Properties of dense cores in clustered massive star-forming regions at high angular resolution Free

Abstract

We aim at characterizing dense cores in the clustered environments associated with intermediate-/high-mass star-forming regions. For this, we present a uniform analysis of Very Large Array NH₃ (1,1) and (2,2) observations towards a sample of 15 intermediate-/high-mass star-forming regions, where we identify a total of 73 cores, classify them as protostellar, quiescent starless, or perturbed starless, and derive some physical properties. The average sizes and ammonia column densities of the total sample are ∼0.06 pc and ∼10¹⁵ cm⁻², respectively, with no significant differences between the starless and protostellar cores, while the linewidth and rotational temperature of quiescent starless cores are smaller, ∼1.0 km s⁻¹ and 16 K, than linewidths and temperatures of protostellar (∼1.8 km s⁻¹ and 21 K), and perturbed starless (∼1.4 km s⁻¹ and 19 K) cores. Such linewidths and temperatures for these quiescent starless cores in the surroundings of intermediate-/high-mass stars are still significantly larger than the typical linewidths and rotational temperatures measured in starless cores of low-mass star-forming regions, implying an important non-thermal component. We confirm at high angular resolutions (spatial scales ∼0.05 pc) the correlations previously found with single-dish telescopes (spatial scales ≳ 0.1 pc) between the linewidth and the rotational temperature of the cores, as well as between the rotational temperature and the linewidth with respect to the bolometric luminosity. In addition, we find a correlation between the temperature of each core and the incident flux from the most massive star in the cluster, suggesting that the large temperatures measured in the starless cores of our sample could be due to heating from the nearby massive star. A simple virial equilibrium analysis seems to suggest a scenario of a self-similar, self-gravitating, turbulent, virialized hierarchy of structures from clumps (∼0.1–10 pc) to cores (∼0.05 pc). A closer inspection of the dynamical state taking into account external pressure effects reveals that relatively strong magnetic field support may be needed to stabilize the cores, or that they are unstable and thus on the verge of collapse.

INTRODUCTION

The initial conditions of the star formation process in clusters are still poorly understood. Studies have unveiled the physical and chemical properties of starless isolated low-mass cores on the verge of gravitational collapse in nearby low-mass star-forming regions, showing that they have dense (n ∼ 10⁵–10⁶ cm⁻³) and cold (T ∼ 10 K) nuclei (e.g. Tafalla et al. 2002, 2004; Schnee et al. 2010), and that the internal motions are thermally dominated, as demonstrated by their close-to-thermal linewidths, even when observed at low angular resolution (see Bergin & Tafalla 2007, for a review). In the cold and dense nuclei of these cores, C-bearing molecular species such as CO and CS are strongly depleted (e.g. Caselli et al. 2002; Tafalla et al. 2002), while N-bearing species such as N₂H⁺ and NH₃ maintain large abundances in the gas phase (e.g. Caselli et al. 2002; Crapsi et al. 2005).

One major issue that has so far been poorly investigated is if, and how, the environment influences the physical and chemical properties of these pre-stellar cores. In clusters containing several forming stars in a small volume (of diameter ≤0.1 pc), turbulence, relative motions and interaction with nearby forming (proto-)stars can affect the less evolved condensations (e.g. Ward-Thompson, André & Crutcher 2007). Such an interaction is expected to be much more important in clusters containing intermediate-/high-mass protostars or newly formed massive stars, given the typical energetic feedback associated with the earliest stages of massive star formation (powerful outflows, strong winds, expanding H ii regions) and the high pressure of the parental pc-scale clumps. There is also vigorous theoretical debate on how star formation proceeds in clustered regions. Specifically: are the local kinematics of the gas dominated by feedback from protostellar outflows of already-forming, generally low-mass stars or from feedback from high-mass stars (Nakamura & Li 2007)? Can a model of star formation starting from quiescent starless cores, which has been successfully developed to explain observations of regions of isolated low-mass star formation, be applied to clustered regions (McKee & Tan 2003)? To constrain theoretical models, it is crucial to measure the main physical and chemical properties of starless and star-forming cores in clustered environments.

An observational effort in this direction has started, but it is mostly concentrated on nearby low-mass star-forming regions like Ophiuchus (e.g. André et al. 2007; Friesen et al. 2009) and Perseus (e.g. Foster et al. 2009), due to the fact that the typical large distances (≥1 kpc) of high-mass star-forming regions make the study of clustered environments very challenging. Foster et al. (2009) and Friesen et al. (2009) show that starless cores (studied at spatial scales ∼0.01–0.05 pc) within low-mass star-forming clusters have typically higher kinetic temperatures (∼13–14 K) than low-mass isolated cores (∼10 K). On the other hand, the kinematics of these low-mass protoclusters seem to be dominated by thermal motions like in more isolated cores, even though the external environment is turbulent (André et al. 2007). On the contrary, in the very few published studies of (proto-)clusters containing an intermediate-/high-mass forming star, the internal motions of starless cores are dominated by turbulence (see e.g. Fontani et al. 2008, 2009 for IRAS 05345+3157; Wang et al. 2008 for G28.34+0.06; Pillai et al. 2011 for G29.96−0.02 and G35.20−1.74; Fontani et al. 2012b for IRAS 20343+4129).

By using ammonia, Palau et al. (2007b) measured the temperature of the starless cores in the high-mass proto-cluster IRAS 20293+3952 at spatial scales of ∼0.05 pc, through Very Large Array (VLA) observations of the NH₃ (1,1) and (2,2) inversion transitions. In fact, NH₃ is the ideal thermometer for cold and dense gas because it is produced by the volatile molecular nitrogen, which is not expected to freeze out even in very cold and dense gas, and the NH₃ (2,2) to (1,1) line ratio is sensitive to temperature (e.g. Ho & Townes 1983). Moreover, because other volatile species (like N₂H⁺) cannot be used to derive the temperature, ammonia is the unique tracer for this purpose. Palau et al. (2007b) found temperatures of 16 K for starless cores in IRAS 20293+3952, i.e. higher than those measured in isolated low-mass starless cores (or infrared dark clouds with no active star formation; e.g. Ragan, Bergin & Wilner 2011), but similar to the values measured in active clustered cores in Perseus and Ophiuchus.

In this paper, we study a sample of 15 massive star-forming regions (see Table 1) observed with the VLA (providing an average spatial resolution of ∼0.05 pc) and analysed them in a uniform way. The main goal is to understand whether the results obtained in the few examples shown above are also obtained when analysing a statistically significant sample. The regions were selected according to the following criteria: (i) regions must be at distances ≲ 3.5 kpc, to obtain spatial resolution ≲ 0.05 pc, similar to the scale of the cores (0.03–0.2 pc: e.g. Bergin & Tafalla 2007); (ii) regions must have bolometric luminosities larger than ∼300 L_⊙, which are the luminosities where clustering seems to be important (e.g. Testi, Palla & Natta 1999; Palau et al. 2013) and (iii) regions must be still associated with important amounts of gas and dust judging from single-dish observations of dust and molecular gas studies (e.g. Molinari et al. 1996; Beuther et al. 2002a; Mueller et al. 2002).

OBSERVATIONS

The VLA¹ was used to observe the ammonia (J, K) = (1,1) and (2,2) inversion transitions towards 15 intermediate-/high-mass star-forming regions. These observations are part of different observational projects carried out on different epochs (from 1999 to 2009), and with the array in compact configurations (C, DnC or D). In Table 1 we list the 15 massive star-forming regions, indicating the name of the VLA project and the coordinates of the phase centre for each region. More technical details of each observational project, such as calibrators and epochs, are provided in Table 2. The full-width at half-maximum of the primary beam at the frequency of the observations (∼23.7 GHz) is approximately 2 arcmin. The spectral setup configuration used in each project (i.e. bandwidth and spectral resolution) is indicated in Table 2. The absolute flux scale was set by observing the quasars 1331+305 (3C286), 0137+331 (3C48) or 0319+415 (3C84), for which we adopted a flux of 2.41 Jy, 1.05 Jy and 16 Jy, respectively. Gain calibration was done against nearby quasars, which were typically observed at regular time intervals of ∼5–10 min before and after each target observation. Flux calibration errors could be up to 20–30 per cent. The data reduction followed the VLA standard guidelines for calibration of high-frequency data, using the National Radio Astronomy Observatory package aips. Final images were produced with the task imagr of aips, with the robust parameter of Briggs (1995) typically set to 5, corresponding to natural weighting. Two sources (AFGL 5142 and 22198+6336) were observed in different projects with different angular resolutions. For these sources we combined the uv-data to improve the sensitivity and uv-coverage of the final images. The resulting synthesized beams and rms noise levels (per channel) are indicated in Table 1.

RESULTS AND ANALYSIS

Core identification and classification

In Fig. 1, we present the zero-order moment (velocity-integrated intensity) maps of the NH₃ (1,1) emission for the 15 massive star-forming regions studied in this work, while in Fig. B1, we present the first-order (intensity-weighted mean v_LSR) and second-order (intensity-weighted mean velocity linewidth) moment maps. The zero-order moment maps were constructed by integrating the emission of all the hyperfine components, while for the first- and second-order moment maps we considered only the main hyperfine component, except for 20126+4104 for which the inner satellite hyperfine component was used (in the zeroth, first- and second-order moments) to avoid the high opacities in the main line. The integrated intensity maps reveal ammonia emission in all the regions, coming from compact condensations surrounded by faint and more extended emission. In the first-order moment maps (see Fig. B1), we identify large-scale velocity gradients (see e.g. AFGL 5142, 20081+3122, G75.78+0.34, 22172+5549N), not only associated with the compact condensations or cores but also with the whole ammonia emission, probably revealing the large-scale kinematics of the cloud. To extract and identify the cores within each region we ran the two-dimensional CLUMPFIND algorithm (Williams, de Geus & Blitz 1994) on the NH₃ (1,1) zero-order moment map. This algorithm requires two input parameters: the ‘bottom’ level, corresponding to the lowest intensity to be included in the core, and the ‘step’, which determines the intensity increment required to differentiate one core from another core (see e.g. Miettinen et al. 2012 for further details). In our case, we used ‘bottom’ values of around 20–40 per cent of the peak intensity of the zero-order moment, and ‘steps’ in the range 5–10 per cent of the peak intensity (see last columns in Table 1). The output parameters defining each core returned by CLUMPFIND are the peak position, peak intensity and the flux density of the core. For each identified core we defined a polygon at the level of the full width at half-maximum (FWHM; see black thick lines in Fig. 1). In Table 3 we list the offset position of each core (relative to the phase centre; listed in Table 1) and the deconvolved FWHM size. A total of 73 cores were identified.

The studied field of view (VLA primary beam at 1.3 cm) is ∼2 arcmin, or 1.5 pc at a distance of 2.5 kpc. On average, we found of the order of 5–6 cores in each region, with diameters ∼0.06 pc. We classify the identified cores as starless or protostellar (see Table 4), based on their infrared properties (from the Spitzer/IRAC, Spitzer/MIPS or WISE² images) and other observational evidence reported in the literature (e.g. molecular outflows, masers, H ii regions, radio jets; see references in Table B1), summarized in Table B1. Within the starless cores we consider two groups: ‘quiescent starless’ and ‘perturbed starless’ cores. The former group includes cores appearing dark in the IRAC images, away ( ≳ 10 arcsec) from strong IR sources or outflows, with or without millimetre continuum. On the other hand, perturbed starless cores are not associated with a point infrared source but lie close ( ≲ 10 arcsec) to a bright IR source and/or along the axis of a molecular outflow, suggesting that these cores might be perturbed.³ A core is classified as ‘protostellar’ if it is associated with an infrared point source, and with other star formation signposts (e.g. maser, outflow, centimetre continuum). Some cores were tentatively classified as ‘protostellar?’ if the only hint of star formation is the association with an infrared point source, which could be a background or foreground star not associated with the dense core. These tentatively classified cores are not included in our statistical analysis when comparing the different types of cores to avoid contamination by misclassified cores. In Fig. 1, the stars indicate the position of centimetre continuum sources, likely tracing H ii regions or thermal radio jets. In many cases, the most massive source of the region, usually associated with a strong centimetre source, tracing an (ultracompact) H ii region is located offset of the core peaks (e.g. 20081+3122, 20293+3952, 20343+4129).

Averaged physical parameters for ammonia dense cores

For each core, we extracted the spectra averaged over the area assigned by the polygons (shown in Fig. 1) in both NH₃ (1,1) and (2,2) lines, and fitted the hyperfine structure of the NH₃ (1,1) transition following the procedure described in Appendix A, and a Gaussian to the NH₃ (2,2) line (see observed and fitted spectra in Fig. B2). This allowed us to obtain the opacity, velocity and linewidth for each core.⁴ We derived the rotational temperature and primary beam corrected ammonia column density following the procedure outlined in the appendix of Busquet et al. (2009). All these parameters are listed in Table 3. The average values of linewidth, opacity of the NH₃ (1,1) main line, rotational temperature and ammonia column density of all the 73 cores are ∼1.4 km s⁻¹, 1.4, 19 K, and 10¹⁵ cm⁻², respectively. Our values of linewidth, rotational temperature and ammonia column density are very similar to the values obtained by Urquhart et al. (2011) for the Red MSX Source (RMS) survey, of 2 km s⁻¹, 22 K and 2 × 10¹⁵ cm⁻², even using very different observing techniques and sampling different spatial scales (single-dish versus interferometry). If we analyse the distributions of linewidth, opacity, rotational temperature and column density for the starless and protostellar populations separately (see Fig. 2 panels A to E), the average values that we obtain are (i) ∼1.0 km s⁻¹, 1.5, 16.0 K, and 10¹⁵ cm⁻² for quiescent starless cores, (ii) ∼1.4 km s⁻¹, 1.2, 19.3 K, and 10¹⁵ cm⁻² for perturbed starless cores, and (iii) ∼1.8 km s⁻¹, 1.2, 21.3 K, and 10¹⁵ cm⁻² for protostellar cores. Thus, quiescent starless cores have, as expected, linewidths and rotational temperatures smaller than protostellar cores (see Fig. 2 panels A and D; Table 5). The linewidths and temperatures of perturbed starless cores are in between the values measured for quiescent starless and protostellar cores, consistent with the fact that these cores were originally quiescent and then perturbed by the passage of outflows or the high radiation of a nearby bright infrared source. These cores might be similar to the ‘warm’ starless cores reported in Motte et al. (2010) using Herschel observations towards Cygnus X, and for some of them a low deuterium fractionation is measured (Fontani et al. 2011). Further studies should be carried out to assess the true nature of these perturbed starless cores.

The average values derived for the rotational temperature of quiescent starless and protostellar cores (of 16.0 K and 21.3 K, respectively, corresponding to kinetic temperatures of 18.8 K and 28.8 K, following Tafalla et al. 2004) can be compared to the values reported in the literature, although derived from observations of lower angular resolution. Olmi et al. (2013) studied the dense clumps in the Galactic field l = 59° (at a distance of 3.6 kpc, similar to the distances of our regions) within the Hi-GAL Herschel project (Molinari et al. 2010), and derived kinetic temperatures of 17 K for starless cores and 20 K for protostellar cores, following the same trend as we found in our cores. Urquhart et al. (2011) estimated the kinetic temperatures for clumps associated with young stellar objects and H ii regions in the RMS survey to be in the range 20–25 K, also in agreement with our protostellar temperatures. However, it is worth noting that the average rotational temperature of 16 K found in the quiescent starless cores of our clustered massive star-forming regions is significantly larger than the values measured in starless cores of low-mass isolated regions (of about 10 K or even less; e.g. Tafalla et al. 2002, 2004; Rathborne et al. 2008; Rosolowsky et al. 2008; Schnee et al. 2010), and of infrared dark clouds with no active star formation (∼10 K; e.g. Ragan et al. 2011). Temperatures of ∼15 K for starless cores are also found by Li, Goldsmith & Menten (2003) in the quiescent cores near the Trapezium cluster. Li et al. find that the temperatures of the massive quiescent cores can be well explained by the dust being heated by the external UV field from the Trapezium cluster, at a distance of ∼1 pc from the massive cores. This possibility is investigated for the regions in our sample in Section 4.1.

The linewidths measured in our starless cores have an important non-thermal component, which is almost negligible in low-mass clustered regions (e.g. Friesen et al. 2009; Foster et al. 2009). To evaluate this component, we assumed the relation |$\sigma _\mathrm{nth} = \sqrt{\sigma _\mathrm{obs}^2- \sigma _\mathrm{th}^2}$| where σ_obs is the measured velocity dispersion of the core [= Δv/(8 ln 2)^1/2 for a Gaussian line profile with Δv the measured FWHM of the line] and σ_th is the thermal velocity dispersion. For NH₃, assuming a Maxwellian velocity distribution, σ_th can be calculated from |$\sqrt{k_\mathrm{B} T_\mathrm{kin}/(\mu m_\mathrm{H})}$|⁠, with k_B the Boltzmann constant, μ the molecular weight (= 17.03 for ammonia), m_H the mass of the hydrogen atom and T_kin the kinetic temperature listed in Column 3 of Table 4. In Columns 5 and 6 of the same table we list the non-thermal velocity dispersion (σ_nth) and the non-thermal velocity dispersion over the isothermal sound speed (σ_nth/c_s), where c_s is calculated using a mean molecular weight μ = 2.33. From the distributions shown in Fig. 2 (panels H and I) we see that protostellar cores have a non-thermal component (0.76 km s⁻¹, or equivalently Δv_nth = 1.8 km s⁻¹) higher than the non-thermal component of the quiescent starless (0.44 km s⁻¹, or Δv_nth = 1.0 km s⁻¹) and perturbed starless (0.56 km s⁻¹, or Δv_nth = 1.3 km s⁻¹) cores. For the σ_nth/c_s we obtain mean ratios of 1.7, 1.9 and 2.2 for quiescent starless, perturbed starless and protostellar cores, respectively (see Table 5), indicating that the cores are characterized by moderately supersonic non-thermal motions. In general, our cores (both starless and protostellar), associated with intermediate- and high-mass star-forming regions, have values of turbulent Mach number ∼2, being greater than those found in Perseus or Ophiucus (with values between 0.5 and 1.5; e.g. André et al. 2007; Friesen et al. 2009; Foster et al. 2009).

From the ammonia column density (listed in Table 3), we derived the mass of the core and the core mass surface density, following the procedures explained in the footnotes of Table 4. These two quantities are listed in Columns 8 and 9 of Table 4, and their distributions are shown in panels F and G of Fig. 2. Starless and protostellar cores show similar mean masses (∼1.0–1.8 M_⊙) and mean surface densities (∼0.10–0.12 g cm⁻²) (see Table 5).

Ammonia correlations

As presented in Section 3.2, we note some differences in the parameters derived for the starless and protostellar cores. In particular, an increase in the temperature and linewidth as we move towards more evolved objects (protostellar cores). In a search for a physical relation between the derived parameters, we plotted several quantities against others, shown as six scattered plots in Fig. 3. In these plots we show the distribution of starless and protostellar core samples in red circles and blue stars, respectively. We performed some statistical tests to search for possible correlations between the physical quantities. In the top right corner of each plot, we give Kendall's τ rank correlation coefficient and the Pearson correlation coefficient (ρ) to a least-squares fit (dotted lines). We find that in five of the six plots there is a possible correlation, with τ coefficients ∼0.3, and ρ in the range 0.4–0.6.

In the top panels of Fig. 3, we show the relation between the temperature, the linewidth and the mass of the core with the bolometric luminosity of the region, while in the bottom panels, we compare the temperature, the ammonia column density and the size of the core with the observed linewidth. We note that we are not able to derive a bolometric luminosity for each individual ammonia core but a single luminosity of the whole region.⁵ Thus, the plots in Fig. 3 must be interpreted as a correlation between the properties of the cores within a region with respect to the luminosity of the region (which is in general dominated by the brightest mid-IR source). We find a correlation in five of the six panels (panels A to E of Fig. 3). Similar trends between the same parameters have been reported from single-dish observational studies (e.g. Churchwell, Walmsley & Cesaroni 1990; Myers, Ladd & Fuller 1991; Jijina, Myers & Adams 1999; Rygl et al. 2010; Urquhart et al. 2011; Sepúlveda et al. 2011). Our correlations found in ammonia at higher angular resolution thus confirm that these relations take place also at the smaller spatial scales (∼0.05 pc) of individual cores, and are not an observational (average) artefact due to the poor angular resolution of single-dish observations when studying clumps of sizes ∼0.1–10 pc. It is worth noting that in panel B (linewidth versus luminosity) there are four cores with linewidths ∼4 km s⁻¹, located well above the trend found for the other cores. These four cores (AFGL 5142–1; 19035+0641–1; 20126+4104–1; G75.78+0.34–1) are known to be associated with powerful outflows that could perturb the motions of the dense gas close to the powering source (see Zhang et al. 2002; Cesaroni et al. 2005; Sánchez-Monge 2011; Sánchez-Monge et al. 2013). Finally, in panel F, we investigate a possible relation between the size of the core and its linewidth. Since the publication of the Larson's scaling relations (Larson 1981), several authors (e.g. Myers, Linke & Benson 1983; Caselli & Myers 1995; Pirogov et al. 2003) found, from single-dish studies, that larger dense cores have broader lines, as expected in virialized cores. In our sample, however, we find no correlation (with τ = −0.03 and ρ = 0.01) between these two quantities. A possible explanation for this could be that a number of cores suffer an important injection of turbulence, e.g. from the passage of powerful outflows, which should affect the gas motions of the cores only at the scales of our sample (∼0.05 pc; see e.g. Palau et al. 2007b; Liu, Ho & Zhang 2010; Nakamura & Li 2011), and is diluted at the larger scales studied in single-dish observations. Alternatively, the large linewidths might indicate that the cores are collapsing. In Section 4.2, we discuss in more detail the dynamics of the cores in our sample, and relate it to previous single-dish studies.

DISCUSSION

Temperature of the gas and IR radiation

In Section 3.3, we reported a correlation between the temperature of the cores and the luminosity of the region (see Fig. 3 panel A). These higher temperatures can result from various heating processes: (i) feedback from low-mass stars, e.g. molecular outflows, as found in some cores of AFGL 5142 or 20293+5932 (e.g. Zhang et al. 2002; Palau et al. 2007b); (ii) shocks from convergent flows (e.g. Csengeri et al. 2011a; Beltrán et al. 2012); (iii) feedback from high-mass stars, e.g. strong radiation (e.g. Li et al. 2003). In the following, we test the feedback from massive stars as a possible agent for the increase of temperature in the dense cores.

Our interferometric observations permit the study of the spatial distribution of the cores, and their physical properties, with respect to e.g. the (strong) infrared sources and hence the massive stars. In our regions, the bolometric luminosity is generally dominated, at mid-infrared (MIR) and far-infrared (FIR) wavelengths, by a single strong source associated with the most massive star. We assume that the main source of radiation that can heat the surrounding gas is the massive star detectable in the MIR. To determine if there is a relation between the temperature of the cores and the proximity of the MIR source, we searched the MSX Point Source Catalog (Price et al. 1999) for the coordinates of the MIR sources and calculated the MSX to NH₃ core separation (⁠|$\Delta _\mathrm{MIR-NH_3}$|⁠; using the coordinates listed in Table 3 for our cores). Using the luminosity and position of the most massive (radiating dominant) source and the separation to each ammonia dense core, we derived the incident flux received by each core as |$L_\mathrm{bol}/(4\pi (\Delta _\mathrm{MIR-NH_3})^2)$|⁠. Note that we are measuring a projected separation, which is a lower limit to the true separation. Thus, for all cores, we actually have an upper limit on the received flux, which affects the absolute normalization of the derived relation and increases the scatter of the data points in this relation. In Fig. 4, we plot the received flux versus the rotational temperature. If the radiation of the most massive star dominates the heating of its surroundings, we expect that the cores closer to the most massive source, i.e. with a large received flux, will have higher temperatures. This is consistent with the trend shown in Fig. 4, where the highest temperatures correspond to the cores with a higher received flux. The black solid line corresponds to the relation |$L_\mathrm{bol}/(4\pi (\Delta _\mathrm{MIR-NH_3})^2)=\sigma _\mathrm{SB}\,T_\mathrm{rot}^4$|⁠, with σ_SB the Stephan–Boltzmann constant, while the dotted line corresponds to a least-squares fit with a correlation coefficient of 0.6. For a given bolometric luminosity, the temperature is a factor of approximately three times lower for a core located at a distance ∼0.5 pc, than for a similar core located at <0.05 pc.

Summarizing, the radiation deposited in the environment by the most luminous star of the cluster can be responsible for the temperatures measured in the cores of our clustered regions. Thus, the large temperatures measured for our starless cores, in comparison with the temperatures measured in low-mass star-forming regions, can be interpreted as external heating by the radiation of the most massive (forming) stars of the cluster.

Dynamical state of the cores

CONCLUSIONS

We present the results of VLA observations of the NH₃ (1,1) and (2,2) inversion transition lines towards a sample of 15 massive star-forming regions. We obtained an average spatial resolution of ∼0.05 pc, and analysed the ammonia emission in a consistent way. Our main conclusions can be summarized as follows.

• We identified a total of 73 ammonia dense cores using the two-dimensional CLUMPFIND algorithm. On average we found of the order of 5–6 cores in each field (of ∼2 arcmin, or 1.5 pc at a distance of 2.5 kpc), with sizes ∼0.06 pc. The cores were classified as quiescent starless, perturbed starless and protostellar based on its association with infrared emission and taking into account other star formation signposts (e.g. outflows, masers, centimetre continuum emission) reported in the literature.

• The average values of linewidth, opacity, rotational temperature and ammonia column density for the 73 dense cores are ∼1.4 km s⁻¹, 1.4, 19 K and 10¹⁵ cm⁻², respectively. We found that protostellar cores have larger temperatures and linewidths (∼21.3 K and 1.8 km s⁻¹) than quiescent starless cores (∼16.0 K and 1.0 km s⁻¹). Similarly, cores classified as perturbed starless have temperatures and linewidths (∼19.3 K and 1.4 km s⁻¹) slightly larger than quiescent starless cores, but smaller than cores harbouring a protostar.

• The average temperatures derived for the quiescent starless cores in our clustered regions (∼16 K) are larger than those measured in starless cores in more isolated regions (∼10 K). Our starless and protostellar cores show important non-thermal supersonic components (σ_nth ∼ 0.44 km s⁻¹ and 0.76 km s⁻¹, respectively) and σ_nth/c_s ∼ 2.0, well above to the close-to-thermal lines measured in isolated star-forming regions.

• We found that the temperature and NH₃ (1,1) linewidth of the cores are correlated with the luminosity of the region, suggesting that the feedback of the luminous massive (forming) stars can affect the surrounding molecular environment.

• We evaluated a possible relation between the temperature of the core and its separation with the most important radiating source in the region in terms of the incident flux received by the core. The highest temperatures are measured for those cores located close to the brightest MIR source (separations <0.05 pc), with the temperature decaying by a factor of ∼3 when the cores are located at distances ∼0.5 pc. Thus, the large temperatures found in starless cores in massive star-forming regions can be interpreted as external heating by the radiation of the most massive star of the cluster.

• We compared the virial masses of our cores (at scales ∼0.05 pc) with those of clumps with sizes ∼0.1–10 pc. A simple virial equilibrium analysis seems to suggest a trend between M_vir and core/clump masses favouring a scenario of a self-similar, self-gravitating, virialized hierarchy of structures from clumps to cores. A closer inspection of the dynamical state at core scales, taking into account external pressure (McKee & Tan 2003), indicates that either another form of support (e.g. from magnetic field) is required to stabilize the cores, or that the cores are close to collapse or even collapsing.

Overall, our data suggest that the cores forming in clustered environments harbouring intermediate-/high-mass stars are more affected/perturbed than cores in clustered low-mass star-forming regions, and thus the initial conditions for star formation in these environments seem to be different to those typically assumed in low-mass star-forming regions.

We are grateful to James di Francesco for support with SCUBA data. We thank the anonymous referee for his/her constructive criticisms. The figures of this paper have been done in GREG of the gildas software package developed at the Institut de Radioastronomie Millimétrique (IRAM) and the Observatoire de Grenoble. AP is supported by a JAE-Doc CSIC fellowship co-funded with the European Social Fund under the programme ‘Junta para la Ampliación de Estudios’, by the Spanish MICINN grant AYA2011-30228-C03-02 (co-funded with FEDER funds), and by the AGAUR grant 2009SGR1172 (Catalonia). GB is funded by an Italian Space Agency (ASI) fellowship under contract number I/005/11/0.

REFERENCES

APPENDIX A: HYPERFINE STRUCTURE (HfS) FITTING

Parameters of the fit

The usual fitting of the hyperfine structure of a transition, for instance, the inversion transition NH₃ (J, K) = (1, 1), estimates four free parameters of the transition, namely

• τ_m, the optical depth of the main component,

• A × τ_m, product of the amplitude (A = f [J_ν(T_ex) − J_ν(T_bg)],

  where f is the filling factor, J_ν(T) is the Planck function in units of temperature, T_ex is the excitation temperature and T_bg is the background temperature) times the optical depth of the main component,

• v_LSR, the central velocity of the main component, and

• Δv, the linewidth of the hyperfine components,

with the usual assumptions that T_ex, v_LSR and Δv are the same for all the hyperfine components.

However, some of the parameters are ill-conditioned in some cases. In the optically thin limit, τ_m ≪ 1, only an upper limit for the value of τ_m can be obtained. However, the parameter A × τ_m gives the peak intensity of the line (provided that the hyperfine components are unresolved, or, in the case NH₃, the hyperfine magnetic components that form part of the main component), and is well constrained. This parameter, in the Rayleigh–Jeans approximation, is necessary to calculate the column density of emitting molecules. In the optically thick limit, τ_m ≫ 1, only lower limits for τ_m and A × τ_m can be obtained (and consequently, a lower limit for the column density).

A better fit parameter than τ_m, with well-defined values in the optically thin and optically thick limits, is |$1-e^{-\tau _m}$|⁠. This parameter always has values between 0 (optically thin limit, τ_m ≪ 1) and 1 (optically thick limit, τ_m ≫ 1). Similarly, |$A\left(1-e^{-\tau _m}\right)$| is a better fit parameter than A × τ_m, since it is well constrained in all cases.

The Hyperfine Structure⁷ (hereafter HfS) fitting procedure used to fit the NH₃ (J, K) = (1, 1) lines in this paper fits the four parameters

• |$1-e^{-\tau _m}$|⁠,

• |$A\left(1-e^{-\tau _m}\right)$|⁠,

• v_LSR,

• Δv.

The values and uncertainties for the parameters needed to derive physical properties of the emitting gas, τ_m and A × τ_m (or their limits in the two limiting cases) can be easily derived from the values and uncertainties for the parameters of the fit.

Fitting procedure

Several sampling methods of the m-dimensional parameter space are possible, i.e. regular grid, random, Halton sequence (Halton 1964). We adopted a Halton quasi-random sequence because it samples the parameter space more evenly than a purely random sequence, and the convergence of the fitting procedure to the minimum of χ² is faster.

Parameter error estimation

Once the best-fitting parameter values for which |$\chi ^2=\chi ^2_\mathrm{min}$| are found, the uncertainty in the fitted parameters, σ(p_k), (k = 1 …m), can be estimated as the projection over each parameter axis of the confidence region of the parameters, the region of the m-dimensional parameter space for which χ² does not exceed the minimum value by a certain amount, |$\chi ^2_\mathrm{min}+\Delta$|⁠.

APPENDIX B: VELOCITY, LINEWIDTH AND SPECTRA IMAGES

In Table B1, we summarize the infrared properties of each core, together with the information of other star formation signposts reported in the literature. In Column 4 of the table, we classify each core as ‘quiescent starless’ (S), ‘perturbed starless’ (S*), ‘protostellar’ (P) or ‘tentatively protostellar’ (P?).

In Fig. B1, we present the first-order (intensity-weighted mean v_LSR) and second-order (intensity-weighted mean linewidth) moment maps for the 15 massive star-forming regions studied in this work. Note that the second-order moment maps have been corrected to show directly the linewidth (Δv) instead of the dispersion (σ_v) by using the relation |$\Delta v = \sqrt{8\ln 2}\,\sigma _v$|⁠.

In Fig. B2, we present the observed and fitted spectra of the NH₃ (1,1) and NH₃ (2,2) transitions for all the cores identified and listed in Table 3.