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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 We measure the molecular gas environment near recent (<100 yr old) supernovae (SNe) using ∼1″ or ≤150 pc resolution CO (2–1) maps from the PHANGS–Atacama Large Millimeter/submillimeter Array (ALMA) survey of nearby star-forming galaxies. This is arguably the first such study to approach the scales of individual massive molecular clouds (M_mol≳ 10^5.3M_⊙). Using the Open Supernova Catalog, we identify 63 SNe within the PHANGS–ALMA footprint. We detect CO (2–1) emission near ∼60% of the sample at 150 pc resolution, compared to ∼35% of map pixels with CO (2–1) emission, and up to ∼95% of the SNe at 1 kpc resolution, compared to ∼80% of map pixels with CO (2–1) emission. We expect the ∼60% of SNe within the same 150 pc beam, as a giant molecular cloud will likely interact with these clouds in the future, consistent with the observation of widespread SN–molecular gas interaction in the Milky Way, while the other ∼40% of SNe without strong CO (2–1) detections will deposit their energy in the diffuse interstellar medium, perhaps helping drive large-scale turbulence or galactic outflows. Broken down by type, we detect CO (2–1) emission at the sites of ∼85% of our 9 stripped-envelope SNe (SESNe), ∼40% of our 34 Type II SNe, and ∼35% of our 13 Type Ia SNe, indicating that SESNe are most closely associated with the brightest CO (2–1) emitting regions in our sample. Our results confirm that SN explosions are not restricted to only the densest gas, and instead exert feedback across a wide range of molecular gas densities. 

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 We measure the low- J CO line ratios R 21 ≡ CO (2–1)/CO (1–0), R 32 ≡ CO (3–2)/CO (2–1), and R 31 ≡CO (3–2)/CO (1–0) using whole-disk CO maps of nearby galaxies. We draw CO (2–1) from PHANGS-ALMA, HERACLES, and follow-up IRAM surveys; CO (1–0) from COMING and the Nobeyama CO Atlas of Nearby Spiral Galaxies; and CO (3–2) from the James Clerk Maxwell Telescope Nearby Galaxy Legacy Survey and Atacama Pathfinder Experiment Large APEX Sub-Millimetre Array mapping. All together, this yields 76, 47, and 29 maps of R 21 , R 32 , and R 31 at 20″ ∼ 1.3 kpc resolution, covering 43, 34, and 20 galaxies. Disk galaxies with high stellar mass, log ( M ⋆ / M ⊙ ) = 10.25 – 11 , and star formation rate (SFR) = 1–5 M ⊙ yr −1 , dominate the sample. We find galaxy-integrated mean values and a 16%–84% range of R 21 = 0.65 (0.50–0.83), R 32 = 0.50 (0.23–0.59), and R 31 = 0.31 (0.20–0.42). We identify weak trends relating galaxy-integrated line ratios to properties expected to correlate with excitation, including SFR/ M ⋆ and SFR/ L CO . Within galaxies, we measure central enhancements with respect to the galaxy-averaged value of ∼ 0.18 − 0.14 + 0.09 dex for R 21 , 0.27 − 0.15 + 0.13 dex for R 31 , and 0.08 − 0.09 + 0.11 dex for R 32 . All three line ratios anticorrelate with galactocentric radius and positively correlate with the local SFR surface density and specific SFR, and we provide approximate fits to these relations. The observed ratios can be reasonably reproduced by models with low temperature, moderate opacity, and moderate densities, in good agreement with expectations for the cold interstellar medium. Because the line ratios are expected to anticorrelate with the CO (1–0)-to-H 2 conversion factor, α CO 1 − 0 , these results have general implications for the interpretation of CO emission from galaxies. 

Abstract We measure empirical relationships between the local star formation rate (SFR) and properties of the star-forming molecular gas on 1.5 kpc scales across 80 nearby galaxies. These relationships, commonly referred to as “star formation laws,” aim at predicting the local SFR surface density from various combinations of molecular gas surface density, galactic orbital time, molecular cloud free fall time, and the interstellar medium dynamical equilibrium pressure. Leveraging a multiwavelength database built for the Physics at High Angular Resolution in Nearby Galaxies (PHANGS) survey, we measure these quantities consistently across all galaxies and quantify systematic uncertainties stemming from choices of SFR calibrations and the CO-to-H₂conversion factors. The star formation laws we examine show 0.3–0.4 dex of intrinsic scatter, among which the molecular Kennicutt–Schmidt relation shows a ∼10% larger scatter than the other three. The slope of this relation rangesβ≈ 0.9–1.2, implying that the molecular gas depletion time remains roughly constant across the environments probed in our sample. The other relations have shallower slopes (β≈ 0.6–1.0), suggesting that the star formation efficiency per orbital time, the star formation efficiency per free fall time, and the pressure-to-SFR surface density ratio (i.e., the feedback yield) vary systematically with local molecular gas and SFR surface densities. Last but not least, the shapes of the star formation laws depend sensitively on methodological choices. Different choices of SFR calibrations can introduce systematic uncertainties of at least 10%–15% in the star formation law slopes and 0.15–0.25 dex in their normalization, while the CO-to-H₂conversion factors can additionally produce uncertainties of 20%–25% for the slope and 0.10–0.20 dex for the normalization. 

ABSTRACT We present improved methods for segmenting CO emission from galaxies into individual molecular clouds, providing an update to the cprops algorithms presented by Rosolowsky & Leroy. The new code enables both homogenization of the noise and spatial resolution among data, which allows for rigorous comparative analysis. The code also models the completeness of the data via false source injection and includes an updated segmentation approach to better deal with blended emission. These improved algorithms are implemented in a publicly available Python package, pycprops. We apply these methods to 10 of the nearest galaxies in the PHANGS-ALMA survey, cataloguing CO emission at a common 90 pc resolution and a matched noise level. We measure the properties of 4986 individual clouds identified in these targets. We investigate the scaling relations among cloud properties and the cloud mass distributions in each galaxy. The physical properties of clouds vary among galaxies, both as a function of galactocentric radius and as a function of dynamical environment. Overall, the clouds in our target galaxies are well-described by approximate energy equipartition, although clouds in stellar bars and galaxy centres show elevated line widths and virial parameters. The mass distribution of clouds in spiral arms has a typical mass scale that is 2.5× larger than interarm clouds and spiral arms clouds show slightly lower median virial parameters compared to interarm clouds (1.2 versus 1.4). 

Abstract We explore the relationship between mid-infrared (mid-IR) and CO rotational line emission from massive star-forming galaxies, which is one of the tightest scalings in the local universe. We assemble a large set of unresolved and moderately (∼1 kpc) spatially resolved measurements of CO (1–0) and CO (2–1) intensity,I_CO, and mid-IR intensity,I_MIR, at 8, 12, 22, and 24μm. TheI_COversusI_MIRrelationship is reasonably described by a power law with slopes 0.7–1.2 and normalizationI_CO∼ 1 K km s⁻¹atI_MIR∼ 1 MJy sr⁻¹. Both the slopes and intercepts vary systematically with choice of line and band. The comparison between the relations measured for CO (1–0) and CO (2–1) allow us to infer that $R_{21}\propto I_{\mathrm{MIR}}^{0.2}$, in good agreement with other work. The 8μm and 12μm bands, with strong polycyclic aromatic hydrocarbon (PAH) features, show steeper CO versus mid-IR slopes than the 22 and 24μm, consistent with PAH emission arising not just from CO-bright gas but also from atomic or CO-dark gas. The CO-to-mid-IR ratio correlates with global galaxy stellar mass (M_⋆) and anticorrelates with star formation rate/M_⋆. At ∼1 kpc resolution, the first four PHANGS–JWST targets show CO-to-mid-IR relationships that are quantitatively similar to our larger literature sample, including showing the steep CO-to-mid-IR slopes for the JWST PAH-tracing bands, although we caution that these initial data have a small sample size and span a limited range of intensities. 

The density structure of the interstellar medium determines where stars form and release energy, momentum and heavy elements, driving galaxy evolution1-4. Density variations are seeded and amplified by gas motion, but the exact nature of this motion is unknown across spatial scales and galactic environments5. Although dense star-forming gas probably emerges from a combination of instabilities6,7, convergent flows8 and turbulence9, establishing the precise origin is challenging because it requires gas motion to be quantified over many orders of magnitude in spatial scale. Here we measure10-12 the motion of molecular gas in the Milky Way and in nearby galaxy NGC 4321, assembling observations that span a spatial dynamic range 10-1-103 pc. We detect ubiquitous velocity fluctuations across all spatial scales and galactic environments. Statistical analysis of these fluctuations indicates how star-forming gas is assembled. We discover oscillatory gas flows with wavelengths ranging from 0.3-400 pc. These flows are coupled to regularly spaced density enhancements that probably form via gravitational instabilities13,14. We also identify stochastic and scale-free velocity and density fluctuations, consistent with the structure generated in turbulent flows9. Our results demonstrate that the structure of the interstellar medium cannot be considered in isolation. Instead, its formation and evolution are controlled by nested, interdependent flows of matter covering many orders of magnitude in spatial scale.