A Study of the c-C3HD/c-C3H2 Ratio in Low-mass Star-forming Regions*

J. Chantzos; S. Spezzano; P. Caselli; A. Chacón-Tanarro; L. Bizzocchi; O. Sipilä; B. M. Giuliano

doi:10.3847/1538-4357/aad2dc

1. Introduction

During the early stages of star formation, self-gravitating starless cores begin to contract (n_H > 10⁴ cm⁻³) and to cool down to a few kelvin (T < 10 K). Under these conditions, the deuteration of molecules is considerably increasing. H₂D⁺ is the main deuterium provider for most molecules in dense cores and is formed from the following deuteron–proton reaction (Millar et al. 1989):

$\begin{eqnarray}&&{{\rm{H}}}_{3}^{+}+\mathrm{HD}\rightleftharpoons {{\rm{H}}}_{2}{{\rm{D}}}^{+}+{{\rm{H}}}_{2}+230\,{\rm{K}}.\end{eqnarray} \tag{ 1 }$

This reaction is exothermic and proceeds mostly in the forward direction at temperatures lower than 30 K, increasing the abundance of H₂D⁺. The abundance of H₂D⁺ also depends on the ortho-to-para-H₂ ratio. The backward direction of Reaction (1) is endothermic if the reactants H₂D⁺ and H₂ are mostly in the para-form (Pagani et al. 1992). An important process in these environments is the freeze-out of molecules onto dust grains. Previous studies have shown that CO depletes heavily toward the center of cores (Willacy et al. 1998; Caselli et al. 1999; Bacmann et al. 2003; Crapsi et al. 2005; Pagani et al. 2007). Since CO destroys ${{\rm{H}}}_{3}^{+}$ and H₂D⁺, its depletion from the gas phase leads to a further enhancement of the total deuteration level (Dalgarno & Lepp 1984). As the starless core continues to contract, it eventually becomes a pre-stellar core, defined as being a self-gravitating core (Ward-Thompson et al. 1999) with signs of contraction motions and high levels of CO freeze-out and deuteration (Crapsi et al. 2005). Pre-stellar cores are a sub-sample of starless cores, i.e., the most dynamically evolved and destined to form one or more protostars. Once the protostar is formed, the central regions of the contracting core warm up and the whole core starts to become affected by the outflow driven by the young stellar object. This causes CO to desorb and also increases the backward rate of Reaction (1), leading finally to a decrease of the total deuteration degree. In summary, the increase and decrease of molecular deuteration is sensitive to the evolutionary stage in the star formation process and is an excellent tool to trace the early stages of star formation.

Species that can be used as evolutionary tracers of high-density and low-temperature gas must have the possibility of deuteration and should be abundant in space. One molecule that has been proven to be a very good evolutionary tracer is diazenylium, N₂H⁺ (Crapsi et al. 2005; Emprechtinger et al. 2009; Friesen et al. 2013; Punanova et al. 2016). It has been shown that the deuteration of N₂H⁺ correlates tightly with important evolutionary indicators, such as the dust temperature, the CO depletion factor, and the central column density of H₂. In addition, the emission maps of N₂H⁺ strongly follow the dust emission maps, indicating that N₂H⁺ is less depleted than C-bearing molecules at higher densities (Bergin et al. 2001; Tafalla et al. 2002). This makes N₂H⁺ a very good tracer of the deuteration level in central regions of dense cores. The resistance of N₂H⁺ to depletion has been ascribed by previous studies (Flower et al. 2006; Le Gal et al. 2014) to the fact that nitrogen in the interstellar medium (ISM) is mainly in atomic form, and N atoms can stay in the gas phase longer because of their lower sticking probabilities and the slow process which transforms N into N₂.

Following the detection of cyclopropenylidene (c-C₃H₂) in the laboratory (Thaddeus et al. 1985), a number of U-lines observed by Thaddeus et al. (1981) were able to be identified as c-C₃H₂ transitions. After its first detection, it was observed in various sources, like cold dark clouds, diffuse clouds, circumstellar envelopes, planetary nebulae, etc. (e.g., Benson et al. 1998; Spezzano et al. 2013, and references therein). Due to the high abundance of the normal species, the singly deuterated species c-C₃HD and the isotopologue c-H¹³CC₂H have also been observed in various sources over the past 30 years. For example, c-C₃HD was detected toward L1498 (Bell et al. 1988), TMC-1C and L1544 (Spezzano et al. 2013), as well as TMC-1 (Turner 2001) in the Taurus Molecular Cloud.

After the first laboratory measurement of the doubly deuterated species by Spezzano et al. (2012), c-C₃D₂ was detected in the ISM for the first time toward the starless cores TMC-1C and L1544 with a high signal-to-noise-ratio (S/N) (Spezzano et al. 2013). The observed single and double deuteration in these two sources could be reproduced by a chemical model including only gas-phase reactions (Aikawa et al. 2012). The possibility of double deuteration and its gas-phase chemistry makes c-C₃H₂ a useful probe for the deuteration processes taking place only in the gas phase. A study of the c-C₃H₂-deuteration as an evolutionary indicator will give complementary information to the deuteration of N₂H⁺, and reveal possible differences between the deuteration of C- and N-bearing species in the gas phase. In fact, unlike N₂H⁺, c-C₃H₂ is believed to be an early-type molecule (Herbst & Leung 1989) in terms of cloud evolution and can therefore trace the early stages of star formation; in particular, in L1544, c-C₃H₂ preferentially traces the side of the core more exposed to the interstellar radiation field, where the chemistry is continually rejuvenated by the photodissociation of CO (Spezzano et al. 2016). However, c-C₃H₂ is also affected by freeze-out or chemical depletion, as it does not trace the central regions of starless cores (e.g., Spezzano et al. 2017). It is therefore important to compare the deuteration of this molecule in starless and protostellar cores in order to investigate the level of deuteration in different stages of low-mass star formation. This can give us insights on possible deuteration processes taking place on grain surfaces during the cold and dense phases just before the switch-on of the protostar.

In this work we present single-pointing observations of c-C₃H₂, the singly and doubly deuterated species, c-C₃HD and c-C₃D₂, as well as the isotopologue c-H¹³CC₂H toward 10 starless cores and five protostars in the Taurus and Perseus Molecular Cloud complexes. In Section 2 we summarize the details concerning the observations. Section 3 describes the calculation of the single and double deuteration of c-C₃H₂ as well as the comparison between the deuterium fraction of N₂H⁺ and c-C₃H₂. In Section 3 we also describe the correlation between the deuteration level of c-C₃H₂ and important evolutionary indicators (dust temperature, CO depletion level, and central column density of H₂). The conclusions are summarized in Section 4.

2. Observations

The observations were done at the IRAM 30 m telescope located at Pico Veleta (Spain) toward 10 starless cores and five protostellar cores in Taurus and Perseus. A summary of the observed objects, their coordinates, and their distances is reported in Table 1. These sources all lie in our Galactic vicinity and represent different stages of star formation, from starless cores to more evolved pre-stellar cores and young Class 0 protostars. Previous observations of these sources showed a significant deuteration of N₂H⁺ which correlates with evolutionary indicators, such as the dust temperature, CO depletion, and central column density of H₂ (Crapsi et al. 2005; Emprechtinger et al. 2009). A special case in our sample is L1521F. Even though some studies (Crapsi et al. 2005) describe this source as an evolved pre-stellar core, successive work (Bourke et al. 2006; Takahashi et al. 2013) has proven that L1521F shows an infrared source and a compact continuum millimeter emission, which indicates the existence of a protostar. The detection of a small outflow and a low bolometric luminosity (0.034–0.07 L_⊙) suggests that this source is a so-called Very Low Luminosity Object (hereafter VeLLO) which could be a very young protostellar source or a protostar at its minimum of activity, if episodic accretion is at work (e.g., Visser et al. 2015).

Table 1. Observed Sources with Their Corresponding Coordinates and Estimated Distances

Source	Object	R.A	Decl.	Distance	References
		J2000.0	J2000.0	(pc)
L1495	starless core	04 14 08.2	+28 08 16	140	2
L1495B	starless core	04 18 05.1	+28 22 22	140	1
L1495AN	starless core	04 18 31.8	+28 27 30	140	1
L1495AS	starless core	04 18 41.8	+28 23 50	140	1
L1400K	starless core	04 30 52.1	+54 51 55	140	2
L1400A	starless core	04 30 56.8	+54 52 36	140	1
CB23	starless core	04 43 27.7	+29 39 11	140	1
L1517B	starless core	04 55 18.8	+30 38 04	140	1
L1512	starless core	05 04 09.7	+32 43 09	140	1
TMC2	pre-stellar core^a	04 32 48.7	+24 25 12	140	1
L1544	pre-stellar core^a	05 04 17.2	+25 10 43	140	3
L1521F	protostellar core	04 28 39.8	+26 51 35	140	1
Per 5	protostellar core	03 29 51.6	+31 39 03	220	4
IRAS03282	protostellar core	03 31 21.0	+30 45 30	220	4
HH211	protostellar core	03 43 56.8	+32 00 50	220	4
L1448IRS2	protostellar core	03 25 22.4	+30 45 12	220	4
IRAS16293	protostellar core	16 32 22.6	−24 28 33	120	5

Note. Here we also include the well studied objects L1544 and IRAS16293-2422.

^aThe definition of a "pre-stellar core" is based on the work of Crapsi et al. (2005).

References. (1) Lee et al. (2001), (2) Tafalla et al. (2002), (3) Ward-Thompson et al. (1999), (4) Cernis (1990), (5) Caux et al. (2011).

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The observations were carried out with the EMIR receiver using the E090 configuration (3 mm atmospheric window). Each sub-band covered a frequency range of 1.8 GHz, leading to a total spectral coverage of 7.2 GHz. All four EMIR sub-bands were connected to the Fast Fourier Transform Spectrometer with a frequency resolution of 50 kHz. Frequency switching was performed with a frequency throw of ±3.9 MHz. Telescope pointing was checked every 2 hr on Mercury and was accurate to 3''–4''. The intensity of the obtained spectra was given in antenna temperature units, ${T}_{{\rm{A}}}^{* }$ . The antenna temperature ${T}_{{\rm{A}}}^{* }$ was converted to the main beam temperature T_MB using the relation ${T}_{\mathrm{MB}}=\tfrac{{F}_{\mathrm{eff}}}{{B}_{\mathrm{eff}}}\cdot {T}_{{\rm{A}}}^{* }$ .

In both samples we observed the main isotopologue c-C₃H₂, the singly and doubly deuterated species c-C₃HD and c-C₃D₂, as well as the isotopologue c-H¹³CC₂H, with one ¹³C being off the principal axis of the molecule. Table 2 summarizes the observed species, the spectroscopic parameters, and telescope settings at the corresponding frequencies: E_up describes the upper state energy and A_ul is the Einstein coefficient of the corresponding transition. The upper state degeneracy is given by g_u. The parameters B_eff and θ_MB describe the main beam efficiency and the main beam size of the telescope at a given frequency, respectively. The system temperature T_sys is given in K. The forward efficiency, F_eff, is in the observing frequency range equal to 95%.

Table 2. Transition Parameters of the Observed Species and Telescope Settings

Species	Transitions	Frequency	References	E_up	A_ul	g_u	B_eff	θ_MB	T_sys
	${J}_{{K}_{a},{K}_{c}}$	(GHz)		(K)	(10⁻⁵ s⁻¹)		(%)	('')	(K)
c-C₃H₂	3_2,2 − 3_1,3	84.727	1	16.14	1.04	7	81	29	80–120
c-C₃HD	3_0,3 − 2_1,2	104.187	2	10.85	3.95	21	79	25	90–151
c-C₃HD	2_1,1 − 1_1,0	95.994	2	7.56	0.45	15	80	27	99–114
c-H¹³CC₂H	2_1,2 − 1_0,1	84.185	2	6.33	2.17	10	81	29	80–116
c-C₃D₂	3_0,3 − 2_1,2	94.371	3	9.85	3.37	21	80	27	82–123
c-C₃D₂	3_1,3 − 2_0,2	97.761	3	9.88	3.87	42	80	26	79–119
c-C₃D₂	2_2,1 − 1_1,0	108.654	3	7.90	4.79	15	78	24	96–105

References. (1) Thaddeus et al. (1985), (2) Bogey et al. (1987), (3) Spezzano et al. (2012).

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3. Results

In the Appendix A we show the observed spectra toward all sources. The 3_2,2 − 3_1,3 transition of c-C₃H₂ at 84.727 GHz was detected in all starless and pre-stellar cores except for L1400K, L1517B, and L1512. The same line of c-C₃H₂ was also detected in all protostars except for L1448IRS2. The c-C₃HD (3_0,3 − 2_1,2) and c-H¹³CC₂H (2_1,2 − 1_0,1) emission was detected in all starless, pre-stellar, and protostellar cores with a very high S/N; the strongest lines have an S/N of 25 and 40, respectively. The 3_1,3 − 2_0,2 transition of c-C₃D₂ at 97.761 GHz was found at a high S/N level (the strongest line was detected at a 27σ level) in the following starless and pre-stellar cores: L1495AN, L1512, L1517B, TMC2, and L1544. In the case of the protostellar cores, c-C₃D₂ was detected in four sources: Per5, HH211, L1521F, and IRAS16293-2422 with S/N levels ranging from 7.8 to 13.5.

3.1. Calculation of the Column Densities and the Deuteration Level

The data reduction and analysis was carried out using the GILDAS¹ software (Pety 2005). In order to subtract the baseline caused mainly by the frequency switching mode, high-order polynomials were fitted. Each line was fitted by using the standard CLASS Gaussian fitting method. The total column density was calculated by using the expression for optically thin transitions:

$\begin{eqnarray}&&{N}_{\mathrm{tot}}=\displaystyle \frac{8\pi {k}_{{\rm{B}}}W{\nu }^{2}}{{A}_{\mathrm{ul}}{{hc}}^{3}}\cdot \displaystyle \frac{J({T}_{\mathrm{ex}})}{J({T}_{\mathrm{ex}})-J({T}_{\mathrm{bg}})}\cdot \displaystyle \frac{{Q}_{\mathrm{rot}}({T}_{\mathrm{ex}})}{{g}_{u}{e}^{-\tfrac{{E}_{\mathrm{up}}}{{k}_{{\rm{B}}}{T}_{\mathrm{ex}}}}},\end{eqnarray} \tag{ 2 }$

where $W=\tfrac{\sqrt{\pi }{\rm{\Delta }}{{vT}}_{\mathrm{MB}}}{2\sqrt{\mathrm{ln}(2)}}$ is the integrated intensity of the line, with ${\rm{\Delta }}v$ being the linewidth (FWHM) (Caselli et al. 2002). $J(T)=\left(\tfrac{h\nu }{{k}_{{\rm{B}}}}\right){({e}^{\tfrac{{\rm{h}}\nu }{{k}_{{\rm{B}}}T}}-1)}^{-1}$ is the Rayleigh–Jeans temperature in K, k_B is the Boltzmann constant, ν is the transition frequency, c is the speed of light, and h is the Planck constant. The partition function of a molecule at a given excitation temperature T_ex is given by Q_rot. T_bg is the cosmic background temperature (2.7 K). For a further extension of our sample we also included in this study the pre-stellar core L1544 (Spezzano et al. 2013) as well as the Class 0 protostar IRAS16293-2422 (hereafter IRAS16293) (Caux et al. 2011). In Tables 3 and 4 we summarize the detected lines in every source and the line properties derived from Gaussian fits. The sources CB23, L1495AN, L1495B, Per5, HH211, L1448IRS2, IRAS03282, and IRAS16293 show differences in the linewidth between the main isotopologue and the isotopic variants ranging in the 0.1–0.5 km s⁻¹ interval. These differences do not exhibit any clear trend and are poorly constrained with errors varying from 36% to 94%. Such discrepancies are likely to be produced by the high noise levels of these latter observations and by the coarse sampling of the line profiles (channel spacing is 0.167 km s⁻¹).

Table 3. Observed Lines in the Starless Core Sample

Source/Molecule	Frequency	T_MB	rms	W	${v}_{\mathrm{LSR}}$	${\rm{\Delta }}v$
	(GHz)	(K)	(mK)	(K km s⁻¹)	(km s⁻¹)	(km s⁻¹)
CB23
c-C₃H₂	84.727	0.05	11	0.017 ± 0.004	6.018 ± 0.037	0.333 ± 0.088
c-C₃HD	104.187	0.23	9	0.056 ± 0.002	6.015 ± 0.005	0.229 ± 0.010
c-H¹³CC₂H	84.185	0.13	3	0.024 ± 0.001	5.987 ± 0.003	0.174 ± 0.017
c-C₃D₂	97.761	<0.02	7	<0.004

L1400A
c-C₃H₂	84.727	0.07	8	0.019 ± 0.002	3.355 ± 0.020	0.246 ± 0.030
c-C₃HD	104.187	0.13	8	0.036 ± 0.002	3.348 ± 0.008	0.263 ± 0.021
c-H¹³CC₂H	84.185	0.06	2	0.020 ± 0.001	3.287 ± 0.006	0.334 ± 0.014

L1400K
c-H¹³CC₂H	84.185	0.06	9	0.018 ± 0.002	3.178 ± 0.023	0.268 ± 0.048
c-C₃HD	104.187	<0.04	15	<0.01

L1495
c-C₃H₂	84.727	0.06	4	0.015 ± 0.001	6.779 ± 0.012	0.244 ± 0.035
c-C₃HD	104.187	0.13	10	0.038 ± 0.002	6.768 ± 0.010	0.269 ± 0.025
c-H¹³CC₂H	84.185	0.07	14	0.021 ± 0.005	6.726 ± 0.036	0.281 ± 0.088

L1495AN
c-C₃H₂	84.727	0.17	14	0.062 ± 0.006	7.259 ± 0.014	0.344 ± 0.039
c-C₃HD	104.187	0.43	22	0.138 ± 0.007	7.275 ± 0.007	0.304 ± 0.019
c-H¹³CC₂H	84.185	0.22	10	0.075 ± 0.004	7.261 ± 0.007	0.329 ± 0.019
c-C₃D₂	97.761	0.04	6	0.011 ± 0.001	7.208 ± 0.020	0.236 ± 0.044

L1495AS
c-C₃H₂	84.727	0.08	8	0.028 ± 0.004	7.302 ± 0.019	0.353 ± 0.046
c-C₃HD	104.187	0.15	9	0.046 ± 0.002	7.281 ± 0.008	0.280 ± 0.018
c-H¹³CC₂H	84.185	0.09	8	0.025 ± 0.002	7.229 ± 0.015	0.254 ± 0.022

L1495B
c-C₃H₂	84.727	0.04	8	0.020 ± 0.004	6.655 ± 0.038	0.460 ± 0.086
c-C₃HD	104.187	0.13	16	0.054 ± 0.006	6.635 ± 0.022	0.403 ± 0.048
c-H¹³CC₂H	84.185	0.06	7	0.018 ± 0.002	6.582 ± 0.020	0.300 ± 0.045

L1512
c-C₃HD	104.187	0.30	19	0.067 ± 0.005	7.095 ± 0.009	0.204 ± 0.015
c-H¹³CC₂H	84.185	0.15	8	0.033 ± 0.002	7.058 ± 0.012	0.211 ± 0.015
c-C₃D₂	97.761	0.03	3	0.008 ± 0.001	7.075 ± 0.017	0.293 ± 0.038

L1517B
c-C₃HD	104.187	0.30	14	0.068 ± 0.004	5.778 ± 0.007	0.249 ± 0.017
c-H¹³CC₂H	84.185	0.10	11	0.029 ± 0.004	5.751 ± 0.018	0.279 ± 0.031
c-C₃D₂	97.761	0.05	8	0.014 ± 0.002	5.777 ± 0.024	0.266 ± 0.054
c-C₃D₂	94.371	0.05	8	0.013 ± 0.002	5.854 ± 0.025	0.271 ± 0.053

TMC2
c-C₃H₂	84.727	0.16	18	0.061 ± 0.007	6.192 ± 0.020	0.365 ± 0.047
c-C₃HD	104.187	0.53	24	0.184 ± 0.007	6.217 ± 0.007	0.325 ± 0.016
c-H¹³CC₂H	84.185	0.16	9	0.065 ± 0.004	6.132 ± 0.010	0.374 ± 0.024
c-C₃D₂	97.761	0.10	4	0.030 ± 0.001	6.237 ± 0.005	0.283 ± 0.012
c-C₃D₂	94.371	0.05	5	0.018 ± 0.001	6.258 ± 0.014	0.330 ± 0.040
c-C₃D₂	108.654	0.03	7	0.012 ± 0.002	6.262 ± 0.036	0.355 ± 0.107

L1544^a
c-C₃H₂	84.727	0.21	10	0.10 ± 0.01	7.210 ± 0.008	0.46 ± 0.01
c-C₃HD	104.187	0.48	10	0.238 ± 0.004	7.181 ± 0.004	0.468 ± 0.009
c-C₃HD	95.994	0.13	10	0.065 ± 0.003	7.17 ± 0.01	0.48 ± 0.03
c-H¹³CC₂H	84.185	0.19	10	0.093 ± 0.003	7.154 ± 0.008	0.44 ± 0.02
c-C₃D₂	97.761	0.13	5	0.059 ± 0.002	7.181 ± 0.007	0.43 ± 0.02
c-C₃D₂	94.371	0.07	5	0.032 ± 0.002	7.20 ± 0.01	0.45 ± 0.03
c-C₃D₂	108.654	0.04	5	0.023 ± 0.002	7.17 ± 0.02	0.54 ± 0.05

Note. The line properties are derived from Gaussian fits.

^aThe values for L1544 were taken from Spezzano et al. (2013).

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Table 4. Observed Lines in the Protostellar Core Sample

Source/Molecule	Frequency	T_MB	rms	W	${v}_{\mathrm{LSR}}$	${\rm{\Delta }}v$
	(GHz)	(K)	(mK)	(K km s⁻¹)	(km s⁻¹)	(km s⁻¹)
Per5
c-C₃H₂	84.727	0.09	9	0.050 ± 0.004	8.102 ± 0.021	0.529 ± 0.051
c-C₃HD	104.187	0.27	21	0.116 ± 0.007	8.174 ± 0.013	0.401 ± 0.032
c-H¹³CC₂H	84.185	0.09	6	0.035 ± 0.002	8.171 ± 0.012	0.362 ± 0.026
c-C₃D₂	97.761	0.09	11	0.029 ± 0.004	8.215 ± 0.021	0.318 ± 0.050

HH211
c-C₃H₂	84.727	0.10	7	0.051 ± 0.002	9.089 ± 0.013	0.461 ± 0.029
c-C₃HD	104.187	0.35	14	0.163 ± 0.005	9.097 ± 0.007	0.432 ± 0.018
c-H¹³CC₂H	84.185	0.05	5	0.022 ± 0.002	9.100 ± 0.019	0.403 ± 0.045
c-C₃D₂	97.761	0.10	7	0.037 ± 0.002	9.102 ± 0.012	0.361 ± 0.032

L1448IRS2
c-C₃HD	104.187	0.20	13	0.105 ± 0.005	4.084 ± 0.011	0.479 ± 0.027
c-H¹³CC₂H	84.185	0.05	6	0.037 ± 0.004	3.977 ± 0.032	0.690 ± 0.082

IRAS03282
c-C₃H₂	84.727	0.02	5	0.020 ± 0.002	7.002 ± 0.062	0.933 ± 0.155
c-C₃HD	104.187	0.12	9	0.064 ± 0.004	6.863 ± 0.015	0.517 ± 0.034
c-H¹³CC₂H	84.185	0.03	5	0.013 ± 0.002	6.812 ± 0.035	0.414 ± 0.072

L1521F
c-C₃H₂	84.727	0.22	6	0.086 ± 0.002	6.407 ± 0.005	0.366 ± 0.010
c-C₃HD	104.187	0.33	17	0.144 ± 0.006	6.433 ± 0.009	0.410 ± 0.018
c-H¹³CC₂H	84.185	0.18	12	0.077 ± 0.005	6.365 ± 0.013	0.404 ± 0.028
c-C₃D₂	97.761	0.05	6	0.018 ± 0.002	6.477 ± 0.020	0.360 ± 0.063

IRAS16293
c-C₃H₂	84.727	0.09	3	0.183 ± 0.006	4.303 ± 0.034	2.011 ± 0.077
c-C₃HD	104.187	0.17	6	0.280 ± 0.012	4.235 ± 0.031	1.573 ± 0.080
c-C₃HD	95.994	0.03	2	0.053 ± 0.004	4.026 ± 0.059	1.914 ± 0.147
c-H¹³CC₂H	84.185	0.03	3	0.089 ± 0.008	3.889 ± 0.108	2.394 ± 0.237
c-C₃D₂	94.371	0.03	4	0.059 ± 0.010	4.342 ± 0.158	1.952 ± 0.375
c-C₃D₂	97.761	0.03	3	0.049 ± 0.006	4.281 ± 0.097	1.516 ± 0.196

Note. The line properties are derived from Gaussian fits.

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For the calculation of the total column densities of c-C₃H₂ and its isotopologues we assumed the same excitation temperature T_ex that was used in the same sources by Crapsi et al. (2005) and Emprechtinger et al. (2009) for N₂H⁺.² We also used the same excitation temperature for the deuterated and the ¹³C species. The effect of underestimating the excitation temperature of the main and the deuterated species by 1 K changes the deuteration level N(c-C₃HD)/N(c-C₃H₂) by up to 30%. In the case of L1544 we used the T_ex derived in Gerin et al. (1987), where detections of c-C₃H₂ and its deuterated counterpart are reported. In particular, there were three transitions of c-C₃HD at 19.419, 79.812, and 104.187 GHz detected in L1544, which gave a T_ex of 5 ± 2 K. An optically thick transition of c-C₃H₂ detected at 85.339 GHz provided a T_ex of 6 K. This excitation temperature is, within the errors, equal to that found in N₂H⁺(1–0) and N₂D⁺(2–1) toward the same source (Crapsi et al. 2005). Due to the large error of T_ex for c-C₃HD, we used for the main and the deuterated species a T_ex of 6 K.

Since c-H¹³CC₂H was detected in every source, we used the total column density of c-H¹³CC₂H to derive N(c-C₃H₂) by considering a ¹²C/¹³C ratio of 77 (Wilson & Rood 1994). This gave us the additional advantage of avoiding ambiguities due to the optical depth of the main species. The carbon isotope ratio was determined in several sources, from different molecular species and can vary up to a factor of 2 (Wilson & Rood 1994). This means that the derived N(c-C₃H₂) suffers from an uncertainty of a factor of 2. The assumed ortho-to-para ratio of c-C₃H₂ and c-C₃D₂ is 3 and 2, respectively. Tables 5 and 6 show the derived column densities for every species in each starless core and protostar, respectively. The error for the column densities was calculated by propagating the uncertainty on the integrated intensity, W, including the 1σ statistical error as well as 10% calibration uncertainty. The column densities for the singly and doubly deuterated species were calculated from the c-C₃HD (3_0,3 − 2_1,2) and c-C₃D₂ (3_1,3 − 2_0,2) transitions.

Table 5. Column Densities of the Species c-C₃H₂, c-C₃HD, c-C₃D₂ and c-H¹³CC₂H in the 11 Starless Cores within the Taurus Molecular Cloud Complex

Starless Core	N(c-C₃H₂)	N (c-C₃HD)	N(c-H¹³CC₂H)	N(c-C₃D₂)
	(10¹² cm⁻²)	(10¹² cm⁻²)	(10¹² cm⁻²)	(10¹² cm⁻²)
CB23	10.9 ± 1.2	1.15 ± 0.13	0.28 ± 0.03	<0.07
L1400A	9.1 ± 1.1	0.74 ± 0.09	0.24 ± 0.03	^a
L1400K	8.0 ± 1.3	<0.26	0.21 ± 0.03	^a
L1495	8.6 ± 2.1	0.66 ± 0.08	0.22 ± 0.06	^a
L1495AN	31.7 ± 3.5	2.50 ± 0.28	0.82 ± 0.09	0.13 ± 0.02
L1495AS	11.4 ± 1.6	0.94 ± 0.11	0.30 ± 0.04	^a
L1495B	7.5 ± 1.2	0.94 ± 0.14	0.20 ± 0.03	^a
L1512	13.2 ± 1.6	1.09 ± 0.13	0.34 ± 0.04	0.08 ± 0.02
L1517B	12.2 ± 1.9	1.23 ± 0.14	0.32 ± 0.05	0.16 ± 0.03
TMC2	25.9 ± 2.9	2.94 ± 0.32	0.67 ± 0.08	0.31 ± 0.03
L1544	34.9 ± 3.7	3.18 ± 0.32	0.91 ± 0.10	0.53 ± 0.06

Note.

^aNo data available.

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Table 6. Column Densities of the Species c-C₃H₂, c-C₃HD, c-C₃D₂ and c-H¹³CC₂H in the Six Protostars

Protostellar	N(c-C₃H₂)	N(c-C₃HD)	N(c-H¹³CC₂H)	N(c-C₃D₂)
Core	(10¹² cm⁻²)	(10¹² cm⁻²)	(10¹² cm⁻²)	(10¹² cm⁻²)
Per5	14.2 ± 1.7	1.4 ± 0.16	0.37 ± 0.04	0.24 ± 0.04
HH211	8.5 ± 1.2	1.9 ± 0.20	0.22 ± 0.03	0.30 ± 0.04
L1448IRS2	13.9 ± 1.9	1.3 ± 0.14	0.36 ± 0.05	^a
IRAS03282	5.1 ± 1.1	0.7 ± 0.09	0.13 ± 0.03	^a
IRAS16293	36.4 ± 5.0	3.6 ± 0.39	0.95 ± 0.13	0.43 ± 0.07
L1521F	31.5 ± 3.7	2.4 ± 0.26	0.82 ± 0.10	0.20 ± 0.03

Notes. The protostars Per 5, HH211, L1448IRS2 and IRAS03282 belong to the Perseus complex, L1521F lies in the Taurus complex, and IRAS16293 is part of the Ophiuchus complex.

^aNo data available.

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Figure 1 shows the deuterium fraction for each species in every starless core. Here one can clearly see that the deuteration for both c-C₃H₂ and N₂H⁺ follows a similar trend and is of the same magnitude, except for the most dynamically evolved object, the pre-stellar core L1544. The deuteration of c-C₃H₂ is in all sources within the 1σ uncertainty consistent with 10%, except for L1400K where the c-C₃HD column density was estimated to be less than 0.26 × 10¹² cm⁻², which resulted in a 3σ upper limit for the N(c-C₃HD)/N(c-C₃H₂) ratio of 0.03. All these sources except for TMC2 and L1544 have been identified by Crapsi et al. (2005) as less evolved starless cores having, among other properties, a deuteration degree ≤0.1 which is also in our case fulfilled (in the source L1495B the deuterium fraction can still be within errors less than or equal to 0.1). L1544 is the only source where the deuteration of N₂H⁺ is larger than that of c-C₃H₂, showing a significant discrepancy of a factor of 2.6. One possible explanation for this can be found in the formation route of N₂H⁺. The progenitor of N₂H⁺ is N₂ which is formed via neutral–neutral reactions: N + C → CN and CN + N → N₂ (Pineau des Forets et al. 1990; Le Gal et al. 2014). Carbon-bearing molecules like c-C₃H₂ on the other hand are formed faster through sequential ion–neutral reactions. For this reason, N₂H⁺ is believed to be a late-type molecule, becoming highly abundant in evolved cores, such as L1544. Furthermore, N₂H⁺ is more resistant to depletion and survives in the gas phase longer than C-bearing molecules, thus tracing regions where the deuterium fractionation is more efficient because of the large amount of freeze-out of neutral species (such as CO and O) which participate in the destruction of the ${{\rm{H}}}_{3}^{+}$ deuterated isotopologues (Dalgarno & Lepp 1984).

The abundance of the doubly deuterated species with respect to the normal species is 0.4%–1.5%. These values are comparable to those calculated by Spezzano et al. (2013) in TMC-1C and L1544. The ratios N(c-C₃HD)/N(c-C₃H₂) and N(c-C₃D₂)/N(c-C₃HD) are quite similar in all starless and pre-stellar cores. This suggests that c-C₃H₂ and c-C₃HD follow the same deuteration route and are not affected by the dynamical evolution of the dense core, as already pointed out in Spezzano et al. (2013). In the source CB23 we find a marginal detection of c-C₃D₂ and therefore derive a 3σ upper limit for the column density. The abundance ratios N(c-C₃HD)/N(c-C₃H₂), N(c-C₃D₂)/N(c-C₃H₂) and N(c-C₃D₂)/N(c-C₃HD) among the starless core sample are listed in Table 7.

Table 7. Column Density Ratios of the Deuterated Species c-C₃HD, c-C₃D₂ with Respect to the Main Species in the Starless Core Sample

Starless Core	N(c-C₃HD)/N(c-C₃H₂)	N(c-C₃D₂)/N(c-C₃H₂)	N(c-C₃D₂)/N(c-C₃HD)
CB23	0.11 ± 0.02	<0.006	<0.06
L1400A	0.08 ± 0.02	^a	^a
L1400K	<0.03	^a	^a
L1495	0.08 ± 0.03	^a	^a
L1495AN	0.08 ± 0.02	0.004 ± 0.001	0.05 ± 0.01
L1495AS	0.08 ± 0.02	^a	^a
L1495B	0.13 ± 0.04	^a	^a
L1512	0.08 ± 0.02	0.006 ± 0.002	0.08 ± 0.02
L1517B	0.10 ± 0.03	0.013 ± 0.005	0.13 ± 0.04
TMC2	0.11 ± 0.03	0.012 ± 0.003	0.10 ± 0.02
L1544	0.09 ± 0.02	0.015 ± 0.003	0.17 ± 0.03

Note.

^aNo data available.

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Also in the observed protostars the deuteration for both species is similar, as we can clearly see in Figure 2. The deuterium fraction peaks in HH211, reaching 23% in case of c-C₃H₂ and 27% in case of N₂H⁺ which is also the highest estimated deuteration among all observed protostellar and starless cores. The abundance ratio N(c-C₃HD)/N(c-C₃H₂) is within the error bars equal to 10%, with the exception of HH211, where the average deuteration level is 0.23 ± 0.06. These results are similar to the N(c-C₃D₂)/N(c-C₃HD) ratio, which ranges from 5% to 17%. Finally, the abundance of the doubly deuterated species with respect to the main isotopologue varies between 0.6% and 3.6%. The single and double deuteration level of c-C₃H₂ in every protostellar core is summarized in Table 8.

Table 8. Column Density Ratios of the Deuterated Species c-C₃HD, c-C₃D₂ with Respect to the Main Species in the Protostellar Core Sample

Protostellar Core	N(c-C₃HD)/N(c-C₃H₂)	N(c-C₃D₂)/N(c-C₃H₂)	N(c-C₃D₂)/N(c-C₃HD)
Per5	0.10 ± 0.02	0.017 ± 0.005	0.18 ± 0.05
HH211	0.23 ± 0.06	0.036 ± 0.009	0.16 ± 0.04
L1448IRS2	0.09 ± 0.02	^a	^a
IRAS03282	0.14 ± 0.05	^a	^a
IRAS16293	0.10 ± 0.02	0.012 ± 0.003	0.12 ± 0.03
L1521F	0.08 ± 0.02	0.006 ± 0.002	0.08 ± 0.02

Note.

^aNo data available.

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In case of IRAS16293, we derived the deuteration of c-C₃H₂ and its isotopologues, as well as the depletion factor of CO using the publicly available data from TIMASSS (Caux et al. 2011). For the calculation of the c-C₃H₂ column density and its isotopologues, we assumed a T_ex of 8.9 K for the main and the ¹³C species, and a T_ex of 6.3 K for the deuterated counterparts, as was derived in Majumdar et al. (2017). The N(c-C₃HD)/N(c-C₃H₂) ratio in IRAS16293 calculated in this work is 0.10 ± 0.02. This is comparable to the deuteration of 14% determined in Majumdar et al. (2017) within the uncertainties.

3.2. Correlation between Deuteration and CO Depletion Factor

In a cold and dense cloud, molecules in the gas phase tend to collide and freeze-out onto dust grains, leading to a gradual decrease of their gas-phase abundance. Molecules are bound on grains through van der Waals forces (Garrod et al. 2007), meaning that species with a non-zero dipole moment, such as CS and CO, will be strongly bound on grain surfaces at the low temperatures typical of starless cores; thus, they deplete from the gas phase by significant amounts. Deuteration is expected to correlate with the CO depletion factor, since CO destroys H₂D⁺ (Dalgarno & Lepp 1984). Previous studies have proven that the deuterium fraction of N₂H⁺ correlates strongly with the degree of CO depletion (Caselli et al. 2002; Crapsi et al. 2005; Emprechtinger et al. 2009). The level of depletion is usually expressed as the depletion factor f_d and is given by:

$\begin{eqnarray}&&{f}_{d}(\mathrm{CO})=\displaystyle \frac{{X}_{\mathrm{ref}}(\mathrm{CO})}{X(\mathrm{CO})},\end{eqnarray} \tag{ 3 }$

where X_ref(CO) is the reference abundance of CO in the local ISM and X(CO) is the observed CO abundance (e.g., Emprechtinger et al. 2009).

Figure 3 shows the N(c-C₃HD)/N(c-C₃H₂) and the N(N₂D⁺)/N(N₂H⁺) ratio versus the CO depletion factor for the starless core sample. The depletion factors for L1544, TMC2, L1495, and L1517B were taken from Crapsi et al. (2005). To search for a statistical correlation between N(c-C₃HD)/N(c-C₃H₂) and f_d(CO) we applied the Kendall's τ and Spearman's ρ rank correlation tests. The Kendall's test gives τ = 0.33 with a significance p of 0.49 and the Spearman's test gives ρ = 0.40 with p = 0.60, indicating that there is no correlation between the c-C₃H₂ deuteration and the CO depletion factor within the starless core sample. In case of the N₂H⁺ deuteration, however, we note a significant jump toward the pre-stellar core L1544. As already mentioned, this indicates that N₂H⁺ is less affected by depletion than c-C₃H₂ and traces the deuteration level in the highest-density regions of the core; in fact the N₂H⁺ abundance also increases where CO is significantly frozen, as CO destroys N₂H⁺ to form HCO⁺.

The correlation between N(c-C₃HD)/N(c-C₃H₂) and the CO depletion factor in the observed protostars is shown in Figure 4. The depletion factors for the sources HH211, IRAS03282, L1448IRS2, and Per5 were taken from Emprechtinger et al. (2009), while the depletion factor for L1521F was reported in Crapsi et al. (2005). For the CO depletion level in IRAS16293 we used the spectral properties of the C¹⁸O (1–0) transition given in Caux et al. (2011) to calculate the column density of C¹⁸O, as was done in Emprechtinger et al. (2009). Here we use X_ref(C¹⁶O) = 9.5 × 10⁻⁵ (Frerking et al. 1982) to allow a fair comparison with Emprechtinger et al. (2009), although other values for X_ref(C¹⁶O) can be found in the literature (Wannier 1980; Lacy et al. 1994). We use the relation X(C¹⁶O)/X(C¹⁸O) = 560 (Wilson & Rood 1994) such that:

$\begin{eqnarray}&&X({{\rm{C}}}^{16}{\rm{O}})=\displaystyle \frac{{N}_{\mathrm{tot}}({{\rm{C}}}^{18}{\rm{O}})\cdot 560}{N({{\rm{H}}}_{2})}.\end{eqnarray} \tag{ 4 }$

**Figure 4.** Deuterium fraction of c-C₃H₂ and N₂H⁺ as a function of CO depletion factor for the protostellar core sample. The deuterium fraction of N₂H⁺ and the CO depletion factors were taken from Emprechtinger et al. (2009), while the N(N₂D⁺)/N(N₂H⁺) ratio and f_d(CO) for L1521F was given in Crapsi et al. (2005).
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The excitation temperature of C¹⁸O was set equal to 43 K which is the dust temperature for IRAS16293 (Schöier et al. 2002). At this temperature no CO depletion is expected. However, the C¹⁸O column density is an average along the line of sight which, apart from the warm central regions, also includes the cold envelope, where CO can be significantly frozen (e.g., Brünken et al. 2014). The hydrogen column density N(H₂) was derived using the Herschel/SPIRE image of IRAS16293 at 250, 350, and 500 μm. These data are publicly available and can be downloaded from the Herschel Science Archive.³ For more information concerning the data reduction, see Section 3.3. The resulting N(H₂) of 1.0 × 10²³ cm⁻² is the mean value of column densities within a beam of 40''. Following Equation (3), the depletion factor for IRAS16293 is equal to

$\begin{eqnarray}&&{f}_{d}(\mathrm{CO})=0.7\pm 0.2.\end{eqnarray} \tag{ 5 }$

This value is consistent with the low ${f}_{d}(\mathrm{CO})$ values measured by Punanova et al. (2016) in various sources toward ρ Ophiuchus. The fact that f_d(CO) is lower than 1 suggests that the adopted X_ref(C¹⁶O) is underestimated by a factor of 2–3. Moreover, one has to keep in mind that the C¹⁸O (1–0) emission was observed within 22'', while the estimation of N(H₂) was done within a 40'' beam. This indicates that the derived depletion factor should be considered as a lower limit.

Figure 4 shows no clear trend between the deuteration of c-C₃H₂ and the CO depletion among the protostellar cores. This is also confirmed by the Kendall's rank test that gives τ = 0.32 with a significance p of 0.45 as well as by the Spearman's rank test that results in ρ = 0.56 with p = 0.32 (without considering the protostar L1521F). The source L1521F deviates strongly from the rest of the sources, having a significant depletion factor of 15 and simultaneously showing a low c-C₃H₂ deuteration of 8%. These values are comparable to those found in L1544, where the CO depletion factor is 14 (Crapsi et al. 2005) and the deuteration of c-C₃H₂ is 9%. The peculiarity of L1521F has been proven already in previous works, where the central column density N(H₂) is high (13.5 × 10²² cm⁻²) despite the low N₂H⁺ deuteration (being a factor of 2 lower than in L1544; Crapsi et al. 2004, 2005).

The large CO depletion factor and low deuteration both in N₂H⁺ and c-C₃H₂ in L1521F could be a signature of episodic accretion of the central protostar. Since L1521F has been classified as a VeLLO (Bourke et al. 2006; Takahashi et al. 2013) it may be in a quiescent phase, following an accretion burst event. During such a burst, CO is expected to return in the gas phase (Visser et al. 2015), thus reducing the deuterium fraction. After the burst, the fast cooling of the dust could quickly lead to CO freeze-out, with short timescales of the order of 10⁹/n_H yr, where n_H is the total number density of hydrogen nuclei (e.g., Caselli et al. 1999), while the deuteration of gas-phase molecules is a slower process, especially if during the burst the ortho-to-para-H₂ ratio (sensitive to the temperature) increases to values larger than 1% (e.g., Flower et al. 2006; Kong et al. 2015). However, the exact physical and chemical conditons of L1521F are beyond the scope of this work and it is clear that further observations are needed to prove this point.

3.3. Correlation between Deuteration and H₂ Column Density

As already pointed out in Section 3.2, an increase in volume density toward the core center is expected to correlate with an increase in deuteration, because of the consequently larger CO freeze-out rates, as long as the temperature remains below 20 K. For this reason we examine how the estimated deuteration of c-C₃H₂ in the starless and the pre-stellar cores correlates with the central column density of molecular hydrogen. For the N(H₂) calculation we use the Herschel/SPIRE image of the Taurus complex at 250, 350, and 500 μm, taken during the Herschel Gould Belt Survey (André et al. 2010).

A modified blackbody radiation is fitted to each pixel, using an emissivity spectral index β = 1.5 and a dust emissivity coefficient κ_250μm = 0.1 g⁻¹ cm² (Hildebrand 1983). The data reduction involves smoothing the 250 μm and 350 μm images to the resolution of the 500 μm image and resampling all images to the same grid. From this fitting procedure we obtain the central column density N(H₂) as well as the dust temperature T_Dust for every pixel. The resulting N(H₂) is the mean value of column densities in a 40'' beam. For the error estimation we take into account calibration uncertainties of 7% according to the SPIRE manual (see Appendix C). In Table 9 we summarize the resulting column densities and their uncertainties. The estimated N(H₂) values are up to a factor of 3 smaller than those calculated in Crapsi et al. (2005) at the 1.2 mm dust continuum peak. This results from the different beam sizes used, 40'' versus 11'', so that the highest-density parts of the central cores (such as L1544, with central densities of ∼10⁶ cm⁻³ within a 1000 au in radius; see Keto & Caselli 2010) are diluted within the Herschel beam.

Table 9. N(H₂) Values for the Starless Core Sample, Derived from the Herschel/SPIRE Images, within a 40'' Beam (This Work), as Well as Those Derived from the 1.2 mm Continuum Emission within a 11'' Beam (Crapsi et al. 2005)

Starless Core	N(H₂)^a	N(H₂)^b
	(10²¹ cm⁻²)	(10²¹ cm⁻²)
L1495	8.3 ± 1.6	31 ± 10
L1495B	10.1 ± 2.0	⋯
L1495AN	15.1 ± 2.7	⋯
L1495AS	22.1 ± 4.1	⋯
TMC2	18.9 ± 3.3	60 ± 12
L1544	27.9 ± 5.1	94 ± 16
L1512	8.6 ± 1.6	⋯
L1517B	11.5 ± 2.3	37 ± 10
CB23	8.5 ± 1.6	⋯

Notes.

^aThis work. ^bCrapsi et al. (2005).

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Figure 5 shows the correlation between N(c-C₃HD)/N(c-C₃H₂) and N(H₂) for the starless core sample. We also included the N(N₂D⁺)/N(N₂H⁺) ratio, calculated in Crapsi et al. (2005) for a direct comparison. The cores L1400K and L1400A were not part of this study, since there were no SPIRE images of these sources available.

No correlation is found between the deuteration level of both species and N(H₂) among the starless cores. However, in L1544, we recognize a substantial increase in the deuteration of N₂H⁺, as was already visible in Figure 1. In Crapsi et al. (2005) there are three additional evolved pre-stellar cores (L183, L429, and L694-2), that show enhanced N₂H⁺ deuteration with increasing N(H₂). This indicates that N₂H⁺ is indeed a late-type molecule and stays in the gas phase at high densities, while c-C₃H₂ is possibly depleted in the central regions, thus it stops tracing the central zone of the core where high levels of deuterium fractions are present. This is in agreement with our current understanding of the chemistry of c-C₃H₂, and its distribution across the pre-stellar core L1544 (Sipilä et al. 2016, see in Appendix B).

Another way of testing this theory is to examine parameters that are related to the kinematics of the gas, such as the width of the detected lines. Figure 6 shows the correlation between the observed linewidth, ${\rm{\Delta }}{v}_{\mathrm{obs}}$ , of c-C₃H₂ (3_2,2 − 3_1,3) and of N₂H⁺ (1–0) among the starless and protostellar core sample. Thermal, turbulent, and systematic motions contribute to the total ${\rm{\Delta }}{v}_{\mathrm{obs}}$ . Thermal broadening does not play a substantial role, since the thermal linewidth of c-C₃H₂ is just 0.11 km s⁻¹ at 10 K (and 0.13 km s⁻¹ for N₂H⁺). As we can clearly see in Figure 6, the observed c-C₃H₂ line has a larger width in most of the cores (except for L1495 and L1495AN, where the observed linewidths are approximately the same).

**Figure 6.** Observed linewidth of N₂H⁺ (Crapsi et al. 2005; Emprechtinger et al. 2009) compared to that of c-C₃H₂ (this work) in the starless and protostellar core sample. The dashed line represents the 1:1 ratio.
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This suggests that c-C₃H₂ traces a different region than N₂H⁺, where turbulent or systematic (i.e., rotation, infall, or outflows in protostellar objects) motion dominates. In both starless and protostellar core samples we see the same trend by studying the linewidth of c-H¹³CC₂H (2_1,2 − 1_0,1) instead, suggesting that the optical depth broadening of c-C₃H₂ (3_2,2 − 3_1,3) is negligible.

3.4. Correlation between Deuteration and Dust Temperature

During the protostellar phase, the core starts to warm up the surrounding material, leading to desorption of CO from dust grains. Moreover, the energetic ouflows by protostars can also contribute to the release of CO molecules in the gas phase via sputtering or grain–grain collisions (e.g., Caselli et al. 1997; Jiménez-Serra et al. 2008). Back in the gas phase, CO can react and destroy H₂D⁺, reducing the total deuteration in molecules. In addition, Reaction (1) can proceed at high temperatures also in the backward direction, leading to a further reduction of H₂D⁺. Therefore, one expects an anticorrelation between the deuteration and the dust temperature (e.g., Ladd et al. 1991; Myers & Ladd 1993) of a protostar, as has already been confirmed (Emprechtinger et al. 2009; Fontani et al. 2011). In Figure 7 we plot the deuterium fraction of c-C₃H₂ against T_Dust in the protostellar core sample. The values for T_Dust were taken from Emprechtinger et al. (2009). As in Section 3.2, here we also include the protostar IRAS16293 (Schöier et al. 2002). Figure 7 shows a clear anticorrelation between deuteration and T_Dust, when excluding L1521F, that has a Kendall's τ coefficient of −0.74 with a significance p of 0.08 and a Spearman's ρ coefficient of −0.82 with a significance p of 0.09. The abundance ratio N(c-C₃HD)/N(c-C₃H₂) peaks in the coldest source, HH211 at 23%, and decreases toward the warmer sources down to 8%.

**Figure 7.** Deuterium fraction of c-C₃H₂ as a function of dust temperature T_Dust in the protostellar core sample, including the VeLLO L1521F.
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The young source HH211 could be an example of a protostar where the accretion burst has recently occurred and/or where ices have been recently evaporated. If this is the case, one way to interpret the large deuteration of c-C₃H₂ is the release of a large amount of deuterated (and non-deuterated) c-C₃H₂ from the ices into the gas phase. Furthermore, this could imply significant deuteration of c-C₃H₂ on the surface of dust grains, maybe due to hydrogen–deuterium exchange reactions known to occur for other molecules, such as CH₃OH during the preceding cold pre-stellar phase (e.g., Parise et al. 2006).⁴

The result for L1521F deviates considerably from the rest of the sources. The dust temperature for L1521F (T_Dust = 9 ± 2 K) was taken from Kirk et al. (2005). As already highlighted in Section 3.2, L1521F hosts a VeLLO which could be a protostar in the very early stages of evolution and/or an example of low activity in protostellar evolution characterized by episodic accretion. This could explain the mismatch between the physical (low T_Dust) and chemical conditions (low deuteration).

4. Conclusion

In this work we presented single-pointing observations of c-C₃H₂, the singly and doubly deuterated species, c-C₃HD and c-C₃D₂, as well as the isotopologue c-H¹³CC₂H toward 10 starless cores and five protostellar cores in the Taurus and Perseus complexes. The pre-stellar core L1544 and the protostellar core IRAS16293 were also included in our study. We calculated the deuterium fractionation N(c-C₃HD)/N(c-C₃H₂) and studied its correlation with the CO depletion factor, the dust temperature, and the H₂ column density toward the core center. We also examined the differences between the deuteration of C- and N-bearing molecules. Here is a summary of our main conclusions.

1.
The ratio N(c-C₃HD)/N(c-C₃H₂) is, within the error bars, equal to 10% in all starless and pre-stellar cores where c-C₃HD has been detected. This also accounts for the protostars except for the source HH211 where we measure a high deuteration level of (23 ± 6)%. The N(c-C₃D₂)/N(c-C₃H₂) ratio ranges from 0.4 to 1.5% in starless and pre-stellar cores, and from 0.6 to 3.6% among the protostellar cores. The deuteration of c-C₃H₂ and N₂H⁺ follows the same trend in both samples. However, in case of the evolved pre-stellar core L1544, the deuteration of N₂H⁺ is significantly higher (factor of 2.6) compared to the N(c-C₃HD)/N(c-C₃H₂) ratio. This can be understood by the well-known fact that N₂H⁺ remains in the gas phase even at densities of about 10⁶ cm⁻³, where the C-bearing molecules (including c-C₃H₂ and its deuterated forms) are highly frozen and where deuterium fractionation proceeds rapidly, thanks to the large abundances of the deuterated ${{\rm{H}}}_{3}^{+}$ isotopologues.
2.
Among the starless cores, we find no correlation between the deuteration of c-C₃H₂ and the CO depletion factor or the central H₂ column density (measured with Herschel). However, the N₂H⁺ deuteration substantially increases toward L1544, which is the most evolved source within the starless core sample. This indicates that N₂H⁺ traces the central dense core, unlike c-C₃H₂, which is more likely tracing an outer shell surrounding the dense region of the pre-stellar core. This theory is also favored by the fact that the observed linewidth of the c-C₃H₂ emission is larger than that of the N₂H⁺ emission among the starless and the protostellar cores. As a consequence, the information resulting from observing c-C₃H₂ and N₂H⁺ is complementary because it brings insights on different regions of the core.
3.
Among the protostellar cores, there is a tight anticorrelation between the deuteration of c-C₃H₂ and the dust temperature (τ = −0.74 and ρ = −0.82), with the exception of L1521F. The N(c-C₃HD)/N(c-C₃H₂) ratio drops with increasing T_Dust, reaching the maximum value of 0.23 in the coolest source, HH211 (T_Dust < 21 K), and decreasing toward the warmest sources, down to a deuteration level of 0.08. The c-C₃H₂ deuteration does not correlate with the CO depletion factor within the protostellar core sample. L1521F differs substantially from the rest of the sources showing, in both species, c-C₃H₂ and N₂H⁺, a low deuteration and at the same time a high depletion factor of 15 (see the comment below for explanation).
4.
The high c-C₃H₂ deuteration of the youngest source, HH211, might be the result of a recent evaporation of c-C₃H₂ and c-C₃HD coming from a recent accretion burst. The timescale must be short enough to avoid the enhanced abundance of CO in the gas phase to significantly alter the c-C₃H₂ abundance and deuterium fraction. As similarly large values are not seen in the pre-stellar phase, deuteration processes taking place also on dust grains would be a possible scenario for the observed high deuteration of c-C₃H₂ in this young protostar.
5.
The source L1521F shows a peculiar behavior, having a low deuteration of 0.08 in spite of a significant CO depletion factor (f_d(CO) = 15 ± 3.6) and a low dust temperature (T_Dust = 9 ± 2 K). The peculiarity of this source has been highlighted in other studies as well (Crapsi et al. 2005, 2004). L1521F could be an episodically accreting low-mass protostar in a quiescent phase (Bourke et al. 2006; Takahashi et al. 2013). The fact that it shows a low deuteration and dust temperature, while having a high CO depletion, might imply that after a recent burst, which heated dust and gas, the ortho-to-para-H₂ ratio possibly increased, thus slowing down the deuteration process in the now cold envelope.

We thank the anonymous referee for his/her comments that significantly improved the present work. S. S. acknowledges the financial support of the Minerva Fast Track fellowship of the Max Planck Gesellschaft.

Appendix A: Observed Spectra of c-C₃H₂ and Its Isotopologues toward the Starless and Protostellar Core Samples

In Figures 8–23 we show the observed spectra toward all sources.

**Figure 8.** Spectra of several isotopologues of c-C₃H₂ toward the protostellar core HH211. The red line plots the CLASS Gaussian fit.
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**Figure 9.** Spectra of the isotopologues of c-C₃H₂ observed toward the protostellar core IRAS03282. The red line plots the CLASS Gaussian fit.
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**Figure 10.** Spectra of the isotopologues of c-C₃H₂ observed toward the protostellar core L1448IRS2. The red line plots the CLASS Gaussian fit.
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**Figure 11.** Spectra of the isotopologues of c-C₃H₂ observed toward the protostellar core L1521F. The red line plots the CLASS Gaussian fit.
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**Figure 12.** Spectra of the isotopologues of c-C₃H₂ observed toward the protostellar core IRAS16293. The red line plots the CLASS Gaussian fit.
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**Figure 13.** Spectra of the isotopologues of c-C₃H₂ observed toward the protostellar core Per5. The red line plots the CLASS Gaussian fit.
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**Figure 14.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core CB23. The red line plots the CLASS Gaussian fit.
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**Figure 15.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core L1400A. The red line plots the CLASS Gaussian fit.
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**Figure 16.** Spectrum of the main species c-C₃H₂ observed toward the starless core L1400K. The red line plots the CLASS Gaussian fit.
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**Figure 17.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core L1495. The red line plots the CLASS Gaussian fit.
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**Figure 18.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core L1495AN. The red line plots the CLASS Gaussian fit.
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**Figure 19.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core L1495AS. The red line plots the CLASS Gaussian fit.
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**Figure 20.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core L1495B. The red line plots the CLASS Gaussian fit.
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**Figure 21.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core L1512. The red line plots the CLASS Gaussian fit.
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**Figure 22.** Spectra of the isotopologues of c-C₃H₂ observed toward the starless core L1517B. The red line plots the CLASS Gaussian fit.
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**Figure 23.** Spectra of the isotopologues of c-C₃H₂ observed toward the pre-stellar core TMC2. The red line plots the CLASS Gaussian fit.
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Appendix B: The c-C₃H₂ and c-C₃HD Distribution across the Pre-stellar Core L1544

We use the chemical/physical model for L1544 described in Sipilä et al. (2016) to simulate the abundances of gaseous and solid c-C₃H₂, c-C₃HD and the ratio c-C₃HD/c-C₃H₂ as functions of distance from the core center, defined by the position of the millimeter dust continuum peak. Figure 24 shows the abundances of the gaseous and solid species as well as the deuteration level c-C₃HD/c-C₃H₂ at three different times: 10⁴, 10⁵, and 10⁶ yr. The depletion of c-C₃H₂ and c-C₃HD toward the center increases with the evolution of the core, as expected. At t = 10⁶ yr the depletion zone of both species reaches a few 1000 au. Here we confirm the fact that c-C₃H₂ and its deuterated counterpart stop tracing the zone where high levels of deuterium fraction are present, as already suggested in Section 3.2. The right panel of Figure 24 shows that the total deuteration level of gaseous and solid c-C₃H₂ is less than 20% at t = 10⁶ yr. This means that one of the most advanced gas–grain chemical codes including deuterium fractionation is not able to reproduce the large deuterium fraction of 23% observed in c-C₃H₂ toward the young protostar HH211 (which represents the next evolutionary state after the evolved pre-stellar core L1544), suggesting either that some important surface processes are missing in the current chemical scheme, or that the relative rates of the currently included processes need to be modified.

**Figure 24.** Abundance profiles of gaseous and solid c-C₃H₂ (red), c-C₃HD (blue), and the ratio c-C₃HD/c-C₃H₂ toward L1544, as functions of distance, from the core center to a radius of 10⁴ au. The solid species are marked with an asterisk. The abundances and abundance ratios are plotted at three different times: 10⁴, 10⁵, and 10⁶ yr.
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Appendix C: Error Estimation of the H₂ Column Density

One source of uncertainty in the estimation of N(H₂), which is derived from the SPIRE images at (250, 350, 500) μm, is the flux uncertainty. The flux calibration of the SPIRE photometer is based on Neptune. Being a bright source, Neptune produces high-S/N spectra and has a well understood submillimeter spectrum. The calibration flux densities for Neptune at (250, 350, 500) μm are (160, 100, 60) Jy and the absolute flux uncertainty is estimated to be 4%, which corresponds to the absolute calibration uncertainty. Considering also the relative calibration and the extended source calibration uncertainty, the total flux uncertainty for the SPIRE bands amounts to 7% according to the SPIRE handbook.

The column density of H₂ and its total error are estimated by applying a Monte Carlo fitting procedure with 1000 iterations. After every iteration, the noise level _noise is added to every map, pixel by pixel, following the equation

$\begin{eqnarray*}&&{\epsilon }_{\mathrm{noise}}={\epsilon }_{1}\cdot 0.07\cdot {I}_{\nu }+\delta {I}_{\nu }\cdot {\epsilon }_{2},\end{eqnarray*}$

where I_ν is the detected intensity at a frequency ν, _1,2 describes a random number taken from a standard normal distribution, and δ I_ν is the statistical error on the flux density value in each pixel produced by the pipeline. The fitting method gives a cube of N = 1000 maps. The fist map with _noise = 0 gives the resulting N(H₂), while its uncertainty is given by the standard deviation of the remaining maps.

A Study of the c-C₃HD/c-C₃H₂ Ratio in Low-mass Star-forming Regions^*

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Abstract

1. Introduction

2. Observations

3. Results

3.1. Calculation of the Column Densities and the Deuteration Level

3.2. Correlation between Deuteration and CO Depletion Factor

3.3. Correlation between Deuteration and H₂ Column Density

3.4. Correlation between Deuteration and Dust Temperature

4. Conclusion

Appendix A: Observed Spectra of c-C₃H₂ and Its Isotopologues toward the Starless and Protostellar Core Samples

Appendix B: The c-C₃H₂ and c-C₃HD Distribution across the Pre-stellar Core L1544

Appendix C: Error Estimation of the H₂ Column Density

Footnotes

A Study of the c-C3HD/c-C3H2 Ratio in Low-mass Star-forming Regions*

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Author e-mails

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ORCID iDs

Dates

Abstract

1. Introduction

2. Observations

3. Results

3.1. Calculation of the Column Densities and the Deuteration Level

3.2. Correlation between Deuteration and CO Depletion Factor

3.3. Correlation between Deuteration and H2 Column Density

3.4. Correlation between Deuteration and Dust Temperature

4. Conclusion

Appendix A: Observed Spectra of c-C3H2 and Its Isotopologues toward the Starless and Protostellar Core Samples

Appendix B: The c-C3H2 and c-C3HD Distribution across the Pre-stellar Core L1544

Appendix C: Error Estimation of the H2 Column Density

Footnotes

A Study of the c-C₃HD/c-C₃H₂ Ratio in Low-mass Star-forming Regions^*

3.3. Correlation between Deuteration and H₂ Column Density

Appendix A: Observed Spectra of c-C₃H₂ and Its Isotopologues toward the Starless and Protostellar Core Samples

Appendix B: The c-C₃H₂ and c-C₃HD Distribution across the Pre-stellar Core L1544

Appendix C: Error Estimation of the H₂ Column Density