Ammonia Observations of Planck Cold Cores

Single-pointing observations of NH$_3$ (1,1) and (2,2) were conducted towards 672 Planck Early Release Cold Cores (ECCs) using the Nanshan 26-m radio telescope. Out of these sources, a detection rate of 37% (249 cores) was achieved, with NH$_3$(1,1) hyperfine structure detected in 187 and NH$_3$(2,2) emission lines detected in 76 cores. The detection rate of NH3 is positively correlated with the continuum emission fluxes at a frequency of 857 GHz. Among the observed 672 cores, ~22% have associated stellar and IR objects within the beam size (~2$\arcmin$). This suggests that most of the cores in our sample may be starless. The kinetic temperatures of the cores range from 8.9 to 20.7 K, with an average of 12.3 K, indicating a coupling between gas and dust temperatures. The ammonia column densities range from 0.36 to 6.07$\times10^{15}$ cm$^{-2}$, with a median value of 2.04$\times10^{15}$ cm$^{-2}$. The fractional abundances of ammonia range from 0.3 to 9.7$\times10^{-7}$, with an average of 2.7 $\times10^{-7}$, which is one order of magnitude larger than that of Massive Star-Forming (MSF) regions and Infrared Dark Clouds (IRDCs). The correlation between thermal and non-thermal velocity dispersion of the NH$_3$(1,1) inversion transition indicates the dominance of supersonic non-thermal motions in the dense gas traced by NH$_3$, and the relationship between these two parameters in Planck cold cores is weaker, with lower values observed for both parameters relative to other samples under our examination. The cumulative distribution shapes of line widths in the Planck cold cores closely resemble those of the dense cores found in regions of Cepheus, and Orion L1630 and L1641, with higher values compared to Ophiuchus. A comparison of NH3 line-center velocities with those of $^{13}$CO and C$^{18}$O shows small differences (0.13 and 0.12 km s$^{-1}$ ), suggesting quiescence on small scales.


Introduction
Molecular cores, representing the earliest stages of potential star formation, are crucial for our understanding of the initial conditions of this important process shaping the morphology of galaxies.One approach is to conduct a statistical study of cold dense clumps from unbiased large surveys in the Milky Way.The Planck satellite has carried out the first all-sky survey in the submm-to-mm range, providing a wealth of galactic cold dust cores (Planck Collaboration et al. 2011a).The first release of the all-sky Cold Clump Catalogue of Planck Objects (C3PO) was presented by the Planck Collaboration et al. (2011c).This comprehensive catalog profiles 10,342 distinctive cold sources that stand out against a warmer background.Within the collection of C3PO clumps, a subset of 915 Early Cold Cores (ECCs) was identified using specific criteria, namely a signalto-noise ratio (S/N) greater than 15 and color temperatures below 14 K.The S/N is based on one of the four matched multifrequency filter (MMF) algorithms (Planck Collaboration et al. 2011b;Melin et al. 2012) This particular ECC sample is included as part of the Planck Early Release Compact Source Catalogue (ERCSC), as presented by the Planck Collaboration et al. (2011b).The Planck Collaboration et al. (2016) released the Planck Catalog of Galactic cold clumps (PGCCs) with 13188 sources as the full version of the ECC catalog.These sources, found in various environments, are useful for investigating the initial conditions of star formation, including dynamic processes and the evolution of cores in molecular clouds, making use of their characteristic low temperatures and low levels of activity (Juvela et al. 2010(Juvela et al. , 2012;;Liu et al. 2012;Tatematsu et al. 2020;Kim et al. 2020;Fehér et al. 2022).
Plenty of works have been dedicated to the PGCCs using different molecular spectral lines.The Purple Mountain Observatory (PMO) 14m telescope was used to observe 12 CO, 13 CO, and C 18 O transitions in multiple regions.Specifically, 674 cores in Planck cold clumps of the ECCs were observed (Wu et al. 2012), along with 71 cores in Taurus, Perseus, and in the California nebula (Meng et al. 2013), 51 cores in Orion (Liu et al. 2012), 96 cores in the second quadrant (Zhang et al. 2016), 65 cores in the first Quadrant, and 31 cores in the Anti-Center direction region (Zhang et al. 2020).Additionally, the J = 1-0 transitions of HCO + and HCN (Yuan et al. 2016) as well as C 2 H N = 1-0 and N 2 H + J = 1-0, were observed toward the 621 CO selected cores (Liu et al. 2019).Two large projects were also conducted to study PGCCs systematically: the Taeduk Radio Astronomy Observatory (TRAO) mapped the J = 1-0 transitions of 12 CO and 13 CO, while the James Clerk Maxwell Telescope (JCMT) surveyed the 850 µm continuum emission of more than 1000 PGCCs selected from the TRAO sample in the SCUBA-2 Continuum Observations of Pre-protostellar Evolution (SCOPE) project (Liu et al. 2018).Further studies of several molecular species toward subsets of the SCOPE objects were made using the SMT 10m, KVN 21m, Atacama Large Millimeter/submillimeter Array, SMA, NRO 45m and Effelsberg 100m telescopes (Liu et al. 2016;Tatematsu et al. 2017Tatematsu et al. , 2020;;Kim et al. 2020;Fehér et al. 2022).Based on these studies above, it has been discovered that PGCCs demonstrate a state of quiescence and are often believed to represent the earliest stage of star formation.
To characterize the physical properties of the interior of these objects in a large, relatively unbiased sample, observations in dense gas tracers are crucial.Ammonia (NH 3 ) has been established as a reliable dense gas tracer of molecular clouds (e.g., Ho & Townes 1983;Walmsley & Ungerechts 1983;Danby et al. 1988).Specifically, NH 3 (1,1) and (2,2), both belonging to the para-species of ammonia, have been proven to be excellent thermometers at T kin < 40 K (Walmsley & Ungerechts 1983).Additionally, the critical densities of NH 3 (1,1) and (2,2) are about 10 3 cm −3 (Evans 1999; Shirley 2015), making them a suitable tracer for dense regions and suffering from minimal freeze-out (Bergin & Tafalla 2007).Therefore, we present a pilot study of NH 3 (1,1), and (2,2) towards ECCs in different environments, complemented by archival CO data, and calculate the characteristics of these cold cores.Fehér et al. (2022) conducted a study of PGCCs using the Effelsberg 100m radio antenna to observe the NH 3 (1,1) and (2,2) lines as a supplement to SCOPE targets.The selection of regions for observation was based on two main criteria.Preference was given to regions covered by Herschel observations and to regions characterized by high column density clumps (Liu et al. 2018).In contrast to the SCOPE targets, our sample consists of the whole ECC sample obtained under good observational conditions.
This paper presents a survey of Planck Early Release Cold Cores (ECCs) using ammonia lines, conducted with the Nanshan 26-m telescope.In Sect.2, we provide a detailed description of the sample and observations.In Sect.3, we describe the sample properties, and in Sect. 4 we present the results of our survey.In Sect.5, a comprehensive discussion of the data is given.Our main findings are summarized in Sect.6.

The sample
To ensure optimal observational conditions, we carefully chose cold cores from the 915 Planck Early Release Cold Cores (ECCs) dataset (as previously mentioned in Sec. 1).Specifically, we focused on ECCs with a declination above −30 degrees (to observe with a sufficiently high elevation for the Nanshan 26m telescope).As a result of this selection process, our dataset comprises a total of 672 sources, achieved after the exclusion of sources situated within the Galactic center region, where Galactic longitudes fell within |l| ≤ 5 • .These exclusions were made due to the complex interstellar medium environment and intense stellar activity prevalent in the central region of the Milky Way (Ao et al. 2013;Ginsburg et al. 2016;Immer et al. 2016).By removing these sources, we aimed to mitigate the potential biases introduced by the unique environment of the Galactic center and obtain a more representative sample of dense cores that better reflect their characteristics in other regions of the galaxy.Subsequently, our observations were conducted with NH 3 lines using the Nanshan 26-m telescope.The selected sources are listed in Table A.4 of Appendix A and shown in the top panel of Fig. 1.
Previous investigations have explored extensive sets of individual sources employing ammonia as a probe to examine the dense cores within molecular clouds (Jijina et al. 1999;Sridharan et al. 2002;Rosolowsky et al. 2008;Dunham et al. 2011;Wienen et al. 2012;Svoboda et al. 2016).By conducting a cross-match analysis with these surveys, we identified 27 our sources that overlap with the sample that has been previously detected in ammonia surveys.We also conducted a cross-match analysis with Planck cold cores observed in ammonia (Fehér et al. 2022): Only six of our sources have been previously observed in ammonia survey specifically targeting Planck cold cores.
To convert antenna temperatures T * A into main beam brightness temperatures T MB , a beam efficiency of ∼0.59 was adopted (Wu et al. 2018), with T MB uncertainty about 14%.The telescope is equipped with a dual-input Digital Filter Bank (DFB) system with 8192 channels.The typical system temperature is ∼50 K (T * A scale) at 23.708564 GHz.The FWHM beam of the telescope is 115 ′′ obtained from point-like continuum calibrators, and the bandwidth is 64 MHz, resulting in a channel spacing of 0.098 km s −1 .All velocities are with respect to the Local Standard of Rest (LSR).The total integration time for each onand off-position was 360 s, with some sources requiring multiple observations to increase the signal-to-noise ratio (S/N).All observations were obtained under good weather conditions and above an elevation of 30 • , resulting in a typical RMS noise level of ∼20 mK.

CO archival data
In this study we also utilized the J=1-0 transitions of 12 CO, 13 CO, and C 18 O from the PMO (Liu et al. 2012;Meng et al. 2013;Zhang et al. 2016Zhang et al. , 2018Zhang et al. , 2020)).The 3×3 beam sideband separation Superconduction Spectroscopic Array Receiver system was used as the front end (Shan et al. 2012).The Half Power Beam Width (HPBW) is 52 arcsec in the 115 GHz band, with a mean beam efficiency of about 50% and the pointing and tracking accuracies are better than 5 ′′ .Fast Fourier Transform Spectrometers (FFTSs) were used with each FFTS providing 16384 channels and a total bandwidth of 1 GHz.The channel spacing is ∼0.16 km s −1 for 12 CO, 13 CO and C 18 O.The On-The-Fly (OTF) observing mode was applied, with the antenna continuously scanning a region of 22 ′ ×22 ′ centered on each clump, while only the central 14 ′ × 14 ′ regions were used due to the noisy edges of the OTF maps.
After matching the spatial resolution of previous PMO mapping observations (Liu et al. 2012;Meng et al. 2013;Zhang et al. 2016Zhang et al. , 2018Zhang et al. , 2020) ) with that of the ammonia data (2 ′ ), we extracted the spectra of the J = 1 -0 transitions of 12 CO, 13 CO, and C 18 O at the 2 ′ × 2 ′ peak position of each source in our sample to construct a data set.In the PMO observations, 195 sources match our NH 3 detected sub-sample (see Sect. 4.1).

Data reduction
The data reduction was performed using the CLASS package of GILDAS 1 , and the python plot packages matplotlib (Hunter 2007).The NH 3 data were spectrally smoothed to better compare and analyze these together with the CO data, resulting in a velocity resolution of 0.16 km s −1 .A feature was considered a genuine detection when the signal-to-noise ratio (S/N) was above 3.To convert hyperfine blended line widths to intrinsic line widths in the NH 3 inversion spectrum (e.g., Barranco & Goodman 1998), we also fitted the averaged spectra using the GILDAS built-in "NH 3 (1,1)" fitting method which can fit all 18 hyperfine components simultaneously.From this NH 3 (1,1) fit we can obtain integrated intensity, line center velocity, intrinsic line widths of individual hyperfine structure (hfs) components, and optical depth (see Table A.2) of AppendixA.
Main beam brightness temperatures T MB are obtained from GAUSS fit.Because the hyperfine satellite lines of the NH 3 (2,2) transition are mostly weak, NH 3 (2,2) optical depths are not determined.A single Gaussian profile was fitted to the main group of NH 3 (2,2) hyperfine components.A total of eight NH 3 cores were fitted with two velocity components.The spectral line of each distinguishable component was fitted with Gaussian and "NH 3 (1,1)" fittings.These components are denoted by the labels "a" and "b" appended to the respective source names, as presented in Table A.2.We treated these two velocity components as separate entities (i.e., plotted them as two distinct cores).However, most of the cores in our observations required only a single velocity component fit.Physical parameters of the dense gas such as rotational temperature (T rot ), kinetic temperature (T kin ), and NH 3 column density (N NH 3 ) were derived (see Sects.3.2 and 3.3).Fig. 2 C.1 of Appendix C).The excitation temperature for CO (T ex(CO) ), 13 CO opacity (τ13 CO ), C 18 O opacity (τ C 18 O ), 13 CO column density (N13 CO ), C 18 O column density (N C 18 O ), and hydrogen column density (N H 2 ) were also calculated (see Table C.2 of Appendix C).

Distances
The distances of our sources were obtained from the literature (Wu et al. 2012;Planck Collaboration et al. 2016).For sources whose distances were unavailable in the literature, we employed the distance with the highest probability from the parallax-based distance estimator of the Bar and Spiral Structure Legacy Survey (Reid et al. 2016).The histogram of the kinematic distances is presented in the lower right panel of Fig. 1.It can be deduced from the distance distribution that the NH 3 (1,1) detection rate is significantly increased beyond 0.6 kpc, and the NH 3 (2,2) detection rate does not exhibit a clear correlation with distance.The distances of all sources range from 0.11 to 4.09 kpc, with a mean of 0.98 kpc and a median of 0.94 kpc.56% of the sources have distances within 0.5 and 1.5 kpc.

Kinetic temperature
With the measured data, the rotational temperature (T rot ), kinetic temperature (T kin ), NH 3 column density (N NH 3 ), thermal velocity dispersion σ Therm , non-thermal velocity dispersion σ NT , thermal-to-non-thermal pressure ratio R p , thermal sound speed c s and Mach number (M) of cores can be calculated.
Once the optical depth is determined by the "NH 3 (1,1)" fitting as described in Sect 2.4, we can calculate the excitation temperature of the NH 3 (1,1) inversion transition through the relation (Ho & Townes 1983), where T MB and τ represent the temperature and the optical depth of the (1,1) line derived using the GILDAS built-in 'GAUSS' and 'NH 3 (1,1)' fitting methods.A histogram of the optical depths of the (1,1) lines for our positions with NH 3 (1,1) signal-to-noise ratios > 3σ is summarized in Fig. 3b.Since the relative populations of the K = 1 and 2 ladders of NH 3 are not directly connected radiatively, they are highly sensitive to collisional processes.This allows us to use them as a thermometer of the gas kinetic temperature.The method described in Ho & Townes (1983), has been used to obtain the rotation temperature.
The rotation temperature is given by the expression where T MB (2,2) is the main beam brightness temperatures of the (2,2) line derived using the GILDAS built-in 'GAUSS' fitting method.
We estimated the kinetic temperature T kin using the approximation of Tafalla et al. (2004) : where the energy gap between the (1,1) and (2,2) states is ∆E 12 = 41.5 K.This approximation has been derived with Monte Carlo models and provides an accuracy of 5% in the range between 5 and 20 K. Most of our sources can be found in this interval.

NH 3 column density
Computing the ammonia column density requires the optical depth and line width of the (1, 1) inversion transition along with the rotational temperature, which is obtained from Eqs. (2).As the optical depth and the rotational temperature depend only on line ratios, the resulting column density is a source-averaged quantity.
Realistically assuming that for our cold sources, the bulk of the ammonia populations resides in the metastable (J = K), (J,K) = (0,0) to (3,3) levels, the total NH 3 column densities can be calculated from NH 3 (1,1) following (Wienen et al. 2012), where N(1,1) is the column density of the NH 3 (1,1) transition, the FWHM line width ∆v is in km s −1 , the line frequency ν is in GHz, and the rotational temperature T rot is in Kelvin.

Velocity dispersions, sound speed, and gas pressure ratio
The observed line widths provide a measure of the internal motions within each Planck source.Here we computed nonthermal velocity dispersion (σ NT ), thermal velocity dispersion (σ TH ), and sound speed (c s ) following Levshakov et al. (2014), Tang et al. (2017Tang et al. ( , 2018aTang et al. ( ,b, 2021)).
The thermal sound speed can be calculated with where µ = 2.37 is the mean molecular weight for molecular clouds (Dewangan et al. 2016).
We also calculated the thermal-to-nonthermal pressure ratio (R P =σ 2 TH /σ 2 NT ; Lada et al. 2003) and Mach number (given as M=σ NT /c s ).
The statistical properties of the sample are summarised in
The highest angular resolution of the Planck survey is 5 arcmin, at a frequency of 857 GHz.We plotted the distribution of observed sources and the NH 3 lines detected in this work as well as the detection rate of the NH 3 (1,1) line as a function of the 857 GHz aperture flux density S 857 of the Planck Sources in the lower left panel of Fig. 1.We observe that sources with S 857 larger than 3 Jy have a 100% detection rate.Furthermore, the detection rate of the NH 3 (1,1) line increases from 0 to 100 percent as the flux density S 857 rises from 1.5 to 4.6 Jy.However, it should be noted that while the detection rates of the NH 3 (1,1) line are 100 percent in the last bins, the number of sources within these bins is limited, with only 8, 6, 4, 3, 2, and 2 sources in total.
In the lower right panel of Fig. 1, we observed an unexpectedly low detection rate of ammonia in regions with small kinematic distances.To understand this phenomenon, we performed a column density analysis of sources situated within a distance of less than 0.45 kpc.Utilizing hydrogen column density data from the Planck Collaboration et al. (2011c), we found a difference in column densities between sources where ammonia was detected and those where it was not, within this near distance (less than 0.45 kpc).Specifically, sources with detected ammonia exhibited an average hydrogen column density of 4.32 × 10 21 cm −2 , while those without ammonia detection had an average hydrogen column density of 1.99 × 10 21 cm −2 .Moreover, it's important to consider that sources in these nearby regions may have relatively extended spatial distributions.This spatial extension implies that during our observations of ammonia point sources, we may inadvertently miss the real peaks of the Planck cold cores.
The top panel of Fig. 1 presents the spatial distribution of the detected sources, which are mainly located in local star-forming regions such as Taurus and Orion and the galactic plane.This trend is shared by all of the ECCs and CO-selected cores in the sample (Wu et al. 2012;Yuan et al. 2016).As mentioned in Sect.2.1, we cross-matched our sample with sources observed by Fehér et al. (2022), owing to distinct criteria detailed in Section. 1. Consequently, there is a disparity in the distribution of sources across the galaxy between the two samples (see also Sect.2.1).

Properties of the NH 3 emitting gas
Figure 3 shows the statistics of observed and physical properties for the NH 3 detected sample.The top left panel shows the intrinsic line width of an individual hfs component, ∆V (NH 3 (1, 1)), which ranges approximately from 0.36 to 2.36 km s −1 , with an average of 0.89 ± 0.29 km s −1 , which suggests that the nonthermal turbulence of these sources is significant (errors correspond to the standard deviations of the mean throughout this article).The top middle panel of Figure 3 shows the sample optical depths, which range from 0.1 to 5.3 with an average value of 1.6, implying that NH 3 (1,1) lines in most of the detected PGCC cores are optically thick (see Table 1).
The top right panel shows the excitation temperature, T ex , which ranges approximately from 2.8 to 5.4 K, with a mean and median of 3.2 and 3.1 K, respectively.The bottom left panel of Figure 3 shows the derived rotational temperature, which exhibits a range of 8.6 to 17.6 K, with an average value of 11.4 ± 2.2 K.The median value of the rotational temperature is 10.7 K, with a typical value of approximately 10 K. Remarkably, 83% of the sources exhibit values lying between 8 and 14 K.The NH 3 kinetic temperature distribution, illustrated in the bottom middle panel of Fig. 3, ranges from 8.9 to 20.7 K, with an average of 12.3 ± 2.9 K and a median value of 11.4 K.The total NH 3 column density ranges from 0.36 to 6.07 × 10 15 cm −2 , with an average of 2.04 × 10 15 cm −2 .The total column densities of NH 3 are presented as a histogram in the bottom right panel of Fig. 3, exhibiting a peak around 10 15.4 cm −2 in our sample.
The thermal velocity dispersion of NH 3 (1,1) lines detected at a >3σ level shows a range of 0.07 to 0.10 km s −1 , with an average of 0.08 ± 0.01 km s −1 and a median of 0.07 km s −1 .The non-thermal velocity dispersion of NH 3 (1,1) for cores ranges from 0.30 to 1.09 km s −1 , with an average of 0.55 ± 0.18 km s −1 and a median of 0.49 km s −1 .The thermal linewidth is significantly smaller than the non-thermal linewidth, which suggests that non-thermal motions dominate the dense gas in the PGCCs.The sound speed of the gas ranges from 0.18 to 0.27 km s −1 , with an average of 0.21 ± 0.02 km s −1 and median of 0.20 km s −1 .The thermal to non-thermal pressure ratio in the gas traced by NH 3 (1,1) ranges from 0.01 to 0.06, with an average of 0.02 ± 0.01, and a median of 0.02.The Mach number ranges from 1.6 to 5.0 with an average of 2.7 ± 0.8, and a median of 2.5.

Thermal and non-thermal motions
The clumps are supported against their gravity by both thermal and non-thermal motions (Cho & Lazarian 2003).The former is a manifestation of the kinetic temperature within a clump, while the latter originates from star-forming activities such as infall motions and outflows that can broaden the non-thermal velocity dispersion.However, the quiescent nature of PGCCs suggests that these motions are not particularly vigorous.Therefore, turbulent motion is the primary contributor to the non-thermal mo-   tion of these cores.Ammonia is one of the few dense gas tracers that allows for the simultaneous computation of line width and kinetic temperature, as well as thermal and non-thermal line widths.Our data are particularly well-suited for investigating these two types of motion.When turbulent energy is converted into heat, a correlation is expected to exist between the kinetic temperature and linewidth (Guesten et al. 1985;Molinari et al. 1996;Ao et al. 2013;Ginsburg et al. 2016;Immer et al. 2016;Tang et al. 2017Tang et al. , 2018aTang et al. ,b, 2021)).In this study, we investigate the existence of a correlation between temperature and turbulence in PGCCs traced by the dense gas.To achieve this, we utilized the NH 3 (1,1) and (2,2) line ratio derived kinetic temperature and NH 3 non-thermal velocity dispersion (σ NT ) as a decent approximation proxy for turbulence.The non-thermal velocity dispersions versus the kinetic temperature for the sources are shown in Fig. 4, with the dotted line representing the thermal sound speed.Our results indicate a weak correlation between non-thermal velocity dispersion and kinetic temperature, suggesting that turbulent heating may contribute to gas temperature in these cold cores.

Associated stellar objects
The associated objects of the cores are crucial for our understanding of their environment and evolutionary stages.Therefore, we investigated the objects associated with the cores, including infrared (IR) objects, young stellar objects (YSOs), and young stellar object candidates (YSO candidates).We obtained the stellar objects from the Simbad website.Statistical properties are given in Tables 2-3.YSOs are distinguished by their manifestation of not only infrared excess but also additional spec-tral features, providing evidence of active star formation processes (Allen et al. 2004;Gutermuth et al. 2004).Conversely, YSO candidates represent potential YSOs necessitating further scrutiny and validation.
In our study, we adopted the ammonia beam size (∼2 ′ ) as a matching criterion.Among the 672 cores observed, our analysis revealed the presence of 131 (∼19%) IR objects, 57 (∼ 8%) YSOs and 58 (∼ 8%) YSO candidates.The rare association may indicate low star formation activity (Lada et al. 2009;Lombardi et al. 2010).However, it cannot be entirely excluded that the associated objects originate from different gas clumps located along the line-of-sight (Wu et al. 2006).It is important to note that certain cores in our sample may encompass multiple IR sources, as well as multiple YSOs or YSO candidates.Notably, the majority of these IR objects correspond to single-point sources detected by the Infrared Astronomical Satellite (IRAS).Overall, our findings indicate that 149 (∼22%) cores have different types of associated objects within a beam size of ∼2 ′ .Additionally, we find that 112 (∼17%) cores contain at least one IR object, 29 (∼4%) cores have YSOs, and 23 (∼3%) cores contain YSO candidates.Among these, 102 sources only associate with IR objects, 18 cores only associate with YSOs and 16 cores only associate with YSO candidates.4 cores are associated with both YSOs and YSO candidates, 7 cores with both YSO and IR objects, 3 cores with both IR objects and YSO candidates.
Considering the 249 cores where NH 3 (1,1) emission was detected, we find 66 (∼27%) IR objects, 48 (∼19%)YSOs, and 52 (∼21%) YSO candidate sources associated with these cores using the aforementioned ∼2 ′ criterion.Notes.Matching criteria refer to associated objects within the ∼2 ′ ammonia beam size.Based on preliminary statistical analysis, the proportion of sources with NH 3 emission matching IR sources and stellar objects is higher than the overall proportion of the total sample matching IR sources and YSOs.The ammonia detection rate of sources matching young stellar objects or their candidates in the 672 observed cores is 66%, while the ammonia detection rate of sources matching IR objects is 45%.The ammonia detection rate is higher in sources with matching stellar objects.Not all sources with matched stellar objects and IR objects have been detected in NH 3 (1,1).There can be several reasons for this.Firstly, distance plays a significant role.If the YSOs or IR objects are located at a large distance, the faint emission signal from ammonia may be too weak to be detected.Secondly, the spatial resolution of the observing instrument can also be a factor.Other factors include line-of-sight effects and environmental conditions, where the physical environment surrounding the YSOs may influence the presence of ammonia molecules.The inescapable issue at hand is that our matching could potentially be limited to lineof-sight coincidence, lacking the necessary distance information for spatial alignment.

NH 3 abundances
The column densities of ammonia in our sample range from 0.36 ∼ 6.07 × 10 15 cm −2 , with a mean value of approximately 2.04 × 10 15 cm −2 and a median value of about 1.83 × 10 15 cm −2 (Table 1).We utilized 13 CO to derive the H 2 column densities as described in Appendix C. The H 2 column densities N H 2 ( 13 CO) range from 7.0 × 10 20 to 2.88 × 10 22 cm −2 , with an average of 7.4 × 10 21 cm −2 .The column densities of NH 3 denoted as N NH 3 , were compared with the column densities of H 2 , denoted as N H 2 , derived from 13 CO to determine the fractional abundance of ammonia in each source.The fractional abundance, χ NH 3 , is defined as the ratio of N NH 3 to N H 2 ( 13 CO).The ammonia abundances in the sources range from 0.3 to 9.7 × 10 −7 , with an average of 2.7 × 10 −7 .
Fig. 5 illustrates the column densities of NH 3 and its abundances, χ NH 3 , as a function of H 2 column density and kinetic temperature T kin .It is observed that the NH 3 column densities and fractional abundances are inversely proportional to the kinetic temperatures.Moreover, there is a trend of decreasing fractional NH 3 abundance, χ NH 3 , with increasing N H 2 .

Column densities and abundances
The ammonia column densities in our results are consistent with the findings of PGCC selected sources from SCUBA-2, whose column densities range from 0.4 to 1.5 × 10 16 cm −2 , with a mean value of approximately 1.3 × 10 15 cm −2 (Fehér et al. 2022).The ammonia column densities we obtained in our observations are also consistent with those reported in most starforming environments (Dunham et al. 2011;Wienen et al. 2012;Cyganowski et al. 2013).
The average value of N H 2 ( 13 CO), 7.4 × 10 21 cm −2 , is consistent with the results obtained from the Planck cold cores observed by PMO (Wu et al. 2012;Meng et al. 2013;Zhang et al. 2016).In the SCOPE-2 follow-up observations, the H 2 column densities of 97 Planck cold cores range from 10 22 to 10 24 cm −2 (Fehér et al. 2022), which are higher than the column densities obtained in our work.This may be attributed to the fact that the SCOPE-2 survey does not include sources with column densities N H 2 < 2 ×10 21 cm −2 (Eden et al. 2019).
Previous observations of NH 3 fractional abundance in highmass star-forming clumps suggest a median value of 2.7 × 10 −8 (Urquhart et al. 2015).Additionally, Dunham et al. (2011), Wienen et al. (2012), andMerello et al. (2019) obtained average abundance values of 1.2 × 10 −7 , 4.6 × 10 −8 , and 1.5 × 10 −8 , respectively, in clumps of the Bolocam Galactic Plane Survey (BGPS), the APEX Telescope Large Area Survey of the GALaxy (ATLASGAL), and the Hi-GAL survey.Furthermore, fractional abundances of 4 × 10 −8 , 8 × 10 −7 and 1 × 10 −8 were derived for infrared dark clouds by Pillai et al. (2006), Ragan et al. (2011), and Chira et al. (2013), respectively.The average NH 3 abundance derived from PGCCs in this study is one order of magnitude greater than that of MSF regions and IRDCs and exhibits a narrow distribution similar to that of IRDCs.The elevated NH 3 fractional abundance in PGCCs relative to other star-forming regions is likely attributable to the earlier phase of cloud evolution of PGCCs compared to Massive Star-forming (MSF) regions or even IRDCs.Ammonia is more abundant in cold, dense cores than most other molecules (Bergin & Langer 1997).The average NH 3 abundances obtained in our study are consistent with those predicted for low-mass pre-protostellar cores by chemical models (Bergin & Langer 1997).
The NH 3 column densities and fractional abundances are inversely proportional to the kinetic temperatures (see in Fig. 5 a,  b), which is consistent with the findings of previous studies on infrared dark clouds (Chira et al. 2013).The NH 3 column densities in all cores tend to increase with N H 2 , as shown in Fig. 5 (c), following the general trend that the NH 3 emission follows the dust continuum emission in the cores.This is in agreement with the results reported by Ragan et al. (2011), who found that IRDCs with no evidence of embedded star formation activity exhibit a strong correlation between ammonia and H 2 column density.A similar trend is observed in the cold cores in our observation.

Comparative analysis of thermal and non-thermal motions
To obtain comprehensive statistics on PGCCs, we conducted a comparative analysis of the non-thermal velocity dispersions and kinetic temperatures.Studies encompass a diverse range of samples, including high-mass star-forming clumps at various evolutionary stages from ATLASGAL and BGPS surveys (Dunham et al. 2011;Wienen et al. 2012) (Harju et al. 1991(Harju et al. , 1993;;Friesen et al. 2009).This comprehensive approach allows us to gain valuable insights into the physical properties of these objects and their evolutionary characteristics.In Table 4, we have compiled a list containing the fundamental information of the sources used for comparison in this study.
As seen in Fig. 4, unlike high-mass star-forming clumps and dense cores in star-forming regions (Dunham et al. 2011;Wienen et al. 2012), the relationship between non-thermal velocity dispersion and kinetic temperatures in PGCCs is much weaker, which is similar to or even less than for infrared dark clouds (Chira et al. 2013).Additionally, the distribution of nonthermal velocity dispersion and kinetic temperatures of Planck cold cores is narrower when compared to the observations of the other samples.Spearman's rank correlation coefficients (ρ) for non-thermal velocity dispersion versus kinetic temperatures in different samples and the resultant ρ-values are presented in Table A.5 of Appendix A. The table presents the obtained ρvalues along with their corresponding P-values.The analysis of this table reveals varying degrees of correlation between nonthermal velocity dispersion and kinetic temperature across different samples.Particularly, a conspicuous positive correlation is discernible in the ATLASGAL, BGPS, Ophiuchus, Cepheus, and Orion L1630/L1641 samples, underscored by small P-values.However, in the High-contrast IRDCs, the correlation is relatively weak, with a Spearman correlation coefficient of 0.07 and a p-value of 0.45, suggesting a weak and non-significant linear relationship between these two variables.The Perseus sample also manifests a relatively weak correlation, featuring a Spearman correlation coefficient of 0.2 and a p-value of 0.16, implying a modest positive correlation trend that lacks statistical significance.In contrast, our Planck cold cores sample displays a pronounced positive correlation between non-thermal velocity dispersion and kinetic temperature.With a Spearman correlation coefficient of 0.33 and a p-value of 4.00 × 10 −3 .Furthermore, gas pressure ratios derived from our results closely align with those obtained by Urquhart et al. (2015), who conducted a study on 66 massive young stellar objects and compact Hii regions from the RMS survey (Red MSX Source survey, Lumsden et al. 2013).Urquhart et al. (2015) obtained gas pressure ratios (R p ) of 0.01-0.02for both massive star-forming and quiescent clumps.In contrast, Lada et al. (2003) reported significantly higher values of R p = 4-5 for low-mass star-forming cores, such as Barnard 68, based on C 18 O and C 34 S data.Our sample, which includes non-thermal movements that significantly con-    Harju et al. (1993Harju et al. ( , 1991) ) Warm, massive clumps 51 tribute to the kinetic energy balance, more closely aligns with samples of massive clumps compared to others.

Correlation between NH 3 and other molecular species
In their survey of 674 Planck cold clumps, Wu et al. (2012) discovered that the velocities of transitions from CO and its isotopologues were highly consistent with one another.We plot the absolute value of the difference between J=1-0 transitions of 13 CO and C 18 O and the NH 3 (1,1) line-center velocities from Gaussian fits in Fig. 6 (a, b).When multiple 13 CO velocities were detected along the line of sight, we assumed that the velocity component closest to the NH 3 velocity is associated with the core (Kirk et al. 2007).
The minute discrepancy in centroid velocity between NH 3 and 13 CO (∼0.17 km s −1 ), and between NH 3 and C 18 O (∼0.18 km s −1 ), can be compared to the distinction in line-center velocities of N 2 H + and C 18 O in low-mass, starless, and protostellar cores Walsh et al. (2004);Kirk et al. (2007).Fig. 6 (a, b) illustrate that the majority of cores (64% for the difference between 13 CO NH 3 (1,1) line-center velocities and 70% for the difference between C 18 O and NH 3 (1,1) line-center velocities) exhibit differences smaller than the sound speed (dotted lines), and the remaining cores have differences that are not much larger.This phenomenon was investigated in the Perseus molecular cloud by Kirk et al. (2007), who found that the relative motions of dense N 2 H + cores and their envelopes (measured in C 18 O) generally exhibit velocity differences lower than thermal mo- tions in the majority of cases (∼ 90%).This is also consistent with the findings of Walsh et al. ( 2004), who measured a coreto-envelope velocity difference that exceeded the sound speed in only 3% of their sample.These samples consisted of isolated low-mass cores.Therefore, these comparisons suggest that the velocity differences between low and high-density tracers in the Planck cores observed by NH 3 are similar to those in low-mass, starless, or prestellar cores.In the survey of CO-selected cores in Planck cold clumps, Yuan et al. (2016) found that the central velocity differences of transitions from 13 CO, HCO + and HCN are strikingly consistent with each other.The central velocities (obtained by fitting Gaussian profiles) between 13 CO and HCO + (V13 CO -V HCO + ), 13 CO and HCN (V13 CO -V HCN ), HCO + and HCN (V HCO + -V HCN ) in their study have mean values of 0.006, 0.05, and 0.002 km s −1 , respectively.The smaller deviations from Yuan et al. (2016) may indicate that 13 CO, HCO + , and HCN are better coupled with each other.It is important to note that the channel spacing employed in their study was 0.21 km s −1 .In this work, the mean value of the velocity difference among the central velocities of 13 CO and NH 3 is 0.17 km s −1 , with channel spacing of 0.16 km s −1 .It is worth noting that the relatively low-velocity resolution might impact the interpretation of the small velocity differences observed in both cases, To address this, future observations with higher resolution would be beneficial for a more accurate comparison.By improving the velocity resolution, we can measure and compare the central velocity differences between different molecular lines more accurately, providing deeper insights.Such observations would help further validate and explain the consistency among these molecular transitions and enhance our understanding of the physical processes occurring within Planck cold clumps.Therefore, fu-ture high-resolution observations will be would help to further validate this matter.The mean intrinsic line width of the NH 3 (1,1) lines obtained from GAUSS fit is approximately 0.89 km s −1 , which is comparable to that of C 18 O J=1-0 (0.8 km s −1 ) in Wu et al. (2012), C 2 H N= 1-0 (1.0 km s −1 ) reported in Liu et al. (2019), and HCN J = 1-0 (1.06 km s −1 ) in Yuan et al. (2016).The differences in line widths among different molecular tracers may result from turbulence at different scales.Fig. 6 (c, d) show the distributions of the differences in line widths between 13 CO and C 18 O with NH 3 .The mean widths of NH 3 and 13 CO are nearly identical, with an average difference of ∼0.14 km s −1 .In contrast to high-mass starforming clumps, where the average difference between NH 3 and 13 CO is 4.3 km s −1 (Wienen et al. 2012), the intrinsic line widths of NH 3 , 13 CO and C 18 O are approximately equal in our sample.This finding is consistent with the notion that these PGCCs are quiescent, as the majority of them appear to be transitioning from clouds to dense cores (Wu et al. 2012).

A comparison with different star formation samples
To investigate the physical conditions and assess the potential for star formation within the cold clumps, we conducted a comparative analysis of various NH 3 molecular line surveys targeting different types of celestial objects.This analysis involved a comprehensive examination of line widths, kinetic temperatures, NH 3 column densities, as well as column densities of H 2 , and fractional abundances.In this particular study, to conduct a more comprehensive comparative analysis, we have incorporated not only the samples mentioned in Sec.4.3, but also included additional statistical samples, ultra-compact Hii (UC Hii) regions or UC Hii region candidates (Molinari et al. 1996), High Infrared (IR) extinction clouds (Rygl et al. 2010) and Extended Green Objects (EGOs) (Cyganowski et al. 2013).The fundamental information regarding these sources has been presented in Table 4.It is crucial to emphasize that not all papers provide data for every parameter.In certain studies, some parameters were not reported.Therefore, in the comparison involving these parameters, we opted to consider only those papers that presented available data.
The kinetic temperatures of the cores range from 8.9 to 20.7 K, with an average of 12.3 ± 2.9 K and a median value of 11.4 K (as mentioned in Sect.4.2), and after crossmatching our NH 3 detected 249 sources with PGCCs from Planck Collaboration et al. ( 2016), we have observed that the dust temperature (T dust ) of these 249 sources falls within the range of 8.6 to 13.9 K, with an average value of 11.5 K.The similarity in temperature ranges between T kin and T dust indicates an efficient coupling of gas and dust.The cumulative distribution of the kinetic temperature of NH 3 for different samples is presented in Fig. 7 (a).The results indicate that the UC Hii candidates exhibit the highest kinetic temperatures (Molinari et al. 1996), while the Planck cold cores show lower temperatures compared to other classes of sources.The temperature distribution of the samples is distinct and follows the expected evolutionary sequence.Hence, the kinetic temperature can serve as a reliable indicator for distinguishing between different evolutionary stages.Fig. 7 (b) depicts the cumulative distribution of NH 3 (1,1) line widths.Our analysis indicates that the line widths of AT-LASGAL sources are the largest.The changes in the ATLAS-GAL and UC Hii regions flatten off when the line width exceeds ∼2.5 km s −1 , and their slopes are nearly identical when the line width is smaller than 2.5 km s −1 .The variation of the cumulative fraction function of line width for the Planck cold cores is narrower when compared to other star-forming samples (Dunham et al. 2011;Wienen et al. 2012;Chira et al. 2013), and exhibits a similar cumulative distribution figure to those found in the dense cores of regions like Cepheus, and Orion L1630 and L1641, and Ophiuchus, as reported in Harju et al. (1991Harju et al. ( , 1993) ) and Friesen et al. (2009).However, the average linewidth in the Planck cold cores is slightly larger than that observed in Ophiuchus (0.62 km s −1 ).Notably, the higher line width values observed in the Planck cold cores, in comparison to the dense cores in Ophiuchus, may imply that they are in more advanced and warmer stages of evolution.However, it is worth highlighting that the line width remains relatively small across the various samples under examination.Fig. 7 (c), (d), and (e) presents the cumulative distribution of column densities for NH 3 , H 2 , and fractional ammonia abundances for various samples.The ammonia column densities of cold cores are generally higher than those of other samples and are even comparable to those of ATLASGAL and EGO sources.Conversely, the cumulative distribution for Planck cold clumps exhibits the smallest H 2 column density range, resulting in high ammonia abundances.Despite the relatively high NH 3 column density observed in Planck cold cores, comprehensive consideration of its lower temperature, linewidth, and other parameters still leads to the conclusion that Planck sources are in an early stage of evolution.
To quantitatively compare the distributions, we conducted two-sample Kolmogorov-Smirnov (K-S) tests using the scipy.stats.ks_2sampprocedure in the scipy package.This statistical test assesses the dissimilarity between two samples, with the K-S statistic serving as a measure of this dissimilarity, ranging from 0 to 1.A K-S statistic of 0 implies that there is no significant difference, suggesting the two samples may be from the same distribution.Conversely, a higher K-S statistic suggests a lower likelihood of the samples originating from the same distribution.Additionally, we computed P-values for each pair of samples, representing the probability that the samples share the same distribution.The outcomes of these tests are summarized in Table A.4 of Appendix A. In summary, the K-S test results for all examined parameters, including kinetic temperature, line width, ammonia column density, hydrogen molecule column density, and ammonia abundance, consistently yielded P-values below 0.05.These findings strongly imply substantial disparities between the Planck cold cores and the comparison samples in the examined parameters, which may reflect variations in their physical properties or the influence of distinct environmental conditions.Nevertheless, it is noteworthy that, in the distributions of kinetic temperature and linewidth, the Perseus, Cepheus, and Orion L1630/L1641 samples exhibit smaller KS statistic values.Moreover, their P-values are comparatively larger than those of other samples.In contrast, there is no pronounced similarity in the distributions of ammonia column density and hydrogen molecule column density among these samples.Additionally, in the abundance distribution, Planck displays relatively smaller KS values and larger P-values when compared to BGPS and AT-LASGAL samples.

Summary
We used the Nanshan 26-m radio telescope to perform singlepointing observations of NH 3 (1,1) and (2,2) inversion transitions towards 672 Planck sources.The main results of this study are as follows: 1.Among the observed 672 Planck sources, 249 (37%) were detected.Among these detections, 187 cores exhibit NH 3 (1,1) hyperfine structure while 76 (11%) cores also show corresponding NH 3 (2,2) emission lines.The observed sources are mainly located in local star-forming regions.The detection rate of NH 3 is positively correlated with the continuum emission fluxes of Planck sources at a frequency of 857 GHz, increasing as the 857 GHz flux density increases.2. Among the observed 672 sources, ∼22% have associated stellar and IR objects within the beam size (∼2 ′ ).This may indicate low star formation activity of the cores in our sample and the ammonia detection rate is higher in sources with matching stellar objects.3. The correlation between thermal and non-thermal velocity dispersion in NH 3 (1,1) indicates the dominance of nonthermal pressure and supersonic non-thermal motions in the dense gas traced by NH 3 .In contrast to high-mass starforming clumps and dense cores in star-forming regions, the relationship between non-thermal velocity dispersion and kinetic temperatures in PGCCs is notably weaker, with lower values observed for both parameters relative to other samples under our examination.4. The comparison of the line-center velocities of NH 3 with those from 13 CO and C 18 O reveals small discrepancies (0.17±0.33 km s −1 , 0.12±0.18km s −1 ).The widths of NH 3 , 13 CO, and C 18 O in our sample were almost undistinguishable.These are consistent with the idea that these PGCCs are quiescent, as the majority of them appear to be transitioning from clouds to dense clumps.5.The ammonia column densities range between 0.36 to 6.07 × 10 15 cm −2 .The mean value is approximately 2.04 × 10 15 cm −2 , and the fractional abundances of ammonia range from regions or even IRDCs.6.The kinetic temperatures of the cores range from 8.9 to 20.7 K, with an average of 12.3 ± 2.9 K. Similar temperature ranges between T kin and T dust indicate that the gas and dust are well coupled.7. The cumulative distribution shapes of line widths in the Planck cold cores closely resemble those of the dense cores found in regions Cepheus, and Orion L1630 and L1641, but with slightly higher values compared to Ophiuchus.However, the higher line width values in the Planck cold cores, when compared to these dense cores in Ophiuchus, suggest that they might be in more advanced and warmer stages of evolution.Nevertheless, it is worth noting that line width values remain small across the various samples under examination.This observation highlights the unique characteristics of the Planck cold cores in the context of their evolutionary stages.

Fig. 1 .
Fig.1.Top panel: The distribution of observed cores in the Galactic plane.The selected cores with and without detections of NH 3 emission lines are denoted by blue and yellow circles, respectively.The red triangles denote Planck sources not only being part of our sample but having also been previously detected in ammonia byFehér et al. (2022).Lower left: Detection rate distribution of NH 3 emission lines.The grey histogram represents the whole sample of 672 sources where we searched for NH 3 lines.The red histogram represents the number of sources that we detected in the NH 3 (1,1) line and the blue histogram refers to sources we also detected in the NH 3 (2,2) line.The green triangles denote the detection rate for a given 857 µm flux density.lower right: Distribution of distances.Here the grey histogram also refers to the entire sample, while the red histogram visualizes those sources detected in NH 3 (1,1).The blue histogram refers to sources we also detected in the NH 3 (2,2) line.
provides examples of reduced and cal-ibrated spectra of NH 3 (1,1), and (2,2) inversion lines.Examples for typical ammonia spectrum in different S/N ratios are shown in Fig.B.1 of Appendix B For the 12 CO, 13 CO and C 18 O spectra, peak main-beam brightness temperature, Local Standard of Rest (LSR) velocities, and line widths have been obtained by fitting Gaussian profiles (see Table

Fig. 3 .
Fig. 3. Histograms of physical parameters derived from NH 3 .(a) Intrinsic line widths of individual NH 3 (1,1) hyperfine structure components with hyperfine structure and a peak line flux threshold of 3σ; (b) peak optical depths of the main group of hf components τ m (1,1) for those positions with NH 3 (1,1) hyperfine structure and S/N > 3 (these line widths and peak optical depths are derived from the GILDAS built-in "NH 3 (1,1)" fitting method); (c) excitation temperature T ex ; (d) rotational temperature T rot ; (e) kinetic temperature T kin ; (f) NH 3 column densities.

Fig. 6 .
Fig. 6.Distributions between differences of line-center velocities (a, b) and line widths (c, d) of 13 CO, C 18 O and NH 3 .The average sound speed is indicated as dotted lines in (a, b).

Fig. 7 .
Fig. 7. Comparisons for the cumulative distribution of the line widths of NH 3 (1,1), kinetic temperatures, column densities, and abundances of different star formation samples.
Table 1 including the mean values and the medians of the derived quantities, as well as the minimal and maximal values.The derived values of T ex , T rot , T kin , N tot , σ TH , σ NT , c s , M and R P for individual Planck sources are listed separately in Table A.2 of Appendix A.

Table 1 .
NH 3 parameters of our sample of PGCC cores

Table 2 .
Numbers of associated stellar objects

Table 3 .
Matching results by types of stellar objects , high contrast Infrared Dark Clouds (IRDCs) (Chira et al. 2013), as well as starless cores in the Perseus region (Rosolowsky et al. 2008; Schnee et al. 2009), and dense cores in the Ophiuchus, Cepheus, and Orion L1630 and L1641 molecular clouds Article number, page 8 of 29 Dilda Berdikhan et al.: Ammonia Observations of Planck Cold Cores

Table 4 .
Fundamental information on different NH 3 samples Table A.1.Basic information of the observed sources
Table A.4. Kolmogorov-Smirnov test results for line widths, kinematic temperatures, columnn densities and abundances distributions in different star formation samples.Table A.5. Spearman correlation of kinetic temperature versus non-thermal velocity dispersion in different star formation samples.Table C.1.Parameters derived from the 12 CO, 13 CO and C 18 O (1-0) lines mb, 12 CO V LSR ( 13 CO) ∆v13 CO T mb, 13 CO V LSR (C 18 O) ∆v C 18 O T mb,C 18 O

Table C .
1. Continued Name V LSR (CO) ∆v CO T mb, 12 CO V LSR ( 13 CO) ∆v13 CO T mb, 13 CO V LSR (C 18 O) ∆v C 18 O T mb,C 18 O mb, 12 CO V LSR ( 13 CO) ∆v13 CO T mb, 13 CO V LSR (C 18 O) ∆v C 18 O T mb,C 18 O