The emission lines of molecules such as 12 CO 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. 2010Lada et al. , 2012)). Extragalactic studies show that CO emission does not distinguish between lower density, bulk molecular gas and the star-forming, dense material with H 2 densities of 10 4 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, N 2 H + , 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. 2021Tafalla et al. , 2023;;Beuther et al. 2022;Santa-Maria et al. 2023). Since N 2 H + 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 N 2 H + 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. N 2 H + / 12 CO ∼ 1/100 at ∼150 pc scales in a starburst galaxy; Eibensteiner et al. 2022, N 2 H + / 12 CO ∼1/140 at kpc scales in M 51 den Brok et al. 2022). Extragalactic observations of N 2 H + 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 N 2 H + . 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 N 2 H + 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 cloudscale (125 pc) extragalactic map of N 2 H + in the central 5-7 kpc of the Whirlpool galaxy (a.k.a M 51). SWAN targets nine molecular lines (C 2 H(1-0), HNCO(4-3), HCN(1-0), HCO + (1-0), HNC(1-0), N 2 H + (1-0), C 18 O(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 (log 10 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 N 2 H + (1-0) at ∼kpc resolution in two 30m pointings in the southwestern spiral arm, and den Brok et al. (2022) presented N 2 H + observations of its center at ∼kpc resolution. In Sect. 2, we describe our observations and data reduction, followed by a comparison of the N 2 H + , HCN, and CO line emission in Sect. 3, a discussion in Sect. 4, and a summary in Sect. 5.
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 12 CO data from PAWS (Schinnerer et al. 2013) were smoothed to a common angular and spectral resolution of 3 and 10 km s -foot_0 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 12 CO 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 12 CO-based 3D mask.
Our SWAN observations have imaged the line emission of both HCN(1-0) (hereafter, HCN) and N 2 H + (1-0) (hereafter N 2 H + ) 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 N 2 H + -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 N 2 H + and HCN emission (Sect. 3.3).
Figure 1 shows the integrated intensity maps of HCN(1-0) and N 2 H + (1-0), their ratio (upper panels), and the PAWS 12 CO(1-0) map (bottom-left). For five beam-sized N 2 H + -bright regions in the disk (see 12 CO map) we extract average spectra of HCN, N 2 H + , and 12 CO (bottom middle panel). N 2 H + emission is detected from various extended regions in the disk, including both spiral arms, the molecular ring and interarm regions. Both tracers (N 2 H + , 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).
On average, N 2 H + is ∼5 times fainter than HCN and ∼80 times fainter than CO, while the line profiles are very similar (FWHM for N 2 H + : ∼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 N 2 H + clumps in the Milky Way suggest a factor of ∼10 smaller N 2 H + 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 12 CO luminosity measured per beam (for details see Appendix B) indicates multiple clouds per beam. We conclude that the similar HCN and N 2 H + linewidths suggest that HCN and N 2 H + spatially coexist inside GMCs at these >100 pc scales and only differ at scales below our resolution.
Our average N 2 H + -to-HCN ratio is ∼0.20 ± 0.09 (see Table 1) in regions with detected N 2 H + emission (>3σ) in the integrated intensity map. Table 1 lists average N 2 H + /HCN, N 2 H + / 12 CO and HCN/ 12 CO ratios derived for the full FoV, the central 1.5 kpc in diameter, as well as the remaining diskfoot_1 . The size of the central region is visually set to conservatively encapsulate the area surrounding the center, where low N 2 H + -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 N 2 H + -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 N 2 H + -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).
To study how well the N 2 H + and HCN emission are correlated, we analyzed the pixel-by-pixel distribution of N 2 H + intensity as a function of HCN intensity 2 (Fig. 2, for N 2 H + and HCN as a function of 12 CO emission see Appendix C).
To first order, the N 2 H + 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 N 2 H + flux while very high HCN fluxes (yellow), and (c) show the highest N 2 H + 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 southwestern arm (pink, hereafter "SW.Arm"). Pixels in the central part of the galaxy thus follow a distribution that is significantly fainter in N 2 H + 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 L20, page 3 of 11 (see Fig. 1). We list values for the full FoV, as well as for the central 1.5 kpc in diameter (center) and the remaining disk. For the N 2 H + -to-HCN ratio we further provide ratios of five N 2 H + -bright beam-sized regions in the disk selected visually (compare Fig. 1). The uncertainty is the standard deviation.
provided in Table 2). Details on the fitting process and the uncertainties derived via jackknifing are given in Appendix D. For all subsets, N 2 H + 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 N 2 H + 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 N 2 H + 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 N 2 H + -to-12 CO and HCN-to-12 CO distributions (Appendix C) behave similarly, as the central data points clearly deviate from the bulk distribution. Similarly to the N 2 H + -to-HCN distribution, the N 2 H + -to-12 CO 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-12 CO 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.
The ratio of emission lines from HCN and 12 CO ( 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 N 2 H + /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).
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 N 2 H + -bright SW.arm subset (c, pink) clusters at higher N 2 H + / 12 CO values.
We discuss which physical conditions might impact the brightness of the potential dense molecular gas tracers based on the found distribution of N 2 H + 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 N 2 H + and HCN (Sect. 4.2).
The N 2 H + -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-12 CO ratio is higher in the center compared to the remaining disk (compare with Very-high-resolution (∼30 pc) observations of HCN and 12 CO 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 12 CO 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-12 CO and the N 2 H + -to-12 CO distributions (Fig. C.1) show an enhancement in HCN or N 2 H + emission in the central data points, the effect is less strong for N 2 H + -to-12 CO, as the fit to its central points agrees with the disk fit unlike the HCN-to-12 CO distribution (Appendix C). This implies that N 2 H + is less affected by the AGN than HCN. Galactic studies do not find correlations between N 2 H + and midinfrared (MIR) photons (e.g. Beuther et al. 2022) suggesting that N 2 H + 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 N 2 H + in contrast to our findings. High cosmic-ray ionization rates in the AGN surroundings might counter this effect by increasing the N 2 H + 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.
L20, page 4 of 11 Notes. Fit parameters for a linear fit in log-log space (log 10 I N 2 H + = a• log 10 I HCN + b) that corresponds to a power-law relation in linear space (I N 2 H + = 10 b • I a HCN ). We added Spearman correlation coefficients ρ Sp and corresponding p-values. We only considered pixels with significant emission (i.e. >3σ).
Our global average N 2 H + -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 N 2 H + -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 powerlaw fit without the central subset being most representative of typical conditions: The N 2 H + emission as a function of HCN emission in the disk at 125 pc can be described as:
Jiménez-Donaire +2023 Fig. 3. I N 2 H + /I CO as function of I HCN /T CO 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.
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 N 2 H + -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 N 2 H + -to-HCN L20, page 5 of 11 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 N 2 H + ) 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 N 2 H + , which is abundant in cold and dense regions where the depletion of CO onto dust grains inhibits the main route of N 2 H + 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 N 2 H + emission, we selected pixels in the disk where N 2 H + is detected. Since N 2 H + 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 N 2 H + emission.
We present the first map of N 2 H + (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 N 2 H + 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 N 2 H + 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 N 2 H + -to-HCN ratio of 0.20 ± 0.09 for regions detected in N 2 H + 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 N 2 H + 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 powerlaw function of index 1.20±0.02, indicating that HCN-bright regions have higher gas densities as traced by N 2 H + than we would infer from their HCN emission alone. 3. The N 2 H + -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 N 2 H + emission in pixels in our FoV where N 2 H + 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, N 2 H + 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).
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 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 N 2 H + (1-0) lines, respectively.
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, 13 CO(1-0).
We created the following sets of integrated moment-0 maps for the NOEMA+30m HCN and N 2 H + datacubes as well as for the 12 CO(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 12 CO emission (see Einig et al. 2023, and reference therein). This method isolates connected structures with 12 CO emission above our selected S/N threshold of 2 in the position-positionvelocity (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 12 CO emission to detect the 'islands' ensures that for all lines the same pixels in the ppv cube are used for integration. Since 12 CO is brighter than the other lines, there are more pixels above a given S/N threshold than in N 2 H + and HCN. Therefore, this can result in otherwise too faint emission being stacked in pixels that would not be selected for integration based on N 2 H + 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. L20, page 8 of 11 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.
When considering Gaussian line profiles and that HCN is on average ∼5 times brighter than N
H + , the inferred linewidths at matched brightness agree for HCN and N 2 H + .2 The maps are regridded to 1.5 pixel size to minimize oversampling effects.
Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany e-mail: stuber@mpia.de
IRAM,
rue de la Piscine, 38400 Saint Martin d'Hères, France 3 Sorbonne Université, Observatoire de Paris, Université PSL, École normale supèrieure, CNRS, LERMA, 75005 Paris, France 4 Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany 5 Observatorio Astronómico Nacional (IGN), C/Alfonso XII 3, Madrid 28014, Spain 6 LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 75014 Paris, France
See the IRAM technical memo IRAM-2008-2, https://cloud. iram.fr/index.php/s/Ney5P2BeN7DAEWX