. During our observations, the line was observed with an S/N of more than 6 after just 30 minutes. Emission from C³⁴S is spread over 10 arcmin² in L1544 (Tafalla et al. 1998). We estimated that an OTF map of 6 arcmin² with a noise level of 20 mK at the IRAM 30 m telescope with the EMIR receivers would be possible in 14 hr, allowing us to map c-C₃H₂ and c-C₃D₂ at the same time. By mapping the core it will be possible to locate the deuteration peak, and put more constraints on current gas–grains models.

The authors thank the referee for useful comments. This work has been supported by SFB956. S. Spezzano has been supported in her research with a stipend from the International Max-Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne. S. Schlemmer and S.B. acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) through project BR 4287/1-1. L.B. acknowledges support from the Science and Technology Foundation (FCT, Portugal) through the Fellowship SFRH/BPD/62966/2009, and he is grateful to the SFB956 for the travel allowance.

The column densities and optical depths given in Table 1 were calculated using the following expressions. The line center opacity τ₀ is

$$\begin{eqnarray*} \tau _0 &=& \ln \left(\frac{J(T_{{\rm ex}}) - J(T_{{\rm bg}})}{J(T_{{\rm ex}}) - J(T_{{\rm bg}}) - T_{{\rm mb}}}\right), \end{eqnarray*}$$

where $J(T) = {({h\nu }/{k})}(e^{\frac{h\nu }{kT}}-1)^{-1}$ is the source function in Kelvin. The upper state column density in case of optically thin emission and the total column density are defined as

$$\begin{eqnarray*} N^{{\rm thin}}_{{\rm up}} &=&\frac{8\pi \nu ^3\sqrt{\pi }\Delta \nu \tau _0}{c^3A_{ul}2\sqrt{\ln 2}(e^{\frac{h\nu }{kT}}-1)}\\ N_{{\rm tot}} &=& \frac{N_uQ_{{\rm rot}}(T_{{\rm ex}})}{g_ue^{(\frac{E_u}{kT_{{\rm ex}}})}}, \end{eqnarray*}$$

where k is the Boltzmann constant, ν is the frequency of the line, h is the Planck constant, c is the speed of light, A_ul is the Einstein coefficient of the transition, Δν is the FWHM, g_u is the degeneracy of the upper state, E_u is the energy of the upper state, Q_rot is the partition function of the molecule at the given temperature T_ex. T_ex, T_bg, and T_mb are the excitation, the background (2.7 K), and the main beam temperatures, respectively, in kelvin. To calculate N_tot and τ, we assumed a T_ex of 7 K for TMC-1C and 5 K for L1544 for all deuterated isotopologues, following Gerin et al (1987), and 8 K for TMC-1C and 6 K for L1544 for the main species and the ¹³C isotopologues as they trace also warmer regions of the cloud. The effect of the excitation temperature on the derived column density ratios in Table 2 was found to be small, with a change of few percent upon a variation of ±1 K. By using these expressions, we assumed that the source fills the beam, and optically thin emission obeying LTE. Since lines of c-C₃H₂ are optically thick, we derived its total column density from the total column density of c-H¹³CC₂H assuming a ¹²C/¹³C ratio of 77, determined by Wilson & Rood (1994) from H₂CO and CO as a function of distance from the Galactic center, N_u and τ were calculated backward.