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Context. Dense and cold molecular cores and filaments are surrounded by an envelope of translucent gas. Some of the low-Jemission lines of CO and HCO⁺isotopologues are more sensitive to the conditions either in the translucent environment or in the dense and cold one because their intensities result from a complex interplay of radiative transfer and chemical properties of these heterogeneous lines of sight (LoSs). Aims. We extend our previous single-zone modeling with a more realistic approach that introduces multiple layers to take account of possibly varying conditions along the LoS. We used the IRAM-30m data from the ORION-B large program toward the Horsehead nebula in order to demonstrate our method’s capability and effectiveness. Methods. We propose a cloud model composed of three homogeneous slabs of gas along each LoS, representing an outer envelope and a more shielded inner layer. We used the non-LTE radiative transfer code RADEX to model the line profiles from the kinetic temperature (T_kin), the volume density (n_H2), kinematics, and chemical properties of the different layers. We then used a fast and robust maximum likelihood estimator to simultaneously fit the observed lines of the CO and HCO⁺isotopologues. To limit the variance on the estimates, we propose a simple chemical model by constraining the column densities. Results. A single-layer model cannot reproduce the spectral line asymmetries that result from a combination of different radial velocities and absorption effects among layers. A minimal heterogeneous model (three layers only) is sufficient for the Horsehead application, as it provides good fits of the seven fitted lines over a large part of the studied field of view. The decomposition of the intensity into three layers allowed us to discuss the distribution of the estimated physical or chemical properties along the LoS. About 80% of the¹²CO integrated intensity comes from the outer envelope, while ~55% of the integrated intensity of the (1 − 0) and (2 − 1) lines of C¹⁸O comes from the inner layer. For the lines of the¹³CO and the HCO⁺isotopologues, integrated intensities are more equally distributed over the cloud layers. The estimated column density ratioN(¹³CO)/N(C¹⁸O) in the envelope increases with decreasing visual extinction, and it reaches 25 in the pillar outskirts. While the inferredT_kinof the envelope varies from 25 to 40 K, that of the inner layer drops to ~15 K in the western dense core. The estimatedn_H2in the inner layer is ~3 × 10⁴cm⁻³toward the filament, and it increases by a factor of ten toward dense cores. Conclusions. Our proposed method correctly retrieves the physical and chemical properties of the Horsehead nebula. It also offers promising prospects for less supervised model fits of wider-field datasets. 

Context.Observations of ionic, atomic, or molecular lines are performed to improve our understanding of the interstellar medium (ISM). However, the potential of a line to constrain the physical conditions of the ISM is difficult to assess quantitatively, because of the complexity of the ISM physics. The situation is even more complex when trying to assess which combinations of lines are the most useful. Therefore, observation campaigns usually try to observe as many lines as possible for as much time as possible. Aims.We have searched for a quantitative statistical criterion to evaluate the full constraining power of a (combination of) tracer(s) with respect to physical conditions. Our goal with such a criterion is twofold. First, we want to improve our understanding of the statistical relationships between ISM tracers and physical conditions. Secondly, by exploiting this criterion, we aim to propose a method that helps observers to make their observation proposals; for example, by choosing to observe the lines with the highest constraining power given limited resources and time. Methods.We propose an approach based on information theory, in particular the concepts of conditional differential entropy and mutual information. The best (combination of) tracer(s) is obtained by comparing the mutual information between a physical parameter and different sets of lines. The presented analysis is independent of the choice of the estimation algorithm (e.g., neural network orχ²minimization). We applied this method to simulations of radio molecular lines emitted by a photodissociation region similar to the Horsehead Nebula. In this simulated data, we considered the noise properties of a state-of-the-art single dish telescope such as the IRAM 30m telescope. We searched for the best lines to constrain the visual extinction,A_V^tot, or the ultraviolet illumination field,G₀. We ran this search for different gas regimes, namely translucent gas, filamentary gas, and dense cores. Results.The most informative lines change with the physical regime (e.g., cloud extinction). However, the determination of the optimal (combination of) line(s) to constrain a physical parameter such as the visual extinction depends not only on the radiative transfer of the lines and chemistry of the associated species, but also on the achieved mean signal-to-noise ratio. The short integration time of the CO isotopologueJ= 1 − 0 lines already yields much information on the total column density for a large range of (A_V^tot,G₀) space. The best set of lines to constrain the visual extinction does not necessarily combine the most informative individual lines. Precise constraints on the radiation field are more difficult to achieve with molecular lines. They require spectral lines emitted at the cloud surface (e.g., [CII] and [CI] lines). Conclusions.This approach allows one to better explore the knowledge provided by ISM codes, and to guide future observation campaigns. 

Abstract Over the past decade, several millimeter interferometer programs have mapped the nearby star-forming galaxy M51 at a spatial resolution of ≤170 pc. This study combines observations from three major programs: the PdBI Arcsecond Whirlpool Survey, the SMA M51 large program, and the Surveying the Whirlpool at Arcseconds with NOEMA. The data set includes the (1–0) and (2–1) rotational transitions of¹²CO,¹³CO, and C¹⁸O isotopologues. The observations cover ther< 3 kpc region, including the center and part of the disk, thereby ensuring strong detections of the weaker¹³CO and C¹⁸O lines. All observations are convolved in this analysis to an angular resolution of 4″, corresponding to a physical scale of 170 pc. We investigate empirical line ratio relations and quantitatively evaluate molecular gas conditions such as temperature, density, and the CO-to-H₂conversion factor (α_CO). We employ two approaches to study the molecular gas conditions: (i) assuming local thermodynamic equilibrium (LTE) to analytically determine the CO column density andα_CO, and (ii) using non-LTE modeling withRADEXto fit physical conditions to observed CO isotopologue intensities. We find that theα_COvalues in the center and along the inner spiral arm are ∼0.5 dex (LTE) and 0.1 dex (non-LTE) below the Milky Way inner disk value. The average non-LTEα_COis 2.4 ± 0.5M_⊙pc⁻²(K km s⁻¹)⁻¹. While both methods show dispersion due to underlying assumptions, the scatter is larger for LTE-derived values. This study underscores the necessity for robust CO line modeling to accurately constrain the molecular interstellar medium’s physical and chemical conditions in nearby galaxies. 

Context.Mapping molecular line emission beyond the bright low-JCO transitions is still challenging in extragalactic studies, even with the latest generation of (sub-)millimetre interferometers, such as ALMA and NOEMA. Aims.We summarise and test a spectral stacking method that has been used in the literature to recover low-intensity molecular line emission, such as HCN(1−0), HCO⁺(1−0), and even fainter lines in external galaxies. The goal is to study the capabilities and limitations of the stacking technique when applied to imaged interferometric observations. Methods.The core idea of spectral stacking is to align spectra of the low S/N spectral lines to a known velocity field calculated from a higher S/N line expected to share the kinematics of the fainter line (e.g. CO(1−0) or 21 cm emission). Then these aligned spectra can be coherently averaged to produce potentially high S/N spectral stacks. Here we used imaged simulated interferometric and total power observations at different S/N levels, based on real CO observations. Results.For the combined interferometric and total power data, we find that the spectral stacking technique is capable of recovering the integrated intensities even at low S/N levels across most of the region where the high S/N prior is detected. However, when stacking interferometer-only data for low S/N emission, the stacks can miss up to 50% of the emission from the fainter line. Conclusions.A key result of this analysis is that the spectral stacking method is able to recover the true mean line intensities in low S/N cubes and to accurately measure the statistical significance of the recovered lines. To facilitate the application of this technique we provide a public Python package, called PYSTACKER. 

ABSTRACT We use new HCN(1–0) data from the ACA Large-sample Mapping Of Nearby galaxies in Dense gas (ALMOND) survey to trace the kpc-scale molecular gas density structure and CO(2–1) data from the Physics at High Angular resolution in Nearby GalaxieS–Atacama Large Millimeter/submillimeter Array (PHANGS–ALMA) to trace the bulk molecular gas across 25 nearby star-forming galaxies. At 2.1 kpc scale, we measure the density-sensitive HCN/CO line ratio and the star formation rate (SFR)/HCN ratio to trace the star formation efficiency in the denser molecular medium. At 150 pc scale, we measure structural and dynamical properties of the molecular gas via CO(2–1) line emission, which is linked to the lower resolution data using an intensity-weighted averaging method. We find positive correlations (negative) of HCN/CO (SFR/HCN) with the surface density, the velocity dispersion, and the internal turbulent pressure of the molecular gas. These observed correlations agree with expected trends from turbulent models of star formation, which consider a single free-fall time gravitational collapse. Our results show that the kpc-scale HCN/CO line ratio is a powerful tool to trace the 150 pc scale average density distribution of the molecular clouds. Lastly, we find systematic variations of the SFR/HCN ratio with cloud-scale molecular gas properties, which are incompatible with a universal star formation efficiency. Overall, these findings show that mean molecular gas density, molecular cloud properties, and star formation are closely linked in a coherent way, and observations of density-sensitive molecular gas tracers are a useful tool to analyse these variations, linking molecular gas physics to stellar output across galaxy discs. 

Abstract We compare mid-infrared (mid-IR), extinction-corrected H α , and CO (2–1) emission at 70–160 pc resolution in the first four PHANGS–JWST targets. We report correlation strengths, intensity ratios, and power-law fits relating emission in JWST’s F770W, F1000W, F1130W, and F2100W bands to CO and H α . At these scales, CO and H α each correlate strongly with mid-IR emission, and these correlations are each stronger than the one relating CO to H α emission. This reflects that mid-IR emission simultaneously acts as a dust column density tracer, leading to a good match with the molecular-gas-tracing CO, and as a heating tracer, leading to a good match with the H α . By combining mid-IR, CO, and H α at scales where the overall correlation between cold gas and star formation begins to break down, we are able to separate these two effects. We model the mid-IR above I ν = 0.5 MJy sr −1 at F770W, a cut designed to select regions where the molecular gas dominates the interstellar medium (ISM) mass. This bright emission can be described to first order by a model that combines a CO-tracing component and an H α -tracing component. The best-fitting models imply that ∼50% of the mid-IR flux arises from molecular gas heated by the diffuse interstellar radiation field, with the remaining ∼50% associated with bright, dusty star-forming regions. We discuss differences between the F770W, F1000W, and F1130W bands and the continuum-dominated F2100W band and suggest next steps for using the mid-IR as an ISM tracer. 

ABSTRACT Feedback from massive stars plays a key role in molecular cloud evolution. After the onset of star formation, the young stellar population is exposed by photoionization, winds, supernovae, and radiation pressure from massive stars. Recent observations of nearby galaxies have provided the evolutionary timeline between molecular clouds and exposed young stars, but the duration of the embedded phase of massive star formation is still ill-constrained. We measure how long massive stellar populations remain embedded within their natal cloud, by applying a statistical method to six nearby galaxies at $$20{-}100~\mbox{$${\rm ~pc}$$}$$ resolution, using CO, Spitzer 24$$\rm \, \mu m$$, and H α emission as tracers of molecular clouds, embedded star formation, and exposed star formation, respectively. We find that the embedded phase (with CO and 24$$\rm \, \mu m$$ emission) lasts for 2−7 Myr and constitutes $$17{-}47{{\ \rm per\ cent}}$$ of the cloud lifetime. During approximately the first half of this phase, the region is invisible in H α, making it heavily obscured. For the second half of this phase, the region also emits in H α and is partially exposed. Once the cloud has been dispersed by feedback, 24$$\rm \, \mu m$$ emission no longer traces ongoing star formation, but remains detectable for another 2−9 Myr through the emission from ambient CO-dark gas, tracing star formation that recently ended. The short duration of massive star formation suggests that pre-supernova feedback (photoionization and winds) is important in disrupting molecular clouds. The measured time-scales do not show significant correlations with environmental properties (e.g. metallicity). Future JWST observations will enable these measurements routinely across the nearby galaxy population.