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We investigate the relationship between CN N = 1 − 0 and HCN J = 1 − 0 emission on scales from 30 to 400 pc using ALMA archival data, for which CN is often observed simultaneously with the CO J = 1 − 0 line. In a sample of nine nearby galaxies ranging from ultra-luminous infrared galaxies to normal spiral galaxies, we measure a remarkably constant CN/HCN line intensity ratio of 0.86 ± 0.07 (standard deviation of 0.20). This relatively constant CN/HCN line ratio is rather unexpected, as models of photon dominated regions have suggested that HCN emission traces shielded regions with high column densities while CN should trace dense gas exposed to high ultraviolet radiation fields. We find that the CN/HCN line ratio shows no significant correlation with molecular gas surface density but shows a mild trend (increase of ∼1.3 per dex) with both star formation rate surface density and star formation efficiency (the inverse of the molecular gas depletion time). Some starburst and active galactic nuclei show small enhancements in their CN/HCN ratio, while other nuclei show no significant difference from their surrounding discs. The nearly constant CN/HCN line ratio implies that CN, like HCN, can be used as a tracer of dense gas mass and dense gas fractionmore »in nearby galaxies.

We measure the molecular-to-atomic gas ratio,R_mol, and the star formation rate (SFR) per unit molecular gas mass, SFE_mol, in 38 nearby galaxies selected from the Virgo Environment Traced in CO (VERTICO) survey. We stack ALMA¹²CO (J= 2−1) spectra coherently using Hivelocities from the VIVA survey to detect faint CO emission out to galactocentric radiir_gal∼ 1.2r₂₅. We determine the scale lengths for the molecular and stellar components, finding a ∼3:5 relation compared to ∼1:1 in field galaxies, indicating that the CO emission is more centrally concentrated than the stars. We computeR_molas a function of different physical quantities. While the spatially resolvedR_molon average decreases with increasing radius, we find that the mean molecular-to-atomic gas ratio within the stellar effective radiusR_e,R_mol(r<R_e), shows a systematic increase with the level of Hi, truncation and/or asymmetry (H_Iperturbation). Analysis of the molecular- and the atomic-to-stellar mass ratios withinR_e,$R_{\star }^{\mathrm{mol}}(r<R_e)$and$R_{\star }^{\mathrm{atom}}(r<R_e)$, shows that VERTICO galaxies have increasingly lower$R_{\star }^{\mathrm{atom}}(r<R_e)$for larger levels of H_Iperturbation (compared to field galaxies matched in stellar mass), but no significant change in$R_{\star }^{\mathrm{m}\mathrm{o}\mathrm{l}}(r<R_e)$. We also measure a clear systematic decrease of the SFE_molwithinR_e, SFE_mol(r<R_e),more »with increasingly perturbed Hi. Therefore, compared to field galaxies from the field, VERTICO galaxies are more compact in CO emission in relation to their stellar distribution, but increasingly perturbed atomic gas increases theirR_moland decreases the efficiency with which their molecular gas forms stars.

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 SFRmore »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.

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 slopesmore »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.