EDP Sciences
Free Access
Issue
A&A
Volume 507, Number 1, November III 2009
Page(s) 369 - 376
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/200811104
Published online 08 September 2009

A&A 507, 369-376 (2009)

The relation between 13CO J = 2-1 line width in molecular clouds and bolometric luminosity of associated IRAS sources[*]

K. Wang1 - Y. F. Wu1 - L. Ran1,2 - W. T. Yu3 - M. Miller4

1 - Department of Astronomy, School of Physics, Peking University, Beijing 100871, PR China
2 - Department of Atmospheric Sciences, School of Physics, Peking University, Beijing 100871, PR China
3 - Institut für Anorganische Chemie, Universität Bonn, Römer St. 164, 53117 Bonn, Germany
4 - I. Physikal. Institut, Universität zu Köln, Zülpicher St. 77, 50937 Köln, Germany

Received 7 October 2008 / Accepted 21 July 2009

Abstract
Aims. We search for evidence of a relation between properties of young stellar objects (YSOs) and their parent molecular clouds to understand the initial conditions of high-mass star formation.
Methods. A sample of 135 sources was selected from the InfraRed Astronomical Satellite (IRAS) point source catalog, on the basis of their red color to enhance the possibility of discovering young sources. Using the Kölner Observatorium für SubMillimeter Astronomie (KOSMA) 3-m telescope, a single-point survey in 13CO J = 2-1 was carried out for the entire sample, and 14 sources were mapped further. Archival mid-infrared (MIR) data were compared with the 13CO emissions to identify evolutionary stages of the sources. A 13CO observed sample was assembled to investigate the correlation between 13CO line width of the clouds and the luminosity of the associated YSOs.
Results. We identified 98 sources suitable for star formation analyses for which relevant parameters were calculated. We detected 18 cores from 14 mapped sources, which were identified with eight pre-UC H  II regions and one UC H  II region, two high-mass cores earlier than pre-UC H  II phase, four possible star forming clusters, and three sourceless cores. By compiling a large (360 sources) 13CO observed sample, a good correlation was found between the 13CO line width of the clouds and the bolometric luminosity of the associated YSOs, which can be fitted as a power law, $\lg~(\Delta V_{13}/~\rm {km~s}^{-1}) = (-0.023\pm 0.044)+(0.135\pm 0.012)\lg~({\it L}_{\rm bol}/{\it L}_{\odot})$. Results show that luminous (> $10^3~L_{\odot}$) YSOs tend to be associated with both more massive and more turbulent ( $\Delta V_{13}>2~\rm {km~s}^{-1}$) molecular cloud structures.

Key words: stars: formation - ISM: clouds - ISM: molecules - ISM: kinematic and dynamics

1 Introduction

The past decade has witnessed significant progress in the study of high-mass star formation. Observations at millimeter and submillimeter wavelengths (Zhang 2005; Beuther et al. 2002; Cesaroni et al. 2007; Zhang et al. 1998; Keto 2002) suggest that massive proto B stars can form by disk mediated accretion, which is similar to the scenario that produces low-mass stars. However, most of the studies focus on relatively evolved stages, when the central star has already formed and hydrogen burning has begun, characterized by surrounding ultra compact (UC) H  II regions and strong emission from complex molecules (Churchwell 2002). In contrast, the extremely early stages are poorly understood to date. In particular, knowledge to evolutionary stages prior to the onset of H  II regions are crucial to understanding the initial conditions of high-mass star formation.

It is known that stars are formed in molecular clouds. Therefore, the relation between forming stars and parent clouds is important to understand the formation process and the properties of the eventual stars. On galaxy scales, star formation activities are usually described by the so-called Schmidt law, which relates the star formation rate (SFR) to the surface density of gas: $\Sigma_{\rm
SFR} \propto \Sigma _{\rm gas}^{N}$, where the index N=1-2(Kennicutt 1998; Gao & Solomon 2004; Schmidt 1959). Studies of Galactic dense cores have shown that this relation may be universal and can be connected to Galactic star formation (Wu et al. 2005a). Larson (1981) studied the turbulence in star forming clouds and found a strong correlation between the internal velocity dispersion $\sigma$ of the region and its size L: $\sigma(\rm {km~s}^{-1}) \propto$  $L(\rm {pc})^{0.38}$. This relation, also called the Larson law, is valid for low-mass cores but is found to be break down in high-mass cores $\gtrsim$103 $M_{\odot}$ (Plume et al. 1997; Caselli & Myers 1995; Guan et al. 2008). This is indicative of the different status of turbulence in low- and high-mass cores. The breakdown of the Larson law can be interpreted as evidence of widespread supersonic turbulence in high-mass cores, in contrast to subsonic turbulent low-mass cores (Plume et al. 1997). A molecular line width is an observational indicator of turbulence in clouds, and bolometric luminosity is an indicator of forming stars. Any relation between these quantities may help us to understand the initial star forming process.

Here we report results from a 13CO J=2-1survey towards 135 IRAS sources using the KOSMA 3-m telescope. To search for high-mass star forming regions in their early stages, we select a sample on the basis of their red IRAS color to enhance the possibility of finding young sources. We present the primary results and investigate the relation between line width in molecular clouds and bolometric luminosity of associated infrared sources. We describe our sample selection in Sect. 2 and observations in Sect. 3. In Sect. 4 we present statistical results of the single-point survey (Sect. 4.1) and follow-up mapping (Sect. 4.2). We discuss the $\Delta V - L$relation as well as other relations in Sect. 5, and summarize the paper in Sect. 6.

2 Sample

We selected the sample from the Infrared Astronomical Satellite (IRAS) point source catalog (PSC, Beichman et al. 1988) version 2.1 according to our developed color criteria (Wu et al. 2003), namely:

(a)
$f_{100~\mu{\rm m}} < 500$ Jy, lg $(f_{25~\mu{\rm m}}/f_{12~\mu{\rm m}}) \geqslant 0.7$, lg $(f_{60~\mu{\rm m}}/f_{12~\mu{\rm m}}) \geqslant 1.4$, where $f_{\lambda}$ is the flux density;
(b)
lack of 6 cm radio continuum radiation to exclude potential H  II associations;
(c)
declination $\delta > -20^{\circ}$, so that targets are accessible to the telescope KOSMA.
Criterion (a) was chosen so that the sample sources were redder and possibly fainter, thus may be younger than those selected based on traditional Wood & Churchwell (1989) color criteria. Criterion (b) helps to exclude any known H  II regions brighter than current detection limit. Therefore, the sample should represent extremely young stellar objects (YSOs), mostly at evolutionary stages earlier than the UC H  II phase. The 6 cm radio continuum data was extracted from three surveys: (1) $0^{\circ}<\delta<75^{\circ}$4.85 GHz radio continuum survey completed by Gregory & Condon (1991) with the 91-m NRAO telescope; (2) $-29^{\circ}<\delta<9.5^{\circ}$4.85 GHz radio continuum survey led by Griffith et al. (1994) with the 64-m Parkes telescope; and (3) $-9.5^{\circ}<\delta<10^{\circ}$ 4.85 GHz radio continuum survey led by Griffith et al. (1995) with the 64-m Parkes telescope.

Criteria (a) and (c) lead to 500 sources being selected from the PSC, which contains 245 889 sources. However, only 135 sources were observed because of limited observing time and after applying criterion (b). These sources represent the sample reported in this paper. The sample sources are concentrated across the Galactic plane and cover a wide range of longitude, $10^{\circ}<l<230^{\circ}$.

3 Observations

A single-point survey in 13CO J= 2-1(220.398 GHz) was carried out from September 2002 to March 2003 using the Kölner Observatorium für SubMillimeter Astronomie (KOSMA[*]) 3-m telescope on Gornergrat near Zermatt in Switzerland. All of the sample sources were surveyed in 13CO J= 2-1. About half of the sample sources were also observed in 12CO J= 2-1(230.538 GHz) and 14 of them were mapped in 13CO J= 2-1.

The beamwidth of the KOSMA at 230 GHz was 130 $^{\prime\prime}$. The pointing accuracy was superior to 10 $^{\prime\prime}$. The telescope was equipped with a dual-channel SIS receiver, which had a noise temperature of 150 K. A high resolution spectrometer with 2048 channels was employed and the spectral resolution was 165.5 KHz, giving a velocity resolution of 0.22  $\rm {km~s}^{-1}$. The main beam temperature ( $T_{\rm {mb}}$) had been corrected for the effects of Earth's atmosphere, antenna cover loss, radiation loss, and forward spillover and scattering efficiency (92$\%$). From the calibrated Jupiter observations, the main beam efficiency $\eta_{\rm mb}$was estimated as 68$\%$ during our observation. On-the-fly mode was adopted during mapping, with a mapping step of 60 $^{\prime\prime}$. Most maps were extended until the line intensity decreased to half of the maximum value or even lower. The GILDAS[*] software package (CLASS/GREG/SIC) was used for the data reduction (Guilloteau & Lucas 2000).

\begin{figure}
\par\includegraphics[width=9cm,clip]{11104f1.eps}
\end{figure} Figure 1:

Example spectra of 13CO J= 2-1towards the IRAS sources given in the text.

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4 Results

4.1 Survey

Among the entire sample of 135 IRAS sources, we identified 98 sources suitable for star formation analyses (another 37 sources were excluded either because they had multiple components or bad baselines, or failed to be detected), of which 60 have both 13CO J= 2-1 and 12CO J= 2-1 data. Figure 1 presents example spectra of 13CO J= 2-1: (a) IRAS 00117+6412, a perfect Gaussian profile; (b) IRAS 02541+6208, a fairly narrow line width; (c) IRAS 06067+2138, a broad line with red wing, also seen in J= 1-0 transition (Wu et al. 2003); (d) IRAS 20326+3757, a blue wing; (e) IRAS 18278-0212, red asymmetry; (f) IRAS 21379+5106, two peaks; (g) IRAS 19348+2229, two components; and (h) IRAS 02485+6902, multiple components.

Observed and derived parameters are listed in an online Table 1, starting with IRAS name and its J2000 equatorial coordinates in Cols. (1) to (3). By Gaussian fit, we obtain the observed parameters including main beam temperature $T_{\rm {mb}}$, local standard of rest velocity $V_{\rm LSR13}$, and 13CO J= 2-1 line width (full width at half-maximum) $\Delta V_{13}$ for each source, listed in Cols. (4) to (7). When a line profile is obviously non-Gaussian, the parameters are measured with a cursor (e.g., Wu & Evans 2003), and the velocity uncertainty is given as the velocity resolution; when the line profile has distinctive multiple components, only the strongest component is shown, indicated by a character m in corresponding $T_{\rm {mb}}$columns.

The distance to most sources was unavailable in the literature. The kinematic distances were calculated based on the radial velocity $V_{\rm LSR13}$ and the velocity field of the outer Galaxy given by Brand & Blitz (1993). When two kinematic distances were available, we selected the closer one, except when the closer distance is too small (<100 pc). For 8 sources, however, no reasonable distances could be calculated in this way and we assumed that the distance to these sources is 1 kpc. These are marked as * in the distance Col. (8) of Table 1.

The bolometric luminosity was calculated based on the distances and the IRAS fluxes in four bands (12, 25, 60, 100 $\mu $m), following the formula given by Casoli et al. (1986)

\begin{eqnarray*}L_{\rm {bol}} &=& 5.4D^{2}(f_{12~\mu{\rm m}}/0.79\\
&& +~f_{25...
...m m}}/2+f_{60~\mu{\rm m}}/3.9+f_{100~\mu{\rm m}}/9.9)~L_{\odot},
\end{eqnarray*}


where D is the distance in kpc and $f_{\lambda}$ is the flux density in Jansky. The uncertainties in luminosity originate in the kinematic distances and the quality of the IRAS source fluxes. Most of the sample sources have high or moderate quality in all the four bands. Twenty-one sources with upper limit fluxes in one or two bands are marked as u luminosity in Col. (9) of Table 1.

Table 2:   Core properties.

Assuming local thermodynamic equilibrium (LTE) and that the 13CO J= 2-1 transition is optically thin (i.e. $\tau_{13}<1$), we derive excitation temperatures, optical depth and column densities for 13CO, using radiation transfer equation (Garden et al. 1991). Based on the assumption of LTE, 13CO and 12CO share the same excitation temperature $T_{\rm ex}$, which can be derived from the main beam temperature of optically thick 12CO, $T_{\rm {mb12}}$. When $\tau_{13}$ >1, an optical depth correction factor $C_\tau =
\tau_{13}/(1-{\rm e}^{-\tau_{13}})$ is multiplied by its corresponding column density. The relative CO abundance [12CO/H2] is estimated to extend from $2.5~\times~10^{-5}$(Rodriguez et al. 1982) to 10-4(Garden et al. 1991), and we adopt the median value of $6.25~\times~10^{-5}$. Using the terrestrial [12C/13C] ratio of 89, we adopt a value for [13CO/H2] of $7.0~\times~10^{-7}$ when computing the column density of H2. These parameters are listed in Cols. (10) to (13). References of former works are given in the last Col. (14) of Table 1.

The distribution of 13CO J= 2-1 line width of this sample has a mean of 3.09  $\rm {km~s}^{-1}$ and a standard deviation of 1.06  $\rm {km~s}^{-1}$. This line width is relatively smaller than that of typical bright/red IRAS sources associated with water masers (3.5  $\rm {km~s}^{-1}$, Wu et al. 2001; note that this value was measured in J= 1-0 transition), while significantly larger than that of a molecular cloud hosting intermediate-mass star formation activities ($\sim$ $\rm {km~s}^{-1}$, Sun et al. 2006, averaged throughout the Perseus cloud). The luminosities are distributed over a wide range, from 20 $L_{\odot}$ to about 105 $L_{\odot}$, with a mean of 104 $L_{\odot}$. The high dispersion of luminosities indicates that these sources are embedded in very different environments. This luminosity distribution is similar to the young ``low'' sources of Molinari et al. (1996, see their Fig. 6), in agreement with the assumption that our sample group may be relatively younger than that chosen by traditional color criteria. The excitation temperature $T_{\rm ex}$ ranges from 4.4 to 22.5 K, with an average of 9.7 K. This suggests that very cold gases surround the sample sources, colder than those surrounding the luminous IRAS sources (Zhu & Wu 2007). The 13CO column densities are $(1.2{-}28.7)~\times~10^{15}~{\rm cm}^{-2}$, with an average of $6.2~\times~10^{15}~{\rm cm}^{-2}$, while H2 column densities are $(1.7{-}40.8)~\times~10^{21}~{\rm cm}^{-2}$, with an average of $8.9~\times~10^{21}~{\rm cm}^{-2}$. These densities are roughly close to the critical value for gravitational collapse (Hartquist et al. 1998).

4.2 Mapping

To improve our understanding of the properties of the surveyed sample, 14 sources were mapped in 13CO J= 2-1and compared with archival mid-infrared (MIR) continuum data. Mapped sources were selected from the surveyed sample as those with only single emission component, and they almost evenly cover longitude $70^{\circ}<l<230^{\circ}$, avoiding low Galactic longitudes, where 13CO lines are often affected by multiple velocity components from the Galactic molecular ring. Using these sources as a guide, maps were extended until at least one core was resolved. We name a map on the basis of its guide source name, as outlined in Fig. 2. In four cases, one map resolved two cores, resulting in 18 cores in total. We found that 13 cores are associated with the original guide sources, two cores are associated with other IRAS sources, and three cores have no embedded infrared source (sourceless hereinafter). A core is named after its associated IRAS source; for a sourceless core, it is named after its nearest IRAS source plus relative direction to the core (e.g., 20067+3415NE). See Table 2 for core properties.

The core size (Col. 2 of Table 2) is defined as an equivalent linear size $R = \sqrt{A/\pi}$, where A is the projected area of each cloud within the 50$\%$ contour (highlighted in Fig. 2). It is corrected for the effect of beam smearing by multiplying its value by a factor ${\sqrt{\theta_{\rm {obs}}^2-\theta_{\rm {mb}}^2}}/{\theta_{\rm {obs}}}$, where $\theta_{\rm {obs}}$ is the angular diameter of the core and $\theta_{\rm {mb}}$is the beamwidth. For three cores, the observed angular diameters are comparable to the beamwidth, so that the cores are just marginally resolved and the corresponding core sizes are highly uncertain. In a few cases, maps were not complete to 50$\%$of the peak intensity, and can only infer lower limits to R(indicated by a symbol ``>''). The average line width of each core (Col. 3) is determined by combining all the spectra in the core and then fitting a Gaussian profile to the average spectrum. In a few cases, the average spectra show line asymmetry/absorption and need to be fitted with two Gaussian profiles, and then the line width of the stronger profile is given. The typical uncertainty in the average line width is 0.04  $\rm {km~s}^{-1}$. Column (4) lists the luminosity also given in Table 1 for reference. Peak volume densities for H2, $n({\rm H}_{2})$ (Col. 5), and the LTE core masses, $M_{{\rm LTE}}$ (Col. 6), are calculated based on both R and the peak 13CO column densities determined by interpolating the maps. For three maps (IRAS 06067+2138, 07024-1102, and 21391+5802), however, no $N(^{13}{\rm CO})$ are available in Table 1 because of a lack of 12CO data. To estimate their core properties, we assume reasonable excitation temperatures: for IRAS 06067 and 07024, we assume a typical $T_{\rm ex}$ of 15 K; and for IRAS 21391, we assume that $T_{\rm ex}$ equals the dust temperature (25 K, Beltrán et al. 2002). Column (7) presents the virial mass derived from the sizes and line widths following MacLaren et al. (1988). The ratio of virial to LTE mass $\alpha = M_{\rm vir}$/ $M_{{\rm LTE}}$is listed in the last Col. (8) of Table 2. We exclude the marginally resolved cores when computing averages except for the line width column.

Overall, the core mass ranges from $\sim$ $10^2~M_{\odot}$to $10^4~M_{\odot}$, the linear size from 0.11 pc to 2.41 pc, and molecular hydrogen density is in the range $\sim$ $10^3{-}10^4~\rm {cm}^{-3}$. The luminosities are once again, distributed across a wide range, from 30 $L_{\odot}$ to $1.7~\times~10^4~L_{\odot}$. Overall, the line width $\overline{\Delta V}_{13}$ > $\sim$ $2~\rm {km~s}^{-1}$, and has an average of 2.80  $\rm {km~s}^{-1}$, smaller than that of the entire surveyed sample. We find an average value of 1.3 for the ratio of virial to LTE core mass, $\alpha$. Overall the mapping sample infers $\alpha\sim 1$, indicating that most of the cores appear to be virialized.

Comparisons between 13CO maps and MIR images are presented in Fig. 2, and a detailed evolutionary identification of individual mapped sources is presented in the online Appendix A.

\begin{figure}
\par\includegraphics[angle=-90,width=5cm,clip]{11104f2a.eps}\hspa...
...degraphics[angle=-90,width=5cm,clip]{11104f2n.eps}\hspace*{2.5cm}}\end{figure} Figure 2:

13CO J= 2-1 integrated intensity contours overlay the Midcourse Space Experiment (MSX; Price et al. 2001) band A (8.28 $\mu $m) images as background, if available. Maps are listed in order of name, except the two without MSX data. IRAS 03258+3104 has no band A data and we use band C instead; IRAS 00557+5612 and 22198+6336 both have no MSX data available, as labeled on the top of their relevant sub-figures. IRAS point sources are denoted by squares while MSX point sources by triangles. Small crosses represent observed points, while large crosses denote the original guide sources (Sect. 4.2), as labeled on the top of each map. Dash lines schematically separate resolved cores. For integration, only intensity over three times of the standard deviation ($3\sigma $) is considered. Contour levels begin from 30% to 90% by 10% of the peak intensity, while 50% level is highlighted by a solid thick contour. For MSX images, the grey scale wedge is shown on the right side; the unit is $W~
\rm{m}^{-2}~\rm{sr}^{-1}$.

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5 Discussion

5.1 The line width-luminosity relation

The empirical correlation of line width versus luminosity has been found by various authors from observations in C18O (Ridge et al. 2003; Saito et al. 2001), as well as in NH3(Myers et al. 1991; Ladd et al. 1994; Jijina et al. 1999; Wouterloot et al. 1988; Harju et al. 1993). The line width is in general found to increase with luminosity, for different $\lg(\Delta
V)/\lg(L_{\rm {bol}})$ slopes: 0.13-0.19 for NH3(Jijina et al. 1999) and 0.11 for C18O (Saito et al. 2001). Given the relatively wide availability of the archival 13CO data, it is helpful to compile an up-to-date 13CO observed sample to investigate the luminosity-line width relation in case of 13CO.

\begin{figure}
\par\includegraphics[width=11cm,clip]{11104f3.eps}\end{figure} Figure 3:

Line width plotted versus bolometric luminosity of 360 13CO observed sources: surveyed sources (open circles), mapped sources (filled circles), and other samples adopted from the literature (diamonds). Solid line represents a least squares fitting to the data, and the dash lines represent the luminosity/line-width criteria (Sect. 5.1).

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In Fig. 3, we plot in logarithmic space the line width versus luminosity from our sample and other 13CO observed samples adopted from the literature (Wu et al. 2004; Ridge et al. 2003; Wu et al. 2001; Beichman et al. 1986; Yamashita et al. 1989; Fischer et al. 1985; Dent et al. 1985). This sample contains 360 sources in total. One finds that the luminosity of the IRAS sources is well correlated with the 13CO line width, as fitted by a power law:

\begin{displaymath}\lg~\bigg(\frac{\Delta V_{13}}{\rm {km~s}^{-1}}\bigg) = (-0.0...
...(0.135\pm 0.012)\lg~\bigg(\frac{L_{\rm
bol}}{L_{\odot}}\bigg),
\end{displaymath}

where the correlation coefficient c.c.= 0.69. This suggests that the mass of the forming stellar objects is linked to the dynamic status of their parent clouds. Saito et al. (2001) measured a similar correlation in the Centaurus tangential region and suggested that the mass of the formed stars is determined by the internal velocity dispersion of the dense cores. If the velocity dispersion is a reliable indicator of the turbulence, this is consistent with the idea that turbulence is different in high-mass and low-mass cores. We note that the 13CO line widths adopted from the literature were measured from J= 1-0transition with smaller beams.

It is generally agreed that embedded infrared point sources of high luminosity ($\geq$ $10^3~L_{\odot}$) but without associated H  II regions are good candidates to be high-mass YSOs in the pre-UC H  II phase (e.g., Wu et al. 2006, and references therein). However, sufficiently young massive objects are not necessarily bright at infrared wavelengths; some of them have no infrared counterparts. High-mass objects at sufficiently young evolutionary stages could be quite faint in infrared ranges either because they are not yet mature enough to have developed infrared emission or they are embedded very deeply in cold dust. For instance, Sridharan et al. (2005) identified several 1.2 mm emitting high-mass starless cores (HMSCs) that exhibit absorption or no emission at the MIR wavelengths; a centimeter-emitting UC H  II region was also found without an infrared counterpart (Forbrich et al. 2008). In our mapped sample, faint (< $10^3~L_{\odot}$) sources associated with very massive (> $10^{3}~M_{\odot}$) cores (20149, 20151) do exist. Although we cannot rule out the possibility that these two sources could evolve to only low-mass stars, it is very likely that the clouds will eventually fragment to form high-mass stars, given the large amount of gas therein.

Hereafter, for clarity, our luminosity criterion refers to bolometric luminosity $L_{\rm bol} \geq 10^{3}~ L_{\odot}$, and our line-width criterion refers to line width $\Delta V
$(13CO J= 2-1) >2  $\rm {km~s}^{-1}$. According to the $\Delta V - L$ relation above, luminosity $L_{\rm
bol}=10^{3}~L_{\odot}$ corresponds to $\Delta V_{13} =
2.42^{+0.49}_{-0.41}~\rm {km~s}^{-1}$. Because high-mass stars are far more luminous than their low-mass counterparts, luminous IRAS sources ($\geq$ $10^3~L_{\odot}$) are likely to be high-mass stellar objects. Therefore, we tentatively (not exclusively) suggest the lower limit, $\Delta V_{13} =2~\rm {km~s}^{-1}$, as a characteristic value for the line-width criterion, analogous to the widely used luminosity criterion. Objects with line width larger than this characteristic value are probably high-mass objects. The line-width criterion includes 94.5% sources that also satisfy the luminosity criterion (Fig. 3), which implies that line width may be a key parameter in measuring the masses of the forming stellar objects in the cores, at least in our sample. We note that this criterion (2  $\rm {km~s}^{-1}$) is larger than the typical line width of low mass cores (1.3  $\rm {km~s}^{-1}$, Myers et al. 1983), and smaller than the average line width of high-mass cores (3.5  $\rm {km~s}^{-1}$, Wu et al. 2001).

Applying the luminosity/line-width criteria to our sample, there are 68 sources satisfying luminosity criterion, 65 (95.6%) of which also satisfy line-width criterion. We suggest that the 65 sources are candidate high-mass star formation regions in a pre-UC H  II phase. For the remaining 30 less luminous sources, 23 of them satisfy the line-width criterion but not the luminosity criterion. We suggest that the 23 sources are high-mass YSO candidates earlier than pre-UC H  II phase.

5.2 Core masses and line widths

The core masses provide a direct test of our line-width criterion. Figure 3 includes 15 cores with luminosities listed in Table 2. We exclude sourceless cores and marginally resolved cores in the discussion in this section, because the former's luminosity cannot be determined and latter's estimated size and mass are highly uncertain. The remaining 14 luminosity-available cores can be divided into two groups: group I, which do not satisfy the luminosity criterion, including 03414, 21391, 03260, 20149, 06067, 20151; and group II, satisfying the luminosity criterion, including 00557, 22198, 03101, 06103, 00117, 05168, 22506, 20067 (in order of increasing line width). All group II cores also satisfy the line-width criterion, and they are located in the upper right panel of Fig. 3. They are very massive, their estimated masses being higher than several $10^2~M_{\odot}$, except core 00117 ( $1.8~\times~10^2~M_{\odot}$). On the other hand, group I cores mostly satisfy the line-width criterion. They are relatively less massive than group II cores, their masses being typically $\sim$ $10^2~M_{\odot}$or more, with two very massive cores 20149 and 20151 (> $10^{3}~M_{\odot}$). The only case that does not satisfy the line-width criterion, core 03414, has the lowest mass in group I. We note that all group I cores are still significantly more massive than the low-mass cores (Myers et al. 1983).

The high-mass nature of group I cores confirms again (in addition to the previously mentioned cores 20149, 20151) that the luminosity criterion cannot be applied to some young sources. On the other hand, the line-width criterion is applicable to our sample. While in terms of inferring mass, line width may not be as direct an indicator as luminosity, it is helpful when luminosity is unavailable or is affected by large uncertainty (e.g., due to distance ambiguity, flux upper limit), which is often the case. In addition, line width can be measured observationally more easily and more accurately than luminosity.

In Fig. 4a, we plot $\lg (\Delta V_{13})$ versus $\lg M_{{\rm LTE}}$. A weak correlation is evident in the data, with a correlation coefficient of 0.38. This may indicate that, for molecular clouds with associated YSOs, the 13CO line width at some degree is related to the cloud mass, and massive cores tend to have larger line widths. This weak correlation, together with the strong $\Delta V - L$ correlation, indicates that massive stars are more likely to form in massive molecular cores. The core mass and associated IRAS luminosity in our mapped sample are indeed well correlated ( c.c. = 0.76). However, this correlation may need to be corrected for distance effects (0.3-6.08 kpc for mapped sample) because both mass and luminosity are proportional to D2. Nevertheless, strong mass-luminosity correlations were reported in other regions or samples that have far smaller distance differences than our sample (Dobashi et al. 1996; Ridge et al. 2003; Saito et al. 2001). Figure 4b plots line width $\Delta V_{13}$and core size R in logarithm. With an average virial mass of $1.1~\times~10^3~M_{\odot}$, the cores exhibit no correlation between size and line width. This indicates that the Larson law is invalid for our mapped sample, consistent with the results of previous works (Plume et al. 1997, $\langle
M_{{\rm vir}} \rangle > 3.8~\times~10^3~M_{\odot}$; Guan et al. 2008, $\langle M_{{\rm vir}} \rangle =
5.6~\times~10^3~M_{\odot}$). The correlations in Fig. 4 are unaffected by distance, because the line width and distance of the plotted cores are not correlated ( c.c.=0.04).

We conclude that, based on the currently available sample, YSOs with higher bolometric luminosity (> $10^3~L_{\odot}$), tend to be associated with more massive molecular cloud structures, which are usually more turbulent, and have a large 13CO line width, $\Delta V_{13}>2~\rm {km~s}^{-1}$. It is important to note that, the characteristic value ( $2~\rm {km~s}^{-1}$) may not be universal, and can vary from region to region and/or from line to line. Further mapping of more clouds, as well as higher angular resolution data if available, are required to examine the line-width criterion proposed here.

\begin{figure}
\par\includegraphics[width=9cm,clip]{11104f4.eps}
\end{figure} Figure 4:

Relations between 13CO line width $\Delta V_{13}$ and other physical parameters of molecular cores: a) LTE mass $M_{{\rm LTE}}$, and b) size R. In both cases, the filed circles represent data and solid lines are linear fitting results to the data. The fitting function and correlation coefficient are labeled in each panel.

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6 Summary

We have carried out a 13CO J= 2-1 survey of 135 IRAS sources selected as potential YSOs earlier than UC H  II regions. Our main findings are summarized as follows:

1.
Ninety-eight sources have good enough emission profile for analysis; some of them show asymmetric line profiles of 13CO J= 2-1. The line width is 3.09  $\rm {km~s}^{-1}$and excitation temperature is 9.7 K, on average. The H2 column densities are $(1.7{-}40.8)~\times~10^{21}~{\rm cm}^{-2}$. Sixty-five sources are suggested to be candidate precursors of UC H  II regions.

2.
Fourteen sources were mapped and resolved as eighteen cores, which have been identified with eight pre-UC H  II regions and one UC H  II region, two high-mass cores earlier than pre-UC H  II phase, four possible star forming clusters, and three sourceless cores.

3.
For molecular clouds with known associated YSOs and measured $L_{\rm {bol}}$, 13CO line width $\Delta V_{13}$ of the clouds is correlated with the bolometric luminosity of the YSOs. Based on the current 13CO observed sample (360 sources in total), this correlation can be fitted as a power law, $\lg~(\Delta V_{13}/~\rm {km~s}^{-1}) = (-0.023\pm 0.044)+(0.135\pm 0.012)\lg~({\it L}_{\rm bol}/{\it L}_{\odot})$.

4.
Luminous (> $10^3~L_{\odot}$) YSOs tend to be produced in more massive and more turbulent ( $\Delta V_{13}>2~\rm {km~s}^{-1}$) molecular cloud structures.

5.
High-mass stars are more likely to form in massive molecular clouds.

Acknowledgements
We are grateful to Q. Zhang, X. Guan, R. Xue and L. Zhu for valuable discussion. We thank H. Du and F. Virgili for their help on the manuscript. We also thank the anonymous referee whose comments and suggestions helped to improve the content and the clarity of this paper. This research is supported by Grants 10733030 and 10873019 of NSFC. It made use of data products from the Infrared Astronomical Satellite (IRAS) and the Midcourse Space Experiment (MSX) retrieved from the NASA/IPAC Infrared Science Archive, which is operated by the JPL/Caltech under a contract with NASA.

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Online Material

Appendix A: individual analyses

In Fig. 2, we compare the integrated intensity of 13CO emissions to IRAS (point sources) and MSX (point sources and images) data. We use the most sensitive band (band A, centered on 8.28 $\mu $m) images of MSX when available. We note that maps in Fig. 2 are labeled by the original guide sources (Sect. 4.2). IRAS 03258+3104 has no band A data and we use band C (centered on 12.13 $\mu $m) instead. IRAS 00557+5612 and 22198+6336 both have no MSX data. Individual analyses of each map are presented as follows.

IRAS 00117+6412: 13CO emission peak coincides well with IRAS and MSX point sources, and there are also strong counterparts in all four MSX bands. This distinctive 13CO core is massive ( $1.8~\times~10^2~M_{\odot}$), in agreement with the conclusion deduced from the luminosity/line-width criteria (Sect. 5.1). We therefore suggest that it is a pre-UC H  II region. Strong 22 GHz water maser (Wouterloot et al. 1993) and outflow activity (Zhao et al. 2003; Zhang et al. 2005) have been detected within this area, providing evidence of active star formation.

IRAS 00557+5612: MSX data are unavailable close to this region, but the IRAS source matches well to the 13CO core peak. A core as massive as $6.6~\times~10^2~M_{\odot}$agrees with the conclusion deduced from the luminosity/line-width criteria. We therefore suggest that it is a pre-UC H  II region. A velocity gradient of 0.36  $\rm {km~s}^{-1}$  $\rm {pc}^{-1}$from northeast to southwest is inferred, yielding a rotating angular velocity of $1.16~\times~10^{-14}~\rm {s}^{-1}$. According to 13CO J= 1-0 and HCO+ mapping by Zhu & Wu (2007), two subcores exist within this core.

IRAS 03101+5821: 13CO emission coincides with infrared point sources and image as well. A core more massive than $5.8~\times~10^2~M_{\odot}$agrees with the conclusion drawn from the luminosity/line-width criteria. We therefore suggest that it is a pre-UC H  II region. A 22 GHz water maser has been detected within this area (Wouterloot et al. 1993).

IRAS 03258+3104: a MSX band A image is unavailable for this region and we use band C instead. 13CO emission within this area is more diffuse than that in former sources. At least two cores (03260+3111 and 03260+3111NE) are resolved within an area of 0.34 pc. The larger core coincides with IRAS 03260+3111, which does not satisfy our color selection criteria and was suggested as an UC H  II region by Churchwell et al. (1990). Taking both their line width and luminosity into account, we suggest that core 03260+3111 is a high-mass object in UC H  II phase, while 03260+3111NE is a sourceless core. The original guide source of the map, IRAS 03258+3104, is not associated with any resolved 13CO core. It has been suggested to be a Class 0 object driving a low-mass bipolar CO outflow (Knee & Sandell 2000).

IRAS 03414+3200: 13CO is quite diffuse across the entire area of 0.34 pc, so that no distinctive 13CO core is found. However, several infrared point sources are evident close to the 90% contour within one beam, superimposed on a steep density gradient. Although its mass (>85 $M_{\odot}$) and line width 1.92  $\rm {km~s}^{-1}$) are relatively low in all the mapped sources, it appears to be a star forming cluster.

IRAS 05168+3634: at least two cores (05168+3634 and 05168+3634SW) are present within 3.01 pc. The dominant northeastern core appears to be associated with the infrared sources. The total core mass higher than $1.5~\times~10^4~M_{\odot}$agrees with the conclusion deduced from the luminosity/line-width criteria. We suggest that the dominant core is a high-mass star forming region in pre-UC H  II phase, and the SW core is a sourceless core. This is consistent with results from Molinari et al. (1996). Strong outflow activity was identified (Zhang et al. 2005; Brand et al. 1994) at the position of the NE core, and the outflow driving source appears deviated to the infrared source IRAS 05168+3634. A 22 GHz water maser was detected by Palla et al. (1991) in this region.

IRAS 06067+2138: 13CO core coincides with the IRAS point source but is without MSX counterpart. The core mass $M_{{\rm LTE}}$ ( $2.5~\times~10^2~M_{\odot}$) is only one third of its virial mass $M_{\rm vir}$ ( $7.8~\times~10^2~M_{\odot}$), indicating that the core is not yet gravitationally bound. Taking its large line width (3.36  $\rm {km~s}^{-1}$) into account, we suggest that it is a high-mass object earlier than pre-UC H  II phase.

IRAS 06103+1523: 13CO emission coincides with both infrared point sources and image. A core as massive as $2.8~\times~10^3~M_{\odot}$agrees with the conclusion deduced from the luminosity/line-width criteria. IRAS 06103+1523 is found to be two point sources by MSX data, implying that a fine structure may exist there. A denser molecular tracer (e.g., N2H+ or HCO+) and a higher resolution (several arcsec) are needed to study these fine structures. We therefore suggest that it is a high-mass star forming cluster.

IRAS 07024-1102: 13CO map is incomplete but a core is clearly evident. The core coincides with the IRAS point source but does not have a MSX counterpart. Although its luminosity (570 $L_{\odot}$) is a little lower than the luminosity criterion, it does generate a line width (1.99  $\rm {km~s}^{-1}$) very close to the line-width criterion. We therefore suggest that it is a high-mass object earlier than pre-UC H  II phase.

IRAS 20067+3415: the 13CO gas distribution is quite complex in this region. At least two cores (20067+3415 and 20067+3415NE) are revealed. The dominant southwestern core coincides with infrared point sources, while the northeastern core is a sourceless core. Several sub-structures are revealed within an area of 2.21 pc with total mass of $4.9~\times~10^3~M_{\odot}$. Thus, we suggest that core 20067+3415 is a high-mass star forming cluster. The MIR emission and luminosity are relatively weak compared to those of other pre-UC H  II regions, indicating a very early evolutionary stage.

IRAS 20149+3913: 13CO emission reveals two cores (20149+3913 and 20151+3911); both also coincide with infrared point sources and image. They do not satisfy the luminosity criterion but have large line widths, consistent with their high masses. Both sources are located in the Cygnus X molecular cloud complex and were mapped in 1.2 mm continuum (Motte et al. 2007), yielding masses 8 $M_{\odot}$ and 23 $M_{\odot}$, respectively (see their Table 1 and Fig. 13). Here we suggest that both cores are pre-UC H  II regions.

IRAS 21391+5802: 13CO emission detects a distinctive core and a belt of gas distributed along the southeast to northwest direction, which is coincident with the MIR background and several point sources. The core mass $M_{{\rm LTE}}$( $1.3~\times~10^2~M_{\odot}$) is roughly half of its virial mass $M_{\rm vir}$( $3.1~\times~10^2~M_{\odot}$), indicating that the core is not yet gravitationally bound, responsible for a large line width (2.78  $\rm {km~s}^{-1}$). Taking its relatively small size (0.32 pc) into account, we suggest that it is a star forming cluster where high-mass stars could eventually form. A 22 GHz water maser and outflow were identified in this region (Zhang et al. 2005; Palla et al. 1991).

IRAS 22198+6336: MSX data are unavailable near this region, but the IRAS source matches the 13CO core peak well. A core as massive as $1.7~\times~10^3~M_{\odot}$agrees with the conclusion deduced from the luminosity/line-width criteria. A 22 GHz water maser and outflow were identified in this region (Zhang et al. 2005; Palla et al. 1991). We therefore suggest that it is a pre-UC H  II region.

IRAS 22506+5944: 13CO core coincides well with a luminous IRAS point source and a bright MSX counterpart. A core as massive as $1.0~\times~10^3~M_{\odot}$ agrees with the conclusion deduced from the luminosity/line-width criteria. Thus, we suggest that it is a pre-UC H  II region. Outflow activity (Zhang et al. 2005; Wu et al. 2005b) and a 22 GHz water maser (Palla et al. 1991) were identified, indicating that active star formation process is underway.

In summary, 13CO J= 2-1 mapping reveals at least 18 massive cores from 14 maps. By means of individual analyses, we identify eight pre-UC H  II regions and one UC H  II region, two high-mass cores earlier than pre-UC H  II phase, four possible star forming clusters, and three sourceless cores.

Table 1:   Observed and derived parameters of surveyed sources.


Footnotes

... sources[*]
Appendix A and Table 1 are only available in electronic form at http://www.aanda.org
... (KOSMA[*]
The KOSMA 3 m radiotelescope at Gornergrat-Süd Observatory is operated by the University of Cologne and supported by special funding from the Land NRW. The Observatory is administered by the Internationale Stiftung Hochalpine Forschungsstationen Jungfraujoch und Gornergrat, Bern.
... GILDAS[*]
Available at http://www.iram.fr/IRAMFR/GILDAS

All Tables

Table 2:   Core properties.

Table 1:   Observed and derived parameters of surveyed sources.

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