EDP Sciences
Free Access
Issue
A&A
Volume 605, September 2017
Article Number L5
Number of page(s) 4
Section Letters
DOI https://doi.org/10.1051/0004-6361/201731123
Published online 14 September 2017

© ESO, 2017

1. Introduction

The relationship between star formation (SF) and the supply of dense gas is of critical importance for our understanding of cosmic SF. We must develop a detailed picture of the relation between dense gas and SF in galaxies if we wish to explain the structure and evolution of galaxies (e.g., Somerville & Davé 2014). This relation can, for example, be explored in the Milky Way. In molecular clouds within ~ 500 pc from the Sun, one can estimate the star formation rate, , by counting individual young stars. Nearby clouds can be resolved spatially, which also simplifies estimating the mass of gas at high density, Mdg. Recent research suggests defining Mdg as the mass residing at high visual extinctions, AVAV,dg with AV,dg ≈ 7 mag, resulting in Mdg (e.g., Heiderman et al. 2010, Lada et al. 2010).

It is very challenging to study and Mdg in galaxies. One might, for example, assume that the light of young stars is absorbed and re-emitted by dust. Then the far-infrared luminosity of a galaxy (i.e., at wavelengths of 8 to 1000 μm) characterizes SF via LFIR. Similarly, one might assume that a certain molecular emission line requires elevated densities to be excited. Then MdgLQ for line luminosities of a suitable transition Q. Gao & Solomon (2004b), in particular, introduced the HCN (J = 1–0) transition as a tracer of dense gas in galaxies (i.e., H2 densities ≫ 104 cm-3), suggesting that MdgLHCN (1–0).

This raises an important question: is Mdg as derived from AV equal to Mdg as obtained from LHCN (1–0)? The LEGO project (Molecular Line Emission as a Tool for Galaxy Observations; led by JK) uses wide-field maps to address such questions. Here we summarize key conclusions from a comprehensive study of Orion A (Kauffmann et al., in prep., hereafter Paper II).

thumbnail Fig. 1

Maps of the peak intensity for transitions near 100 GHz. The left panel gives AV as inferred from Herschel data. Contours at 5 and 30 mag are drawn and repeated in all panels, and the peak intensity is stated for every transition. Line emission maps are smoothed to resolution before filled contours are drawn at signal-to-noise ratios of 3, 5, 10, 30, 50, and 100. Panels are ordered by increasing critical density, ncr.

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2. Preparation of observational data

Data on emission lines at ~ 100 GHz frequency (Fig. 1) were obtained with the 14 m telescope of the Five College Radio Astronomy Observatory (FCRAO). Maps of the CCH (N = 1–0, J = 1 / 2–1/2), HCN (J = 1–0), N2H+ (J = 1–0), C18O (J = 1–0), and CN (N = 1–0, J = 3 / 2–1/2) transitions are taken from Melnick et al. (2011). Data on the (J = 1–0) and 13CO (J = 1–0) lines are from Ripple et al. (2013). The full width at half maximum (FWHM) beam size for a given frequency ν is ϑbeam = 52″·(ν/ 100 GHz)-1. An efficiency ηmb = 0.47 is used for conversion to the main beam intensity scale, . This paper focuses on the integrated intensities, .

Dust-based estimates of the H2 column density N(H2) are derived from Herschel observations of Orion at wavelengths of 250 to 500 μm (André et al. 2010) using modified methods from Guzmán et al. (2015) described in Kauffmann et al. (2017). We assume thin ice coatings and dust coagulation for 105 yr at a molecular volume density of 106 cm-3 to select dust opacities from Ossenkopf & Henning (1994). Paper II describes how we calibrate these data against an extinction-based map from Kainulainen et al. (2011) to predict the visual extinction, AV/ mag = N(H2) / 9.4 × 2020 cm-2, at a resolution of 38″.

We fit the filamentary cloud north of 5:14:00 (J2000) with a truncated cylindrical power-law density profile, n(r) = nR·(r/R)k, where r is the distance from the filament’s main axis. We then obtain the median density along any line of sight for an offset s from the filament main axis, nmed(s). For given s, half of the mass resides above (and half below) this density, so that nmed(s) can be considered a representative density. Further algebraic operations relate s, nmed(s), and AV(s) (Fig. 3; see Paper II).

3. Molecules as tracers of cloud material

We seek to explore molecular line emission under conditions that are representative for the Milky Way. We therefore ignore the region south of 5:10:00 declination (J2000). First, much of this region is subject to intense radiation emitted by young stars in the Orion Nebula. This is probably not typical for molecular clouds. Second, the well-shielded southerly regions (with dust temperatures ≤ 22 K) are devoid of embedded stars that are characteristic of SF regions (Megeath et al. 2012). Finally, we ignore pixels where AV< 2 mag because of observational uncertainties.

3.1. Line emission per unit cloud mass

The line-to-mass ratio, hQ = W(Q) /AV, indicates how the emission from transition Q relates to the mass reservoir characterized by AV. Given AVN(H2), the ratio W(Q) /AV essentially measures the intensity of line emission per H2 molecule.

It is plausible to assume that hQ is a function of n and therefore N(H2). This is, for example, expected if the molecular abundance or the excitation is a function of the density. This is explored in Fig. 2. For this analysis we sort the data into logarithmically spaced bins in AV, and we then derive the mean of hQ and its uncertainty from counting statistics in this bin. We see that hQ is indeed a strong function of AV, which justifies our ansatz to explore the trend of hQ versus AV. We normalize hQ to a maximum value of 1 in the well-detected bins of Fig. 2 in order to simplify comparisons between molecular species.

The trend of hQ versus AV is non-trivial, and it differs between molecules. Most molecules start with a significant value of hQ at low AV, their line-to-mass ratio increases towards a maximum at an AV of 5 to 20 mag, and hQ steadily decreases with increasing AV at even higher extinction. One single molecule defies this trend: the line-to-mass ratio of N2H+ begins near or at zero at low AV, and hQ then begins to steadily rise at AV ≳ 10 mag, possibly to level out (or decrease) at AV ≳ 100 mag.

This is a critical result. This means that the N2H+ (J = 1–0) transition is the only transition among those observed here that selectively traces gas at high (column) density. All other transitions are, by contrast, most sensitive to material at AV ~ 10 mag. Pety et al. (2017) conclude the same in Orion B, using an argument that relates more to the following section.

thumbnail Fig. 2

Normalized line-to-mass ratio, hQ, for the reference region. Shading indicates the uncertainty at a confidence level ≈ 68%, while gray dashes indicate the limits of bins. N2H+ is a good tracer of dense gas since hQ increases with increasing AV.

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3.2. Characteristic (column) density traced by a line

Figure 2 characterizes whether or not a given molecular emission line traces the cloud material well under given conditions. It would be desirable if this information could be collapsed into a single number. One could, for example, attempt to establish the typical H2 (column) density of material that is traced by a given transition. We use the line luminosities for this purpose. Integration over the map area at column densities corresponding to gives the luminosity as a function of the cutoff value , (1)where is the area element measured in pc2. Let be the total luminosity. We then define the characteristic column density of transition Q to be the column density that contains half of the total line luminosity, (2)We then use the density model to define a characteristic density . We also obtain the characteristic column density for the spatial gas mass distribution, , by replacing WQ with AV in Eqs. (1)–(2). Figure 3 shows how and nmed increase towards deeper layers of the cloud.

thumbnail Fig. 3

Top panel: cumulative fraction of emission for various transitions (and mass for dust) indicated by various colors. Dashed vertical lines indicate where selected transitions achieve . Shaded regions indicate uncertainties as described in Sect. 3.2. Bottom panel: estimated median density. Shading indicates confidence ranges of ± 10% and ± 40% around the median estimate.

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This analysis is greatly influenced by the choice of the region analyzed. For example, it is generally known that most of a cloud’s mass resides at low column densities. The field north of 5:10:00 declination considered here does, however, not fulfill this condition. For example, in the area shown in Fig. 1, while holds for the entire Orion A cloud. We therefore use the AV map from Kainulainen et al. (2011) to correct for this relative lack of lower-density material. Specifically, we interpolate the binned information on hQ (i.e., W [ Q ] vs. AV) summarized in Fig. 2 to derive a predicted value of W(Q) for every pixel in the Kainulainen et al. map. We then use these predicted W(Q) in Eqs. (1)–(2) to derive predictions of and for the entire Orion A region. We do not treat CCH because of overly large uncertainties in hQ.

We use the observed values of hQ from Fig. 2 if the measurements exceed their uncertainty by a factor ≥ 3. Around this detection limit we use linear fits to hQ versus lg(AV) to determine the AV for which hQ = 0. We then use linear interpolation in hQ between the point where the transition is safely detected and the point where the emission is predicted to vanish. The latter point has an uncertainty resulting from the aforementioned linear fit. Variation of this point changes and thereby . Further, one might assume that the actual mass distribution (i.e., dM/ dAV) might actually deviate from the one derived from the Kainulainen et al. map. Here we explore a scenario in which we vary dM/ dAV by a factor 2 up and down at AV = 2 mag, leave dM/ dAV unchanged at AV ≥ 10 mag, and interpolate linearly at intermediate AV. Figure 3 shows how extremes in both these modifications might influence the results for HCN and N2H+.

Figure 3 recovers the trends already seen in Fig. 2: most transitions trace lower-density material and have , where for HCN (J = 1–0). The only exception is N2H+ (J = 1–0) with . This transition is the only true tracer of higher column densities. Pety et al. (2017) studied in Orion B how cloud sectors at different AV contribute to LQ. They do not calculate , but their results seem broadly consistent with ours.

4. Tracing the dense gas in star forming galaxies

4.1. HCN as a tracer of moderately dense gas

The constraints on hQ = W(Q) /AV and are of critical importance for the study of star-forming galaxies. For example, Gao & Solomon (2004b) speculate that gas at densities ≳ 3 × 104 cm-3 is traced by emission in the HCN (J = 1–0) transition. More recently, Usero et al. (2015) assumed threshold densities as large as 3 × 105 cm-3 (they deem 104to5 cm-3 likely), while Jimenez-Donaire et al. (2016) estimate threshold densities ≥ 5 × 105 cm-3 from H13CN–to–H12CN line ratios in galaxies. More generally, it is often argued that the high critical density of the HCN (1–0) line, ncr = 1 × 106 cm-3, implies that this transition traces gas of very high density. However, the analysis presented here shows that , which suggests that . This does not fundamentally question the interpretation of trends like the Gao & Solomon relation, but it critically affects the detailed analysis of data.

The low value of is not entirely surprising. Evans (1999) and Shirley (2015; also see Linke et al. 1977) point out that HCN should become detectable at “effective” densities neff ≈ (1 to 3) × 104 cm-3 for gas at 10 K and regular abundances, for which neffncr. Further, HCN can be excited by electrons at H2 densities ncr if fractional electron abundances X(e−) > 10-5 prevail (Goldsmith & Kauffmann 2017, following a suggestion by S. Glover). Here we provide solid observational evidence supporting such work.

Critical densities simply do not control how line emission couples to dense gas. This is already evident from Fig. 1.

The low characteristic density ≈ 870 cm-3 for the HCN (1–0) line has important implications for modeling. Theoretical studies often relate and Mdg via the free-fall time at density , , and a SF efficiency, εSF ≤ 1, via = εSF·Mdg/τff. A landmark paper by Krumholz & Tan (2007), for example, assumes , infers εSF ≈ 0.01, and concludes that SF is “slow” in regions sampled by HCN (1–0). Our measurements indicate that is a factor ≈ 70 smaller, τff a factor ≈ 701 / 2 ≈ 8 larger, and SF thus by a similar factor more efficient and “faster”. Determinations of for HCN and other molecules are thus of essential importance for SF theory.

thumbnail Fig. 4

Star formation in the Milky Way and galaxies. The reference relation for the Milky Way does not describe galaxies. This might hint at unknown reservoirs of HCN emission.

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4.2. Galactic vs. extragalactic star formation relations

We initially set out to investigate whether Mdg as derived from AV is equal to Mdg as obtained from LHCN (1–0). We now return to this question. Lada et al. (2010) argue that Mdg if Mdg is calculated as the cloud mass residing at AVAV,dg = 7 mag. In Sect. 3.2 we show that for the HCN (1–0) transition, similar to AV,dg. This suggests that about half of LHCN(1–0) originates directly in the dense star-forming gas of galaxies. The remaining fraction of LHCN(1–0) does not directly trace Mdg. Still, this emission might be an efficient probe of the gas surrounding and shaping Mdg. From this perspective one might postulate (3)where αHCN(1–0) is a constant. Gao & Solomon (2004b), for example, suggested that αHCN(1–0) ≈ 10 M/ (K km s-1 pc2), based on simple models. But αHCN(1–0) has never been estimated using observations, in particular not down to densities < 103 cm-3 that we suggest are traced by the HCN (1–0) line.

We estimate , following the procedure described in Sect. 3.2. Recall that this is a lower limit since we cannot predict WQ for AV< 2 mag (Sect. 3). We further derive Mdg ≈ 1.6 × 104M by evaluating the mass of material residing at AV ≳ 7 mag in the Kainulainen et al. (2011) extinction map. We thus find αHCN(1–0) ≲ 20 M/ (K km s-1 pc2). This is in good agreement with modeling by Gao & Solomon (2004b); but for the wrong reasons, given their models essentially assume , which exceeds the true value by a factor ≈ 30. Shimajiri et al. (2017) estimate αHCN(1–0) ≈ 10 M/ (K km s-1 pc2) from observations of Aquila, Ophiuchus, and Orion B. Their work assumes a scaling factor to include gas at AV< 8 mag. Our work differs from theirs in that we actually measure this factor (Fig. 3) while Shimajiri et al. implement a sophisticated treatment of interstellar radiation fields.

In Fig. 4 we use our new observational determination of αHCN(1–0) to compare SF in the Gao & Solomon (2004a) galaxies to SF in molecular clouds near the Sun (Lada et al. 2010) and in the Galactic Center (GC; Longmore et al. 2013; Kauffmann et al. 2017). For the galaxies we adopt = βFIR·LFIR with (Eq. (4) and the offset from Fig. 3 of Murphy et al. 2011). Lada et al. (2010) suggest a reference relation describing SF rates in clouds within ~ 500 pc of the Sun, ,MW = (4.6 ± 2.6) × 10-8M yr-1·(Mdg/M), from which GC clouds appear to deviate by a factor ~ 10.

Figure 4 also shows that galaxies deviate from ,MW by an average factor ,MW/ ⟩ ≲ 4.5. Given that ,MW/ ⟩ ∝ αHCN(1–0), could αHCN(1–0) in galaxies be smaller than estimated here? Significant contributions to LHCN(1–0) from reservoirs outside those considered here, for example from diffuse cloud envelopes, could indeed reduce αHCN(1–0) = Mdg/LHCN(1–0).

5. Summary

We study the relationship between various emission lines and dense gas. This analysis is based on observations of various molecules at frequencies near 100 GHz (, , C18O, CN, CCH, HCN, and N2H+). We focus on the HCN (1–0) transition, for which we find that it typically traces gas at , corresponding to a characteristic H2 density ≈ 870 cm-3 (Sect. 3.2). The only molecular transition clearly connected to dense gas is the N2H+ (1–0) transition, characteristic of AV ≈ 16 mag and densities ≈ 4000 cm-3. The low characteristic densities derived for the HCN (1–0) line are about two orders of magnitude below values commonly adopted in extragalactic research (Sect. 4.1). This impacts theoretical discussions of SF trends in galaxies. We use this new knowledge on the emission from HCN to compare SF in galaxies to SF in the Milky Way (Sect. 4.2). The comparisons indicate that galaxies either deviate from SF relations holding in the Milky Way, or hitherto unknown reservoirs of emission contribute to LHCN(1–0).

Acknowledgments

We thank a knowledgeable anonymous referee for helping to significantly improve the paper. This research was conducted in part at the Jet Propulsion Laboratory, which is operated by the California Institute of Technology under contract with the National Aeronautics and Space Administration (NASA). A.G. acknowledges support from Fondecyt under grant 3150570.

References

All Figures

thumbnail Fig. 1

Maps of the peak intensity for transitions near 100 GHz. The left panel gives AV as inferred from Herschel data. Contours at 5 and 30 mag are drawn and repeated in all panels, and the peak intensity is stated for every transition. Line emission maps are smoothed to resolution before filled contours are drawn at signal-to-noise ratios of 3, 5, 10, 30, 50, and 100. Panels are ordered by increasing critical density, ncr.

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In the text
thumbnail Fig. 2

Normalized line-to-mass ratio, hQ, for the reference region. Shading indicates the uncertainty at a confidence level ≈ 68%, while gray dashes indicate the limits of bins. N2H+ is a good tracer of dense gas since hQ increases with increasing AV.

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In the text
thumbnail Fig. 3

Top panel: cumulative fraction of emission for various transitions (and mass for dust) indicated by various colors. Dashed vertical lines indicate where selected transitions achieve . Shaded regions indicate uncertainties as described in Sect. 3.2. Bottom panel: estimated median density. Shading indicates confidence ranges of ± 10% and ± 40% around the median estimate.

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In the text
thumbnail Fig. 4

Star formation in the Milky Way and galaxies. The reference relation for the Milky Way does not describe galaxies. This might hint at unknown reservoirs of HCN emission.

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In the text

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