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Nitrogen hydrides such as NH3 and N2H+ are widely used by Galactic observers to trace the cold dense regions of the interstellar medium. In external galaxies, because of limited sensitivity, HCN has become the most common tracer of dense gas over large parts of galaxies. We provide the first systematic measurements of N2H+ (1-0) across different environments of an external spiral galaxy, NGC 6946. We find a strong correlation (r > 0.98, p < 0.01) between the HCN (1-0) and N2H+ (1-0) intensities across the inner ∼8 kpc of the galaxy, at kiloparsec scales. This correlation is equally strong between the ratios N2H+ (1-0)/CO (1-0) and HCN (1-0)/CO (1-0), tracers of dense gas fractions (fdense). We measure an average intensity ratio of N2H+ (1-0)/HCN (1-0) = 0.15 ± 0.02 over our set of five IRAM-30m pointings. These trends are further supported by existing measurements for Galactic and extragalactic sources. This narrow distribution in the average ratio suggests that the observed systematic trends found in kiloparsec-scale extragalactic studies of fdense and the efficiency of dense gas (SFEdense) would not change if we employed N2H+ (1-0) as a more direct tracer of dense gas. At kiloparsec scales our results indicate that the HCN (1-0) emission can be used to predict the expected N2H+ (1-0) over those regions. Our results suggest that, even if HCN (1-0) and N2H+ (1-0) trace different density regimes within molecular clouds, subcloud differences average out at kiloparsec scales, yielding the two tracers proportional to each other. 

We present new HCN and HCO⁺(J= 3–2) images of the nearby star-forming galaxies (SFGs) NGC 3351, NGC 3627, and NGC 4321. The observations, obtained with the Morita ALMA Compact Array, have a spatial resolution of ∼290–440 pc and resolve the innerR_gal ≲ 0.6–1 kpc of the targets, as well as the southern bar end of NGC 3627. We complement this data set with publicly available images of lower excitation lines of HCN, HCO⁺, and CO and analyse the behaviour of a representative set of line ratios: HCN(3–2)/HCN(1–0), HCN(3–2)/HCO⁺(3–2), HCN(1–0)/CO(2–1), and HCN(3–2)/CO(2–1). Most of these ratios peak at the galaxy centres and decrease outwards. We compare the HCN and HCO⁺observations with a grid of one-phase, non-local thermodynamic equilibrium (non-LTE) radiative transfer models and find them compatible with models that predict subthermally excited and optically thick lines. We study the systematic variations of the line ratios across the targets as a function of the stellar surface density (Σ_star), the intensity-weighted CO(2–1) (⟨I_CO⟩), and the star formation rate surface density (Σ_SFR). We find no apparent correlation with Σ_SFR, but positive correlations with the other two parameters, which are stronger in the case of ⟨I_CO⟩. The HCN/CO–⟨I_CO⟩ relations show ≲0.3 dex galaxy-to-galaxy offsets, with HCN(3–2)/CO(2–1)–⟨I_CO⟩ being ∼2 times steeper than HCN(1–0)/CO(2–1). In contrast, the HCN(3–2)/HCN(1–0)–⟨I_CO⟩ relation exhibits a tighter alignment between galaxies. We conclude that the overall behaviour of the line ratios cannot be ascribed to variations in a single excitation parameter (e.g., density or temperature).