© The Authors 2023

1. Introduction

The emission lines of molecules such as ¹²CO are considered to be good tracers of the bulk molecular mass distribution (e.g. BIMA-SONG, Helfer et al. 2003; PAWS, Schinnerer et al. 2013; PHANGS, Leroy et al. 2021) and found to correlate with (e.g. infrared) emission tracing recent star formation (e.g. Kennicutt & Evans 2012; Bigiel et al. 2008). However, molecular clouds contain a wide range of densities, with star formation typically associated with the densest gas (e.g. Lada et al. 2010, 2012). Extragalactic studies show that CO emission does not distinguish between lower density, bulk molecular gas and the star-forming, dense material with H₂ densities of ≳10⁴ cm⁻³ (e.g. Gao & Solomon 2004; Jiménez-Donaire et al. 2019; Querejeta et al. 2019)

Tracers of dense gas are by definition challenging to observe due to the lower abundances of these molecules relative to CO and the smaller volume occupied by the dense phase, which both lead to a significantly reduced line brightness when compared to CO. With typical HCN-to-CO line ratios in disk galaxies of ∼1/30 or lower (Usero et al. 2015; Bigiel et al. 2016), extragalactic studies were focusing on HCN(J = 1 − 0) finding a tighter correlation between HCN line emission with star formation rate (SFR) than for CO emission (Gao & Solomon 2004; Jiménez-Donaire et al. 2019). The higher critical density (n_crit) of HCN(1–0) has led to the common interpretation that this line preferentially traces the denser sub-regions of molecular clouds (Shirley 2015), making HCN a commonly used tracer of dense molecular gas in extragalactic studies (Bigiel et al. 2016; Gallagher et al. 2018; Jiménez-Donaire et al. 2019; Querejeta et al. 2019; Bešlic et al. 2021; Eibensteiner et al. 2022; Neumann et al. 2023; Kaneko et al. 2023).

Galactic studies have questioned the use of HCN as a dense gas tracer at cloud scales (< 10 pc) and favour the use of another molecule, N₂H⁺, which has successfully been detected towards several molecular clouds in the Milky Way (e.g. Pety et al. 2017; Kauffmann et al. 2017; Barnes et al. 2020; Tafalla et al. 2021, 2023; Beuther et al. 2022; Santa-Maria et al. 2023). Since N₂H⁺ is destroyed in the presence of CO, it is linked to the dense clumps of clouds, where CO freezes to dust grains (e.g. Bergin & Tafalla 2007). This makes N₂H⁺ not only a chemical tracer of cold and dense cores within clouds, but also leads to its emission being beam-diluted and, thus, even fainter than HCN (e.g. N₂H⁺/¹²CO ∼1/100 at ∼150 pc scales in a starburst galaxy; Eibensteiner et al. 2022, N₂H⁺/¹²CO ∼1/140 at kpc scales in M 51 den Brok et al. 2022). Extragalactic observations of N₂H⁺ are thus challenging and limited to low-resolution studies (e.g. ∼kpc scales; den Brok et al. 2022; Jiménez-Donaire et al. 2023) or individual regions of galaxies (e.g. the center of starburst galaxy NGC 253; Martín et al. 2021). Jiménez-Donaire et al. (2023) summarize Galactic and extragalactic observations of HCN and N₂H⁺. Although it may stand as a challenging task, the IRAM Northern Extended Millimetre Array (NOEMA) is capable of obtaining high sensitivity and high angular resolution observations needed to map the distribution of the faint emission of N₂H⁺ and HCN in star-forming galaxy disks.

We present the first results from Surveying the Whirpool at Arcsecond with NOEMA (SWAN) IRAM Large Program (PIs: E. Schinnerer & F. Bigiel), including the first cloud-scale (125 pc) extragalactic map of N₂H⁺ in the central 5–7 kpc of the Whirlpool galaxy (a.k.a M 51). SWAN targets nine molecular lines (C₂H(1–0), HNCO(4–3), HCN(1–0), HCO⁺(1–0), HNC(1–0), N₂H⁺(1–0), C₁₈O(1–0), HNCO(5–4), 13 CO(1–0)) at ∼3″ (∼125 pc) to study the role of dense gas in the star formation process across galactic environments.

M 51 (NGC 5194) is a nearby (D = 8.58 Mpc; McQuinn et al. 2016) close to face-on (i = 22°, PA=173°; Colombo et al. 2014), massive (log₁₀ M_*/M_⊙ = 10.5; den Brok et al. 2022), spiral galaxy that hosts a low-luminosity AGN (Ho et al. 1997; Dumas et al. 2011; Querejeta et al. 2016). The HCN emission has been mapped at 3″ resolution (125 pc) for three circular regions of ∼3 kpc diameter (Querejeta et al. 2019) in M 51, at 4″ in the outer spiral arm at ∼5 kpc galactocentric distance (Chen et al. 2017) and out to ∼8 kpc in the disk at 1–2 kpc resolution by EMPIRE (Bigiel et al. 2016; Jiménez-Donaire et al. 2019). Watanabe et al. (2014) detected both HCN and N₂H⁺(1–0) at ∼kpc resolution in two 30m pointings in the south-western spiral arm, and den Brok et al. (2022) presented N₂H⁺ observations of its center at ∼kpc resolution. In Sect. 2, we describe our observations and data reduction, followed by a comparison of the N₂H⁺, HCN, and CO line emission in Sect. 3, a discussion in Sect. 4, and a summary in Sect. 5.

2. Data

We used observations from the IRAM large program LP003 (PIs: E. Schinnerer, F. Bigiel) that combine NOEMA (integration time of ∼214 h) and the 30 m single dish observations (about ∼69 h integration time from EMPIRE, CLAWS, and this program) to map 3–4 mm emission lines from the central 5 × 7 kpc of the nearby galaxy M 51. A detailed description of the observations and data reduction is presented in Appendix A.

The combined data as well as ¹²CO data from PAWS (Schinnerer et al. 2013) were smoothed to a common angular and spectral resolution of 3″ and 10 km s⁻¹ per channel. We integrated each line by applying the so-called GILDAS-based “island method” (see Einig et al. 2023, and references therein), where structures with ¹²CO emission above a selected S/N of 2 in the position-position-velocity cube are selected. For all lines, the emission is then integrated over the same pixels from the ¹²CO-based 3D mask.

3. Results on dense gas in M 51

Our SWAN observations have imaged the line emission of both HCN(1–0) (hereafter, HCN) and N₂H⁺(1–0) (hereafter N₂H⁺) in M 51 at 125 pc resolution. In order to analyze which physical conditions might impact the brightness of these potential dense molecular gas tracers, we study the N₂H⁺-to-HCN ratio across the disk of M 51 (Sect. 3.1), identify regions where the ratio deviates from the global trend (Sect. 3.2), and quantify the correlation between N₂H⁺ and HCN emission (Sect. 3.3).

3.1. Distribution of N₂H⁺ and HCN in the disk of M 51

Figure 1 shows the integrated intensity maps of HCN(1–0) and N₂H⁺(1–0), their ratio (upper panels), and the PAWS ¹²CO(1–0) map (bottom-left). For five beam-sized N₂H⁺-bright regions in the disk (see ¹²CO map) we extract average spectra of HCN, N₂H⁺, and ¹²CO (bottom middle panel). N₂H⁺ emission is detected from various extended regions in the disk, including both spiral arms, the molecular ring and interarm regions. Both tracers (N₂H⁺, HCN) roughly follow the CO brightness distribution with the brightest regions being the galaxy center (denoted as region 1), the southwestern spiral arm (2) as well as the northwestern part of the inner molecular ring (4).

Fig. 1. Integrated intensity maps of N2H+ (top left) and HCN (top center), as well as their ratio (top right) at 3″ (∼125 pc) resolution of the central 5 kpc  ×  7 kpc in M 51a. The ratio map shows emission above 3σ for both lines. The beam of ∼3″ is shown in the bottom left corner of the N2H+ map for reference; the location of the galactic center is marked (green ×). We further display 12CO emission at 3″ resolution from the PAWS survey (bottom left; Schinnerer et al. 2013) for comparison and show the 30 K km s−1 contour of 12CO for reference in all maps. The central 1.5 kpc (in diameter) is indicated by a cyan circle in the 12CO map. Average spectra of five beam-sized regions in the disk (see the 12CO map) are shown for N2H+, HCN and 12CO (bottom center). We scale the spectra by a factor of 3 (N2H+) and 0.05 (12CO) for easier comparison. The full-disk spectra contain all pixels in the FoV, shown on top of a HST image (bottom right).

On average, N₂H⁺ is ∼5 times fainter than HCN and ∼80 times fainter than CO, while the line profiles are very similar (FWHM for N₂H⁺: ∼20 km s⁻¹, HCN ∼30 km s⁻¹)¹, in agreement with ∼kpc observations in NGC 6946 (Jiménez-Donaire et al. 2023). This remains true, even when imaging our data at 1 km s⁻¹ spectral resolution. As observations of ∼0.1 pc N₂H⁺ clumps in the Milky Way suggest a factor of ∼10 smaller N₂H⁺ linewidths relative to HCN (e.g. 1–2 km s⁻¹; Tatematsu et al. 2008), our linewidths probably trace cloud-to-cloud velocity dispersion or turbulence scaling with physical lengths. Further, the typical ¹²CO luminosity measured per beam (for details see Appendix B) indicates multiple clouds per beam. We conclude that the similar HCN and N₂H⁺ linewidths suggest that HCN and N₂H⁺ spatially coexist inside GMCs at these > 100 pc scales and only differ at scales below our resolution.

3.2. N₂H⁺-to-HCN line ratios

Our average N₂H⁺-to-HCN ratio is ∼0.20 ± 0.09 (see Table 1) in regions with detected N₂H⁺ emission (> 3σ) in the integrated intensity map. Table 1 lists average N₂H⁺/HCN, N₂H⁺/¹²CO and HCN/¹²CO ratios derived for the full FoV, the central 1.5 kpc in diameter, as well as the remaining disk². The size of the central region is visually set to conservatively encapsulate the area surrounding the center, where low N₂H⁺-to-HCN ratios are observed (see Fig. 1), but also to avoid other morphological structures such as the molecular ring at larger radii. For these ≳kpc regions, the N₂H⁺-to-HCN line ratio in the center (disk) is lower (higher) by a factor of ∼1.3 (∼1.2) compared to the full FoV value, but still agrees within the uncertainties.

On approximately cloud-size scales (125 pc), the N₂H⁺-to-HCN ratio is significantly (> 3σ) lower in the center (1) than in region 2 in the south-western spiral arm (see Fig. 1 and Table 1) and deviates by a factor of 2.5 from the full FoV average. These findings suggest the presence of systematic trends that drive the high scatter of the full FoV line ratios (see next section).

3.3. Correlation of HCN and N₂H⁺ line emission

To study how well the N₂H⁺ and HCN emission are correlated, we analyzed the pixel-by-pixel distribution of N₂H⁺ intensity as a function of HCN intensity² (Fig. 2, for N₂H⁺ and HCN as a function of ¹²CO emission see Appendix C).

Fig. 2. Comparison of N2H+ and HCN emission. (a) Pixel-by-pixel distribution of integrated N2H+ and HCN emission in linear (left panel) and logarithmic (right panel) scaling. Subsets of pixels are visually isolated based on their high N2H+ (pink, SW.Arm) or HCN (yellow, AGN) values. Their location relative to the distribution of HCN emission in M 51 is shown in b) (contour marks 5σ N2H+ integrated intensity). Power-law fits are applied to all data points (black dashed line), the subsets identified (solid lines), as well as all data points excluding the yellow (AGN-affected) subset (black dotted line). Fit parameters and Spearman correlation coefficients for all data points and the subsets are given in Table 2. Data points below the 3σ noise level are presented as grey crosses. The N2H+-to-HCN relation from Jiménez-Donaire et al. (2023) is shown as a green dotted line.

To first order, the N₂H⁺ emission is strongly correlated with the HCN emission (Spearman correlation coefficient ρ_Sp = 0.832 ± 0.009, see Table 2). Although some data deviate from the correlation. The linear presentation (left panel) reveals two clusters with different mean slopes. We visually devise subsets of pixels that: (a) belong to the main cluster containing the bulk of the data points (grey), (b) have comparably low N₂H⁺ flux while very high HCN fluxes (yellow), and (c) show the highest N₂H⁺ intensities where the apparently linear trend becomes exponential (pink). Locating these pixels in the HCN moment-0 map (Fig. 2b) reveals that subset (b) originates from the galaxy center (yellow, hereafter “AGN”) and subset (c) from the south-western arm (pink, hereafter “SW.Arm”). Pixels in the central part of the galaxy thus follow a distribution that is significantly fainter in N₂H⁺ emission than in HCN emission compared to the rest of the sample. We discuss the impact of the AGN in Sect. 4.1.

The logarithmic presentation (right panel of Fig. 2a) confirms that subset (c, pink) from the south-western arm follows the bulk data (grey) for a power-law distribution. The comparably large scatter in this subset (c, SW.arm) emerges from two different spatial locations that have slightly different slopes than the subset’s average one (see also Appendix E.1).

We fit all data points plus the subsets (emission > 3σ) with linear functions in logarithmic scaling. The fit parameters as well as Spearman correlation coefficients (ρ_Sp) and p-values are provided in Table 2). Details on the fitting process and the uncertainties derived via jackknifing are given in Appendix D. For all subsets, N₂H⁺ emission is (similarly) aptly (ρ_Sp >  0.75) and super-linearly (best-fit power a >  1) correlated with HCN emission. However, the fit of the central (yellow) data points significantly deviates from the fit for all data points including and excluding the central ones (black dashed and dotted line, see also Appendix D). The central subset contributes ∼7% of the total HCN and ∼4% of the total N₂H⁺ flux in our FoV, and contains most of the brightest HCN pixels. Although the disk data points (without AGN and SW.arm, grey points), can be best described with a linear relation (power a = 0.97 ± 0.013), the power index monotonically increases when the upper limit of the range in integrated N₂H⁺ emission used to select the fitted point is increased. This is likely due to the scatter around the power law decreasing at the same time as the data explores a larger part of the power law, increasing the range spanned by the data.

The N₂H⁺-to-¹²CO and HCN-to-¹²CO distributions (Appendix C) behave similarly, as the central data points clearly deviate from the bulk distribution. Similarly to the N₂H⁺-to-HCN distribution, the N₂H⁺-to-¹²CO distribution (Fig. C.1) is best described by a super-linear power-law, with its brightest end being mainly populated by the pixels from subset (c, SW.arm) (Table C.1). In contrast, the HCN-to-¹²CO distribution is best described by a sub-linear to linear power-law. We quantified the scatter of these distributions in Appendix E.2 and find that for all distributions, the scatter is of order ∼0.14 dex, while the total range covered by the lines cover ≳1.5 dex.

3.4. Density-sensitive line ratio

The ratio of emission lines from HCN and ¹²CO (f = I_HCN/I_CO) has been commonly used as an indication of the (average) gas density f_dense (e.g. Usero et al. 2015; Bigiel et al. 2016; Jiménez-Donaire et al. 2019). We compare I_N2H⁺/I_CO to f in Fig. 3 and find them to be correlated (ρ_Sp = 0.70, p-value  <   0.001). Overall, 82% (97%) of our data points agree within 3σ (5σ) with the fit from Jiménez-Donaire et al. (2023, Eq. (2)) with a power-law index of 1.0 obtained when fitting all available Galactic and extragalactic data (green line).

Fig. 3. IN2H+/ICO as function of IHCN/TCO for all data points and subsets above a 3σ noise level. We show the average uncertainty in the bottom right corner, as well as the best-fit from Jiménez-Donaire et al. (2023, Eq. (2)) with a power law slope of 1.0 derived for extragalactic and Galactic data points (green line). Contours indicate the number density of data points.

Our result indicates that to a first order, both line ratios are correlated. Although the difference has a low statistical significance, the AGN subset (b, yellow) is offset from the remaining data, and the N₂H⁺-bright SW.arm subset (c, pink) clusters at higher N₂H⁺/¹²CO values.

4. Discussion on molecular gas density in M 51

We discuss which physical conditions might impact the brightness of the potential dense molecular gas tracers based on the found distribution of N₂H⁺ and HCN in the disk (Sect. 3.1), the high and low line ratios in isolated regions (Sect. 3.2), and the correlations between the emission of N₂H⁺ and HCN (Sect. 4.2).

4.1. The AGN impacts the central emission in M 51

The N₂H⁺-to-HCN line ratio is significantly lower in the center of M 51 compared to regions in the disk, and the central data points are offset from those in the disk (Fig. 2). In contrast, the HCN-to-¹²CO ratio is higher in the center compared to the remaining disk (compare with Fig. C.1), in agreement with Jiménez-Donaire et al. (2019) at ∼kpc scales. Very-high-resolution (∼30 pc) observations of HCN and ¹²CO in M 51 by Matsushita et al. (2015) reveal extraordinarily high HCN/CO ratios (> 2) at the location of the AGN, which they explain by infrared pumping, possibly weak HCN masing and an increased HCN abundance. Electron excitation in the XDR of the AGN might also contribute to the enhanced HCN emission (Goldsmith & Kauffmann 2017). Blanc et al. (2009) identified [NII]λ6584/Hα line ratios typical of AGN in M 51’s central ∼700 pc and spatially coincident with X-ray and radio emission. HCN and ¹²CO arise both from the outflow associated with nearly coplanar radio jet, with significant effects seen out to a distance of 500 pc (Querejeta et al. 2016). While the central 1.5 kpc (diameter) region as used for the line ratios likely overestimates the area of influence of the AGN, our visually selected subset (b) likely underestimates the area impacted.

While both the HCN-to-¹²CO and the N₂H⁺-to-¹²CO distributions (Fig. C.1) show an enhancement in HCN or N₂H⁺ emission in the central data points, the effect is less strong for N₂H⁺-to-¹²CO, as the fit to its central points agrees with the disk fit unlike the HCN-to-¹²CO distribution (Appendix C). This implies that N₂H⁺ is less affected by the AGN than HCN. Galactic studies do not find correlations between N₂H⁺ and mid-infrared (MIR) photons (e.g. Beuther et al. 2022) suggesting that N₂H⁺ is not affected by infrared-pumping via the AGN. While an increased temperature in the AGN vicinity can also increase HCN emission (Matsushita et al. 2015; Tafalla et al. 2023), this would lead to CO sublimating, reacting with and destroying N₂H⁺ in contrast to our findings. High cosmic-ray ionization rates in the AGN surroundings might counter this effect by increasing the N₂H⁺ abundance (Santa-Maria et al. 2021), which is not seen for HCN (Meijerink et al. 2011). The complex mechanisms happening in the AGN vicinity will be explored in a future paper.

4.2. The emerging N₂H⁺-to-HCN relation

Our global average N₂H⁺-to-HCN ratio of 0.20 ± 0.09 agrees well with ratios obtained at ∼kpc resolution in M 51 of ∼0.14 for the galaxy center and ∼0.19 in the southern spiral arm (Watanabe et al. 2014; Aladro et al. 2015). A recent literature compilation (Jiménez-Donaire et al. 2023) reported that a N₂H⁺-to-HCN ratio of 0.07 − 0.22 for extragalactic regions and ∼0.05 − 0.23 when including Galactic sources. Line ratios of five ∼kpc size regions in NGC 6946 range between 0.12 − 0.20, leading to a global ratio of 0.15 ± 0.03, or a linear fit in log-space of power 0.99 ± 0.04 and offset 0.87 ± 0.04 (Jiménez-Donaire et al. 2023) shown for reference in Fig. 2. This fit agrees with our fit to the central subset (b), but shows a significant (> 3σ) deviation from our fits focusing on the disk.

Given the AGN impact (Sect. 4.1), we considered the power-law fit without the central subset being most representative of typical conditions: The N₂H⁺ emission as a function of HCN emission in the disk at 125 pc can be described as:

$$\begin{array}{c}\hfill {\log }_{10}{I}_{{\mathrm{N}}_2{\mathrm{H}}^{+}}=(1.20\pm 0.02)·{\log }_{10}{I}_{\mathrm{HCN}}-(0.825\pm 0.009).\end{array}$$(1)

The super-linearity in our relation, driving the discrepancy between our results and the literature, comes from the bright south-western spiral arm, where our N₂H⁺-to-HCN ratio is the highest (Table 1, region 2). Strong streaming motions present in the southern spiral arm are likely stabilizing the gas resulting in low star formation efficiencies (Meidt et al. 2013). This region (at ∼28 − 38″) is at the transition between the normal star formation efficiency and the extremely low star formation efficiency seen further south (Querejeta et al. 2019) and has a high dynamical complexity (i.e. coinciding with the co-rotation radius of a m = 3 mode; Colombo et al. 2014). Although its N₂H⁺-to-HCN ratio is larger than the global average, it extends the general distribution in a smooth manner (Fig. 2), unlike the clearly offset emission from M 51’s center. We speculate the following:

Firstly, HCN-bright regions have more dense gas (as traced by N₂H⁺) than what we would expect from the HCN intensities. This effect should potentially be correlated with the resolution, as higher-resolution observations able to resolve clouds would be able to better to isolate the spatially smaller dense clumps.

Secondly, galactic studies find that HCN luminosity is sensitive to far-UV light from young massive stars (e.g. Pety et al. 2017; Kauffmann et al. 2017; Santa-Maria et al. 2023). The HCN emission is linked to dense molecular clouds, but it is also well correlated with regions of recent star formation. This effect is not seen for N₂H⁺, which is abundant in cold and dense regions where the depletion of CO onto dust grains inhibits the main route of N₂H⁺ destruction. In the southern-spiral arm, where star-formation is found to be comparably lower, this could explain our power law of 1.2.

As the focus of this study is the comparison of HCN to N₂H⁺ emission, we selected pixels in the disk where N₂H⁺ is detected. Since N₂H⁺ is a chemical tracer of dense gas, we thus selected regions where dense gas can be expected. This can introduce a bias towards higher values, as we potentially mask out regions of low N₂H⁺ emission.

5. Summary and conclusion

We present the first map of N₂H⁺(J = 1 − 0) and HCN(1–0) from the NOEMA+30m large program SWAN in the central 5 × 7 kpc of the nearby star-forming disk galaxy M 51 at cloud-scale resolution of 125 pc (3″). We study where the chemical dense gas tracer N₂H⁺ emits with respect to larger-scale dynamical features and how it relates to emission from other molecules, such as HCN and CO. Comparing these lines, we have drawn the following conclusions:

1. Extended N₂H⁺ emission is detected from various regions across the disk, with the brightest emission found in the south-western spiral arm, followed by the center and the north-western end of the molecular ring. Overall, HCN emission is bright in the same regions, but it shows the highest intensity in the center.

2. We find an average N₂H⁺-to-HCN ratio of 0.20 ± 0.09 for regions detected in N₂H⁺ emission (> 3σ) with strong variations throughout the disk of up to a factor of ∼2 − 3 in the south-western spiral arm and the center that hosts an AGN. The N₂H⁺ and HCN emission are strongly correlated (ρ_Sp ∼ 0.83), but the central 1.5 kpc clearly deviates. The disk emission can be described with a super-linear power-law function of index 1.20 ± 0.02, indicating that HCN-bright regions have higher gas densities as traced by N₂H⁺ than we would infer from their HCN emission alone.

3. The N₂H⁺-to-HCN ratio is significantly lower in the M 51’s center where an AGN is present and its distribution is offset from the bulk of the disk data. The affected region accounts for ∼9% of the total HCN emission and ∼4% of total N₂H⁺ emission in pixels in our FoV where N₂H⁺ is detected. MIR pumping might be one explanation for the bright and enhanced HCN flux surrounding the AGN.

Our ∼120 pc observations in M 51 demonstrate that to first order, N₂H⁺ and HCN are strongly super-linearly correlated. In addition to first-order correlations with gas-density, the peculiar line ratio present near the AGN and the scatter of the power-law fit suggest additional second-order physics (such as optical depth, gas temperature) or chemistry (abundance variations).

Acknowledgments

This work was carried out as part of the PHANGS collaboration. We thank the anonymous referee for their constructive feedback. This work is based on data obtained by PIs E. Schinnerer and F. Bigiel with the IRAM-30 m telescope and NOEMA observatory under project ID M19AA. S.K.S. acknowledges financial support from the German Research Foundation (DFG) via Sino-German research grant SCHI 536/11-1. J.P. acknowledges support from the French Agence Nationale de la Recherche through the DAOISM grant ANR-21-CE31-0010 and from the Programme National “Physique et Chimie du Milieu Interstellaire” (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. E.S. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694343). A.U. acknowledges support from the Spanish grant PID2019-108765GB-I00, funded by MCIN/AEI/10.13039/501100011033. M.Q. and M.J.J.D. acknowledge support from the Spanish grant PID2019-106027GA-C44, funded by MCIN/AEI/10.13039/501100011033. J.d.B. acknowledges support from the Smithsonian Institution as a Submillimeter Array (SMA) Fellow. L.N. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 516405419. The work of A.K.L. is partially supported by the National Science Foundation under Grants No. 1615105, 1615109, and 1653300. C.E. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) Sachbeihilfe, grant number BI1546/3-1. Y.-H.T. acknowledges funding support from NRAO Student Observing Support Grant SOSPADA-012 and from the National Science Foundation (NSF) under grant No. 2108081. M.C. gratefully acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) through an Emmy Noether Research Group, grant number CH2137/1-1. COOL Research DAO is a Decentralized Autonomous Organization supporting research in astrophysics aimed at uncovering our cosmic origins. S.C.O.G. acknowledges support from the DFG via SFB 881 “The Milky Way System” (sub-projects B1, B2 and B8) and from the Heidelberg cluster of excellence EXC 2181-390900948 “STRUCTURES: A unifying approach to emergent phenomena in the physical world, mathematics, and complex data”, funded by the German Excellence Strategy. H.A.P. acknowledges support by the National Science and Technology Council of Taiwan under grant 110-2112-M-032-020-MY3.

References

Appendix A: Data

We utilized observations from the IRAM large program LP003 (PIs: E. Schinnerer, F. Bigiel) that used the Northern Extended Millimetre Array (NOEMA) and 30m single dish to map the 4-3 mm line emission from the central 5×7 kpc of the nearby galaxy M 51. The observations, data calibration and imaging resulting in our final datasets are briefly described below.

A.1. NOEMA data

NOEMA observations were taken with 9-11 antennas between January 2020 and December 2021, resulting in a total of 214 hours under average to excellent observing conditions with an average water vapor of ∼4 mm split across C (59%; 126h) and D (41%; 88h) configuration. Observations of the phase and amplitude calibrators (J1259+516 and J1332+473, replaced by 1418+546 if one of the two was not available) were executed every ∼20 minutes. The mosaic consists of 17 pointings in a hexagonal grid. Data reduction was carried out using the IRAM standard calibration pipeline in GILDAS (Gildas Team 2013). Average to excellent temporal subsets of the observed data were selected based on the relative seeing of the different tracks. Absolute flux calibration was done using IRAM models for MWC349 and LkHa101 providing about 50 independent measurements of the flux of J1259+516 and J1332+473 over a period of about 1 year. This allowed us to confirm that the time variations of the flux of these quasars were relatively smooth.

We detect emission from 9 molecular lines between ∼80 and 110 GHz, including HCN(1–0; 88.6 GHz) and N₂H⁺(1–0; 93 GHz) presented in this paper, but also C₂H(1–0), HNCO(4–3), HCO⁺(1–0), HNC(1–0), C¹⁸O(1–0), HNCO(5–4) and ¹³CO(1–0). Continuum was subtracted from the uv visibilities by fitting a baseline of the order of 0 for each visibility, excluding channels in a velocity range of 300 km s⁻¹ around the redshifted-frequency of each line. For each line, the NOEMA data were resampled to a spectral axis with 10 km s⁻¹ resolution, relative to the systemic velocity of v_sys = 471.7 km s⁻¹ (Shetty et al. 2007).

B.1. IRAM-30m single-dish data

In order to sample all the spatial scales, we needed to combine the NOEMA interferometric imaging with single dish data of the HCN (1–0) and N₂H⁺(1–0) emission lines from both archival and new observations.

The HCN (1–0) emission line was observed as part of the IRAM-30m survey EMPIRE (Jiménez-Donaire et al. 2019), using the 3 mm band (E090) of the dual-polarization EMIR receiver (Carter et al. 2012). N₂H⁺(1–0) was observed by the IRAM-30m CLAWS survey (055-17, PI: K. Sliwa; den Brok et al. 2022), where EMIR was also used to map the 1 mm (220 GHz) and 3 mm (100 GHz) emission lines in M 51. In both surveys, the integration time was spread over the full extent of M 51, while the required field of view (FoV) for the 30m imaging is the interferometric FoV plus a guard-band to avoid edge effects amounting to 5 square arcmin. We estimate that the EMPIRE and CLAWS projects obtained each about 14 hours of 30m integration time over the relevant field of view. As a rule of thumb to achieve an optimum combination one needs to observe with the 30m telescope the same amount of time as is spent in the compact D configuration³. Hence, we obtained 55 hours of additional IRAM 30m observations (project 19-238 observed in February and April 2020) with a similar tuning as the NOEMA one. In all three cases, we used the on-the-fly-position switching (OTF-PSW) mode, with emission-free reference positions close to the galaxy. The fast Fourier transform spectrometers (FTS) were used to record the data. We refer to Jiménez-Donaire et al. (2019) and den Brok et al. (2022) for details of the observations.

The data were (re)-reduced (1) to ensure a homogeneous treatment and (2) to avoid unnecessary spatial or spectral regridding. In short, for each observed spectrum, we first extracted a frequency range of 300 MHz centered on each target line. We then converted the temperature scale from $T_A^{\star }$ to T_mb by applying the relevant Ruze formula with the CLASS command MODIFY BEAM_EFF /RUZE. We computed the velocity scale corresponding to each line’s redshifted velocity, and we reprojected the spatial offsets of each observed spectrum to the NOEMA projection center of RA=13:29:52.532, Dec=47:11:41.982. We also subtracted a polynomial baseline of the order of one fitted by excluding a velocity range of [ − 170, +170 km s⁻¹]. Finally, we gridded all the data on the same spatial and spectral grid as the NOEMA data. The achieved noise levels are 2.5 K at 29.3″ and 2.4 K at 27.9″ for the HCN and N₂H⁺ (1–0) lines, respectively.

C.1. NOEMA+30m imaging

The 30m data are then merged with the NOEMA data in the uv plane using the GILDAS UV_SHORT command (see Pety & Rodríguez-Fernández 2010, for details). The combined data were imaged with UV_MAP on a grid of 768 × 1024 pixels of 0.31″ size. Högbom-cleaning without cleaning mask was run in order to achieve residuals consistent with a Gaussian distribution of the noise. In practice, we ran it until a stable number of clean components, which depends on the line, was reached. The intensity scale was finally converted from Jy/beam to K. The resulting dataset has a rms of ∼20 mK per 10 km s⁻¹ channel at a nominal resolution of 2.1 × 2.4″ for the brightest line, ¹³CO(1–0).

We created the following sets of integrated moment-0 maps for the NOEMA+30m HCN and N₂H⁺ datacubes as well as for the ¹²CO(J = 1–0) data from PAWS (Schinnerer et al. 2013). All data are convolved to a common angular and spectral resolution of 3″ (125 pc) and 10 km s⁻¹ per channel. We integrated each line by applying the so-called ’island-method’ based on ¹²CO emission (see Einig et al. 2023, and reference therein). This method isolates connected structures with ¹²CO emission above our selected S/N threshold of 2 in the position-position-velocity (ppv) cube and integrates the emission of selected lines over the identified structures along the velocity axis. To avoid misleading oversampling effects, we regridded our maps to pixels with sizes of half the beam major axis for all calculations (i.e. 1.5″). Using ¹²CO emission to detect the ’islands’ ensures that for all lines the same pixels in the ppv cube are used for integration. Since ¹²CO is brighter than the other lines, there are more pixels above a given S/N threshold than in N₂H⁺ and HCN. Therefore, this can result in otherwise too faint emission being stacked in pixels that would not be selected for integration based on N₂H⁺ emission, for instance.

For comparison, we also integrated each line individually, by selecting ’islands’ based on each line’s intensity. This reduces the noise for each line individually while conserving faint emission from connected structures. However, this also introduces some bias, as the emission is integrated over a varying amount of pixels in different structures for each line. While some values slightly change due to these effects, we confirm that all trends and conclusions remain unchanged.

Pixels where the N₂H⁺ integrated emission is significantly (> 3σ) detected, contain ∼50% of significant ¹²CO flux in our FoV and ∼70% of significant HCN emission in the FoV. Pixels where HCN is significantly detected contain ∼90% of the significant ¹²CO emission in our FoV. Since the our analysis in section 3 is based on regions where N₂H⁺ is detected, we limited our analysis to a smaller area in the FoV.

Appendix B: Typical cloud mass per beam

As N₂H⁺ is abundant in small dense cores, we generally expect the N2H+ emission to arise from regions with sizes much smaller than our resolution of 125 pc, which is slightly worse than the size of massive GMCs. Thus, the pixel-by-pixel variations in our observations reflect average physical trends affecting ensembles of multiple clumps. Our finding (see Sect. 3.1 that linewidths of N₂H⁺ are comparable to HCN in selected beam-size regions, suggests that at our 125 pc scales, we are indeed averaging emission from several dense clouds. This is further supported by the typical emission found in these regions. In the selected beam-size regions (see Fig. 1), we find typical integrated ¹²CO intensities of I_CO ∼ 1 × 10² K km s⁻¹. A typical large molecular cloud with cloud masses of M_cloud ∼ 1 × 10⁵ M_⊙ would (at our resolution) correspond to integrated intensities of 1.3 K km s⁻¹ using a standard CO-to-H₂ conversion factor of α_CO = 4.35 M_⊙ pc⁻² (K km s⁻¹)⁻¹. Therefore, we can confirm that at our resolution we are likely to be averaging the emission from several clouds.

Appendix C: N₂H⁺-to-¹²CO and HCN-to-¹²CO relation

In addition to the N₂H⁺-to-HCN distribution (Fig. 2), we show the N₂H⁺-to-¹²CO and HCN-to-¹²CO distributions in Fig. C.1. We mark the same subset of pixels (AGN, SW.arm) identified in the N₂H⁺-to-HCN distribution accordingly. We fit power-laws to all the data (dashed line), the data without the central points (dotted line), as well as the subsets of data (subset (b) AGN, subset (c) SW.arm). Fit parameters can be found in Table C.1 and more details on the fitting process are provided in Appendix D. Similarly to our previous findings, we see that the central data points follow a steeper trend than the rest of the data points. While the central points in the HCN-to-¹²CO distribution do not overlap with the rest of the data, the central N₂H⁺-to-¹²CO distribution mostly overlaps with the rest of the data points and the central N₂H⁺-to-¹²CO trend is only slightly steeper than the global trend.

Fig. C.1. Pixel-by-pixel distribution of integrated N2H+ (top panels) and HCN (bottom panels) as a function of 12CO emission, similar to Fig. 2 (a) in linear (left panels) and logarithmic (right panels) scaling. Subsets of pixels isolated in Fig. 2 are marked accordingly (pink: subset (c) SW.Arm, yellow: Subset (b) AGN). Power-law fits to the full data (black dashed), the data without the central points (black dotted) and the subsets are added (colors respectively). Fit uncertainties are only shown in log space to ease visibility.

The N₂H⁺-bright data points from the southern spiral arm (subset (c): pink) are also the brightest pixels in ¹²CO. These points constitute a super-linear relation in the N₂H⁺-to-¹²CO plane. This is less clear for the HCN-to-¹²CO distribution. While all fits to the N₂H⁺-to-¹²CO data and subsets are super-linear (a >  1), all fits to the HCN-to-¹²CO data and subsets are sub-linear (a <  1) except for the fit to subset (c). We note, however, that there are additional data points in the HCN-to-¹²CO distribution, which are elevated above the bulk distribution that might instead belong to the central subset (b), but are not selected since our selection of these subsets is visually determined based on the N₂H⁺-to-HCN distribution. While the fit to all data points shows a large increase in offset due to the central data points, the fit without the central subset might still be elevated due to the likely imperfect selection of data points impacted by the AGN.

The fit to the central subset (b) of the HCN-to-¹²CO distribution significantly deviates from the fit to the disk data without this subset, similar to our findings for the N₂H⁺-to-HCN distribution. Unsuprisingly, this is not the case for the central fit of the N₂H⁺-to-¹²CO distribution, which agrees well with the fit to the disk data, as most of the central subset (b) overlaps with the disk data. This indicates that the mechanism driving the offset in line emission affects N₂H⁺ less than HCN (see discussion in Section 4).

Appendix D: Fitting the N₂H⁺-to-HCN, N₂H⁺-to-¹²CO and HCN-to-¹²CO distribution

We fit all data points, the data subsets (b,c) as well as all disk data, namely, all data without subset (b) AGN, of the N₂H⁺-to-HCN, N₂H⁺-to-¹²CO and HCN-to-¹²CO distributions with linear functions in logarithmic scaling. We only considered pixels with significant emission (> 3σ). Parameters are fitted with curve-fit (python scipy-optimize tool; Virtanen et al. 2020). We fit a linear function of shape f(x)=ax + b to the logarithmic data with slope a and offset b. Following error propagation, the corresponding uncertainty at each x value is $\mathrm{\Delta }f(x)=\sqrt{{\left(\mathrm{\Delta }ax\right)}^2+{\left(\mathrm{\Delta }b\right)}^2}$, with uncertainties Δa, Δb accordingly. The discrepancy to the literature fit is measured as $\sigma =|f-f_{\mathit{lit}}|/\sqrt{\mathrm{\Delta }{f}^2+\mathrm{\Delta }{f}_{\mathit{lit}}^2}$, which is dependent on x. We provide the average discrepancy in the range over which our data are measured.

Uncertainties are estimated by perturbing each pixel by a random Gaussian value with standard deviation at the corresponding noise value, and randomly jackknifing 10% of the data before either calculating fit-parameters or Spearman correlation coefficients. Repeating this 100 times yields the standard deviation as uncertainty.

Appendix E: Quantifying the scatter of line ratios

We investigated regions with increased scatter, as well as quantify the scatter between N₂H⁺ and HCN, HCN, and ¹²CO as well as N₂H⁺ and ¹²CO.

E.1. Disentangling emission from the southern spiral arm

In Sect. 4.2 we isolated pixels that are bright in HCN and N₂H⁺. The region with pixels brightest in N₂H⁺ (subset c: pink points in Fig. 2) shows a comparably large scatter in N₂H⁺ emission, with the emission varying by nearly a factor of 2 at similar levels of HCN flux (at I_HCN ∼ 18 K km s⁻¹ we find I_N2H⁺ ∼ 4 − 7.5 K km s⁻¹). A closer look (Fig. E.1) reveals that this emission originates from different spatial locations in the disk, one with a shallower N₂H⁺-to-HCN distribution located in the north-western part of the molecular ring (pink circles), the other with a steeper N₂H⁺-to-HCN distribution from the south-western part of the same spiral arm (dark red circles).

As noted in Sect. 4.2, the data points from the southern spiral arm (red points in Fig. E.1) drive the non-linear but logarithmic relation between N₂H⁺ and HCN emission. Interestingly, the northern region is located close to the AGN jet major axis (Querejeta et al. 2016) and might be potentially impacted by the AGN as well, though the number of data points is lower.

E.2. Measuring the scatter of line ratios

We quantified the scatter of the N₂H⁺-to-HCN, HCN-to-¹²CO and the N₂H⁺-to-HCN distribution as follows. For this analysis, we excluded the central subset (b) as it exhibits a quite different distribution from the rest of the data, as well as data points below the 3σ noise level. We subtracted the corresponding best-fit value (using the fit parameters when excluding the center) from each data point in the according distribution. The obtained data has an average scatter of ∼0.14 dex for N₂H⁺ as a function of HCN emission, 0.19 dex for N₂H⁺ as a function of ¹²CO emission and 0.29 dex for HCN as a function of ¹²CO emission.

Fig. E.1. Close-up of HCN and N2H+ emission (left panel) of N2H+-bright pixels from subset (c), as in Fig. 2, as well as their location in the disk (right panel, compare to panel b of Fig. 2). We separate the pixels into two sub-regions (red, pink)

We drew the following conclusion: a) While all lines span a range of ≳1.5 dex in intensity, we find ∼10% scatter, indicating that all lines are well correlated. b) The scatter of N₂H⁺ as a function of HCN is least, indicating a tighter correlation between N₂H⁺ and HCN than any of those lines with ¹²CO. Since these results are strongly dependent on the fit and thus the fitting tool used, we suggest these results be taken with caution.

All Tables

All Figures

Fig. 1. Integrated intensity maps of N2H+ (top left) and HCN (top center), as well as their ratio (top right) at 3″ (∼125 pc) resolution of the central 5 kpc  ×  7 kpc in M 51a. The ratio map shows emission above 3σ for both lines. The beam of ∼3″ is shown in the bottom left corner of the N2H+ map for reference; the location of the galactic center is marked (green ×). We further display 12CO emission at 3″ resolution from the PAWS survey (bottom left; Schinnerer et al. 2013) for comparison and show the 30 K km s−1 contour of 12CO for reference in all maps. The central 1.5 kpc (in diameter) is indicated by a cyan circle in the 12CO map. Average spectra of five beam-sized regions in the disk (see the 12CO map) are shown for N2H+, HCN and 12CO (bottom center). We scale the spectra by a factor of 3 (N2H+) and 0.05 (12CO) for easier comparison. The full-disk spectra contain all pixels in the FoV, shown on top of a HST image (bottom right).

In the text

Fig. 2. Comparison of N2H+ and HCN emission. (a) Pixel-by-pixel distribution of integrated N2H+ and HCN emission in linear (left panel) and logarithmic (right panel) scaling. Subsets of pixels are visually isolated based on their high N2H+ (pink, SW.Arm) or HCN (yellow, AGN) values. Their location relative to the distribution of HCN emission in M 51 is shown in b) (contour marks 5σ N2H+ integrated intensity). Power-law fits are applied to all data points (black dashed line), the subsets identified (solid lines), as well as all data points excluding the yellow (AGN-affected) subset (black dotted line). Fit parameters and Spearman correlation coefficients for all data points and the subsets are given in Table 2. Data points below the 3σ noise level are presented as grey crosses. The N2H+-to-HCN relation from Jiménez-Donaire et al. (2023) is shown as a green dotted line.

In the text

	Fig. 3. IN2H+/ICO as function of IHCN/TCO for all data points and subsets above a 3σ noise level. We show the average uncertainty in the bottom right corner, as well as the best-fit from Jiménez-Donaire et al. (2023, Eq. (2)) with a power law slope of 1.0 derived for extragalactic and Galactic data points (green line). Contours indicate the number density of data points.
In the text

Fig. C.1. Pixel-by-pixel distribution of integrated N2H+ (top panels) and HCN (bottom panels) as a function of 12CO emission, similar to Fig. 2 (a) in linear (left panels) and logarithmic (right panels) scaling. Subsets of pixels isolated in Fig. 2 are marked accordingly (pink: subset (c) SW.Arm, yellow: Subset (b) AGN). Power-law fits to the full data (black dashed), the data without the central points (black dotted) and the subsets are added (colors respectively). Fit uncertainties are only shown in log space to ease visibility.

In the text

	Fig. E.1. Close-up of HCN and N2H+ emission (left panel) of N2H+-bright pixels from subset (c), as in Fig. 2, as well as their location in the disk (right panel, compare to panel b of Fig. 2). We separate the pixels into two sub-regions (red, pink)
In the text