© The Authors 2025

1 Introduction

Deuterated molecules are useful tools for studying the physical conditions and astro-chemical evolution of molecular clouds (Roberts et al. 2002; Guilloteau et al. 2006). The deuterium fractionation, that is, the abundance ratios of deuterated molecules to their hydrogenated counterparts, are much enhanced over the cosmic D/H elemental abundance ratio ~1.5 × 10⁻⁵ (Roberts & Millar 2000). Due to the lower zeropoint energy of deuterated molecules compared to their nondeuterated counterparts, which ensures that deuterium is preferentially bonded into molecules compared to hydrogen, deuterated molecules can be synthesized effectively in the cold gas-phase during the early stage of the evolution of molecular clouds (Roberts & Millar 2000). The process of deuterium fractionation is sensitive to various physical conditions such as temperature, density, CO depletion (Millar et al. 1989; Feng et al. 2020), and ionization (Caselli 2002), and low temperatures and high densities have particularly significant effects (Fontani et al. 2011; Pillai et al. 2011). Therefore, deuterated molecules are considered as excellent tracers for cold (T ~ 10 K) and dense (n ≥10⁴ cm⁻³) regions within molecular clouds (Roberts & Millar 2007).

After the detection of DCN in the Orion Nebula molecular cloud (Jefferts et al. 1973), many other deuterated species were identified in molecular clouds over the past decades. These include DCO⁺ (Hollis et al. 1976; Tiné et al. 2000; Caselli 2002), DNC (Snell & Wootten 1977; van der Tak et al. 2009; Yang et al. 2024), N₂D⁺ (Snyder et al. 1977; Crapsi et al. 2005; Fontani et al. 2006), deuterated NH₃ (Turner et al. 1978; Roueff et al. 2005; Pillai et al. 2007; Li et al. 2022b), and deuterated H₂CO (Watson et al. 1975; Roberts et al. 2002; Roberts & Millar 2007). Among these deuterated molecules, DCO⁺ and DCN are particularly valuable for studying the physical conditions and astro-chemical evolution of molecular clouds. This is due to their relatively high abundances, simple rotational spectra, accessible rotational transitions (Yang et al. 2024), and their synthetic pathways, which are closely linked to the deuterium fractionation process (Millar et al. 1989). Observational studies (Watson 1973; Roberts et al. 2002; Feng et al. 2020) and theoretical models (Herbst 1982; Millar et al. 1989) of deuterium chemistry suggest that DCO⁺ and DCN are important for understanding the evolution of a molecular cloud.

The deuterated fraction (D_frac) is defined as the abundance ratio of a deuterated molecule to its hydrogenated counterpart. This ratio was studied for many deuterated species (Hirota et al. 2001; Turner 2001; Caselli 2002; Roberts et al. 2002), including DCO⁺ and DCN. DCO⁺ was first detected in the molecular clouds NGC 2264, and DR (OH) was studied with H¹³CO⁺/DCO⁺ abundance ratios of 0.54 and 1.18 (Hollis et al. 1976). The DCO⁺/HCO⁺ ratio was found to be ~0.18 in the dark cloud L134N and 0.02 in TMC1-N (Tiné et al. 2000). For massive starless clump candidates, the DCO⁺/HCO⁺ and DCN/HCN ratios were estimated to be 0.011−0.040 and 0.004– 0.045, respectively (Yang et al. 2024). The DCN/HCN ratio increases from 0.001 in the hot core gas close to the infrared source IRc2 to values of 0.01−0.06 in the OMC-1 ridge region (Schilke et al. 1992). The abundance of deuterated molecules is considered crucial for understanding the physical conditions and deuterium chemistry in the cold gas-phase of molecular clouds.

However, large-sample surveys of DCO⁺ and DCN lines toward cold dense cores are still lacking in the literature. This gap limits our understanding of the enhancement of deuterated molecules in the phase from diffuse molecular gas to cold cores, including the measurements of D_frac for these molecules. The Planck cold clumps from the Early Cold Core Catalogue (ECC), which were selected from Wu et al. (2012), lack feedback from star formation, represent some of the most quiescent regions, and are ideal for such large-sample surveys. These Planck cold clumps have a typical mass of ~5 M_⊙, a size of ~0.5 pc (Planck Collaboration XXVIII 2016), and an excitation temperature of ~10 K (Wu et al. 2012).

We present a single-pointing survey of DCO⁺ and DCN 1−0 toward the 559 Planck cold clumps observed to date. The observational details are described in Sect. 2, the results are presented in Sect. 3, and the discussion and summary are provided in Sect. 4 and Sect. 5, respectively.

2 Observations

In total, 559 sources selected from the 674 Planck cold clumps with CO line detections (Wu et al. 2012) were observed using the Arizona Radio Observatory (ARO) 12-meter telescope in 2020 and 2023. The masses of 83 of the 559 observed sources can be found in Planck Collaboration XXVIII (2016), with mass values ranging from 0.29 to 1.85 × 10⁴ M_⊙. There are 75 sources with masses below 100 M_⊙, 6 sources with masses between 100 and 1000 M_⊙, and only 2 sources with masses exceeding 1000 M_⊙. The kinematic distances of these 559 sources range from 0.10 to 21.58 kpc, while the excitation temperatures derived from CO 1– 0 (T_ex(CO) hereafter) range from 3.9 to 27.1 K (Wu et al. 2012). The beam size at 72 GHz is ~87″. The focus was checked at the beginning of each observing block. The pointing was checked every two hours on a nearby quasar or planet. The main-beam brightness temperature (T_mb) was calculated from $T_{\text{A}}^{*}=T_{\text{mb}}\times \eta$, where $T_{\text{A}}^{*}$ is the antenna temperature, and η is the average beam efficiency of the 4 mm receiver, with a value of 0.92 ± 0.06.

In early 2020, 258 sources were observed in DCO⁺ and DCN 1−0 using the 4 mm receiver (66–90 GHz) with dual polarizations and the ARO Wideband Spectrometer (AROWS) with mode 3, which provides a 78.125 kHz channel spacing (~0.32 km s⁻¹ at 72 GHz) and 500 MHz bandwidth, covering DCO⁺ 1−0 at 72.039312 GHz and DCN 1−0 at 72.414927 GHz simultaneously. Due to the limited velocity resolution of ~0.32 km s⁻¹ with AROWS mode 3, accurate measurements of the full width at half maximum (FWHM) for sources with narrow line widths were challenging. To address this, high spectral resolution supplementary observations were conducted for 32 sources with narrow DCO⁺ 1−0 lines using AROWS mode 5, which provides a 19.531 kHz channel spacing (~0.081 km s⁻¹ at 72 GHz) and 125 MHz bandwidth. To derive D_frac, 41 sources with DCO⁺ 1−0 detections were observed for H¹³CO⁺ 1−0 at 86.754288 GHz and H¹³CN 1−0 at 86.3401764 GHz simultaneously, using AROWS mode 3 with a velocity resolution ~0.27 km s⁻¹ at 86 GHz. Standard position-switching mode was used with 3 minutes on and 3 minutes off for each source. The typical system temperatures (T_sys) were 150 K at 72 GHz and 120 K at 86 GHz, resulting in a root-mean-square (rms) noise level of ~50 mK at 78.125 kHz channel spacing for the final spectrum after averaging both polarizations.

In 2023, 51 sources were observed for DCO⁺ and DCN 1−0, with 30 sources additionally observed for H¹³CO⁺ and H₁₃CN 1−0. The same setup was used as in 2020.

In 2023, 250 sources were observed using the 4 mm receiver and the newly updated AROWS multiwindow mode 13, which provides up to eight spectral windows of the same size with a 19.53 kHz channel spacing (~0.081 km s⁻¹ at 72 GHz) and a bandwidth of 40 MHz. This setup covers DCO⁺ and DCN 1−0 in the lower sideband (LSB) and H¹³CO⁺ and H¹³CN 1-0 in the upper sideband (USB) simultaneously. The standard positionswitching mode was used with 30 seconds on and 30 seconds off, repeating six times for each source. The typical T_sys values are 150 K at 72 GHz and 120 K at 86 GHz, resulting in an rms noise level of ~100 mK at the 19.53 kHz channel spacing for the final spectrum after averaging both polarizations. As a result of a software bug in the multiwindow configuration code during the shared-risking period for the wrong sign of the Doppler correction for the second sideband in observations using AROWS mode 13 in 2023, the V_LSR measurements of H¹³CO⁺ and H₁₃CN 1−0 in USB exhibit offsets of 1 to 7 km s⁻¹, even though all the parameters were obtained for the lines in the first sideband (which is the LSB, including DCO⁺ and DCN 1−0), but all the other parameters are correct. Therefore, the V_LSR values of H¹³CO⁺ and H₁₃CN 1−0 are not provided in Sect. 3 and were not used for the scientific discussion.

The data reduction was performed using the CLASS package in the GILDAS¹ software. After checking each scan, we discarded poor scans (fewer than 3%). A first-order baseline was applied to all spectral lines, and a single-component Gaussian fitting was applied to obtain parameters, including the velocity- integrated intensity (∫T_mbdv denoted as W hereafter), V_LSR, and FWHM for each source.

3 Results

Sources considered with detections were judged by W greater than 3σ, where both W and σ were obtained from the Gaussian fitting in CLASS. W of the DCO⁺ 1−0 line is denoted as W(DCO⁺) hereafter, and an analogous notation is applied to the DCN, H¹³CO⁺, and H₁₃CN 1−0 lines. Examples of detections for the DCO⁺ and DCN 1−0 lines toward G091.73+04.3 observed in 2020 using the low-velocity resolution mode (AROWS mode 3) are shown in Figure 1. The detections toward G159.21- 20.1 observed in 2023 using high-resolution mode (AROWS mode 13) are shown in Figure 2. Since each source was observed for approximately the same duration of six minutes, the noise levels of the spectra are similar, although the different rms levels are caused by a different velocity resolution. DCN and H¹³CN J = 1−0 exhibit hyperfine splitting into the F = 1−0, 2−1, and 0−0 components, and F = 2−1 is the strongest. For the results and discussion in this paper, we focused on the J = 1−0, F = 2−1 lines of DCN and H¹³CN, which are written as DCN 1−0 and H₁₃CN 1−0 hereafter.

Fig. 1 Spectral lines of DCO+ and DCN 1−0 (black line) overlaid with the Gaussian fitting results (green line) toward G091.73+04.3, as observed in 2020 using the low-velocity resolution mode (AROWS mode 3) with a velocity resolution of ~0.32 km s−1. The hyperfine components of DCN 1−0 are visible.

3.1 Detection rates of DCO⁺, DCN, H¹³CO⁺, and H¹³CN 1−0

Using the low-velocity resolution mode (AROWS mode 3), we detected DCO⁺ and DCN 1−0 in 79 and 11 out of 309 sources with detection rates of 25.6% and 3.6%, respectively. Using the high-velocity resolution mode (AROWS mode 13), we detected DCO⁺, DCN, H¹³CO⁺, and H¹³CN 1−0 in 58, 9, 57, and 13 out of 250 sources with detection rates of 23.2%, 3.6%, 22.8%, and 5.2%, respectively. The detection rates of DCO⁺ and DCN 1−0 are similar in the two AROWS modes. Overall, the detection rates for DCO⁺ and DCN 1−0 are 24.5% and 3.6%, with detections in 137 and 20 out of 559 sources, respectively. The detection rates are summarized in Table 1. The detailed detection status is presented in Table A.1 (see Appendix A).

The detection rates of DCO⁺ and H¹³CO⁺ 1−0 are similar in the 250 sources observed with the high-velocity resolution mode (AROWS mode 13), and detections of these two lines occurred simultaneously in most sources. In 46 sources, both DCO⁺ and H¹³CO⁺ 1−0 were detected, with a median W(DCO⁺) of 6.0σ and a median W(H¹³CO⁺) of 7.0σ. Twelve sources only showed detections of DCO⁺ 1−0, with a median W (DCO⁺) of 4.0σ. These sources are G168.85-15.8, G161.85-08.6, G163.32- 08.4, G165.69-09.1, G178.48-06.7, G195.00-16.9, G177.14-01.2, G200.34-10.9, G185.33-02.1, G181.84+00.3, G199.88+00.9, and G201.13+00.3. Eleven sources only had H¹³CO⁺ 1−0 detections, suggesting that deuterium enhancement may not occur, with median a W(H¹³CO⁺) of 6.6σ, These sources are G159.23- 34.4, G162.64-31.6, G168.00-15.6, G170.13-16.0, G170.99- 15.8, G165.16-07.5, G195.09-16.4, G159.34+11.2, G191.00-04.5, G215.00-15.1, and G216.18-15.2.

Fig. 2 Spectral lines of DCO+ and DCN 1−0 (black line) overlaid with the Gaussian fitting results (green line) toward G159.21-20.1, as observed in 2023 using the high-velocity resolution mode (AROWS mode 13) with a velocity resolution of ~0.081 km s−1. The hyperfine components of DCN 1−0 are visible.

3.2 Derived parameters of the detected DCO⁺ and DCN 1−0

The parameters for sources with DCO⁺ 1−0 detections are listed in Table A.2, and those with DCN 1−0 detections are listed in Table A.3 (see Appendix A). DCO⁺ and DCN 1−0 were detected in 137 and 20 out of 559 sources, respectively. Sixten sources had detections of both DCO⁺ and DCN 1−0, 121 sources with DCO⁺ but without DCN, 4 sources with DCN but without DCO⁺, and 418 sources with no detection of either molecule. The distributions of W(DCO⁺) and W(DCN) are shown in Figure 3. W(DCO⁺) ranges from 0.06 to 2.40 K km s⁻¹ with a median value of 0.35 K km s⁻¹, and the FWHM ranges from 0.2 to 2.5 km s⁻¹ with a median value of 0.7 km s⁻¹. W(DCN) ranges from 0.10 to 0.44 K km s⁻¹ with a median value of 0.15 K km s⁻¹, and the FWHM ranges from 0.2 to 1.2 km s⁻¹ with a median value of 0.4 km s⁻¹.

In G209.28-19.6 and G206.10-15.7, multiple velocity components of DCO⁺ 1−0 were found. In G209.28-19.6, W was derived by directly integrating the velocity range of the line. In G206.10- 15.7, two components are shown in Figure 4, with W values derived from a double-component Gaussian fitting.

Fig. 3 Distribution of W(DCO+) (red bars) and W(DCN) (blue bars).

3.3 Derived parameters of the detected H¹³CO⁺and H¹³CN 1−0

We observed a total of 71 sources, selected from 79 sources with DCO⁺ 1−0 detections using the low-velocity resolution mode (AROWS mode 3), for H¹³CO⁺ and H¹³CN 1−0 simultaneously in the low-velocity resolution mode (AROWS mode 3). H¹³CO⁺ 1−0 was detected in 66 of these 71 observed sources. Twenty of these 66 sources with H¹³CO⁺ 1−0 had H¹³CN 1−0 detections.

H¹³CO⁺ and H¹³CN 1−0 were detected using the high- velocity resolution mode (AROWS mode 13) in 57 and 13 out of 250 sources, respectively, and 12 sources showed detections of both H¹³CO⁺ and H¹³CN 1-0. The distributions of W(H¹³CO⁺) and W (H¹³ CN) with this mode are shown in Figure 5.

The parameters for H¹³CO⁺ and H¹³CN 1−0 are listed in Table A.4 and Table A.5 (see Appendix A), respectively. W(H¹³CO⁺) ranges from 0.06 to 1.11 K km s⁻¹ with a median value of 0.24 K km s⁻¹ , and the FWHM ranges from 0.1 to 2.4 km s⁻¹ with a median value of 0.5 km s⁻¹. W(H¹³CN) ranges from 0.05 to 0.28 km s⁻¹ with a median value of 0.10 K km s⁻¹ , and the FWHM ranges from 0.2 to 1.5 km s⁻¹ with a median value of 0.4 km s⁻¹ .

As mentioned in Sect. 3.2, G206.10-15.7 and G209.28-19.6 also exhibited multiple velocity components of H¹³CO⁺ 1−0. For G209.28-19.6, W(H¹³CO⁺) was derived by directly integrating the velocity range of the line. For G206.10-15.7, the parameters for H¹³CO⁺ 1−0 with two velocity components are listed in Table A.4 (see Appendix A).

Fig. 4 Spectral lines of DCO+ and H13CO+ 1−0 (black line) overlaid with the Gaussian fitting results (green line) toward G206.10-15.7. Double-velocity components in DCO+ and H13CO+ 1−0 were detected.

Fig. 5 Distribution of W(H13CO+) (orange bars) and W(H13CN) (green bars).

3.4 Deuterated fraction of HCO⁺and HCN

The D_frac values of HCO⁺ and HCN were estimated by calculating the column density ratios of deuterated molecules to their hydrogenated counterparts, using their ¹³C-isotopolog counterparts. The column densities were derived from Eq. (1), assuming local thermodynamic equilibrium (LTE) and that the two deuterated molecules and their ¹³C-isotopolog counterparts are optically thin, $$N_{\text{tot}}=\frac{8\pi k{v}^{2}Q\left(T_{\text{ex}}\right)}{h{c}^3{𝑔}_u{A}_{ul}}{e}^{\frac{E_l+hv}{k\text{Tex}}}{\displaystyle \int T_{\text{mb}}}dv\left({\text{cm}}^{-2}\right)$$(1)

Here, k = 1.38 × 10⁻¹³ erg K⁻¹ is the Boltzmann constant, v is the frequency of the transition, h = 6.624 × 10⁻²⁷ erg s is the Planck constant, c = 2.998 × 10¹⁰ cm s⁻¹ is the speed of light, T_ex is the excitation temperature (assumed to be 9.375 K), Q(T_ex) is the partition function dependent on the T_ex, A_ul is the Einstein emission coefficient, g_u is the upper-level degeneracy, and E_l is the energy of the ground state. Q(T_ex), A_ul, g_u, and E_l for the four transitions are given by the CDMS (van der Tak et al. 2009). Since all the four lines are the transitions between J =1 and J = 0, E_l is zero for each line.

According to Eq. (1), the column density ratios of deuterated molecules to their ¹³C-isotopolog counterparts are given by N(DCO⁺)/N(H¹³CO⁺)≈1.33×W(DCO⁺)/W(H¹³CO⁺) and N(DCN)/N(H¹³CN)≈1.30×W(DCN)/W(H¹³CN). T_ex = 9.375 K is a reasonable assumption, since these sources are cold cores. Even when the gas density is below the critical densities of these lines, which might invalidate the LTE assumption, the derived column densities of DCO⁺ and H¹³CO⁺ may have large uncertainties. However, the relative abundance ratio of DCO⁺/H¹³CO⁺ estimated based on there J = 1−0 lines does not vary much because the two molecules have similar excitation conditions, which can cancel the bias in the column density estimation. This also holds for estimating the relative abundance ratio of DCN/H¹³CN.

The kinematic distances of the Planck cold clumps were obtained for 741 ¹³CO components, with 51% ranging from 0.5 to 1.5 kpc (Wu et al. 2012), indicating that these sources are in the solar neighborhood. The corresponding physical scale of the beam size 87″ for source at 1 kpc is ~4 pc. The ¹²C/¹³C ratio as a function of Galactocentric distance D_GC, ¹²C/¹³C = 6.21 D_GC + 18.71, provided in Milam et al. (2005), where the D_GC of the sun is 8.15 kpc (Reid et al. 2019). A ¹²C/¹³C ratio of 68, representative of the local interstellar medium, was used for these Planck cold clumps. The D_frac values were derived from the ¹²C/¹³C ratios and column density ratios: D_frac(HCO⁺) = 1/68×N(DCO⁺)/N(H¹³CO⁺) and D_frac(HCN) = 1/68×N(DCN)/N(H¹³CN), which are listed in Table A.6 (see Appendix A). The 3σ upper limit values are also provided, calculated as $3rms\sqrt{\delta v\cdot \text{Δ}v}$(K ⋅ km ⋅ s⁻¹), where δv is the channel spacing of the velocity, and ∆v is the FWHM.

D_frac(HCO⁺) was derived for 113 components from 112 sources, including two velocity components in G206.10-15.7, ranging from 0.89% to 7.4% with a median of 3.1%. Dfr_ac(HCN) was derived for 11 sources, ranging from 1.5% to 5.5% with a median of 2.3%. Four of the 9 sources with both Dfrac(HCO⁺) and Dfrac(HCN) values show Dfrac(HCO⁺) greater than Dfrac (HCN), and the remaining 5 sources show the opposite (see Figure 6).

Fig. 6 Dfrac(HCO+) vs. Dfrac(HCN) for nine sources with both deuterated fractions.

3.5 FWHMs of DCO⁺ and H¹³CO⁺ 1−0

Of the 250 sources observed using the high-velocity resolution mode (AROWS mode 13), the number distributions of the FWHM of DCO⁺ and H¹³CO⁺ 1−0 in 46 sources with detections of both molecules are shown in the top of Figure 7. The FWHMs of these detections are mainly below 1 km s⁻¹, and the peak at 0.3−0.4 km s⁻¹ corresponds to 11 and 12 out of 46 detections for DCO⁺ and H¹³CO⁺, respectively. The number distributions of FWHM of DCO⁺ and H¹³CO⁺ 1−0 in the 12 sources for which only DCO⁺ 1−0 was detected and the 11 sources for which only H¹³CO⁺ 1−0 was detected are shown in the bottom panle of Figure 7. The FWHM of the sources with single detections shows no significant difference compared to those for which DCO⁺ and H¹³CO⁺ 1−0 are both detected. A comparison of the FWHMs between DCO⁺ and H¹³CO⁺ is shown in Figure 8, which demonstrates that the line widths are roughly similar within the error bars, with DCO⁺ 1−0 having a slightly larger line width than H¹³CO⁺ 1−0. Figure 9 displays the comparisons between FWHM of DCO⁺ and Dfrac(HCO⁺) and between FWHM of H¹³CO⁺ and D_frac(HCO⁺), without a clear trend. The FWHM of DCO⁺ 1−0 seems to be larger than that of H¹³CO⁺ 1−0 in sources with D_frac greater than 5%. However, it is hard to conclude clearly for these differences because the signal-to-noise ratios of H¹³CO⁺ 1−0 are too low in these sources.

Fig. 7 Top: distributions of FWHM for DCO+ (red bars) and H13CO+ (orange bars) 1−0 in 46 sources where DCO+ and H13CO+ 1−0 were detected using the high-velocity resolution mode (AROWS mode 13). Bottom: distribution of FWHM of DCO+ in sources for which only DCO+ 1−0 was detected (red bars) and distribution of FWHM of H13CO+ in sources for which only H13CO+ 1−0 was detected (orange bars).

Fig. 8 FWHM of DCO+ 1−0 vs. H13CO+ 1−0 of 46 sources in which both lines were detected with the high-velocity resolution mode (AROWS mode 13).

Fig. 9 Top: comparison between the FWHM of DCO+ and Dfrac(HCO+). Bottom: comparison between the FWHM of H13CO+ and Dfrac(HCO+). Each plot contains 113 data points.

Fig. 10 Distribution of Tex(CO) in sources where DCO+ 1−0 is detected (red bars) and where it is not detected (pink bars).

4 Discussion

4.1 Properties of these Planck cold clumps with and without a DCO⁺ 1−0 detection

In order to determine whether the properties of sources with DCO⁺ 1−0 detections differ from those without detections, the distributions of T_ex(CO) and W(HCO⁺) for sources with and without DCO⁺ 1−0 detections are provided. The W(HCO⁺) data are from Yuan et al. (2016). The distributions of T_ex(CO) for sources with and without a DCO⁺ 1−0 detection are similar, as shown in Figure 10. The T_ex (CO)s of these Planck cold clumps are below 30 K. They mainly range from 7 to 12 K. The distributions of W(HCO⁺) for sources with and without a DCO⁺ 1−0 detection are also similar (see Figure 11). The detection rates of DCO⁺ 1−0 are slightly higher in sources with higher W(HCO⁺) than in those with lower W(HCO⁺). The similarity of distributions suggests that the detection or nondetection status of DCO⁺ 1−0 is not limited by T_ex(CO) and W(HCO⁺).

Fig. 11 Distribution of W(HCO+) in sources where DCO+ 1−0 is detected (red bars) and where it is not detected (pink bars).

4.2 Possible reason for the different detection rates and similar Dfracs of HCO⁺ and HCN in Planck cold clumps

The detection rates for DCO⁺ and H¹³CO⁺ 1−0 are 24.5% and 22.8%, respectively, whereas those for DCN and H¹³CN 1–0 are 3.6% and 5.2%. This indicates that both the deuterated and¹³ C-isotopolog counterparts of HCO⁺ are detected more frequently than their HCN counterparts. The higher detection rates of DCO⁺ compared to DCN 1−0 are consistent with the studies of 70 µm dark high-mass clumps (Li et al. 2022a) and massive starless clump candidates (Yang et al. 2024).

The D_frac(HCO⁺) values in 112 sources range from 0.89% to 7.4% with a median value of 3.1%, and the D_frac(HCN) values in 11 sources range from 1.5% to 5.5% with a median value of 2.3%. These values do not show a significant difference between the two molecular pairs. The D_frac values are consistent with those observed in molecular clouds (e.g., Hollis et al. 1976), low-mass starless cores (e.g., Tafalla et al. 2006), and massive starless clump candidates (e.g., Yang et al. 2024). Four of the nine sources where both D_frac(HCO⁺) and D_frac(HCN) were estimated show D_frac(HCO⁺) greater than D_frac (HCN), and the remaining five sources show the opposite (see Figure 6). Therefore, the significantly lower detection rate of DCN 1–0 compared to DCO⁺ 1−0, despite similar noise levels, cannot be attributed to differences in D_frac values.

The deuterium fractionation is generally regarded as starting from the molecule-ion reaction primarily at temperature below 30 K. At these low temperatures, the reaction $\text{HD}+{\text{H}}_3^{+}\rightleftharpoons {\text{H}}_2+{\text{H}}_2{\text{D}}^{+}+\text{ΔE}$ (where ∆E = 232 K) proceeds forward, enhancing the abundance of H₂D⁺, which is a precursor of many deuterated molecules (Millar et al. 1989). DCO⁺ is thought to form in the gas phase and to be abundant below ∼30 K, while DCN is thought to form through multiple pathways in the interstellar medium, and its abundance peaks at higher temperatures than DCO⁺ (Millar et al. 1989). Consequently, deuterated molecules are often used as chemical clocks to trace the evolutionary stages during star formation (Fuente et al. 2005; Busquet et al. 2010; Fontani et al. 2014; Sakai et al. 2022). For example, Kim et al. (2020) suggested that the detection rates of deuterated molecules signify chemical evolutionary stages, while the Dfrac s should be used for this study.

Because of the similar D_frac values for HCO⁺ and HCN in Planck cold clumps, we propose that the disparity in the detection rates between DCO⁺ and DCN 1−0 is primarily due to differences in their critical densities. This explanation was also suggested for massive starless clump candidates (Yang et al. 2024). When we ignore the background emission, the optically thin critical density can be approximated by $n_{\mathit{crii}}^{\mathit{thin}}~A_{jk}/{\gamma }_{jk}$, where A_jk (s⁻¹) is the Einstein A, and γ_jk (cm³ s⁻¹) is collision rate out of the upper level j to the level k (Shirley 2015). At 10 K, the critical densities for DCO⁺ and DCN 1−0 are 3.2 × 10⁴ and 2.6 × 10⁵ cm⁻³ (Feng et al. 2020) , and those for H¹³CO⁺ and H¹³CN 1−0 are 6.2 × 10⁴ and 5.3 × 10⁵ cm⁻³ (Shirley 2015). Although the A_jk values for DCO⁺ and DCN 1–0 are similar, γ_jk related to the collision cross section for collisions with H₂ for DCO⁺ (a molecular ion) is larger than DCN (a neutral molecule), resulting in a critical density for DCO⁺ that is lower by an order of magnitude than DCN (Shirley 2015). This also holds for H¹³CO⁺ and H¹³CN as well as for DCO⁺ and DCN.

Fig. 12 Comparison of Tex and Dfrac (HCO+) (red points), including the 3σ upper and lower limit value of Dfrac(HCO+) (red points and arrows) for sources with only H13 CO+ and only DCO+ detections, respectively.

4.3 Origin of the deuterium fractionation

The comparison between T_ex(CO) and D_frac (HCO⁺) shows no trend, including the upper and lower limits of D_frac (HCO⁺) (see Figure 12). Most upper and lower limits of D_frac (HCO⁺) fall within the expected ranges, suggesting that most sources with detections of only DCO⁺ or H¹³ CO⁺ do not exhibit significantly different properties compared to sources with both detections. The small range of T_ex(CO)s for these sources makes it challenging to discuss a relation between T_ex (CO) and the deuterium fractionation. Observations of the deuterium fractionation in late stages of star-forming regions are needed for further study. Chemical models suggest that deuterated molecules can be destroyed in hot molecular gas (Millar et al. 1989; Hatchell et al. 1998). Observations suggest that in hot cores, D_frac(HCN) generally decreases from off-core to on-core positions, where temperatures vary significantly (Hatchell et al. 1998).

Twelve of the observed sources exhibit lower limits of D_frac(HCO⁺), with only DCO⁺ 1–0 detections, possibly due to the lower critical density of 3.2 × 10⁴ cm⁻³ for DCO⁺ 1−0 compared to 6.2 × 10⁴ cm⁻³ for H¹³CO⁺ 1−0 at 10 K (Shirley 2015; Feng et al. 2020). Four of these 12 sources exhibit particularly high D_frac values, namely G177.14-01.2, G181.84+00.3, G199.88+00.9, and G201.13+00.3 (see Figure 12). They deserve further study.

Conversely, 11 sources have upper limits of D_frac(HCO⁺), with only H¹³CO⁺ 1–0 detections, corresponding to low D_frac values. No significant differences in the number distributions of T_ex(CO) are found between sources with only DCO⁺ 1–0 detections, only H¹³CO⁺ 1–0 detections, and those with both detections (see Figure 12). The FWHM number distributions for sources with only DCO⁺ 1–0 detections, only H¹³CO⁺ 1–0 detections, and both detections show no significant differences, and the FWHMs are mainly within 1 km s⁻¹ (see Figure 7). It was suggested that D_frac may decrease with increasing microturbulent velocity fields (Gerner et al. 2015; Li et al. 2022b). However, our results do not reveal any trend between the Dfrac and line widths for either DCO⁺ or H¹³CO⁺ 1–0 (see Figure 9). The limited range of the FWHMs for these emission lines in Planck cold clumps makes it difficult to discuss the relation between D_frac and FWHM.

The deuterium chemistry suggests that the deuterium fractionation starts during the pre-collapse phase of the molecular cloud evolution, when the gas becomes cold (T ~10 K) and dense (n ≥ 10⁴ cm⁻³) (Roberts & Millar 2000; Ceccarelli et al. 2001; Roberts & Millar 2007). This mechanism was used to explain the high D_frac observed in cold molecular cores (Ceccarelli et al. 2001; Caselli et al. 2003). According to this framework, in the early stages of cold-core formation (T ~ 15-20 K, n ~10⁴ cm⁻³), D_frac would remain too low (~10⁻⁴–10⁻³) to produce detectable DCO⁺ 1–0, while H¹³CO⁺ 1–0 could be detected. However, among our 250 observed sources using the high-velocity resolution mode (AROWS mode 13), DCO⁺ and H¹³CO⁺ 1–0 are detected in 58 and 57 sources with similar detection rates of 23.2% and 22.8%, respectively. More importantly, there are 46 sources with both DCO⁺ and H¹³CO⁺ 1–0 detections. DCO⁺ and H¹³CO⁺ 1–0 emissions are detected almost simultaneously in the same sources. These results indicate that DCO⁺ can already be widespread in cold molecular clouds, rather than just beginning to become abundant. Thus, the phenomenon of high D_frac observed in cold cores may not necessarily be explained by cold-core deuterium chemistry.

Moreover, the D_frac values for HCO⁺ and HCN, reflecting the enhancement of deuterium for these two species, are similar. They range from 0.89% to 7.4% and 1.5% to 5.5%, respectively. The detection rates of DCN and H¹³CN 1–0 of 3.6% and 5.2%, respectively, are significantly lower than those of DCO⁺ and H¹³CO⁺ 1–0 of 24.5% and 22.8%, respectively. This might due to the higher critical densities of DCN and H¹³ CN 1–0 compared to those of DCO⁺ and H¹³CO⁺ 1–0, respectively. Thus, perhaps because the volume density is not high enough to excite DCO⁺ and DCN to the J = 1 energy level, the DCO⁺ and DCN lines cannot be detected in diffuse gas. The method for testing the origin of DCO⁺ and DCN in diffuse molecular clouds is to observe the DCO⁺ and DCN absorption lines toward diffuse molecular clouds with background quasar-emitting millimeterwave continuum sources. The differences in D_frac during the evolution of molecular clouds and late stages of star formation are caused by the synthesis and depletion of deuterated molecules in different physical conditions. Thus, a comparison with large-sample surveys of deuterated molecular lines toward hot molecular cores at late stages of star formation, as well as updated astro-chemical models for these deuterated molecules, is needed to fully understand the enhancement of deuterium in molecular clouds.

5 Summary

With the aim to understand the enhancement of deuterated molecules from diffuse molecular gas to cold cores, we conducted a single-pointing survey toward 559 Planck cold clumps of ECC for DCO⁺ and DCN 1–0 using the ARO 12m telescope. This included observations of 309 cores for DCO⁺ and DCN 1– 0 simultaneously, followed by 71 of these cores in which DCO⁺ 1–0 was detected for H¹³CO⁺ and H¹³CN 1–0 simultaneously, with the aim to determine D_frac . Additionally, 250 cores were observed for DCO⁺, DCN, H¹³CO⁺, andH¹³CN 1–0 simultaneously. The observed parameters, including W, V_LSR, and FWHM, were presented. The detection rates and D_frac for HCO⁺ and HCN were also presented. Potential reasons for the different detection rates and the similar D_frac for HCO⁺ and HCN in Planck cold clumps were discussed. The main results of this survey are listed below:

1. DCO⁺ and DCN 1–0 were detected in 79 and 11 out of 309 sources with the low-velocity resolution mode (AROWS mode 3), which gives detection rates of 25.6% and 3.6%, respectively. DCO⁺, DCN, H¹³CO⁺, and H¹³CN 1–0 were detected in 58, 9, 57, and 13 out of 250 sources with the highvelocity resolution mode (AROWS mode 13), which gives detection rates of 23.2%, 3.6%, 22.8%, and 5.2%, respectively. Overall, DCO⁺ and DCN 1–0 were detected in 137 and 20 out of 559 sources, with detection rates of 24.5% and 3.6%, respectively, with about 6 minutes of telescope time for each source;

2. The D_frac(HCO⁺) values in 112 sources range from 0.89% to 7.4%, with a median value of 3.1%, and the D_frac(HCN) values in 11 sources range from 1.5% to 5.5%, with a median value of 2.3%;

3. The line widths (FWHMs) of the DCO⁺ and H¹³CO⁺ 1–0 detections are mainly distributed within 1 km s⁻¹ , and most measurements fall between 0.3 and 0.4 km s⁻¹;

4. The similar D_frac values for DCO⁺ and DCN suggest that the higher detection rate of DCO⁺ compared to DCN is due to the lower critical density of DCO⁺ ;

5. The nearly simultaneous detections of DCO⁺ and H¹³CO⁺ 1–0 in the same sources suggest that deuterium fractionation may start during diffuse molecular gas phase prior to coldcore formation.

Data availability

Tables A.1 to A.6, B.1, E.1 and E.2 are only available in electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/696/A140. More information about DCO⁺, DCN, H¹³CO⁺ and H¹³CN 1–0 lines from our sample in Appendix D is available on Zenodo under the following link: https://zenodo.org/records/15013446

Acknowledgements

We would like to acknowledge the help of the staff of the ARO 12-m for assistance with the observations. This work is supported by National Key R&D Program of China under grant 2023YFA1608204, the National Natural Science Foundation of China (NSFC) grant 12173067 and the Guangxi Talent Programme (Highland of Innovation Talents). S.L. is supported by NSFC grant 11988101.

Appendix A Detection statuses and parameters of spectral lines

Appendix B High spectral resolution supplementary observations with AROWS mode 5

As described in Sect. 2, high spectral resolution supplementary observations with AROWS mode 5 were conducted for DCO⁺ 1-0 narrow lines toward 32 sources. The fluxes of DCO⁺ 1-0 observed with the high-velocity resolution mode (AROWS mode 5) are similar to those observed with the low velocity resolution mode (AROWS mode 3) (see Table B.1).

The FWHMs of DCO⁺ 1-0 using the high-velocity resolution mode (AROWS mode 5) are compared with those using the low velocity resolution mode (AROWS mode 3) in Fig. B.1, showing similar values within the error bars. Therefore, even though the FWHMs from low spectral resolution observations may not be precise, they are still useful as a reference.

Fig. B.1 Comparison between FWHM of DCO+ with velocity resolution ~0.081 km s−1 with mode 5 and FWHM of DCO+ with velocity resolution ~0.32 km s−1 with mode 3. There are 32 points in the plot.

Appendix C The relationships of the kinematic distances of sources and detection results

To determine whether DCO⁺ 1-0 detection is limited by distance, the distributions of kinematic distances for sources with and without DCO⁺ 1-0 detections are shown in Fig. C.1. To reduce uncertainty in kinematic distances, sources located at galactic longitudes 0º±l5º and 90º±l5º, as well as those with a galactic scale height greater than 1 kpc, were excluded. Among the observed sources, the kinematic distances for 378 sources that meet the coordinate requirements are from Wu et al. (2012). The kinematic distances of these sources, regardless of DCO⁺ 1-0 detection, show a similar distribution (see Fig. C.1). The kinematic distances of 82 sources with DCO⁺ 1-0 detections range from 0.11 to 5.75 kpc, with a mean of 1.08 kpc and a median value of 0.81 kpc. For the 296 sources without DCO⁺ 1-0 detections, kinematic distances range from 0.10 to 5.42 kpc, with a mean of 1.11 kpc and a median value of 1.01 kpc. The kinematic distances of sources with and without detections show similar distributions, means, and medians, which rules out the effect of beam dilution on the detection or non-detection status.

Fig. C.1 Distribution of kinematic distance of sources where DCO+ 1-0 is detected or not.

Appendix D The spectral lines of DCO⁺, DCN, H¹³CO⁺, and H¹³CN 1-0

The spectra of deuterated molecules (black lines) and the spectra of¹³ C–isotopologue counterparts (red lines) are presented in Figs. D.1 to D13, grouped by HCO⁺ and HCN respectively.

Figures D.1 to D3 show the spectral lines of DCO⁺ 1-0. Figure D.1 displays the spectra for 8 sources where DCO⁺ 1-0 was detected using the low velocity resolution mode (AROWS mode 3), but H¹³CO⁺ 1-0 was not observed. Figure D2 presents spectra for 5 sources with DCO⁺ 1-0 detections and no H¹³CO⁺ 1-0 detections using the low velocity resolution mode (AROWS mode 3). Figure D3 shows spectra for 12 sources with DCO⁺ 1-0 detections and no H¹³ CO⁺ 1-0 detections using the high-velocity resolution mode (AROWS mode 13).

Figures 4~6 show the spectral lines of DCN 1-0. Figure 4 shows spectra for 2 sources with DCN 1-0 detection and no H¹³CN 1-0 observation using the low velocity resolution mode (AROWS mode 3). Figure 5 shows spectra for 5 sources with DCN 1-0 detections but without H¹³CN 1-0 detections using the low velocity resolution mode (AROWS mode 3). Figure 6 presents spectra for 2 sources with DCN 1-0 detections and no H¹³CN 1-0 detections using the high-velocity resolution mode (AROWS mode 13).

Figure D7 displays the spectral lines of H¹³CO⁺ 1-0, with 11 sources showing H¹³CO⁺ 1-0 detections but without DCO⁺ 1-0 detections with the high-velocity resolution mode (AROWS mode 13).

Figures D8 and D9 show the spectral lines of H¹³CN 1- 0. Figure D8 shows spectra for 16 sources with H¹³CN 1-0 detections but no DCO⁺ 1-0 detections using the low velocity resolution mode (AROWS mode 3). Figure D9 shows spectra for 6 sources with H¹³CN 1-0 detections and no DCN 1-0 detections using the high-velocity resolution mode (AROWS mode 13).

Figures D10 and D11 show the spectral lines of both DCO⁺ and H¹³CO⁺ 1-0. Figure D10 shows spectra for 66 sources with detections of both DCO⁺ and H¹³CO⁺ 1-0 using the low velocity resolution mode (AROWS mode 3). Figure D11 displays spectra for 46 sources with detections of both species using the highvelocity resolution mode (AROWS mode 13). Due to errors in the Doppler tracking with mode 13, H¹³ CO+ 1-0 lines were manually aligned with DCO+ 1-0 lines in Figure D11.

Figures D12 and D13 show the spectral lines of DCN and H¹³CN 1-0. Figure D12 includes spectra for 4 sources with both DCN and H¹³CN 1-0 detections using the low velocity resolution mode (AROWS mode 3). Figure D13 presents spectra for 7 sources with both detections using the high-velocity resolution mode (AROWS mode 13). Due to errors in the Doppler tracking with mode 13, H¹³CN 1-0 lines were manually aligned with DCN 1-0 lines in Figure D13.

Fig. D.1 Line profiles of DCO+ 1-0 with the low velocity resolution mode (AROWS mode 3). The transitions of H13CO+ 1-0 have not been observed in these sources. Additional Figures D1∼D13 are available on Zenodo. https://zenodo.org/records/15013446

Appendix E The sources without any detection

A total of 228 sources were observed for DCO⁺ and DCN 1- 0 using the low velocity resolution mode (AROWS mode 3), with no detections of either molecule. The details for these 228 sources, including name, R.A., and Decl., are provided in Table E.1. Additionally, Table E.2 lists details for 180 sources observed with the high-velocity resolution mode (AROWS mode 13) that showed no detection of DCO⁺, DCN, H¹³CO⁺, or H¹³CN 1-0.

References

All Tables

All Figures

	Fig. 1 Spectral lines of DCO+ and DCN 1−0 (black line) overlaid with the Gaussian fitting results (green line) toward G091.73+04.3, as observed in 2020 using the low-velocity resolution mode (AROWS mode 3) with a velocity resolution of ~0.32 km s−1. The hyperfine components of DCN 1−0 are visible.
In the text

	Fig. 2 Spectral lines of DCO+ and DCN 1−0 (black line) overlaid with the Gaussian fitting results (green line) toward G159.21-20.1, as observed in 2023 using the high-velocity resolution mode (AROWS mode 13) with a velocity resolution of ~0.081 km s−1. The hyperfine components of DCN 1−0 are visible.
In the text

	Fig. 3 Distribution of W(DCO+) (red bars) and W(DCN) (blue bars).
In the text

	Fig. 4 Spectral lines of DCO+ and H13CO+ 1−0 (black line) overlaid with the Gaussian fitting results (green line) toward G206.10-15.7. Double-velocity components in DCO+ and H13CO+ 1−0 were detected.
In the text

	Fig. 5 Distribution of W(H13CO+) (orange bars) and W(H13CN) (green bars).
In the text

	Fig. 6 Dfrac(HCO+) vs. Dfrac(HCN) for nine sources with both deuterated fractions.
In the text

	Fig. 7 Top: distributions of FWHM for DCO+ (red bars) and H13CO+ (orange bars) 1−0 in 46 sources where DCO+ and H13CO+ 1−0 were detected using the high-velocity resolution mode (AROWS mode 13). Bottom: distribution of FWHM of DCO+ in sources for which only DCO+ 1−0 was detected (red bars) and distribution of FWHM of H13CO+ in sources for which only H13CO+ 1−0 was detected (orange bars).
In the text

	Fig. 8 FWHM of DCO+ 1−0 vs. H13CO+ 1−0 of 46 sources in which both lines were detected with the high-velocity resolution mode (AROWS mode 13).
In the text

	Fig. 9 Top: comparison between the FWHM of DCO+ and Dfrac(HCO+). Bottom: comparison between the FWHM of H13CO+ and Dfrac(HCO+). Each plot contains 113 data points.
In the text

	Fig. 10 Distribution of Tex(CO) in sources where DCO+ 1−0 is detected (red bars) and where it is not detected (pink bars).
In the text

	Fig. 11 Distribution of W(HCO+) in sources where DCO+ 1−0 is detected (red bars) and where it is not detected (pink bars).
In the text

	Fig. 12 Comparison of Tex and Dfrac (HCO+) (red points), including the 3σ upper and lower limit value of Dfrac(HCO+) (red points and arrows) for sources with only H13 CO+ and only DCO+ detections, respectively.
In the text

	Fig. B.1 Comparison between FWHM of DCO+ with velocity resolution ~0.081 km s−1 with mode 5 and FWHM of DCO+ with velocity resolution ~0.32 km s−1 with mode 3. There are 32 points in the plot.
In the text

	Fig. C.1 Distribution of kinematic distance of sources where DCO+ 1-0 is detected or not.
In the text

	Fig. D.1 Line profiles of DCO+ 1-0 with the low velocity resolution mode (AROWS mode 3). The transitions of H13CO+ 1-0 have not been observed in these sources. Additional Figures D1∼D13 are available on Zenodo. https://zenodo.org/records/15013446
In the text