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A&A
Volume 622, February 2019
Article Number A32
Number of page(s) 18
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/201834411
Published online 24 January 2019

© ESO 2019

1 Introduction

The Planck satellite (Tauber et al. 2010; Planck Collaboration I 2011) carried out the first all sky survey in the submillimeter to millimeter range with unprecedented sensitivity and provides a catalog of cold clumps of interstellar matter in the Galaxy. The Cold Clump Catalog of Planck Objects (C3POs) released by Planck Collaboration XXIII (2011) consists of 10 342 cold sources that stand out against a warmer environment. The C3PO clumps are cold with dust temperatures ranging from 7 to 19 K, peaking around 13 K. Among the C3PO clumps, 915 early cold cores (ECCs) were identified with most valid detection and lowest dust temperatures (<15 K). Planck Collaboration XXVIII (2016) released 13 188 Planck Catalog of Galactic cold clumps (PGCCs) as the full version of the ECC catalog. The characteristics of coldness and quiescence make them good targets to investigate the initial conditions of star formation, including both dynamic processes and chemical states (Juvela et al. 2010, 2012, 2015, 2018; Parikka et al. 2015; Tatematsu et al. 2017).

Soon after the release of ECC data, surveys with different molecular spectral lines were conducted. Observations with the J = 1 − 0 transitions of 12CO, 13CO, and C18 O toward 674 Planck cold clumps selected from the ECC catalog were performed by Wu et al. (2012) using the 13.7 m telescope of the Purple Mountain Observatory (PMO). Mapping observations of the same transitions were followed up soon (Liu et al. 2012, 2013, 2015, 2016, 2018a,b; Meng et al. 2013; Zhang et al. 2016, 2018; Tang et al. 2018). Meanwhile, single-point observations of HCO+ J = 1 − 0 and HCN J = 1 − 0 toward 621 CO-selected cores associated with PGCCs were performed (Yuan et al. 2016). Thanks to these follow-up studies, the morphologies and dynamic properties of PGCCs are fairly well understood. However, their locations in the evolutionary sequence are still unclear. The chemical properties, essential for understanding the evolutionary states of PGCCs, were not given enough attention. To investigate the chemical evolutionary states of PGCCs, probing a large sample of such sources with molecule pair of the early formed molecule ethynyl radical (C2 H; Beuther et al. 2008) and the daughter molecule diazenylium (N2 H+; Aikawa et al. 2003; Tatematsu et al. 2017) will be helpful.

C2H is the simplest hydrocarbon molecule with the carbon-carbon triple bond (C ≡ C). Since being firstly detected by Tucker et al. (1974), C2H is found to bewidely distributed and detected in all evolutionary stages of star-forming regions (Sanhueza et al. 2013; Jiang et al. 2015). Beuther et al. (2008) suggest that this molecule could also be used to study the cold gas of forming stars to investigate their initial conditions. Meanwhile, N2 H+ is also an excellent tracer of dense molecular cloud cores (Caselli et al. 2002). N2 H+ is durable in cold and dense regions owing to the depletions of its destroyers such as CO and the delayed freeze-out of its precursors such as N2. We expect that C2H and N2 H+ are enhanced in different evolutionary states of PGCCs.

In this paper, we report a survey of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 toward the gas structures enclosed by emission of 13CO J = 1 − 0 in the PGCCs (Liu et al. 2012; Meng et al. 2013; Zhang et al. 2016). We have compared the spectra of our detected species with those of CO and its isotopologues as well as HCO+ and HCN (Wu et al. 2012; Yuan et al. 2016) to reveal the characteristics of C2 H and N2 H+ in PGCCs. We have also compared the abundances of C2 H and N2 H+ with those predicted by gas-grain chemical model to investigate the evolutionary states of single PGCC and PGCCs in different regions. This paper is arranged as follows. We present a description of the sample and observations in Sect. 2. The results of the molecular line observations are presented in Sect. 3. We discuss the properties of these two species and the chemical evolutionary states of detected sources in Sect. 4. We summarize the paper in Sect. 5.

thumbnail Fig. 1

Spatial distribution in the Galactic plane of observed sources. The CO-selected cores with and without detections of C2 H are denoted by the yellow and blue stars, respectively. The background image represents the Hα emission (Finkbeiner 2003) in unit of R (106/4π photons cm−2 s−1 sr−1). The green contours represent CO (1–0) integrated emission detected by Planck HFI (Planck Collaboration XIII 2014). The red contours show the Planck 353 μm continuum emission. The contour levels are (0.05, 0.1, 0.3, 0.5, 0.7, 0.9) × maximum value. Famous star forming regions such as Taurus-Perseus-California (Lombardi et al. 2010), Cepheus, Orion complex (Dame et al. 2001) are sketched with the black line.

2 Sample and observation

2.1 Sample characteristics

A sample consisting of 121 CO-selected cores with strongest emission of 13CO J = 1 − 0 (Wu et al. 2012) was selected to be observed in C2 H N = 1 − 0 and N2 H+ J = 1 − 0. Spectra of J = 1 − 0 of CO, 13CO and C18O at the center of observed cores were extracted from previous mapping observations (Liu et al. 2012; Meng et al. 2013; Zhang et al. 2016). The preliminary work of deriving line parameters from these CO data was done as described in Yuan et al. (2016). Basic information about our detected sources including their equatorial coordinates, distances, H2 column densities of host PGCCs derived from dust continuum (Nd (H2); Planck Collaboration XXVIII 2016), and CO parameters are listed in Table A.1.

Distances of these sources are adopted from the literature (Wu et al. 2012; Planck Collaboration XXVIII 2016). For sources with no available distances in the literature, distances are adopted as the values with the highest probabilities given by a Bayesian distance calculator (Reid et al. 2016). The distances calculated by the Bayesian distance calculator are on average 30% higher than those adopted from the literature (Table A.1). Figure 1 shows the spatial distribution of the observed sources. These sources are biased toward nearby star-forming regions while the Galactic plane is under-represented. These properties are inherited from the whole sample of ECCs and CO-selected cores (Wu et al. 2012; Yuan et al. 2016). The red and green contours represent Planck 353 μm continuum emission and Planck CO J = 1 − 0 emission detected by the High Frequency Instrument on the Planck satellite (Planck HFI; Planck Collaboration XIII 2014), respectively. Distribution of Planck 353 μm continuum is well correlated with that of CO J = 1 − 0 detected by Planck HFI. The Planck HFI CO emission traces relatively dense regions on Galactic scale, and our CO-selected cores tend to locate at the margins of these regions.

The excitation temperatures of CO J = 1 − 0 (Tex(CO)) for our CO-selected cores range from 9 to 21 K. The mean value of Tex (CO) is 14 K with a standard error of 0.3 K, and it is slightly larger than the value in Wu et al. (2012) and the average dust temperature (13 K) for C3POs (Planck Collaboration XXIII 2011). Sources in our sample generally have higher H2 column densities than those of CO cores in other PGCC samples. The H2 column densities of CO cores in nearby star-forming regions range from 1 × 1021 to 10 × 1021 cm−2 with a mean value of 2.2 × 1021 cm−2 (Meng et al. 2013), and those in the Galactic second quadrant range from 0.6 × 1021 to 36 × 1021 cm−2 with a mean value of 8 × 1021 cm−2 (Zhang et al. 2016). The H2 column densities (NCO(H2)) of our CO-selected cores are derived from N(13CO) adopting the 12C/13C isotope ratioand CO abundance (X[CO]) as the values in the solar neighbor with a Galactocentric distance ~8 kpc (Wilson & Rood 1994; Pineda et al. 2013), 63 and 9 × 10−5, respectively. NCO(H2) cover the range of (3–70) × 1021 cm−2 with a mean value of 2.2 × 1022 cm−2.

Futhermore, 20 cores with valid detection of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 were selected to perform mapping observations.

2.2 Observations

Single-point observations of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 (Table 1) were carried out with the PMO 13.7 m telescope from 2015 May to June. The nine-beam Superconducting Spectroscopic Array Receiver (SSAR) was working as the front end in sideband separation mode (see Shan et al. 2012). An FFTS spectrometer was used as back end, which has a total bandwidth of 1 GHz and 16 384 channels, corresponding to a velocity resolution of 0.21 km s−1 for C2 H N = 1 − 0 and 0.20 kms−1 for N2 H+ J = 1 − 0. C2 H N = 1 − 0 was observed in the lower sideband (LSB), while N2 H+ J = 1 − 0 was observed simultaneously in the upper sideband (USB). The half-power beam width and main beam efficiency at 90 GHz are about 56′′ and 0.5, respectively. The pointing accuracy of the telescope was better than 4′′. The typical system temperature(Tsys) is around 170 K and varies about ten percent. Spectra of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 were integrated till the rms of Ta ranged from 20 to 50 mK.

Mapping observations were performed in June 2015 using the PMO 13.7 m telescope. Same front and back ends were employed as in single-point observations. The on-the-fly (OTF) observation mode was applied. The antenna continuously scanned a region of 18′ × 18′ centered on CO-selected cores with a scan speed of 20′′ s−1. Only the central 10′ × 10′ regions were cut out for further analyses because the edges of the OTF maps are very noisy. Data were meshed with a grid spacing of 30′′.

The GILDAS1 package including CLASS and GREG (Guilloteau & Lucas 2000; Pety 2005) was used to reduce the data. All figures were plotted using the open source Python package, Matplotlib.

Table 1

Line parameters.

3 Results

Among the 121 observed CO-selected molecular cores, 71 have detection of C2 H N = 1 − 0 and 58 have detection of N2 H+ J = 1 − 0. Cores with or without detection of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 are denoted in Fig. 1 with stars in different colors, and their projected spatial distributions have no obvious deviations. Typical spectra of several cores with antenna temperature (Ta) of C2 H N = 1 − 0, J = 3∕2 − 1∕2, F = 2 − 1 larger or smaller than or comparable with that of N2 H+ F1 = 2 − 1 are shown in Fig. 2 as examples.

Mapping observations of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 are performed toward 20 cores. Both lines are detected in all sources except N2 H+ J = 1 − 0 in G167.2-15A1.

3.1 Line parameters

All six hyperfine structure (HFS) components are well resolved for C2 H N = 1 − 0 of detected sources, while only the spectra of the main component C2 H N = 1 − 0, J = 3∕2 − 1∕2, F = 2 − 1 are exhibited in Fig. 2. However, only three groups of HFS components of N2 H+ J = 1 − 0, as listed in Table 1, are well resolved for most of the sources. F1 = 2 − 1 is the main group of N2 H+ J = 1 − 0 and consists of two hyperfine lines labeled as F = 2 − 1 and F = 3 − 2 with a velocity separation ~1 km s−1.

Using the HFS fitting program in GILDAS/CLASS, we performed hyperfine structure fitting toward spectra of C2 H N = 1 − 0 and N2 H+ J = 1 − 0. In the HFS fitting, the optical depths of different hyperfine lines are all assumed as Gaussian with the same width, and the excitation temperatures for different HFS components are the same (Feng et al. 2016). Hyperfine structure fitting can give the parameters such as line width (ΔV) and velocity (VLSR) very precisely. The results of HFS fittings are listed in Table A.2, including Ta, VLSR, ΔV, and integrated intensities (∫ TadV) of C2 H N = 1 − 0, J = 3∕2 − 1∕2, F = 2 − 1 and N2 H+ J = 1 − 0, F1 = 2 − 1. The optical depths are not listed because most of the lines we detect are optical thin (τ < 0.1), and hence HFS fitting can not provide accurate values of optical depths.

The Ta of C2 H N = 1 − 0, J = 3∕2 − 1∕2, F = 2 − 1 ranges from 0.08 to 0.93 K with a median value of 0.50 K. The Ta of N2 H+ N = 1 − 0, J = 1 − 0, F1 = 2 − 1 ranges from0.10 to 1.03 K with a median value of 0.45 K. The sources with detection of N2 H+ J = 1 − 0 all have detection of C2 H N = 1 − 0. Only 10 sources have Ta of N2 H+ J = 1 − 0, F1 = 2 − 1 larger than that of C2 H N = 1 − 0, J = 3∕2 − 1∕2, F = 2 − 1 by more than 3 σ (Table A.2), and all of them have line widths of C2 H N = 1 − 0 and C18O larger than the average line width of C2 H (~1.0 km s−1) except G104.4+06A1.

Figure 3a shows the correlation between the VLSR of C2 H N = 1 − 0 and N2 H+ J = 1 − 0. They agree with each other very well, with smaller than three, where . From Fig. 3b, one can see that line widths of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 are also quite consistent with each other and δ ((-) is smaller than 1.5, where . The mean widths of 13CO J = 1 − 0 and C18 O J = 1 − 0 of these CO-selected cores with valid detection of C2 H N = 1 − 0 are 2.0 and 1.3 km s−1, slightly larger than the mean width of C2 H N = 1 − 0. However, from Fig. 3c it can be clearly seen that the larger mean width of C18 O mainly results from several sources (shown as red dots) with smaller than 1 km s−1. The ΔV of C2 H N = 1 − 0 are well consistent with those of C18O J = 1 − 0 for the rest of the sources, especially for sources with widest line widths. Figure 3d shows the cumulative distribution functions of nonthermal velocities (Eq. (5)) traced by C2 H N = 1 − 0 and N2 H+ J = 1 − 0. Nonthermal velocity dispersions, σNT, traced by C2 H N = 1 − 0 and N2 H+ J = 1 − 0 can be better fitted with lognormal distributions than Gaussian distributions. The probability density function function of lognormally distributed random variable X (fX) can be expressed with three parameters (a, b, c) as (1)

The mean (μ) and variance (σ2) of lognormally distributed random variable X can be expressed as

The three parameters of the best lognormal fits are (0.88, 0.14, 0.20) and (0.87, 0.13, 0.16; Fig. 3d), corresponding to mean values and standard deviations (μ, σ) of the fitted curves (0.43, 0.32) km s−1 and (0.36, 0.25) km s−1, respectively.

thumbnail Fig. 2

Example spectra of CCH (blue) and N2H+ (red).

3.2 Derived parameters

The dispersions of thermal velocity (σtherm) and one dimensional nonthermal velocity (σNT) can be calculated as

where , Ttherm is the gas kinetic temperature which is adopted as excitation temperature of CO, k the Boltzmann’s constant, mX the molecular mass, mH the mass of atomic hydrogen, and = ρ/n(H2) the mean molecular weight of the gas (Kauffmann et al. 2008). is adopted as 2.72 assuming n(He)/n(H) = 0.18 and ignoring the mass contributions of metals. The σNT derived from emission of C2 H N = 1 − 0 and that of N2 H+ J = 1 − 0 are listed in the second and third columns of Table A.3, respectively.

Under the assumption of local thermal equilibrium (LTE), column densities of C2 H and N2 H+ can be calculated through (e.g. Mangum & Shirley 2015)

where J(T) = , Tbg (2.73 K) is the temperature of the cosmic background radiation, h is the Planck constant, and the beam-filling factor f is assumed as unit. The permanent dipole moment μ, line strengthSij, partition function Q and upper level energy Eu were adopted from the Cologne Database for Molecular Spectroscopy2 and partly listed in Table 1.

Unfortunately, the excitation temperatures cannot be given by HFS fittings because most lines we detected areoptical thin and the exact beam filling factors are unknown for single-point sources. Besides, the assumption that the excitation temperatures of different hyperfine components stay the same is not always valid. For example, the differences among the excitation temperatures of different hyperfine components of C2 H N = 1 − 0 can be as large as several K in L1498 (Padovani et al. 2009). Therefore, the excitation temperatures Tex~ 5 K were adopted. For optical thin lines, the assumption, Tex = Eu∕k, was usually made to give the lower limits to the column densities (Miettinen 2014). It is also consistent with the typical excitation temperatures of the N2 H+ J = 1 − 0 (5 K) in dense cloud cores (Caselli et al. 2002). To explore how large uncertainties are brought in under this estimation, we also calculated the column densities with excitation temperatures deduced from spectra of J = 1 − 0 of 12CO and 13CO. The column densities of C2H and N2 H+ as well as their ratios calculated based on the two set of Tex assumptionsare listed in the fourth-to-sixth and seventh-to-ninth columns of Table A.3, respectively.It is clear from Table A.3 that column densities calculated based on the two set of Tex assumptionsdo not deviate much from each other, and most of them have deviations less than 15%. An underestimation of Tex (5 K) would introduce a higher τ through Eq. (7), which compensates for the reduced column densities introduced by it in Eq. (6). The values of N(C2H)/N(N2H+) change little within a wide range of temperatures (Pan et al. 2017). The column densities calculated with Tex = 5 K are adopted for further discussions.

thumbnail Fig. 3

Panela: correlation between the centroid velocity of C2H N = 1 − 0 and that of N2H+ J = 1 − 0. The green solid line represents the result of linear least-squares fitting. Panel b: correlation between the line width of C2 H N = 1 − 0 and that of N2H+ J = 1 − 0. Blue dashed line represents ΔV = ΔV. Panel c: correlation between line width of C2H N = 1 − 0 and the difference between the line width of C2H N = 1 − 0 and that of C18O. The two dashed lines denote the 1 σ values for the distribution of line width differences. Panel d: fittings of the cumulative distribution functions of nonthermal velocities. Red and yellow solid lines show results of lognormal fittings. The three parameters (Eq. (1)) of the best lognormal fits are (0.88, 0.14, 0.20) and (0.87, 0.13, 0.16), respectively. Dashed pink lines show results of standard-normal fittings.

3.3 Mapping parameters

Among sources with detection of C2 H N = 1 − 0 and N2 H+ J = 1 − 0, 20 were performed with mapping observations, and all have detection of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 with a σ ~ 0.08 K km s−1 except G167.2-15A1. The nondetection of N2 H+ J = 1 − 0 for G167.2-15A1 might be due to its weak emission (Ta ~ 0.33 K) and shorter integration time (σ ~ 0.13 K) compared with other mapped sources. The integrated intensities of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 are shown as blue and red contours in Fig. 4, respectively.

From each map shown in Fig. 4, one or several substructures are resolved in one CO-select core. The contour with half maximum value is taken as the border line of a substructure. Additional labels are used to distinguish different substructures if there are two or more substructures resolved within a single map, for example “NE” if one substructure was in the northeast relative to its neighbor substructure. Since the emission regions of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 are well correlated with each other, each substructure resolved from C2 H N = 1 − 0 map is matched with its nearest substructure resolved from N2 H+ J = 1 − 0 map, and asame location label is given to them. The radius (r) of a substructure is defined as the radius of a circle whose area is equal to the area enclosed by the border line of that substructure. In total there are 26 substructures resolved with r > 0.5′. The average value of the radius for C2H substructures is 1.3 ± 0.1 arcmin (0.28 ± 0.05 pc), and it is larger than that for N2 H+ substructures, 0.9 ± 0.1 arcmin (0.22 ± 0.05 pc). The names of their harboring CO-selected cores and their location labels are listed in the first two columns of Table A.4. Process of calculating the peak column densities is the same as that in Sect. 3.2. Parameters including peak positions, VLSR, ΔV, and column densities of peak points as well as the radii of these substructures are also listed in Table A.4.

Because the abundances of C2 H are less variant than those of N2 H+, the masses of substructures (Msub) are calculated based on emission of C2 H N = 1 − 0 through the equation (8)

where the abundance of C2 H (X[C2H]) is assumed as 10−8. It is reasonable because abundances of C2H are nearly constant in diffuse molecular gas (4 ± 2 × 10−8; Beuther et al. 2008), starless cores such as TMC-1 (3–5 × 10−8; Liszt et al. 2018) and prestellar cores such as L1498 (0.8 ± 0.1 × 10−8; Padovani et al. 2009) as well as PGCCs (Sect. 4.2). The uncertainty of calculated Msub contributed by the assumption of fixed X[C2H] can be as high as a factor of five. Virial masses (Mvir) of dense cores assumed as gravitationally bounded spheres with ρ ∝ R−2 can be calculated though (MacLaren et al. 1988; Williams et al. 1994) (9)

where ), G is the gravitational constant, γ = 5∕3. The Msub, Mvir and virial parameters α = Mvir/Msub are listed in the last three columns of Table A.4.

The derived virial parameters range from 1.2 to 21.8 with a median value of 4.8. Among the 26 substructures resolved, 20 have virial parameters smaller than five. Considering the possible underestimations of the masses of substructures for the overestimations of X[C2H], most of these substructures in PGCCs are approximately virialized and slightly confined by external pressures (Pattle et al. 2015).

thumbnail Fig. 4

Contours of integrated intensities of C2H N = 1 − 0 (blue) and N2H+ J = 1 − 0 (red) from 45 to 95% stepped by 10% of maximum value. Background shows 13CO emission. Yellow triangles and green stars represent 2MASS sources and IRAS sources quoted from Simbad, respectively.

4 Discussion

4.1 Kinematics

All sources have only one velocity component with single peak, except for G120+03A1 and G133.4+09A1 whose spectra exhibit blue asymmetry. A double-peaked line is blue or red asymmetric if its higher peak skews to the blue or red side. Combining with an optically thin line, an optically thick double-peaked line can be further identified as a blue profile if its higher peak is shifted blueward with δV = (Vthick − Vthin)/ΔVthin < −0.25 (Myers et al. 1996; Mardones et al. 1997). A red profile would have δV > 0.25 (Wu et al. 2007; Yuan et al. 2013). However, the characteristic blue profile will appear only if the molecular tracer has a suitable optical depth and critical density (Wu & Evans 2003; Evans et al. 2005) within a source with warmer center regions (Zhou et al. 1993). Blue profiles are not expected to be common in PGCCs with dark and cold center regions.

Similar profiles may also be produced by multicomponents of target sources. In G120+03A1, spectrum of HCO+ J = 1 − 0 was identified as red profile (with higher red peak) by Yuan et al. (2016). Although emission of N2 H+ J = 1 − 0 is weak and blended by several hyperfine structures, a small blue component can still be resolved. Spectrum of C18 O J = 1 − 0 has two peaks similar to that of C2 H N = 1 − 0 while that of 13CO J = 1 − 0 shows a flat-topped single peak (Yuan et al. 2016). In G133.4+09A1, both spectra of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 show two resolvable peaks. A small red component can also be resolved with C18 O J = 1 − 0, but not with HCN J = 1 − 0 and HCO+ J = 1 − 0 (Yuan et al. 2016). Spectrum of HCO+ J = 1 − 0 shows broad line wings and there are multiple peaks in the spectrum of 12CO J = 1 − 0. These two sources may consist of two or more velocity components. Only the main velocity components are fitted since the remaining velocity components can not be resolved fully in spectra of different species.

The widths of different lines might be the result of the different level of turbulence on different spatial scales. ΔV of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 agrees with each other well (Fig. 3c) because they have similar critical densities (Ungerechts et al. 1997) and both trace the inner dense regions of PGCCs. The mean width of C2 H N = 1 − 0 is about 1.0 km s−1 and it is similar to that of HCN J = 1 − 0 in Yuan et al. (2016) and that of C18O J = 1 − 0 in Wu et al. (2012). It is also close to the mean width of 13CO J = 1 − 0 for CO-selected cores in the molecular complexes of Orion (0.9 km s−1), Taurus (1.1 km s−1), and California (1.4 km s−1; Liu et al. 2012; Meng et al. 2013). For most of these PGCC sources, the line widths seem to be uniform on different scales. It may indicate that turbulence has been dissipated on smaller scales. The entire PGCC region is nearly “transition-to-coherence” because of the low density, thus cutoff wavelength below which Alfven waves cannot propagate and support turbulence (Goodman et al. 1998) is large. Below coherence scale, constant residual line widths persist throughout the volume (Tafalla 2005). The region outside such a coherent core is more like filled with cloud components with a radially power-law distributed velocity field. The Larson’s ΔV–r relationship (Larson 1981) can not be applied to PGCCs (Zhang et al. 2016) because the H2 column densities of PGCCs are lowest compared with other star formation samples such as infrared dark clouds (IRDCs; Wu et al. 2012) thus 13CO and C18 O traced the relatively dense components in PGCCs. It is also compatible with the concept that these PGCCs are quiescent and most of them seem to be in transitions from clouds to dense clumps (Wu et al. 2012). The cloud components may contribute to the broad line widths of C18 O of several sources with narrow C2H lines. Sources with broad line widths of C2H and N2 H+ may be more evolved since sources with emission of N2 H+ stronger than that of C2H all have line widths broader than 1 km s−1.

The typical nonthermal velocity traced by C2 H N = 1 − 0 in CO-selected cores is comparable with that in dense cloud cores (Caselli et al. 2002), whose typical line width of NH3 is ~ 0.5 km s−1 which corresponds to a σNT ~ 0.2 km s−1. The ratio between σNT and σtherm ranges from0.7 to 4.7 with a median value of 1.6. Among 71 sources, 12 have σNT/σtherm < 1. It is consistentwith the idea that supersonic isothermal turbulence is well developed with a lognormal velocity distribution (Veltchev et al. 2016) in outer part of PGCC and decays as the radius decreases. The residual line width in coherent region persists due to subsonic or low supersonic turbulence (Goodman et al. 1998; Myers 1998). Emission of C2 H and N2 H+ traces the inner coherent regions of PGCCs, where radial density distributions of pressure-confined Bonnor–Ebert spheres (Pattle et al. 2015)may be established.

All these characteristics indicate that most of our selected cores in PGCCs are very cold (with an average gas temperature 14 K), quiescent and with single component, while still turbulence dominant. However, there are still some obviously more envolved sources. Our sample is made up of different components including clouds, relatively isolated cold clumps and evolved gas cores. Emission of C2 H and N2 H+ originates from the inner dense regions but may have different states of chemical evolutions (Sect. 4.2).

thumbnail Fig. 5

Panela: relation between the abundances of C2H and N2 H+ of CO-selected cores and the H2 column densities of their host PGCCs (Nd(H2)). The abundances of C2H and N2 H+ of our sourceslocate in two different regions separated by the green line. The dashed red line shows the result of linear least-square fitting on data represented by red circles. Panel b: blue line shows number density distribution of log(N(N2H+)/N(C2H)) for our detected PGCC sources. The value of this parameter for typical sources are also shown, including well known starless cores TMC-1 (Hirota et al. 2004; Liszt et al. 2018), L1498 and CB246 (Padovani et al. 2009), massive clumps associated with infrared dark clouds I18151-1208 MM3 (abbreviated as I18151MM3) and G019.27+0.07 MM1 (abbreviated as G019MM1; Sakai et al. 2008, 2010), as well as the infrared dark cloud G028.23-00.19 (Sanhueza et al. 2013).

4.2 Abundances of C2H and N2 H+

These early cores in our sample with low temperatures but high enough column densities to shield interstellar radiation field (Tatematsu et al. 2017) are good sites to test the evolutions of those two kind of molecules. C2 H is generally the most abundant hydrocarbon (Liszt et al. 2018) in diffuse molecular gas and dark cloud gas. It has been known to be a tracer of photo-dissociation regions (PDRs; Fuente et al. 1993). Recent evidences suggest that it could also trace the cold and dense gas associated with the early stage of star formation. In dark clouds, C2 H has an extended distribution (Beuther et al. 2008). In the early stage of dark clouds, C2 H is thought to reside in the inner regions instead of in the external photo-dissociated layers of clumps (Sanhueza et al. 2013). In the latter stages C2 H can still has a high abundance in the outer region when it is oxidized to form other species such as CO, OH and H2 O in the dense center regions (Beuther et al. 2008; Miettinen 2014; Feng et al. 2016). However, N2 H+ usually shows centrally peaked emission for its durability in dense regions. N2 H+ forms through proton transfer reaction (Aikawa et al. 2001). N2 H+ is impeded if CO is present in the gas phase for the competition of CO to react with its precursor H through . Furthermore, CO also plays the role of the direct destroyer of N2 H+ through reaction N2H+ + CO →HCO+ + N2 (Bergin et al. 2002). Anticorrelation between N2 H+ and gas-phase CO was presented in envelopes around the pre-stellars and protostars, such as L1544 (Caselli et al. 1999) and IC 5146 (Bergin et al. 2001). In star-forming cores, heating and radiations of protostars will lead to the generation of C2 H and the destruction of N2 H+, which make it hard to predict the evolution trends of the abundances of these two species.

Figure 5a shows the relation between the abundances of C2 H and N2 H+ of CO-selected cores and the H2 column densities of their host PGCCs (Nd (H2)). The H2 column densities of CO-selected cores derived from emission of 13CO J = 1 − 0 (NCO(H2)) are adopted to calculate the abundances of C2H and N2 H+. Nd (H2) are much lower than NCO(H2) for relatively large beams (~4.3′ at 350 μm; Planck Collaboration XXVIII 2016) and should be treated as the densities of the environments of CO-selected cores. N2 H+ abundances of CO-selected cores are positively correlated with Nd (H2), but with a large dispersion (Fig. 5a). It suggests that N2 H+ abundances are positively correlated with the evolutionary ages if the cores in PGCCs with larger Nd (H2) tend to be more evolved. On the other hand, the abundances of C2 H are weakly correlated with Nd (H2). From Fig. 5a, it is clear to see that the abundances of C2 H and N2 H+ of our sources locate in two different regions separated by a green line. Our sources all have N(C2H) > N(N2H+) thus in pretty young states (< 5 × 105 yr). The abundances of C2H and N2 H+ as well as their ratios can serve as intrinsic parameters to trace the evolutionary states of PGCC gas cores. Figure 5b shows the number density distribution of the ratio between the column density of N2 H+ and that of C2 H (N(N2H+)/N(C2H)). The value of N(N2H+)/N(C2H) for typical starless cores and IRDCs are also shown in Fig. 5b. Our PGCC cores generally have N(N2H+)/N(C2H) higher than those of starless cores such as TMC-1 and L1498, but lower than those of IRDCs such as G028.34S, which is consistent with the result of Tatematsu et al. (2017).

We built a very simple gas-grain chemical model to unveil the evolution of C2 H and N2 H+ in cold gas. In this simulation, a single-point (zero-dimension) chemical code is run under an ordinary differential equation solver DVODE (Brown et al. 1989) with most physical parameters fixed and dynamical processes are not coupled. The temperature is adopted as 10 K, the visible extinction Av = 5, the grain radius σg = 0.03 μm, and the rate of ionization by cosmic-ray γ is set as 1.2 × 10−17 s−1 (Lee et al. 2004). At such a low temperature that is lower than the thermal evaporation temperature of CO 22–25 K (Bergin et al. 1995; Ripple et al. 2013), there is nearly no feedback of gas particles except H2 from grain surfaces, although grain surface reactions are very active. The gas phase reactions were downloaded from UMIST Database for Astrochemistry 2012 (McElroy et al. 2013) with 6173 reactions for 467 kind of species. The metal abundances are adopted as the low-metal abundance case of Graedel et al. (1982). Initially, the elements are all ionized except the hydrogen atoms. The volume density n(H2) is fixed as 105 cm−3, and the results of the simulation are shown in Fig. 6a. Adopting a lower or higher n(H2) has little influence on the evolution trends of the abundances except the timescale, especially for the early stages when the chemical processes are mainly driven by the atoms and ions generated from photo-dissociation and photo-ionization during prior more diffuse phase instead of externally induced ionizations. It is natural that the abundances of species will evolve slower or faster under a lower or higher n(H2) (Pan et al. 2017). The values along the x-axis of Fig. 6a have limited meanings and should not be interpreted as the exact chemical ages considering the variances of volume densities of PGCCs. Instead, we find that X[C2H]/X[N2H+] is an intrinsic parameter to trace the evolutionary state of a PGCC.

In early stage, the abundance of N2 H+ increases with time while that of C2H stays nearly constant. The abundance of C2H drops down quickly after the carbon atoms are depleted, while that of N2 H+ keeps growing. As shown in Fig. 6b, the ratio between the abundance of N2 H+ and that of C2H can trace the evolution states of PGCCs quite well. The cores with the lowest abundances of N2 H+ (< 10−10) are in the youngest evolutionary states compared with other sources, and most of them are located in the green band shown in Fig. 6b whose center line has a power-law index of 0.75. The power law index is slightly lower than one maybe because of the depletions of CO (Liu et al. 2012) and thus the H2 column densities in evolved regions are underestimated. For more evolved cores, X[N2H+] versus X[C2H]/X[N2H+] deviates from the green band for dropping down of the abundances of C2 H. The cores with high abundances of N2 H+ (~ 10−9) but still located in the green band may have the harshest depletions of CO. Another possibility is that the C2 H emission regions in these cores are dominated by the outer regions where the abundances of C2 H have not yet dropped down. Observations with higher resolutions will be helpful to investigate the depletions in the most inner dense regions of PGCCs, and exam the validity and general applicability of this molecule pair as a tracer of evolutionary state.

thumbnail Fig. 6

Panel a: time evolution of species according to the result of gas-grain chemical model. Panel b: relation between abundances of N2H+ and N[C2H]/N[N2H+]. The color of each dot represents according CO excitation temperature, and dot-size represents column density of H2 induced from 13CO (NCO (H2)). The green line represents the center line of the green band. The blue line shows the result of the gas-grain chemical model.

4.3 Emission regions

Most of our mapped sources are located in nearby star forming regions such as Taurus and Cepheus (Wu et al. 2012, and the references therein). Cepheus region consists of two velocity components called feature A (300–500 pc) and feature C (800 pc), and they are associated with the Gould belt and the local arm or Orion arm, respectively (Olano et al. 2006). The distance of taurus ranges from 130 to 160 pc (Loinard et al. 2011). Among these 20 mapped CO-selected cores in PGCCs, six are associated with IRAS and eight with 2MASS objects, both within CO emission regions. There are no cores associated with both IRAS and 2MASS objects. This is unlike the case of PGCCs in the second quadrant (with 98° < l < 180° and −4° < b < 10° as defined by Dame et al. 1987) in which most of the associated IR objects are IRAS point sources and the rest are 2MASS objects (Zhang et al. 2016). However, the ratio of the count of cores associated with IR objects to the size of the sample (referred as core-associated-ratio below) of our sample (~70%) is similar to that in nearby star forming regions (Meng et al. 2013). However, among the eight cores in Taurus region (see Table A.4), only three (G159.2-20A1, G168.7-15A2, G173.3-16A1) are associated with IRAS or 2MASS objects. The high core-associated-ratio is mainly contributed by cores in Cepheus region. Among the eight cores in Cepheus region (see Table A.4), only one (G110.6+09A1) is starless. The C2 H and N2 H+ substructures are much smaller than their host clumps and CO emission regions. The average value of r(CO)/r(C2H) and r(CO)/r(N2H+) is 2.3 and 2.9, respectively. Objects locating within the border line of a substructure are considered as its associated objects. In total there are ten substructures associated with IRAS or 2MASS objects. Among them, six are in Cepheus and only one in Taurus. The PGCCs in Cepheus region may be generally more evolved than those in the Taurus Complex.

The average value of line widths of substructures in Cepheus, 1.13 km s−1, is larger than that in Taurus region, 0.88 km s−1 (Table A.4). The average value of r(C2H)/r(N2H+) for the cores in Taurus, 1.33, is larger than that in Cepheus, 1.15. Similarly the average value of the N(C2H)/N(N2H+) in Taurus, 23, is larger than that in Cepheus, 13. These characteristics again confirm that PGCCs in Taurus are less evolved than those in Cepheus. For young sources such as PGCCs in Taurus, distribution of C2 H is much more extended than that of N2 H+. For more evolved sources like PGCCs in Cepheus, N2 H+ is generated in the dense region (Tatematsu et al. 2017) and the area of emission region of N2 H+ continuously expands till close to that of C2H.

Our finding is compatible with the statistics of Myers (1998). Among four complexes, Taurus, Perseus, Orion, and Cepheus, the percentage of supercritical and cluster associated cores is lowest in Taurus, while highest in Cepheus. The cores in Cepheus tend to be dynamically and chemically more evolved than those in Taurus, because the Taurus complex is younger than Cepheus complex as a whole. Another possibility is that the materials in Cepheus are significantly affected by the large void between Cassiopeia and Cepheus (Grenier et al. 1989; Tachihara et al. 2005).

Among the four mapped cores not located in Taurus and Cepheus, C2 H emission regions of two cores (G192.3-11A2, G172.8+02A1) is quite compact, while those of the other two cores (G070.4-01A2, G084.7-01A2) are extended. Emission of C2H with annular distribution is detected in G070.4-01A2 (Fig. 4). Similar emission distribution had been detected by Tatematsu et al. (2017) in PGCC with C2 S surrounding centrally peaked N2 H+. Abundance of C2H is positively correlated with that of C2S in dark cloud cores beacuse of the reactions (Suzuki et al. 1992). Emission of C2H shows annular distribution attributed to the depletion of C2H in the central regions of prestellar cores such as L1498 (Padovani et al. 2009). Similar C2 H distributions are also observed in various massive star formation regions (Li et al. 2012) such as NGC 6334I (Walsh et al. 2010) and PDRs around H II regions (Pilleri et al. 2013). Although the depletion factors of CO are usually not high (<2) in early PGCC cores (Liu et al. 2013), the depletion factors in C2 H N = 1 − 0 emission dominant region can not be ignored considering the dipole moment of C2 H (0.77 D; Wilson & Green 1977) is about seven times higher than that of CO. Depletions in the densest places of PGCCs may produce the annular distributions of C2H emission regions.

5 Summary

We have made C2 H N = 1 − 0 and N2 H+ J = 1 − 0 single-point observations toward 121 CO-selected cores of PGCCs. The detection rate is 59% for C2 H J = 1 − 0 and 48% for N2 H+ J = 1 − 0. Line parameters were derived through HFS fittings. Our column densities calculated assuming Tex equal to 5 K and excitation temperatures of CO J = 1 − 0 are well consistent with each other, and most of them (65%) have deviations of less than 15%. We also mapped 20 sources with the same transitions. Substructures were resolved from maps of C2 H and N2 H+ with peaks slightly dislocated. Our main findings are as follows:

  • 1.

    Mostspectra of detected sources are single peaked. Sources that show red and blue profiles in HCO+ are identified with multicomponents under joint analysis of spectra of C2 H, N2 H+, CO as well as HCN and HCO+. Centroid velocities and line widths of C2 H N = 1 − 0 and N2 H+ J = 1 − 0 are consistent with each other. Most sources (83%) have nonthermal velocities comparable with or larger than thermal velocities. All those characteristics indicate that most of our CO-selected cores in PGCCs are very cold (9–21 K) and quiescent while still dominanted by turbulence.

  • 2.

    We find that the ratio between the abundance of C2 H and N2 H+ is a good tracer of evolution for PGCCs. Gas grain chemical model based on UMIST network is applied to fit N(C2H)/N(N2H+) versus N(N2H+). At the most early stage (N(C2H)/N(N2H+) > 10), abundance of C2 H is nearly invariable while that of N2 H+ increases continuously. Later on (N(C2H)/N(N2H+) < 10), abundance of N2 H+ keeps growing while that of C2H drops rapidly as the exhaustion of carbon atoms. These PGCCs in our sample are in quite early stages and chemistry driven by residual atoms and ions generated from photo-dissociation and photo-ionization during prior more diffuse phase still plays a important role.

  • 3.

    The PGCC cores mapped are approximately virialized (α < 5) and slightly confined by external pressures. Sources in Cepheus have lower ratios between N(C2H) and N(N2H+) and larger line widths compared with those in Taurus. The probability of finding an associated IR source within PGCC substructures in Cepheus, 55%, is larger than that in Taurus, 10%. These indicate that PGCCs in Taurus are less chemically evolved than those in Cepheus. The C2 H emission region of G074.4+01A2 shows an annular distribution.

Acknowledgements

We are grateful to the staff of PMO Qinghai Station. We also thank Ken’ichi Tatematsu and Junzhi Wang for the helpful discussions. This project was supported by the grants of the National Key R&D Program of China No. 2017YFA0402600, NSFC Nos. 11433008, 11373009, 11373026, 11503035, 11573036 and U1631237, and the China Ministry of Science and Technology under State Key Development Program for Basic Research (No.2012CB821800), and the Top Talents Program of Yunnan Province (2015HA030). J.Y. is supported by the Young Researcher Grant of National Astronomical Observatories, Chinese Academy of Sciences.

Appendix A Additional tables

Table A.1

Source sample.

Table A.2

Line parameters.

Table A.3

Derived parameters.

Table A.4

Mapping parameters.

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All Tables

Table 1

Line parameters.

In the text
Table A.1

Source sample.

In the text
Table A.2

Line parameters.

In the text
Table A.3

Derived parameters.

In the text
Table A.4

Mapping parameters.

In the text

All Figures

thumbnail Fig. 1

Spatial distribution in the Galactic plane of observed sources. The CO-selected cores with and without detections of C2 H are denoted by the yellow and blue stars, respectively. The background image represents the Hα emission (Finkbeiner 2003) in unit of R (106/4π photons cm−2 s−1 sr−1). The green contours represent CO (1–0) integrated emission detected by Planck HFI (Planck Collaboration XIII 2014). The red contours show the Planck 353 μm continuum emission. The contour levels are (0.05, 0.1, 0.3, 0.5, 0.7, 0.9) × maximum value. Famous star forming regions such as Taurus-Perseus-California (Lombardi et al. 2010), Cepheus, Orion complex (Dame et al. 2001) are sketched with the black line.
In the text
thumbnail Fig. 2

Example spectra of CCH (blue) and N2H+ (red).
In the text
thumbnail Fig. 3

Panela: correlation between the centroid velocity of C2H N = 1 − 0 and that of N2H+ J = 1 − 0. The green solid line represents the result of linear least-squares fitting. Panel b: correlation between the line width of C2 H N = 1 − 0 and that of N2H+ J = 1 − 0. Blue dashed line represents ΔV = ΔV. Panel c: correlation between line width of C2H N = 1 − 0 and the difference between the line width of C2H N = 1 − 0 and that of C18O. The two dashed lines denote the 1 σ values for the distribution of line width differences. Panel d: fittings of the cumulative distribution functions of nonthermal velocities. Red and yellow solid lines show results of lognormal fittings. The three parameters (Eq. (1)) of the best lognormal fits are (0.88, 0.14, 0.20) and (0.87, 0.13, 0.16), respectively. Dashed pink lines show results of standard-normal fittings.
In the text
thumbnail Fig. 4

Contours of integrated intensities of C2H N = 1 − 0 (blue) and N2H+ J = 1 − 0 (red) from 45 to 95% stepped by 10% of maximum value. Background shows 13CO emission. Yellow triangles and green stars represent 2MASS sources and IRAS sources quoted from Simbad, respectively.
In the text
thumbnail Fig. 5

Panela: relation between the abundances of C2H and N2 H+ of CO-selected cores and the H2 column densities of their host PGCCs (Nd(H2)). The abundances of C2H and N2 H+ of our sourceslocate in two different regions separated by the green line. The dashed red line shows the result of linear least-square fitting on data represented by red circles. Panel b: blue line shows number density distribution of log(N(N2H+)/N(C2H)) for our detected PGCC sources. The value of this parameter for typical sources are also shown, including well known starless cores TMC-1 (Hirota et al. 2004; Liszt et al. 2018), L1498 and CB246 (Padovani et al. 2009), massive clumps associated with infrared dark clouds I18151-1208 MM3 (abbreviated as I18151MM3) and G019.27+0.07 MM1 (abbreviated as G019MM1; Sakai et al. 2008, 2010), as well as the infrared dark cloud G028.23-00.19 (Sanhueza et al. 2013).
In the text
thumbnail Fig. 6

Panel a: time evolution of species according to the result of gas-grain chemical model. Panel b: relation between abundances of N2H+ and N[C2H]/N[N2H+]. The color of each dot represents according CO excitation temperature, and dot-size represents column density of H2 induced from 13CO (NCO (H2)). The green line represents the center line of the green band. The blue line shows the result of the gas-grain chemical model.
In the text

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