EDP Sciences
Free Access
Issue
A&A
Volume 604, August 2017
Article Number A74
Number of page(s) 25
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/201730633
Published online 09 August 2017

© ESO, 2017

1. Introduction

A close connection between dense molecular gas (with nH2> 104 cm-3) and star formation has been established for quite some time on both Galactic and extragalactic scales. On small scales, individual stars of low to intermediate masses are known to form from the collapse of prestellar dense cores (e.g., Myers 1983; Ward-Thompson et al. 1994; André et al. 2000), themselves often embedded in dense cluster-forming gas clumps within molecular clouds (e.g., Lada 1992; Myers 1998). On galaxy-wide scales, the global star-formation rate (SFR) is linearly correlated with the total amount of dense molecular gas as traced by HCN observations (Gao & Solomon 2004a,b), while the correlation between the SFR and the amount of either atomic (HI) or low-density molecular (CO) gas is non linear and not as tight (e.g., Kennicutt 1989). Moreover, as pointed out by Lada et al. (2012), essentially the same relation between SFR and mass of dense gas Mdense is found in nearby Galactic clouds (SFR = 4.6 × 10-8M yr-1 × (Mdense/M)Lada et al. 2010) and external galaxies (SFR = 2 × 10-8M yr-1 × (Mdense/M)Gao & Solomon 2004b). The only exception seems to be the extreme star-forming environment of the central molecular zone (CMZ) of our Galaxy, where a very low star-formation efficiency in dense gas has been reported (Longmore et al. 2013). Investigating the nature and origin of this quasi-universal “star formation law” in the dense molecular gas of galaxies is of fundamental importance for our understanding of star formation and galaxy evolution in the Universe.

Table 1

Observations.

Key insight is provided by the results of recent submillimeter imaging surveys of Galactic molecular clouds with the Herschel Space Observatory, which emphasize the role of interstellar filaments in the star formation process (e.g., André et al. 2010; Molinari et al. 2010). The presence of filamentary structures in molecular clouds was already known long before Herschel (e.g., Schneider & Elmegreen 1979; Myers 2009), but Herschel observations now demonstrate that molecular filaments are truly ubiquitous, make up a dominant fraction of the dense gas in molecular clouds, and present a high degree of universality in their properties (e.g., Arzoumanian et al. 2011; Hill et al. 2011; Schisano et al. 2014; Könyves et al. 2015). A detailed analysis of the radial column density profiles of nearby Herschel filaments shows that they are characterized by a narrow distribution of central widths with a typical full width at half maximum (FWHM) value of ~ 0.1 pc and a dispersion of less than a factor of two (Arzoumanian et al. 2011). Another major result from the Herschel Gould Belt survey (HGBS – André et al. 2010) is that the vast majority of prestellar cores are found in dense, “supercritical” filaments for which the mass per unit length exceeds the critical line mass of nearly isothermal, long cylinders (e.g., Inutsuka & Miyama 1997),  pc-1, where cs ~ 0.2 km s-1 is the isothermal sound speed for molecular gas at T ~ 10 K (e.g., Könyves et al. 2015). These Herschel findings in nearby Galactic clouds support a scenario of star formation in two main steps (cf. André et al. 2014): first, large-scale compression of interstellar material in supersonic flows (turbulent or not) generates a quasi-universal web of filaments in the cold interstellar medium (ISM); second, the densest filaments fragment into prestellar cores (and subsequently protostars) by gravitational instability above Mline,crit.

The realization that, at least in nearby clouds, prestellar core formation occurs primarily along dense filaments of roughly constant inner width has potential implications for our understanding of star formation on global galactic scales. Remarkably, the critical line mass of a filament, , depends only on gas temperature (i.e., T ~ 10 K for the bulk of Galactic molecular clouds, away from the immediate vicinity of massive stars). Given the common filament width Wfil ~ 0.1 pc (Arzoumanian et al. 2011) this may set a quasi-universal threshold for core/star formation in the giant molecular clouds (GMCs) of galaxies at Mline,crit ~ 16 M pc-1 in terms of filament mass per unit length, or Mline,crit/Wfil ~ 160 M pc-2 in terms of gas surface density (corresponding to a visual extinction AV ~ 8), or in terms of gas density (i.e., a number density nH2 ~ 2.3 × 104 cm-3). Indeed, independent Spitzer infrared studies of the SFR as a function of gas surface density in nearby cloud complexes (e.g., Heiderman et al. 2010; Lada et al. 2010; Evans et al. 2014) show that the SFR tends to be linearly proportional to the mass of dense gas above a surface density threshold and drops to negligible values below . The observed star formation threshold corresponds to within a factor of ≪ 2 to the line-mass threshold above which interstellar filaments are expected to be gravitationally unstable.

While the observational results summarized above are very encouraging and tentatively point to a unified picture for star formation on GMC scales in both Galactic clouds and external galaxies, there are at least two caveats. First, direct comparison between Galactic (e.g., Lada et al. 2010) and extragalactic (e.g., Gao & Solomon 2004b) studies of the dense gas – star formation connection is difficult at this stage because different tracers have been used to probe dense gas in Galactic and extragalactic situations so far. For instance, Lada et al. (2010) used column density maps from near-infrared extinction and derived the total mass above the extinction/surface density threshold mentioned earlier (i.e., AV> 8), while Gao & Solomon (2004b) used HCN (1–0) data and estimated the mass of dense gas Mdense above the effective density ~ 3 × 104 cm-3 of the HCN (1–0) transition from the HCN (1–0) line luminosity, i.e., LHCN with αGS04 − HCN ~ 10 M (K km s-1 pc2)-1 (see also Wu et al. 2005). While the effective density of the HCN(1–0) transition (cf. Evans 1999) turns out to be close to the critical threshold density ~ 2.3 × 104 cm-3 quoted above for ~ 0.1-pc-wide supercritical filaments, the relation between and remains to be properly calibrated in nearby Galactic clouds. Second, significant variations in the apparent star-formation efficiency in dense gas as a function of stellar surface density or galactocentric radius have been found in resolved observations of the disks of several nearby galaxies (Usero et al. 2015; Chen et al. 2015; Leroy et al. 2016; Bigiel et al. 2016). To confirm that there is a universal star formation law converting the dense molecular gas of GMCs into stars, wide-field line mapping observations of Galactic clouds in the same dense gas tracers as used in extragalactic work and at a spatial resolution high enough to resolve ~0.1-pc-wide molecular filaments are crucially needed.

With the advent of sensitive heterodyne receivers and wideband spectrometers on millimeter-wave telescopes, wide-field mapping observations in several lines simultaneously are now feasible at an angular resolution down to ~10–30. In this paper, we present wide-field imaging data in the HCN (1–0), H13CN (1–0), HCO+ (1–0), and H13CO+ (1–0) transitions toward three nearby star-forming clouds, Aquila, Ophiuchus, and Orion B. The paper is organized as follows. In Sect. 2, we describe our IRAM 30 m, MOPRA 22 m, and Nobeyama 45 m observations. In Sect. 3, we present the results of the HCN, H13CN, HCO+, and H13CO+ mappings and estimate the far ultraviolet (FUV) field strength from Herschel HGBS 70 μm and 100 μm data. In Sect. 4, we discuss evidence of significant variations in the conversion factor αHCN between HCN luminosity and mass of dense gas, and, in particular, the dependence of αHCN on the FUV field strength. We then revisit the question of the universality of the star-formation efficiency in the dense molecular gas of galaxies and propose an interpretation of this universality in terms of the filamentary structure of GMCs. Our conclusions are summarized in Sect. 5.

2. Millimeter line observations

We carried out observations in the HCN (J = 1 − 0, 88.6318473 GHz), H13CN (J = 1 − 0, 86.340167 GHz), HCO+ (J = 1 − 0, 89.188526 GHz), and H13CO+ (J = 1 − 0, 86.75433 GHz) transitions toward three nearby star-forming regions, Aquila, Ophiuchus, and Orion B using the IRAM 30 m, MOPRA 22 m, and Nobeyama 45 m telescopes. The effective excitation densities1 of the HCN (1–0), H13CN (1–0), HCO+ (1–0), and H13CO+ (1–0) lines at 10 K are 8.4 × 103 cm-3, 3.5 × 105 cm-3, 9.5 × 102 cm-3, and 3.9 × 104 cm-3, respectively (Shirley 2015). Table 1 shows a summary of our molecular line observations. We describe the details of each observation below.

2.1. IRAM 30 m observations toward the Aquila cloud

During two observing runs (18 December 2014–29 December 2014 and 2 September 2015–9 September 2015), we carried out mapping observations toward a 0.4 deg2 region in the Aquila cloud, including the three subregions Aquila/W40, Aquila/Serp. South, and Aquila/cold (see Figs. 1 and A.1), with the Eight MIxer Receiver (EMIR) receiver on the IRAM-30 m telescope. All molecular line data were obtained simultaneously. At 86 GHz, the 30 m telescope has a beam size of 28.6 (HPBW) and the forward and main beam efficiencies (Feff and Beff) are 95% and 81%. As backend, we used the FTS50 spectrometer, providing a bandwidth of 1820 MHz and a frequency resolution of 50 kHz. The latter corresponds to a velocity resolution of ~0.15 km s-1 at 86 GHz. The standard chopper wheel method was used to convert the observed signal to the antenna temperature in units of K, corrected for the atmospheric attenuation. The data are given in terms of the main beam brightness temperature corresponding to . During the observations, the system noise temperatures ranged from 80 K to 330 K. The telescope pointing was checked every hour by observing the quasar source 1741-038 and was found to be better than 3 throughout the two runs. Our mapping observations were made with the on-the-fly (OTF) mapping technique. We chose the positions (RAJ2000, DecJ2000) = (16:29:06.4, − 24:26:57.0), (16:25:34.5, − 24:36:44.0), and (16:26:14.5, − 24:02:00.0) as our reference (off) positions. We decomposed the target field into a series of 10′ × 10′ subfields and took pairs of OTF maps toward each subfield using two perpendicular scanning directions (along the RA or Dec axes). Combining such pairs of OTF maps reduces scanning artifacts. We smoothed the data spatially with a Gaussian function resulting in an effective beam size of 40. The 1σ noise level of the final mosaiced data cube at an effective angular resolution of 40 and a velocity resolution of ~0.15 km s-1 is 0.07 K in TMB.

thumbnail Fig. 1

a) Column density map of the Aquila region derived from Herschel Gould Belt survey (HGBS) data (André et al. 2010; Könyves et al. 2015) at an angular resolution of 18.2 and in units of AV. b) FUV field strength map derived from HGBS 70 μm and 100 μm data smoothed to an angular resolution of 18.2 in Habing units, and integrated intensity maps of c) HCN(1–0); d) HCO+(1–0); e) H13CN(1–0); f) H13CO+(1–0) in units of K km s-1 (TMB). The angular resolutions of the HCN, HCO+, H13CN, and H13CO+ maps are 40, 40, 40, and 50, respectively. In each panel, a green polygon outlines the field observed in molecular lines. The HCN and H13CN integrated intensity includes all components of the hyperfine structure (HFS). The white contour in panel a and the magenta dotted contours in panels e and f show the AV = 8 level obtained after smoothing the Herschel column density map to 40 resolution. In panel b, green open circles indicate the positions of the Class II objects identified by Dunham et al. (2015). In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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2.2. MOPRA observations toward the Ophiuchus cloud

Between 26 July 2015 and 2 August 2015, we carried out mapping observations toward a 0.21 deg2 region in the Ophiuchus cloud, including the two subregions Oph/main (L1688) and Oph/cold (see Fig. A.2), with the 3 mm receiver installed on the MOPRA-22 m telescope. All molecular line data were obtained simultaneously. At 86 GHz, the telescope has a beam size of 39 (HPBW) and a main beam efficiency ηMB of 49% (Ladd et al. 2005). As backend, we used the Mopra spectrometer (MOPS) in zoom mode, providing a bandwidth of 137.5 MHz and a frequency resolution of 33.8 kHz. The latter corresponds to a velocity resolution of ~0.1 km s-1 at 86 GHz. The standard chopper wheel method was used to convert the observed signal to the antenna temperature in units of K, corrected for atmospheric attenuation. The data are given in main beam brightness temperature, /ηMB. During the observations, the system noise temperatures ranged from 240 K to 420 K. The telescope pointing was checked every hour by observing the SiO maser sources AH Sco, VX Sgr, and W Hya, and was better than 5 throughout the entire run. Our mapping observations were made with the OTF mapping technique. The positions (RAJ2000, DecJ2000) = (16:29:06.4, − 24:26:57.0), (16:25:34.5, − 24:36:44.0), and (16:26:14.5, − 24:02:00.0) were used as off positions. We obtained a series of OTF maps with two different scanning directions along the RA or Dec axes covering a subfield of 6′ × 6′ each and combined them into a single map to reduce scanning effects as much as possible. We smoothed the data spatially with a Gaussian function of 19.5″ (FWHM), resulting in an effective beam size of 50. The scanning effects were minimized by combining scans along the RA and Dec directions with the Emerson & Graeve (1988) PLAIT algorithm. The 1σ noise level of the final data at an effective angular resolution of 50 and a velocity resolution of 0.1 km s-1 is 0.5 K in TMB.

Table 2

Physical parameters derived from H13CO+ (1–0) observations.

2.3. NRO 45 m observations toward the Orion B cloud

Between 7 May and 21 May 2015, we carried out mapping observations toward a 0.14 deg2 region in the Orion B cloud, including the four subregions NGC 2023, NGC 2024, NGC 2068, and NGC 2071 (see Figs. A.3A.6), with the TZ receiver on the Nobeyama 45 m telescope. All molecular line data were obtained simultaneously. At 86 GHz, the telescope has a beam size of 19.1″ (HPBW) and a main beam efficiency ηMB of ~50%. As backend, we used the SAM45 spectrometer which provides a bandwidth of 31 MHz and a frequency resolution of 7.63 kHz. The latter corresponds to a velocity resolution of ~0.02 km s-1 at 86 GHz. The standard chopper wheel method was used to convert the observed signal to the antenna temperature in units of K, corrected for the atmospheric attenuation. The data are given in terms of the main beam brightness temperature, /ηMB. During the observations, the system noise temperatures ranged from 140 K to 630 K. The telescope pointing was checked every hour by observing the SiO maser source Ori-KL, and was better than 3 throughout the entire observing run. Our mapping observations were made with the OTF mapping technique. We chose the positions (RAJ2000, DecJ2000) = (5:39:21.819, − 2:9:8.54) and (5:44:41.15, 0:33:4.98) as off positions. We obtained OTF maps with two different scanning directions along the RA or Dec axes covering a subfield of 6′ × 6′ and combined them into a single map to reduce the scanning effects as much as possible. As a convolution function, we adopted a Gaussian function with a FWHM of half the beam size. The scanning effects were minimized by combining scans along the RA and Dec directions with the Emerson & Graeve (1988) PLAIT algorithm. We also applied spatial smoothing to the data with a Gaussian function resulting in an effective beam size of 30. The 1σ noise level of the final data at an effective resolution of 30 and a velocity resolution of 0.1 km s-1 is 0.28 K in TMB.

3. Results and analysis

3.1. H13CO+(1–0) and H13CN(1–0) emission

Figures 1 and A.1A.6 compare the H13CO+(1–0), and H13CN(1–0) integrated intensity maps observed toward Aquila, Ophiuchus, Orion B/NGC 2023, Orion B/NGC 2024, Orion B/NGC 2068, and Orion B/NGC 2071 with the column density maps derived from HGBS data toward the same sub-regions. Above the AV = 16 contour in the Herschel column density maps (assuming NH2/AV = 0.94 × 1021 cm-2, Bohlin et al. 1978), it can be seen that the spatial distribution of the H13CO+(1–0) emission is closely correlated with the texture of the dense gas (e.g., filamentary structure) seen by Herschel. In particular, the H13CO+(1–0) emission traces the dense “supercritical” filaments detected by Herschel very well. Likewise, the spatial distribution of the H13CN (1–0) emission is closely correlated with the column density distribution above the AV = 20 level, especially in the Aquila and Orion B/NGC 2024 regions. As apparent in Figs. 1 and A.1A.6, and in agreement with the effective excitation densities quoted in Sect. 2, the H13CN (1–0) emission traces higher column density gas compared to the H13CO+ (1–0) emission. Figure A.7 displays mean H13CN(1–0) spectra, obtained by averaging the data over the detected portion of each region and sub-region.

Table 3

Virial masses from H13CO+.

Table 4

Virial masses from H13CN.

The 1 K km s-1 level in the H13CO+(1–0) integrated intensity map roughly matches the AV = 30 level in the Herschel column density map (see Fig. 1f), which in turn corresponds to a volume density ~ 8.6 × 104 cm-3 assuming most of the dense gas is concentrated in ~ 0.1 pc filaments (cf. Sect. 1). This is roughly consistent with the H13CO+ (1–0) effective excitation density of ~ 4 × 104 cm-3, suggesting that local thermodynamical equilibrium (LTE) may not be too bad an approximation for H13CO+(1–0). Under the LTE assumption, the column density of H13CO+ can be derived as follows (cf. Tsuboi et al. 2011): (1)We further assume that the excitation temperature Tex of the H13CO+ (1–0) transition is equal to the dust temperature Tdust derived from the HGBS data. The dust temperature ranges from 11 K to 46 K. Table 2 summarizes the results. The mean H13CO+ column densities range from 2.9 × 1010 cm-2 to 1.6 × 1012 cm-2. The H13CO+ abundances relative to H2, XH13CO+NH13CO+/NH2, have mean values in the range (1.5–5.8) × 10-11, using NH13CO+ values estimated from the present data and NH2 values from HGBS data (André et al. 2010; Könyves et al. 2015). These abundance estimates are consistent within a factor of a few with the findings of previous studies in other regions (1.1 ± 0.1 × 10-11 in OMC2-FIR4: Shimajiri et al. 2015b; and 1.8 ± 0.4 × 10-11 in Sagittarius A: Tsuboi et al. 2011).

thumbnail Fig. 2

a) vs. and b) vs. relations. The black dashed lines indicate = and the red lines indicate the best-fit results: and . (The uncertainty in was derived from the uncertainties in and in (see Ikeda et al. 2007; Shimajiri et al. 2015a.) The x- and y-axis ranges are the same in both panels.

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Assuming spherical shapes and uniform density, the virial masses of the detected clumps and structures can be estimated as (see Ikeda et al. 2007; Shimajiri et al. 2015a), (2)The radius of each clump or cloud was estimated as . The velocity dispersion σ was determined as /, where is the mean FWHM velocity width among pixels where the emission was detected. The derived values , , , and are given in Tables 3 and 4.

We also estimated the total virial mass of the area above AV = 8 for each cloud by scaling the virial mass derived for the detected subregion using the well-known linewidth-size relation σVL0.5 (Larson 1981; Heyer et al. 2009). In practice, we assumed (3)and we estimated the cloud radius as [pc] = , where is the projected area of each observed cloud above AV = 8. The total virial mass, , was then estimated from the scaled velocity width () using Eq. (2).

The mass of each cloud was also estimated from HGBS data as where MX (either or ) is the mass integrated over the area of the corresponding Herschel column density map where (H13CO+ or H13CN) line emission was detected or where AV> 8. AY is the surface area (either or ), mH is the hydrogen atom mass, and μH2 = 2.8 is the mean molecular weight per H2 molecule. The uncertainties in and are typically a factor 2, mainly due to uncertainties in the dust opacity (cf. Roy et al. 2014). The total gas masses derived from Herschel, and , range from 6.5 M to 707 M and from 16 M to 954 M, respectively.

Tables 3 and 4 also include estimates of the virial mass ratios, and , defined as (6)and (7)The and ratios range from ~0.30 to ~1.1 and from ~0.40 to ~2.0, respectively, suggesting that all the dense clumps we observed are gravitationally bound, especially the portions detected in H13CO+. Figure 2a plots against , and shows that these two estimates of the mass of dense (AV> 8) gas agree to within better than 50% in each region (see also Table 3).

We also estimated and for the regions where H13CN emission was detected, i.e., Aquila/W40, Aquila/Serp. South, Oph/main, Orion B/NGC 2024, Orion B/ NGC 2068, and Orion B/NGC 2071. The virial mass ratios and range from 0.3 to 2.5 and from 0.5 to 2.9, respectively (see also Fig. 2b).

3.2. HCN (1–0) & HCO+ (1–0) emission

In contrast to the H13CO+ emission, the spatial distributions of HCN(1–0) and HCO+(1–0) emission differ significantly from the column density distribution derived from Herschel data, as shown in Figs. 1 and A.1A.6. The HCN(1–0) and HCO+(1–0) maps appear to trace more extended regions than the denser filaments traced in the Herschel column density maps. In the Aquila cloud, the HCN(1–0) and HCO+ (1–0) integrated intensities are strongest toward the W40 HII subregion, while column density is highest in the Serpens South subregion. The W40 HII region is known to be excited by the luminous stars IRS 1A North of spectral type O9.5 and IRS 1A South of spectral type B1V (Shuping et al. 2012). In the Ophiuchus cloud, the HCN(1–0) and HCO+(1–0) integrated intensities tend to be strong around the compact HII region excited by the B3 star S1 (Grasdalen et al. 1973; André et al. 1988). These findings suggest that the HCN(1–0) and HCO+(1–0) intensities depend on the strength of the local FUV radiation field.

Figure 4 shows comparisons of the mean H13CO+(1–0), HCO+(1–0) and HCN(1–0) spectra observed toward each region. Clear dips in the HCN(1–0) and HCO+(1–0) spectra can be seen at VLSR ~ 7, 4, 10 km s-1 in Aquila/W40, Oph/main, and Orion B/NGC 2071, respectively. Furthermore, the velocities of these dips coincide with the peak velocities of the H13CO+(1–0) spectra. This suggests that the HCN(1–0) and HCO+(1–0) spectra are strongly affected by self-absorption effects. In these subregions, the blueshifted components of the HCN(1–0) and HCO+(1–0) spectra are stronger than the redshifted components. This type of asymmetric spectral shape, known as blue-skewed asymmetry, suggests the presence of infalling motions in the clouds (cf. Myers et al. 1996; Schneider et al. 2010). Thus, the Aquila/W40, Oph/main, and Orion B/NGC 2071 clumps may be undergoing large-scale collapse.

Assuming the same excitation temperature for the two isotopic species and a 12C/13C isotopic ratio Ri = 62 (Langer & Penzias 1993), we also estimate the optical depth of HCN(1–0) and HCO+(1–0) as follows: (8)where Tpeak(i) is the peak intensity of the rare isotopic species [H13CN(1–0) or H13CO+(1–0)] derived from mean spectra averaged over the observed area (see Fig. 4), whereas Tpeak(n) and τ(n) are the peak intensity and optical depth of the normal species [HCN(1–0) or HCO+(1–0)] at the peak velocity of the rare isotopic species in the averaged spectra. In all observed regions, the HCN(1–0) and HCO+(1–0) lines are optically thick (see also Table A.1).

thumbnail Fig. 3

Comparison of the HCN, HCO+, and H13CO+(1–0) spectra averaged over the observed area in a) Aquila/W40; b) Aquila/Serp–South; c) Aquila/cold; d) Oph/main; e) Oph/cold; f) Orion B/NGC 2023; g) Orion B/NGC 2024; h) Orion B/NGC 2068; and i) Orion B/NGC 2071. In each panel, blue, red, and gray lines show the mean HCN, HCO+, and H13CO+(1–0) spectra in the corresponding subregion; the vertical dashed line marks the peak velocity of the H13CO+(1–0) line.

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Recently, Braine et al. (2017) observed a significant dependence of the IHCN/IHCO+ intensity ratio on metallicity, with IHCN/IHCO+ increasing from ~1/4 at 0.3 solar metallicity to ~1 at solar metallicity among galaxies of the local group. In the nearby clouds observed here, the median IHCN/IHCO+ intensity ratio ranges from 0.7 to 1.6 (see Table 5), consistent with the solar or near solar metallicity of these clouds.

Table 5

HCN (1–0) to HCO+ (1–0) line intensity ratios.

thumbnail Fig. 4

Comparison of the HCN, HCO+, and H13CO+(1–0) spectra averaged over the observed area in a) Aquila/W40; b) Aquila/Serp–South; c) Aquila/cold; d) Oph/main; e) Oph/cold; f) Orion B/NGC 2023; g) Orion B/NGC 2024; h) Orion B/NGC 2068; and i) Orion B/NGC 2071. In each panel, blue, red, and gray lines show the mean HCN, HCO+, and H13CO+(1–0) spectra in the corresponding subregion; the vertical dashed line marks the peak velocity of the H13CO+(1–0) line.

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3.3. Estimating the strength of the FUV radiation field

The FUV field strength, G0, can be derived from Herschel 70 μm and 100 μm photometric data using the following equations (Kramer et al. 2008; Schneider et al. 2016): where IFIR is the far-infrared (FIR) intensity, and B60 μm − 80 μm and B80 μm − 125 μm are the bandwidths of the Herschel/PACS broad-band filters at 70 μm and 100 μm, respectively. The G0 values are in units of the local interstellar radiation field (Habing 1968).

According to Hollenbach et al. (1991), G0 can also be estimated from the dust temperature Tdust based on the following relations: where, τ100, T0, and ν0 are the effective optical depth at 100 μm, the dust temperature of the cloud surface, and the frequency at 0.1 μm.

Figure A.8 shows the pixel-to-pixel correlation between the G0 values estimated in our target clouds from Herschel 70 μm and 100 μm data using Eqs. ((9), (10)) and the G0 values estimated from the Herschel Tdust maps using Eqs. ((11)–(13)). The best-fit results are G0(Tdust) = 1.38 × G0(70,100 μm) for Aquila, G0(Tdust) = 0.62 × G0(70,100 μm) for Oph, and G0(Tdust) = 2.60 × G0(70,100 μm) for Orion B. In Orion B, the highest G0 values come from pixels in NGC 2024 and affect the best-fit results. The best-fit results for pixels with G0(70,100 μm) < 100 is G0(Tdust) = 1.04 × G0(70,100 μm). In summary, our two estimates of G0 generally agree to within a factor 2 to 3. Pety et al. (2017) also estimated the strength of the FUV radiation field toward NGC 2023/2024 in Orion B using Eq. (12). Their estimate agrees with our G0(70,100 μm) value within 30%.

Table 6

Derived parameters for the dense portions of the target nearby clouds where AV> 8 mag.

4. Discussion

4.1. Evidence of large variations in the αHCN and αHCO+ conversion factors

In many extragalactic studies (e.g., Gao & Solomon 2004a), the mass of dense gas Mdense is estimated from the HCN(1–0) luminosity LHCN using the relation Mdense = αHCNLHCN and assuming a fixed conversion factor αHCN. Gao & Solomon derived a simple formula for the conversion factor, namely /Tb = 10 M (K km s-1 pc2)-1, under the assumption that the HCN(1–0) emission originates from gravitationally-bound “cores” or clumps with volume-averaged density n(H2) ~ 3 × 104 cm-3 and brightness temperature Tb ~ 35 K. On this basis, they adopted the single value αGS04 − HCN = 10 M (K km s-1 pc2)-1 in their seminal HCN study of galaxies (Gao & Solomon 2004a). Clearly, however, if the brightness temperature of the HCN emitting clumps is larger than 35 K or if their volume-averaged density is less than 3 × 104 cm-3, the αGS04 − HCN factor can become smaller than 10 M (K km s-1 pc2)-1. Calibrating the conversion factor αHCN in Galactic clouds and assessing its potential variations is thus of crucial importance. For a sample of massive Galactic clumps, Wu et al. (2005) investigated the relationship between virial mass (estimated from C34S observations) and HCN luminosity and found a logarithmic mean value αWu05 − HCN = 7 ± 2 M (K km s-1 pc2)-1 for the conversion factor. The fact that the αWu05 − HCN and αGS04 − HCN values differ by only ~ 30% is very encouraging for extragalactic studies, but the HCN excitation conditions in the massive clumps studied by Wu et al. (2005) are not necessarily representative of the bulk of the HCN-emitting dense gas in galaxies.

Here, we have both high-resolution HCN data and independent estimates of the mass of dense gas (from Herschel data) for a sample of nearby clouds/clumps spanning a broad range of radiation-field conditions, and are thus in a good position to calibrate the αHCN factor. To do so, we used the mass estimates derived from the Herschel column density maps, , and the HCN(1–0) luminosities from the present observations to compute a factor for each cloud in our sample. As explained in Sect. 1, because most of the dense gas is distributed in filaments of ~ 0.1 pc width, the AV> 8 level in Herschel column density maps of nearby molecular clouds is an excellent tracer of the gas denser than nH2 ~ 2.3 × 104 cm-3, corresponding to supercritical, star-forming filaments (cf. André et al. 2014). The H2 volume density of 2 × 104 cm-3 is also very close to the typical gas density of ≳ 3 × 104/τ cm-3 traced by the HCN(1–0) line in normal spiral galaxies (Gao & Solomon 2004a, where τ ≳ 1 is the optical depth of the line) and lies between the effective excitation density (8.4 × 103 cm-3) and the critical density (≳ 3 × 105 cm-3) of HCN(1–0) (Shirley 2015). The masses derived from Herschel data therefore provide good reference estimates of the mass of dense gas in nearby clouds. The estimated values of αHerschel − HCN range from ~35 to ~454 M (K km s-1 pc2)-1 (see Table 6). Clearly, large variations in αHerschel − HCN are present.

thumbnail Fig. 5

Correlations between αHerschel − HCN and G0 (blue line and filled circles) and between αHerschel − HCO+ and G0 (red line and filled circles). The blue and red lines correspond to the best-fit relations: [M (K km s-1 pc2)-1] and [M (K km s-1 pc2)-1]. The horizontal line marks αGS04 − HCN = 10 [M (K km s-1 pc2)-1]. The uncertainties in αHerschel − HCN and αHerschel − HCO+ as estimated from the uncertainties are a factor of 2 (Roy et al. 2014). The uncertainties in G0 are also a factor of 2 (see Sect. 3.3).

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thumbnail Fig. 6

a)Mdense,HCN against , and b)Mdense,HCO+ against . Red lines correspond to best-fit linear relations to the red data points: and . The red filled circles use Mdense,mol values derived from the relation . In panel a, the black open squares use Mdense,HCN values derived from the “extragalactic” relation Mdense,HCN = αGS04 − HCN × LHCN, where αGS04 − HCN = 10 M (K km s-1 pc2)-1; the black line corresponds to the best-fit linear relation to the open squares: Mdense,HCN (αGS04 − HCN.

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As described in Sect. 3.2, the HCN emission tends to be strong in areas where the FUV radiation field is strong. Meijerink et al. (2007) demonstrated that the HCN emission is stronger in photon-dominated regions (PDRs) by a factor of two for densities larger than 105 cm-3. Therefore, the variations we observe in αHerschel − HCN may be due to variations in the strength of the FUV field among the sub-regions.

The blue filled circles in Fig. 5 show a correlation plot between αHerschel − HCN and the mean FUV radiation field strength, G0, estimated from Herschel 70 μm and 100 μm data (cf. Sect. 3.3). The correlation coefficient between the two variables is − 0.82, showing the presence of a clear anti-correlation. Quantitatively, αHerschel − HCN decreases as G0 increases according to the following empirical relation: (14)Figure 6a plots the mass of dense gas Mdense,HCN estimated from HCN for each cloud in our sample, using both the standard extragalactic conversion factor αGS04 − HCN [=10 (K km s-1 pc2)-1] (black open squares) and the conversion factor from Eq. (14) (red filled circles), as a function of the reference mass estimate . As can be seen, the Mdense,HCN values obtained with the αGS04 − HCN conversion factor underestimate the reference masses by an order of magnitude on average in nearby clouds. In contrast, the Mdense,HCN estimates using the G0-dependent conversion factor agree well with the reference dense gas mass estimates .

The HCO+(1–0) line is another tracer of dense gas which can be used in extragalactic studies (Braine et al. 2017). Like the HCN emission, the HCO+ emission tends to be strong in areas where the FUV radiation field is strong (see Sect. 3.2). The red filled circles in Fig. 5 show a correlation plot between αHerschel − HCO+ and G0. Here again, a clear anti-correlation is present with a correlation coefficient of − 0.77. The values are slightly larger than the values, but the basic trend as a function of G0 is the same. The αHerschel − HCO+ conversion factor decreases as G0 increases according to the following best-fit relation: (15)Figure 6b plots the mass of dense gas Mdense,HCO+ derived from the HCO+ luminosity using the conversion factor from Eq. (15) as a function of the reference mass estimate . As can be seen, the Mdense,HCO+ estimates using agree well with the reference dense gas mass estimates .

We conclude that both the HCN(1–0) luminosity and the HCO+(1–0) luminosity can be used as reasonably good tracers of the total mass of dense gas down to molecular cloud scales ≳ 1 pc, provided that appropriate G0-dependent conversion factors are employed (and the strength of the radiation field can be estimated). This is true despite the fact that the HCN(1–0) and HCO+(1–0) lines are optically thick and do not trace well the details of the filamentary structure of the dense molecular gas (cf. Sect. 3.2).

thumbnail Fig. 7

Empirical conversion factor against column density (expressed in AV units) for the sub-regions of our sample. and represent the mass derived from Herschel column density data and the HCN luminosity for the portion of each sub-region corresponding to a given column density bin. The width of each column density bin is 4 mag in AV units. The horizontal lines indicate αHerschel − HCN for the various regions (see Table 6).

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4.2. Relationship between star-formation rate and dense gas mass

In this subsection, we use our results on nearby clouds, e.g., our finding of a G0-dependent conversion factor αHerschel(G0), to make a new detailed comparison between the star-formation efficiency within dense molecular gas found in nearby star-forming complexes on one hand and in external galaxies on the other hand.

4.2.1. Estimates of the star-formation rate and star-formation efficiency in the observed clouds

We first estimated the SFR in each of our target regions/sub-regions from direct counting of young stellar objects (YSOs) using the available Spitzer census of YSOs in nearby clouds (Evans et al. 2009). Under the assumption that the median lifetime of Class II YSOs is 2 Myr (Evans et al. 2009; Covey et al. 2010; Lada et al. 2010; Dunham et al. 2015) and that their mean mass is 0.5 M (Muench et al. 2007), the SFR can be derived from the number of YSOs observed with Spitzer as follows: (16)To evaluate the number of YSOs in each subregion observed here, we used the Spitzer catalog of Dunham et al. (2015) for Aquila and Ophiuchus, and the catalog of Megeath et al. (2012) for Orion B. To count YSOs at each evolutionary stage from these catalogs, we selected objects with an infrared spectral index2aIR in the ranges 0.3 ≤ aIR for Class 0/I YSOs, − 0.3 ≤ aIR< 0.3 for Flat Spectrum sources, and − 1.6 ≤ aIR< − 0.3 for Class II objects in agreement with standard YSO classification criteria (Greene et al. 1994).

Dunham et al. (2015) used 2MASS and Spitzer data between 2 μm and 24 μm. Megeath et al. (2012) used Spitzer data between 4.5 μm and 24 μm. While Dunham et al. (2015) published aIR values both before and after correction for extinction, Megeath et al. (2012) used uncorrected aIR values. For the sake of consistency, we used uncorrected aIR values to select Class II YSOs in all regions. The resulting YSO number counts and corresponding SFRs are reported in Table 7 for each region/sub-region observed in molecular lines. The blue filled circles in Fig. 8a show the correlation between SFRYSO and for the clouds of our sample, which can be expressed as /M). This relationship is in good agreement with previous studies of nearby Galactic clouds using extinction maps to estimate the mass of dense gas (Lada et al. 2010, 2012; Evans et al. 2014).

Table 7

Number of YSOs and star-formation rate in each subregion.

4.2.2. Calibration of the dense gas mass in external galaxies

In Sect. 4.1, we showed that reliable HCN-based estimates of the dense gas mass in nearby clouds could be obtained using the G0-dependent conversion factor given by Eq. (14). In this subsection, we try to account for this G0 dependence in galaxies with published HCN data in an effort to improve the current estimates of their dense gas masses. Before doing so, it is important to notice that the values derived for the nearby clouds of our sample are a factor of ≳ 3 to ~ 50 higher than the standard extragalactic conversion factor αGS04 − HCN = 10 M (K km s-1 pc2)-1 (see Fig. 5). Since the mean G0 value in a typical galaxy cannot be much higher than the highest G0 found in our regions (G0 ~ 4000 for NGC 2024), another effect besides the G0 dependence must explain this large difference in conversion factor.

thumbnail Fig. 8

a) SFR against Mdense and b) SFE against Mdense. Blue filled squares indicate the SFRMdense(=) and SFE(=SFR/Mdense) – Mdense relations for the regions observed in this paper. Black open circles indicate the relation between SFR and Mdense in nearby star-forming clouds (Lada et al. 2010). Red filled circles indicate the SFR-Mdense and SFE Mdense relations obtained for external galaxies (Gao & Solomon 2004b), assuming Mdense = αHCN × LHCN with the corrected αHCN values from our Eq. (17). Green, brown, pink, purple, magenta, and orange filled circles indicate the SFR-Mdense and SFE – Mdense relations in the SMC, LMC, M31, M33, and M51 galaxies (Chin et al. 1997, 1998; Brouillet et al. 2005; Buchbender et al. 2013; Chen et al. 2015, 2017) using our relation of Eq. (17). The uncertainties in the extragalactic SFR values are a factor of ~2 (cf. Bell 2003). The black triangle indicates the position of the central molecular zone (CMZ: |l| < 1 deg, |b| < 0.5 deg) in each plot, where SFR and Mdense were estimated from the number count of massive YSOs and Herschel column density, respectively (Longmore et al. 2013). In both panels, the black solid line and black dashed lines display the simple empirical relation expected from the “microphysics” of prestellar core formation within filaments described in Sect. 4.3 (see also André et al. 2014; Könyves et al. 2015): SFR = (4.5 ± 2.5) × 10-8M yr-1 × (Mdense/M), i.e., SFE = (4.5 ± 2.5) × 10-8 yr-1.

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While our HCN/HCO+ observations were specifically focused on the densest (AV> 8) portions of the target clouds, they also cover a small fraction of the lower density gas in these clouds, and our data clearly show that the HCN(1–0) and HCO+(1–0) lines are tracing molecular gas down to much lower column densities than the AV = 8 fiducial limit. In a recent independent molecular line study of the southern part of the Orion B cloud (including NGC 2023 and NGC 2024) with the IRAM 30 m telescope, Pety et al. (2017) found that 36% of the HCN(1–0) line flux was emitted from low extinction (2 ≤ AV< 6) areas, with > 98% of the line flux coming from AV ≥ 2 areas. Likewise, the results of the CHaMP census of molecular clumps in the southern Milky Way with the MOPRA telescope (e.g., Barnes et al. 2016) demonstrate that the HCO+(1–0) line emission is generally tracing gas down to volume densities of ~ 103 cm-3 or less. Dividing the regions and sub-regions observed in our study in various column density bins, we can investigate possible variations of the empirical conversion factor with column density (see Fig. 7). Significant variations in from region to region can be seen, in agreement with the dependence of αHerschel − HCN on the strength of the FUV radiation field discussed in Sect. 4.1. Figure 7 nevertheless suggests that, in any given sub-region (i.e., for a given G0 value), the conversion between gas mass and HCN(1–0) luminosity remains approximately constant, irrespective of gas (column) density or AV, down to AV ~ 2. This means that, in addition to the dense molecular gas nH2 ≳ 2 × 104 cm-3 (corresponding to AV ≳ 8 in resolved nearby clouds), extragalactic HCN(1–0) studies with spatial resolutions from ~ 8 pc to ~ 36 kpc (Chin et al. 1997, 1998; Gao & Solomon 2004b; Brouillet et al. 2005; Buchbender et al. 2013; Chen et al. 2015, 2017) must also probe essentially all of the molecular gas corresponding to 2 <AV< 8 in the observed galaxies. Using typical column density probability distribution functions (PDFs) observed toward Galactic molecular clouds (e.g., Schneider et al. 2013), we can estimate the relative amount of molecular gas at AV> 8 and 2 <AV ≤ 8 in GMCs, M(AV> 2) /M(AV> 8). In practice, we adopt the combined column density PDF derived from Herschel HGBS data in the Aquila and Orion B complexes, which is well described by a power law, (Könyves et al. 2015, and in prep.), as our template. Such a column density PDF implies that M(AV> 2) /M(AV> 8) = (2 / 8)− 1.7 ± 0.2 ≈ 10, at least in molecular clouds such as Aquila and Orion B. Clearly, if extragalactic HCN measurements of dense gas include low-density gas down to AV ~ 2, then the effective αHCN conversion factor for these measurements must be an order of magnitude lower than the factor given by Eq. (14) and thus within a factor of a few of the standard extragalactic conversion factor αGS04 − HCN = 10 M (K km s-1 pc2)-1.

To go further and to improve current extragalactic Mdense,HCN estimates for radiation-field effects, we also need to account for the fact that the minimum column density or extinction AV,min(HCN) down to which significant HCN(1–0) line flux is emitted itself depends on G0. The values of the effective excitation density of HCN(1–0) calculated by Shirley (2015) scale approximately as , where Tgas is the gas kinetic temperature. Assuming TgasTdust and using the simplified relation between Tdust and G0 given by Eq. (12), this means that . For both a spherical and a cylindrical cloud with a density gradient ρrα, column density scales as r1 − α or . Adopting α = 1.75 ± 0.25, a value intermediate between 1.5 (free-falling cloud onto a point mass) and 2 (isothermal spheres) which is also consistent with the logarithmic slope of − 2.7 for the column density PDF (cf. Könyves et al. 2015), we may thus expect the minimum column density probed by HCN(1–0) to scale as . Normalizing this scaling relation using the fact that AV,min(HCN) ≈ 2 for NGC 2023/2024 in Orion B where G0 ≈ 20 (Pety et al. 2017), we obtain the following conversion factor for external galaxies, under the assumption that extragalactic HCN observations sample all of the molecular gas down to AV,min(HCN): (17)Using the total infrared luminosities LIR listed in the Gao & Solomon (2004b) paper and adopting LFIR = LIR/ 1.3 (Graciá-Carpio et al. 2008), we can derive relevant G0 values from Eq. (9) and , where d and θbeam are the distance to each galaxy and the telescope beam size of the corresponding HCN measurement respectively (cf. Buchbender et al. 2013). We can then estimate an effective conversion factor for each galaxy in the Gao & Solomon sample. The resulting G0 and values range from 44 to 3.9 × 104 (mean: 1.7 × 103) and from 1.8 M (K km s-1 pc2)-1 to 17.7 M (K km s-1 pc2)-1 (mean: 10.2 M (K km s-1 pc2)-1), respectively. Using these values for the HCN conversion factor, the corrected masses of dense gas range from 4.3 × 107M to 4.9 × 1010M. Under the assumption that the average gas densities of normal galaxies and extreme starbursts are 2 × 102 cm-3 and 1 × 105 cm-3, respectively, García-Burillo et al. (2012) advocated revised conversion factors αGB12 − HCN ~ 3 − 4 M (K km s-1 pc2)-1 for normal galaxies (LIR< 1011L corresponding to SFR< 2 × 10 M yr-1) and αGB12 − HCN ~ 1 − 2 M (K km s-1 pc2)-1 for extreme starbursts (LIR> 1011L corresponding to SFR> 2 × 10 M yr-1). The revised conversion factors αGB12 − HCN of García-Burillo et al. (2012) are roughly consistent with our suggested values of 1.8–17.7 M (K km s-1 pc2)-1 for the galaxies sampled by Gao & Solomon (2004b) (LIR ~ 1010 − 12L). This agreement suggests that the dependence of the αHerschel − HCN conversion factor on the strength of the FUV radiation field is not restricted to Galactic clouds and also applies to external galaxies. Figure 8a compiles observations of the SFR–Mdense relation from the present study, Lada et al. (2010), and Gao & Solomon (2004b). The SFR-Mdense relation found in our study is consistent with that of Lada et al. (2010), as expected since both are focused on nearby Galactic clouds. The initial SFR-Mdense relation from Gao & Solomon (2004b) lies a factor of ~2–3 below the best-fit relation found for nearby star-forming regions, namely SFR = 4.6 × 10-8Mdense (Lada et al. 2010). Conversely, the corrected SFR-Mdense relation for the Gao & Solomon (2004b) sample lies above the nearby-cloud relation by a factor of ~3. We also compiled data points for nearby galaxies of the local group, namely the Small Magellanic Cloud (SMC), the Large Magellanic Cloud (LMC), M31, M33, and M51 from Chin et al. (1997, 1998), Brouillet et al. (2005), Buchbender et al. (2013), and Chen et al. (2015, 2017). The SFR for each galaxy was estimated using SFR = 2.0 × 10-10 (LIR/L) M yr-1 following Gao & Solomon (2004b). As can be seen in Fig. 8a, the observed trend is basically a linear relation between SFR and dense gas mass, and the nearby-cloud relation provides a good overall fit to most data points.

Figure 8b provides a blow-up view of the scatter around the nearby-cloud star formation law by plotting the star-formation efficiency SFEdenseSFR/Mdense against Mdense for the same objects as in Fig. 8a. As can be seen, SFEdense remains roughly constant within a scatter of less than 1.5 orders of magnitude over 8 orders of magnitude in Mdense from ~ 102M to 1010M. This scatter in SFEdense is significantly smaller than the scatter in SFEtotal, defined as SFR divided by total molecular gas mass Mtotal, observed among nearby clouds and massive Galactic clouds, which exceeds 2 to 3 orders of magnitude over only 4 orders of magnitude in gas mass (cf. Lada et al. 2010; Vutisalchavakul et al. 2016). The mean and standard deviation of (the logs of) all the data points in Fig. 8b (including the CMZ point) are ⟨ log SFEdense (yr-1) = − 7.85 ± 0.31. This is in excellent agreement with the results of Vutisalchavakul et al. (2016) who found ⟨ log SFEdense (yr-1) = − 7.74 ± 0.50 toward star-forming regions in the Galactic plane using masses derived from the Bolocam Galactic Plane Survey (BGPS) data at 1.1 mm and SFR values estimated from WISE mid-infrared data.

The vertical scatter in Fig. 8b can almost entirely be attributed to uncertainties in the αHCN conversion factor used to estimate the dense gas mass for galaxies. In nearby clouds, for which assumptions about this conversion factor are not needed, the observed scatter in SFEdense is less than a factor of ~ 3. To conclude, our results support the view that the relationship between star-formation rate and dense gas mass, i.e., the star-formation efficiency in the dense molecular gas of galaxies, is quasi-universal on a wide range of scales from ~ 1–10 pc to >10 kpc.

4.3. Origin of the quasi-universal star-formation efficiency in dense molecular gas

On the grounds that filaments dominate the mass budget of dense molecular gas in GMCs and that most, if not all, prestellar cores form in filaments (see Sect. 1), André et al. (2014) proposed that the quasi-universal star-formation efficiency in dense gas discussed above and summarized in Fig. 8 originates from the physics of filament evolution and core formation along filaments. Following André et al. (2014), we suggest that the star-formation efficiency in dense gas, SFEdense ≡ SFR /Mdense, is primarily set by three parameters characterizing dense cores along filaments, namely the typical fraction of dense filament gas in the form of prestellar cores (or “core formation efficiency”), fpre, the typical lifetime of prestellar cores, tpre, and the efficiency of the conversion from prestellar core mass to stellar mass (or stellar system mass), ϵcore, according to the simple relation: SFEdense = fpre × ϵcore/tpre. This relation assumes that, in steady state, each supercritical filament has converted a fraction fpre of its mass into prestellar cores, and that each prestellar core converts a fraction ϵcore of its mass into either a single star or a small stellar system on a timescale tpre. The latter assumption is supported by the similarity between the prestellar core mass function (CMF) and the stellar initial mass function (IMF; e.g., Motte et al. 1998; Enoch et al. 2008; André et al. 2010). Observationally, it seems that the three parameters fpre, tpre, ϵcore have reasonably constant values with little variations from cloud to cloud, at least in Gould Belt regions. Based on the results of the HGBS in the Aquila, Ophiuchus, Orion B, and Taurus/L1495 clouds, the prestellar core formation efficiency in the dense (AV> 8) gas of supercritical filaments is estimated to be (e.g., Könyves et al. 2015; Könyves et al., in prep.; Ladjelate et al., in prep.). The typical lifetime of low- to intermediate-mass prestellar cores is known to be Myr (e.g., Lee & Myers 1999; Jessop & Ward-Thompson 2000; Könyves et al. 2015). In reality, tpre likely depends on both core density (Jessop & Ward-Thompson 2000) and core mass (Hatchell & Fuller 2008), but what matters here is the characteristic lifetime of the bulk of prestellar cores near the peak of the CMF and forming in filaments just above the critical line mass Mline,crit. The efficiency of the conversion process from core mass to stellar mass, as estimated from the global shift between the CMF and the IMF is believed to be (e.g., Alves et al. 2007; Nutter & Ward-Thompson 2007; Könyves et al. 2015). Combining these estimates leads to the following “prediction” for SFEdense from the microphysics of star formation in filaments: (18)which is plotted as a solid straight line and strip in Fig. 8. As can be seen, SFE provides a reasonably good fit to both the Galactic and extragalactic data points of Fig. 8b.

4.4. Comments on apparent SFE variations in resolved galactic disks

Recently, Usero et al. (2015), Chen et al. (2015), and Bigiel et al. (2016) reported significant variations in the apparent star-formation efficiency in dense gas, , across the spatially-resolved disks of several nearby galaxies such as M51. In particular, the LFIR/LHCN ratio was observed to decrease as LFIR increases from the outskirts to the center of the M51 disk (see for instance the map of the LIR/LHCN ratio presented by Chen et al. 2015). One plausible interpretation of this trend was a decrease in the star-formation efficiency SFEdense from the outer disk to the center of the M51 galaxy (e.g., Bigiel et al. 2016). We note, however, that since the FUV radiation field is significantly stronger near the center of the disk compared to the outer parts of the galaxy, and since LIR/LHCN scales as , the trend observed in M51 can at least partly originate from the expected decrease in the αHCN factor toward the center of the disk according to Eq. (14), with the efficiency SFEdense remaining approximately constant.

We can further quantify this statement using the detailed results published by Usero et al. (2015) for 29 nearby disk galaxies. These authors found an anti-correlation between the apparent local star-formation efficiency in dense gas SFEUsero − denseIFIR/IHCN and the mass surface density of stars Σstar, expressed as SFEUsero − dense (Myr-1) = 10−0.78 ± 0.30 (M pc-2) (Fig. 2 of Usero et al. 2015). Usero et al. (2015) evaluated the mass surface density of dense gas Σdense as αUsero − HCN × IHCN and the mass surface density of old stars ΣUsero − star values from the 3.6 μm intensity I3.6 μm (with ΣUsero − starI3.6 μm). Since the I3.6 μm intensity is directly proportional to the FUV intensity IFUV across the disk of nearby galaxies (e.g., Ford et al. 2013), the anti-correlation can be rewritten as . The dependence of αHCN on G0 found in Sects. 4.1 and 4.2.2 and expressed by Eq. (17), i.e., , can largely account for the Usero et al. (2015) anti-correlation, and suggests that SFEdense actually depends at most very weakly on Σ as .

Significant variations in SFEdense may still exist in the most extreme star-forming environments like the central molecular zone (CMZ) of our Milky Way (e.g., Longmore et al. 2013, see also Fig. 8) or extreme starburst galaxies (e.g., García-Burillo et al. 2012), especially at high redshift (e.g., Gao et al. 2007). By and large, however, the results summarized in Fig. 8b suggest that SFEdense is remarkably constant over a wide range of scales and environments.

5. Summary and conclusions

In an effort to calibrate dense gas tracers commonly used in extragalactic studies, we carried out wide-field mapping observations at a spatial resolution of ~0.04 pc in HCN (J = 1 − 0), H13CN (J = 1 − 0), HCO+ (J = 1 − 0), and H13CO+ (J = 1 − 0) toward the nearby molecular clouds in Ophiuchus, Aquila, and Orion B using the MOPRA 22 m, IRAM 30 m, and Nobeyama 45 m telescopes. Our main results can be summarized as follows:

  • 1.

    The spatial distributions of the H13CO+(1–0) and H13CN(1–0)emission are tightly correlated with the filamentary texture of thedense gas seen in Herschel column density maps, showing that theH13CO+(1–0) and H13CN(1–0) lines are good tracers of the densest(“supercritical”) filaments seen in Herschel submillimetercontinuum images. Quantitatively, H13CO+(1–0) and H13CN(1–0)trace Herschel filaments very well above AV> 16 (i.e., Mline ≳ 30 M pc-1) and AV> 20 (i.e., Mline ≳ 40 M pc-1)respectively. Moreover, the virial mass estimates derived fromthe H13CO+(1–0) and H13CN(1–0) velocity dispersions agree wellwith the dense gas mass estimates derived from Herschel data forthe same sub-regions.

  • 2.

    In contrast, the spatial distributions of the HCN(1–0) and HCO+(1–0) emission differ significantly from the column density distribution derived from Herschel data. The HCN(1–0) and HCO+ (1–0) lines are only poor tracers of the supercritical filaments seen with Herschel and tend to be stronger around HII regions. Based on a detailed comparison of the HCN(1–0)and HCO+(1–0) integrated intensity maps with the Herschel 70/100 μm and dust temperature maps, it appears that the HCN(1–0) and HCO+(1–0) integrated intensities are strongly correlated with the strength of the local FUV radiation field (G0). The luminosities of the HCN and HCO+ lines can nevertheless be used to derive reasonably good estimates of the masses of dense gas in the nearby clouds we observed, provided that appropriate G0-dependent conversion factors αHerschel − HCN(G0) and αHerschel − HCO+(G0) are adopted when converting LHCN and LHCO+ to Mdense.

  • 3.

    Using the masses derived from Herschel column density maps above AV> 8 as reference estimates of the mass of dense gas in each nearby cloud, we found that the conversion factors αHCN and αHCO+ are anti-correlated with the strength of the local FUV radiation field according to the following best-fit empirical relations: M (K km s-1 pc2)-1 and M (K km s-1 pc2)-1.

  • 4.

    The relation between the star-formation rate, estimated from direct counting of Spitzer YSOs, and the mass of dense gas, derived from Herschel data above AV> 8, for the nearby clouds/clumps of our sample can be expressed as SFRYSO = (2.1 − 5.0) × 10-8M yr/M). This is consistent within errors with the relation found by Lada and collaborators for another and broader sample of nearby star-forming clouds based on Spitzer and near-infrared extinction data (SFR = (4.6 ± 2.6) × 10-8M yr-1× (Mdense/M), Lada et al. 2010, 2012).

  • 5.

    In nearby molecular clouds, the optically thick HCN(1–0) and HCO+(1–0) lines are tracing both moderate column density areas (2 ≤ AV ≤ 8) and high column density areas (AV> 8) (see also Pety et al. 2017). Therefore, published extragalactic HCN(1–0) studies, which have spatial resolutions between ~ 10 pc and ~ 50 kpc, must be tracing all of the moderate density gas down to nH2 ≲ 103 cm-3 in the observed galaxies, in addition to the dense gas with nH2> 104 cm-3. Estimating the contribution of this moderate density gas from the typical column density PDFs observed in nearby clouds, we obtained the following effective HCN conversion factor for external galaxies: .

  • 6.

    Using this G0-dependent conversion factor to improve the dense gas mass estimates of external galaxies with published HCN data, we found that the star-formation efficiency in dense molecular gas, SFEdenseSFR/Mdense, is remarkably constant, with a scatter of less than 1.5 orders of magnitude around the nearby-cloud value of 4.5 × 10-8 yr-1, over 8 orders of magnitude in Mdense from ~ 102M to 1010M. This suggests that the star-formation efficiency in the dense molecular gas of galaxies is quasi-universal on a wide range of scales from ~ 1–10 pc to > 10 kpc.

  • 7.

    Following André et al. (2014), we suggest that SFEdense is primarily set by three parameters characterizing the “microphysics” of core/star formation along molecular filaments, namely the typical fraction of dense filament gas in the form of prestellar cores, , the typical lifetime of solar-type prestellar cores, Myr, and the efficiency of the conversion from prestellar core mass to stellar mass, , according to the simple relation: .


1

The effective excitation density of a molecular transition at a given gas kinetic temperature is defined as the density which results in a spectral line with an integrated intensity of 1 K km s-1 (Shirley 2015).

2

The spectral index aIR is defined as the slope of the near-/mid-infrared spectral energy distribution (SED), aIR = dlog (λSλ) / dlog (λ), where λ and Sλ denote wavelength and flux density at that wavelength, respectively.

Acknowledgments

We thank the referee for useful suggestions that improved the clarity of the paper. The Mopra radio telescope is part of the Australia Telescope National Facility which is funded by the Australian Government for operation as a National Facility managed by CSIRO. The 45-m radio telescope is operated by Nobeyama Radio Observatory, a branch of National Astronomical Observatory of Japan. This research has made use of data from the Herschel Gould Belt survey (HGBS) project (http://gouldbelt-herschel.cea.fr). The HGBS is a Herschel Key Programme jointly carried out by SPIRE Specialist Astronomy Group 3 (SAG 3), scientists of several institutes in the PACS Consortium (CEA Saclay, INAF-IFSI Rome and INAF-Arcetri, KU Leuven, MPIA Heidelberg), and scientists of the Herschel Science Center (HSC). Our work was supported by the ANR-11-BS56-010 project “STARFICH” and the European Research Council under the European Union’s Seventh Framework Programme (ERC Advanced Grant Agreement No. 291294 – “ORISTARS”). N.S. acknowledges support from the DFG through project number Os 177/2-1 and 177/2-2, and central funds of the DFG-priority program 1573 (ISM-SPP). Y.G. acknowledges support from the National Natural Science Foundation of China (grants 11390373 and 11420101002) and the Chinese Academy of Sciences’ Key Research Program of Frontier Sciences.

References

Appendix A: Complementary figures and tables

Figures A.1A.9 are complementary figures. The optical depths of the HCN (1–0) and HCO+ (1–0) lines in each AV bin are listed in Table A.1. Table A.2 summarizes the definition of each notation used in this paper.

thumbnail Fig. A.1

Same as Fig. 1, but for Aquila/cold. The H2 column density map of the Aquila region is from Herschel Gould Belt Survey (HGBS) data (André et al. 2010; Könyves et al. 2015). The white contour in panel a and magenta dotted contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 40 resolution. In panel f, the magenta solid contour indicates the rough AV column density level above which significant H13CO+ (1–0) emission is detected, i.e., AV = 16.

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thumbnail Fig. A.2

Same as Fig. 1, but for Ophiuchus. The H2 column density map of the Ophiuchus region is from HGBS data (Ladjelate et al., in prep.). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 50, 50, 50, and 60. The white contour in panel a and magenta dotted contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 50 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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thumbnail Fig. A.3

Same as Fig. 1, but for NGC 2023 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dotted contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panel f, the magenta solid contour indicates the rough AV column density level above which significant H13CO+ (1–0) emission is detected, i.e., AV = 16.

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thumbnail Fig. A.4

Same as Fig. 1, but for NGC 2024 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dashed contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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thumbnail Fig. A.5

Same as Fig. 1, but for NGC 2068 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dashed contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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thumbnail Fig. A.6

Same as Fig. 1, but for NGC 2071 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dashed contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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thumbnail Fig. A.7

Comparison of H13CN spectra averaged over pixels where has 5σ emission at a) Oph/main; b) Oph/cold; c) Aquila/W40; d) Aquila/Serp. South; e) Aquila/cold; f) NGC 2023; g) NGC 2024; h) NGC 2068; and i) NGC 2071. For Oph/cold, Aquila/cold, and NGC 2023, the H13CN emission is not detected. Thus, we show the spectra averaged over observing area.

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thumbnail Fig. A.8

Pixel to pixel correlation between the G0 value estimated from Tdust, G0(Tdust), using Eqs. ((11)–(13)) map and G0 values estimated from Herschel 70 and 100 μm data, G0(70,100 μm), using Eqs. ((9), (10)) toward a) Aquila; b) Ophiuchus; c) Orion B. The dashed red lines indicate G0(Tdust) = G0(70,100 μm). The solid red lines indicate the best-fit results: G0(Tdust) = (1.38 ± 0.01) × G0(70,100 μm) for Aquila, G0(Tdust) = (0.62 ± 0.01) × G0(70,100 μm) for Ophiuchus, and G0(Tdust) = (2.63 ± 0.09) × G0(70,100 μm) for Orion B. The blue lines in panel c indicate the best-fit result for pixels with G0(Tdust) < 1000: G0(Tdust) = (1.04 ± 0.02) × G0(70,100 μm).

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thumbnail Fig. A.9

Comparison of the HCO+ (1–0, red), HCN (1–0, blue), H13CO+ (1–0, black), and H13CN (1–0, orange) spectra averaged over the observed area in each AV range for a) Aquila/W40; b) Aquila/Serp-South; c) Aquila/cold; d) Oph/main; e) Oph/cold; f) Orion B/NGC 2023; g) Orion B/NGC 2024; h) Orion B/NGC 2068; and i) Orion B/NGC 2071. In each panel, the vertical grey line marks the peak velocity of the H13CO+ line toward the 16 ≤ AV area, and the spectra shown from top to bottom correspond to the 16 ≤ AV, 12 ≤ AV< 16, 8 ≤ AV< 12, and AV< 8 areas, respectively.

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Table A.1

Optical depths of the HCN (1–0) and HCO+ (1–0) lines.

Table A.2

Definition of each notation used in the paper.

All Tables

Table 1

Observations.

Table 2

Physical parameters derived from H13CO+ (1–0) observations.

Table 3

Virial masses from H13CO+.

Table 4

Virial masses from H13CN.

Table 5

HCN (1–0) to HCO+ (1–0) line intensity ratios.

Table 6

Derived parameters for the dense portions of the target nearby clouds where AV> 8 mag.

Table 7

Number of YSOs and star-formation rate in each subregion.

Table A.1

Optical depths of the HCN (1–0) and HCO+ (1–0) lines.

Table A.2

Definition of each notation used in the paper.

All Figures

thumbnail Fig. 1

a) Column density map of the Aquila region derived from Herschel Gould Belt survey (HGBS) data (André et al. 2010; Könyves et al. 2015) at an angular resolution of 18.2 and in units of AV. b) FUV field strength map derived from HGBS 70 μm and 100 μm data smoothed to an angular resolution of 18.2 in Habing units, and integrated intensity maps of c) HCN(1–0); d) HCO+(1–0); e) H13CN(1–0); f) H13CO+(1–0) in units of K km s-1 (TMB). The angular resolutions of the HCN, HCO+, H13CN, and H13CO+ maps are 40, 40, 40, and 50, respectively. In each panel, a green polygon outlines the field observed in molecular lines. The HCN and H13CN integrated intensity includes all components of the hyperfine structure (HFS). The white contour in panel a and the magenta dotted contours in panels e and f show the AV = 8 level obtained after smoothing the Herschel column density map to 40 resolution. In panel b, green open circles indicate the positions of the Class II objects identified by Dunham et al. (2015). In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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In the text
thumbnail Fig. 2

a) vs. and b) vs. relations. The black dashed lines indicate = and the red lines indicate the best-fit results: and . (The uncertainty in was derived from the uncertainties in and in (see Ikeda et al. 2007; Shimajiri et al. 2015a.) The x- and y-axis ranges are the same in both panels.

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In the text
thumbnail Fig. 3

Comparison of the HCN, HCO+, and H13CO+(1–0) spectra averaged over the observed area in a) Aquila/W40; b) Aquila/Serp–South; c) Aquila/cold; d) Oph/main; e) Oph/cold; f) Orion B/NGC 2023; g) Orion B/NGC 2024; h) Orion B/NGC 2068; and i) Orion B/NGC 2071. In each panel, blue, red, and gray lines show the mean HCN, HCO+, and H13CO+(1–0) spectra in the corresponding subregion; the vertical dashed line marks the peak velocity of the H13CO+(1–0) line.

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In the text
thumbnail Fig. 4

Comparison of the HCN, HCO+, and H13CO+(1–0) spectra averaged over the observed area in a) Aquila/W40; b) Aquila/Serp–South; c) Aquila/cold; d) Oph/main; e) Oph/cold; f) Orion B/NGC 2023; g) Orion B/NGC 2024; h) Orion B/NGC 2068; and i) Orion B/NGC 2071. In each panel, blue, red, and gray lines show the mean HCN, HCO+, and H13CO+(1–0) spectra in the corresponding subregion; the vertical dashed line marks the peak velocity of the H13CO+(1–0) line.

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In the text
thumbnail Fig. 5

Correlations between αHerschel − HCN and G0 (blue line and filled circles) and between αHerschel − HCO+ and G0 (red line and filled circles). The blue and red lines correspond to the best-fit relations: [M (K km s-1 pc2)-1] and [M (K km s-1 pc2)-1]. The horizontal line marks αGS04 − HCN = 10 [M (K km s-1 pc2)-1]. The uncertainties in αHerschel − HCN and αHerschel − HCO+ as estimated from the uncertainties are a factor of 2 (Roy et al. 2014). The uncertainties in G0 are also a factor of 2 (see Sect. 3.3).

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In the text
thumbnail Fig. 6

a)Mdense,HCN against , and b)Mdense,HCO+ against . Red lines correspond to best-fit linear relations to the red data points: and . The red filled circles use Mdense,mol values derived from the relation . In panel a, the black open squares use Mdense,HCN values derived from the “extragalactic” relation Mdense,HCN = αGS04 − HCN × LHCN, where αGS04 − HCN = 10 M (K km s-1 pc2)-1; the black line corresponds to the best-fit linear relation to the open squares: Mdense,HCN (αGS04 − HCN.

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In the text
thumbnail Fig. 7

Empirical conversion factor against column density (expressed in AV units) for the sub-regions of our sample. and represent the mass derived from Herschel column density data and the HCN luminosity for the portion of each sub-region corresponding to a given column density bin. The width of each column density bin is 4 mag in AV units. The horizontal lines indicate αHerschel − HCN for the various regions (see Table 6).

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In the text
thumbnail Fig. 8

a) SFR against Mdense and b) SFE against Mdense. Blue filled squares indicate the SFRMdense(=) and SFE(=SFR/Mdense) – Mdense relations for the regions observed in this paper. Black open circles indicate the relation between SFR and Mdense in nearby star-forming clouds (Lada et al. 2010). Red filled circles indicate the SFR-Mdense and SFE Mdense relations obtained for external galaxies (Gao & Solomon 2004b), assuming Mdense = αHCN × LHCN with the corrected αHCN values from our Eq. (17). Green, brown, pink, purple, magenta, and orange filled circles indicate the SFR-Mdense and SFE – Mdense relations in the SMC, LMC, M31, M33, and M51 galaxies (Chin et al. 1997, 1998; Brouillet et al. 2005; Buchbender et al. 2013; Chen et al. 2015, 2017) using our relation of Eq. (17). The uncertainties in the extragalactic SFR values are a factor of ~2 (cf. Bell 2003). The black triangle indicates the position of the central molecular zone (CMZ: |l| < 1 deg, |b| < 0.5 deg) in each plot, where SFR and Mdense were estimated from the number count of massive YSOs and Herschel column density, respectively (Longmore et al. 2013). In both panels, the black solid line and black dashed lines display the simple empirical relation expected from the “microphysics” of prestellar core formation within filaments described in Sect. 4.3 (see also André et al. 2014; Könyves et al. 2015): SFR = (4.5 ± 2.5) × 10-8M yr-1 × (Mdense/M), i.e., SFE = (4.5 ± 2.5) × 10-8 yr-1.

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In the text
thumbnail Fig. A.1

Same as Fig. 1, but for Aquila/cold. The H2 column density map of the Aquila region is from Herschel Gould Belt Survey (HGBS) data (André et al. 2010; Könyves et al. 2015). The white contour in panel a and magenta dotted contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 40 resolution. In panel f, the magenta solid contour indicates the rough AV column density level above which significant H13CO+ (1–0) emission is detected, i.e., AV = 16.

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In the text
thumbnail Fig. A.2

Same as Fig. 1, but for Ophiuchus. The H2 column density map of the Ophiuchus region is from HGBS data (Ladjelate et al., in prep.). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 50, 50, 50, and 60. The white contour in panel a and magenta dotted contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 50 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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In the text
thumbnail Fig. A.3

Same as Fig. 1, but for NGC 2023 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dotted contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panel f, the magenta solid contour indicates the rough AV column density level above which significant H13CO+ (1–0) emission is detected, i.e., AV = 16.

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In the text
thumbnail Fig. A.4

Same as Fig. 1, but for NGC 2024 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dashed contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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In the text
thumbnail Fig. A.5

Same as Fig. 1, but for NGC 2068 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dashed contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

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In the text
thumbnail Fig. A.6

Same as Fig. 1, but for NGC 2071 in Orion B. The H2 column density map of the Orion B region is from HGBS data (Könyves et al., in prep.; see also Schneider et al. 2013). The angular resolutions of HCN, HCO+, and H13CO+, and H13CN maps are 30, 30, 30, and 40. The white contour in panel a and magenta dashed contours in panels e and f indicate the AV = 8 level derived from the Herschel column density map smoothed to 30 resolution. In panels e and f, the magenta solid contour indicates the rough AV column density level above which significant line emission is detected, i.e., AV = 20 for H13CN (1–0) and AV = 16 for H13CO+ (1–0).

Open with DEXTER
In the text
thumbnail Fig. A.7

Comparison of H13CN spectra averaged over pixels where has 5σ emission at a) Oph/main; b) Oph/cold; c) Aquila/W40; d) Aquila/Serp. South; e) Aquila/cold; f) NGC 2023; g) NGC 2024; h) NGC 2068; and i) NGC 2071. For Oph/cold, Aquila/cold, and NGC 2023, the H13CN emission is not detected. Thus, we show the spectra averaged over observing area.

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In the text
thumbnail Fig. A.8

Pixel to pixel correlation between the G0 value estimated from Tdust, G0(Tdust), using Eqs. ((11)–(13)) map and G0 values estimated from Herschel 70 and 100 μm data, G0(70,100 μm), using Eqs. ((9), (10)) toward a) Aquila; b) Ophiuchus; c) Orion B. The dashed red lines indicate G0(Tdust) = G0(70,100 μm). The solid red lines indicate the best-fit results: G0(Tdust) = (1.38 ± 0.01) × G0(70,100 μm) for Aquila, G0(Tdust) = (0.62 ± 0.01) × G0(70,100 μm) for Ophiuchus, and G0(Tdust) = (2.63 ± 0.09) × G0(70,100 μm) for Orion B. The blue lines in panel c indicate the best-fit result for pixels with G0(Tdust) < 1000: G0(Tdust) = (1.04 ± 0.02) × G0(70,100 μm).

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In the text
thumbnail Fig. A.9

Comparison of the HCO+ (1–0, red), HCN (1–0, blue), H13CO+ (1–0, black), and H13CN (1–0, orange) spectra averaged over the observed area in each AV range for a) Aquila/W40; b) Aquila/Serp-South; c) Aquila/cold; d) Oph/main; e) Oph/cold; f) Orion B/NGC 2023; g) Orion B/NGC 2024; h) Orion B/NGC 2068; and i) Orion B/NGC 2071. In each panel, the vertical grey line marks the peak velocity of the H13CO+ line toward the 16 ≤ AV area, and the spectra shown from top to bottom correspond to the 16 ≤ AV, 12 ≤ AV< 16, 8 ≤ AV< 12, and AV< 8 areas, respectively.

Open with DEXTER
In the text

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