A panchromatic spatially resolved analysis of nearby galaxies – II. The main sequence – gas relation at sub-kpc scale in grand-design spirals

ABSTRACT

In this work, we analyse the connection between gas availability and the position of a region with respect to the spatially resolved main-sequence (MS) relation. Following the procedure presented in Enia et al. (2020), for a sample of five face-on, grand design spiral galaxies located on the MS we obtain estimates of stellar mass and star formation rate surface densities (Σ_⋆ and Σ_SFR) within cells of 500 pc size. Thanks to H i 21cm and ¹²CO(2–1) maps of comparable resolution, within the same cells we estimate the surface densities of the atomic (Σ_H i) and molecular (⁠|$\Sigma _{\rm {H_2}}$|⁠) gas and explore the correlations among all these quantities. Σ_⋆, Σ_SFR, and |$\Sigma _{\rm {H_2}}$| define a 3D relation whose projections are the spatially resolved MS, the Kennicutt–Schmidt law and the molecular gas MS. We find that |$\Sigma _{\rm {H_2}}$| steadily increases along the MS relation and is almost constant perpendicular to it. Σ_H i is nearly constant along the MS and increases in its upper envelope. As a result, Σ_SFR can be expressed as a function of Σ_⋆ and Σ_H i, following the relation log Σ_SFR = 0.97log Σ_⋆ + 1.99log Σ_H i − 11.11. We show that the total gas fraction significantly increases towards the starburst regions, accompanied by a weak increase in star formation efficiency. Finally, we find that H₂/H i varies strongly with the distance from the MS, dropping dramatically in regions of intense star formation, where the UV radiation from newly formed stars dissociates the H₂ molecule, illustrating the self-regulating nature of the star formation process.

galaxies: evolution, galaxies: star formation, galaxies: spirals

1 INTRODUCTION

In the current model of galaxy formation and evolution, stars form in dense clouds of molecular gas, thanks to the interplay of different physical mechanisms (magnetic fields, turbulence, shielding, feedback). Despite its complexity, this interplay translates in tight correlations between different physical quantities: (i) between the surface density of the star formation rate (Σ_SFR) and the surface density of the gas (Σ_gas), and (ii) between the stellar mass surface density (Σ_⋆) and Σ_SFR. The first relation, originally formulated by Schmidt (1959) using the gas volume density and the number of stars formed in the solar neighbourhood, was subsequently derived by Kennicutt (1998) for radially averaged surface densities in external galaxies, and it is thus called the Kennicutt–Schmidt (KS) relation. The second, called main sequence (MS), was initially found using integrated quantities of star-forming galaxies (thus the total SFR and stellar mass M_⋆) in Brinchmann et al. (2004) for local galaxies and later confirmed for high-redshift galaxies by several works (e.g. Daddi et al. 2007; Elbaz et al. 2007; Noeske et al. 2007; Salim et al. 2007). As both relations are intrinsically related to the process of star formation and thus to galaxy evolution as a whole, and because they are fundamental ingredients of theoretical models and simulations, they have been intensively studied in the past (e.g. Tan 2000; Boissier et al. 2003; Springel & Hernquist 2003; Krumholz & McKee 2005; Rodighiero et al. 2011; Kennicutt & Evans 2012; Krumholz, Dekel & McKee 2012; Whitaker et al. 2012; Kashino et al. 2013; Hopkins et al. 2014; Speagle et al. 2014; Genzel et al. 2015; Schreiber et al. 2015; Kurczynski et al. 2016; Tacchella et al. 2016; Santini et al. 2017; Orr et al. 2018; Pearson et al. 2018; Morselli et al. 2019; Popesso et al. 2019).

The KS law relates the fuel of star formation to its end product, stars; its shape has important effects on the depletion time of the gas (t_depl = M_gas/SFR, with M_gas the total gas mass), or equivalently on the efficiency of the star formation process (SFE = t_depl ⁻¹ = SFR/M_gas). In one of the earliest works, Kennicutt (1998) finds a super-linear correlation (slope = 1.4–1.5) between the total gas and the SFR surface densities. Following this result, several papers investigate the relation between star formation and gas availability, considering different gas phases and star formation tracers, as well as exploring this link at different cosmic epochs (e.g. Wyder et al. 2009; Genzel et al. 2010; Tacconi et al. 2010; Genzel et al. 2012). Bigiel et al. (2008), Leroy et al. (2008), Leroy et al. (2013), and Schruba et al. (2011) exploit molecular and neutral gas observations of nearby galaxies to investigate how the relation between gas and star formation activity varies within galaxies and as a function of local and integrated properties. Overall, their findings indicate that the connection between star formation and molecular gas is a linear relation (i.e. slope ∼1), thus implying a constant molecular SFE and t_depl (around 2.2 Gyr). Leroy et al. (2013) find second-order variations in the molecular gas t_depl and study how some of them can be related to variations in the α_CO conversion factor between CO luminosity and H₂ mass, while further variability might arise as a consequence of galaxy properties. Bigiel et al. (2010), instead, study the relation between recent SF activity and H i outside the optical disc, in regions where H i represents the totality of the ISM, and find significant spatial correlation between FUV (tracing recent dust-unobscured star formation) and H i density. They also find that the SFE (t_depl) decreases (increases) with increasing radius. Similarly, Roychowdhury et al. (2015) study the spatially resolved KS relation on sub-kpc and kpc scales in the H i-dominated regions of nearby spirals and irregular galaxies and find that gas consumption time-scales are longer compared to H₂-dominated regions (lower SFE). Other works investigated, at earlier cosmic epoch, the spatially resolved (e.g. Freundlich et al. 2013; Genzel et al. 2013) and integrated (Freundlich et al. 2019) KS relation. In particular, Freundlich et al. (2019) obtain a linear galaxy-averaged molecular KS relation, implying that galaxies at different cosmic epochs have similar star formation time-scales. This is consistent with the results of Peng & Renzini (2020), which find that the sSFR (SFR/M_⋆) and M|$_{\rm H_2}$|/M_⋆ have the same redshift evolution, thus implying a linear KS law. On the other hand, galaxy-to-galaxy variations in the molecular gas–star formation relation have also been reported. For example, Ford et al. (2013), Shetty, Kelly & Bigiel (2013), Shetty, Clark & Klessen (2014b), and Shetty et al. (2014a) find evidence for a sub-linear relation within galaxies and for the combined samples. Also, Casasola et al. (2015) find galaxy-to-galaxy variations of the spatially resolved KS relation, and underline that the slope can be both sub-linear and super-linear, depending on the spatial scale. de los Reyes & Kennicutt (2019) revisit the integrated KS law in local, normal star-forming galaxies and find that spirals lie on a tight log-linear relation with slope 1.41 ± 0.07 (when considering both the neutral and molecular gas) while dwarfs populate the region below it.

The second fundamental relation, the MS, relates stars that have already formed to the ongoing SFR. The existence of the MS up to z ∼ 4 (characterized by a non-evolving slope and scatter and an increasing normalization with increasing redshift, e.g. Speagle et al. 2014; Popesso et al. 2019) was interpreted in the framework of gas-regulated galaxy evolution, according to which galaxies grow along the MS thanks to the continuous replenishment of their gas supply (e.g. Dekel et al. 2009; Bouché et al. 2010; Lilly et al. 2013). The observation of outliers located above the MS relation (starburst are generally classified in literature as galaxies having an SFR that is a factor of 4 higher that the MS value at fixed stellar mass, e.g. Rodighiero et al. 2011) at different cosmic epochs sparkled the interest on whether these sources: (i) have larger gas reservoirs [thus a higher gas fraction, f_gas = M_gas/(M_gas + M_⋆), e.g. Lee et al. 2017], (ii) are more efficient in converting gas into stars (thus a higher SFE, e.g. Solomon et al. 1997; Daddi et al. 2010; Silverman et al. 2015, 2018; Ellison et al. 2020a), or (iii) a combination of both (e.g. Saintonge et al. 2011a, 2012; Huang & Kauffmann 2014; Scoville et al. 2017; Tacconi et al. 2018). In the recent years, the advent of large integral field spectroscopic (IFS) surveys revealed that the integrated MS relation originates at smaller scales (up to the sizes of molecular clouds), thus implying that the star formation process is regulated by physical process that act on sub-galactic scales (Cano-Díaz et al. 2016; Abdurro’uf & Akiyama 2017; Hsieh et al. 2017; Lin et al. 2017; Hall et al. 2018; Medling et al. 2018; Cano-Díaz et al. 2019; Vulcani et al. 2019; Bluck et al. 2020; Enia et al. 2020). Despite a general consensus on the existence of the spatially resolved MS, the slope, intercept, and scatter of the relation vary significantly among different works, depending on the sample selection, SFR indicator, dust correction, and fitting procedure. Moreover, some authors find that the spatially resolved relation vary dramatically from galaxy to galaxy. Recently, the combination of MaNGA (Mapping Nearby Galaxies at APO, Bundy et al. 2015) and ALMaQUEST (the ALMA-MaNGA QUEnching and STar formation survey) allowed the study of the link between the spatially resolved MS and gas reservoirs and the investigation of the nature of starburst regions within galaxies. By analysing 14 MS galaxies, Lin et al. (2019) suggest that the MS relation originates from two more fundamental relations: the molecular KS and the so-called MGMS, a relation between Σ_⋆ and Σ_H2. Ellison et al. (2020b) exploit 34 galaxies in ALMaQUEST to study the nature of variations in the SFR on kpc scales. They find that while the average SFR is regulated by the availability of molecular gas, the scatter of the spatially resolved MS (and thus variations with respect to the average SFR value) originates in variations of the SFE. Dey et al. (2019), using optical IFU and CO observations collected in the EDGE-CALIFA survey (CARMA Extragalactic Database for Galaxy Evolution Bolatto et al. 2017, see also Barrera-Ballesteros et al. 2020), find that Σ_SFR is a function of both Σ_⋆ and |$\Sigma _{\rm H_2}$|⁠, but different from Lin et al. (2019), the relation with the stellar mass is statistically more significant than the one with the molecular gas. Early works on the formation of molecular hydrogen in the ISM, such as Elmegreen (1993) and Blitz & Rosolowsky (2006), have underlined the role of the disc hydrostatic pressure, and hence of Σ_⋆, in promoting the formation of molecules. Also the works of Shi et al. (2011) and Shi et al. (2018), that propose an extended KS law expressed as a proportionality between Σ_SFE and Σ_⋆, emphasize the role of existing stars in setting the current production of stars, which indeed is the very nature of the MS.

In this paper, we build on the work presented in Enia et al. (2020, hereafter Paper I) and analyse the sub-kpc relation between the surface densities of star formation, gas in different phases, and stellar mass in five local grand-design spirals. In Paper I, we exploit multiwavelength observations in more than 20 photometric bands to obtain spatially resolved estimates of Σ_⋆ and Σ_SFR on different physical scales, from few hundred parsecs to 1.5 kpc, via SED fitting. We use these estimates to study the spatially resolved MS relation and find the slope to be consistent for different spatial scales, as well as with the slope of the integrated relation. Here, we aim at analysing under which gas properties different spatial regions populate different loci of the spatially resolved MS, thus trying to understand whether the SFR is more connected to the gravity of the disc (dominated by stars up to ∼2/3 of the optical radius) or with the availability of fuel, or a combination of both. We exploit observations in more than 20 photometric bands to derive accurate SFR and M_⋆ maps to compare to H i and H₂ maps. We discuss the origin of the spatially resolved MS, in terms of its slope and scatter.

The structure of the paper is the following. In Section 2, we give a short description of the data used in this work; in Section 3, we present our results at 500 pc resolution; in Section 4, we analyse the implications of our results on the existence of the MS relation and on how SFE and f_gas vary with varying SFR. Finally, in Section 5 we summarize our findings. The assumed IMF is Chabrier (2003), cosmology is ΛCDM with parameters from Planck Collaboration XIII (2016).

2 DATA

This work is based on multiwavelength observations of five nearby face-on spiral galaxies: NGC 0628, NGC 3184, NGC 5194, NGC 5457, and NGC 6946. Four out of five galaxies are in common with Paper I: they are the ones observed in 23 photometric bands, and included in the THINGS and HERACLES surveys. NGC 6946 was initially excluded from the Paper I sample, since it lacked optical observations (the five Sloan optical filters). We tested for the sample in Paper I how the SED fitting routine results change excluding these five photometric points, finding that they are nearly unchanged. Following this, we are including NGC 6946 in this analysis. The observations in 23 different bands (18 for NGC 6946) have been collected in the DustPedia ¹ (Davies et al. 2017; Clark et al. 2018) archive; more details on the data set can be found in Paper I and references therein. The main properties of the galaxies in this sample are shown in Table 1. We highlight two properties of our sample: (i) according to the integrated SFR and M_⋆ values, the objects in our sample are MS galaxies, located within 0.2 dex from the relation obtained in Paper I, and (ii) three out of five sources are classified as SAB spirals (NGC 3184, NGC 5457, and NGC 6946), thus show evidence of a bar component.

Table 1.

Properties of the galaxies in our sample: (1) galaxy name; (2,3) RA and Dec coordinates in J2000; (4) total M_⋆ from SED fitting; (5) total SFR computed from equation (1) with L_UV and L_IR from SED fitting; (6,7) distance in Mpc and radius in kpc at which the optical surface brightness falls below 25 mag arcsec⁻², both taken from the HyperLEDA data base; (8) total H i mass in R₂₅; (9) total H₂ mass in R₂₅; (10) morphological T type, taken from HyperLEDA; (11) central metallicity computed using the O3N2 index, and taken from the DustPedia archive.

Galaxy name	RA	Dec.	logM⋆	SFR	D	R25	logMH i	logM|$_{\rm H_2}$|	T	12 + log(O/H)
	(deg)	(deg)	(M⊙)	(M⊙ yr−1)	(Mpc)	(kpc)	(M⊙)	(M⊙)
NGC 0628 (M74)	24.174	15.7833	10.31 ± 0.15	1.78 ± 0.41	10.14	14.74	9.54 ± 0.18	9.39 ± 0.20	5.2	8.693 ± 0.001
NGC 3184	154.5708	41.4244	10.13 ± 0.10	1.02 ± 0.10	11.64	12.55	9.38 ± 0.14	9.20 ± 0.24	5.9	8.766|$^{+0.014}_{-0.013}$|
NGC 5194 (M51a)	202.8025	47.1952	10.74 ± 0.20	3.68 ± 0.26	8.59	17.23	9.43 ± 0.17	9.86 ± 0.22	4.0	8.824|$^{+0.017}_{-0.016}$|
NGC 5457 (M101)	210.8025	54.3491	10.37 ± 0.13	3.00 ± 0.15	7.11	24.81	10.15 ± 0.14	9.41 ± 0.18	5.9	8.528|$^{+0.006}_{-0.007}$|
NGC 6946	308.71905	60.15361	10.61 ± 0.13	3.51 ± 0.15	6.73	24.81	9.41 ± 0.15	9.74 ± 0.17	5.9	8.746|$^{+0.067}_{-0.070}$|

2.1 SFRs, stellar mass, and distance from the MS

The spatially resolved measurements at 500 pc resolution of Σ_⋆, Σ_SFR, and distance from the MS (Δ_MS), have been obtained following the procedure presented in Paper I. Briefly, we select 8 nearby, face-on, grand design spiral MS galaxies with log M_⋆ ∼ 10.4–10.6 M_⊙, and perform spatially resolved SED fitting to 23 photometric bands using magphys (da Cunha, Charlot & Elbaz 2008). In particular, we performed SED fitting on cells having two different side measurements: 8 arcsec (thus a varying physical scale between 290 and 700 pc, depending on the distance of the galaxies) and 1.5 kpc. Here, we implement an improved procedure and performed SED fitting at a common resolution of 500 pc (as discussed in Paper I, these scales are higher than the ones where the energy-balance criterion holds, ∼200–400 pc). The procedural improvements are the following: (i) we estimate the noise on the photometry of each cell from the rms maps (while in Paper I we used the DustPedia photometry signal-to-noise ratio); (ii) if a cell has more than 10 bands with SNR < 2 it is automatically excluded from the SED fitting procedure, thus reducing computational time. These improvements influence the χ² estimation in magphys, increasing the number of accepted points within the optical radius, and leading to cleaner results in the outer part of galaxies, where the photometry is fainter. The slope and intercept of the spatially resolved MS given in Paper I do not change when these improvements are implemented in the pipeline.

In each cell, the SFR is computed as the sum of unobscured (SFR_UV) and obscured (SFR_IR) star formation activity, obtained using the relations of Bell & Kennicutt (2001) and Kennicutt (1998) (reported to Chabrier IMF):

$$\begin{eqnarray*} {\rm SFR} = 0.88\times 10^{-28}L_{\rm {UV}} + 2.64\times 10^{-44}L_{\rm IR}, \end{eqnarray*}$$

(1)

where L_UV and L_IR are taken from the best-fitting SED and are the luminosity (in erg s⁻¹ Hz⁻¹) at 150 nm and the one (in erg s⁻¹) integrated between 8 and 1000 μm, respectively. As shown in fig. 3 of Paper I, the SFR computed following equation (1) and the one that magphys gives as output are highly consistent. Here, for consistency with Paper I, we use the SFRs estimated with equation (1), but the results would not change when considering the SFRs given as output of the SED-fitting procedure.

As the sample of galaxies used here differs from the one of Paper I, we decided to recompute the spatially resolved MS for this sample, but following the same procedure, i.e. (1) by fitting with a log-linear relation the median values of logΣ_SFR in bins of logΣ_⋆, using emcee (Foreman-Mackey et al. 2013) and considering 10 bins in the logΣ_⋆ range [6.5:8.5] M_⊙ pc⁻², plus an additional bin to include the few points between [8.5:9.5] M_⊙ pc⁻², and (2) by implementing an orthogonal distance regression (ODR) technique. The slope and intercept of the MS are 0.76(±0.20) and −8.15(±1.63) with the first method, and 0.87(±0.01) and −8.94(±0.06) with the second. These estimates are consistent with the ones in Paper I. In the following analysis we make use of the distance from the MS relation computed with the binning technique, but our results do not change when considering the ODR MS relation.

For each region, we compute the distance from the MS as the difference between log Σ_SFR and the MS value (in log) estimated for the Σ_⋆ of the region, thus Δ_MS = log Σ_SFR − (0.76log Σ_⋆ − 8.15). The left-hand panel of Fig. 1 shows, as an example, the Δ_MS map of NGC 0628; cells in red are located below the spatially resolved MS, while the ones in blue are located above the relation (the Δ_MS maps of the other galaxies in the sample are shown in Appendix  B). Within the optical radius (the dashed circle), we are able to recover most of the cells, especially at r < 0.9 R₂₅.² We emphasize here that the MS relation we obtain is well defined also in the outer parts of the optical disc, where the SFR and M_⋆ are small in absolute values. We refer the reader to Paper I for details on the SED-fitting procedure, as well as for how the spatially resolved MS relation is obtained.

Figure 1.

Spatially resolved properties of NGC 0628: Δ_MS in the left-hand panel, log Σ_H i in the central panel, and |$\log \Sigma _{\rm H_2}$| in the right-hand panel. The dashed circle has a radius equal to the optical radius of the galaxy, R₂₅. In the left-hand and right-hand panels, small dots are the cells where the SED fitting is characterized by a large χ² and are thus rejected. In the central panel, the dotted points are the ones with measured log Σ_H i but no (or rejected) Δ_MS.

2.2 Neutral gas: H i 21 cm observations

Neutral hydrogen mass surface densities (Σ_H i) are measured from 21cm maps available from the THINGS survey (The H i Nearby Galaxy Survey; Walter et al. 2008). These observations have been carried out with the Very Large Array (VLA) and are characterized by a high angular resolution (6 arcsec and 10 arcsec in the robust and natural weighting, respectively). To compute the H i surface brightness, Σ_H i, we first convolve the 21 cm natural-weighted intensity maps, given in Jy beam⁻¹ m s⁻¹, to the resolution of the worst of the 23 photometric bands used in the SED fitting (the one of SPIRE350, 24 arcsec, see Paper I) using a Gaussian kernel. We used the beam sizes given in table 2 of Walter et al. (2008) and equation 1 to obtain the flux in K km s⁻¹ and then estimate Σ_H i from equation  5 of Walter et al. (2008) (that does not include a correction for helium). We compute the sensitivity limit from our maps of Σ_H i at 500 pc resolution and find |$\Sigma _{\rm H\,{\small I},lim}\, \sim 2$|  M_⊙ pc⁻². The central panel of Fig. 1 shows the distribution of Σ_H i in NGC 0628. As in several other spiral galaxies, the H i is centrally depressed (e.g. Casasola et al. 2017), and it extends on radius that are significantly larger that the optical radius (Swaters et al. 2002; Wang et al. 2013). The values of M_H i within R₂₅ are reported in Table 1. For the galaxies in our sample, the H i gas-to-stellar mass ratio (M_H i/M_⋆) within R₂₅ varies from 5 per cent to 60 per cent.

2.3 Molecular gas: CO observations

The molecular gas surface density, |$\Sigma _{\rm {H_2}}$|⁠, is computed using the ¹²CO(2−1) intensity maps from the HERACLES survey (The HERA CO-Line Extragalactic Survey; Leroy et al. 2009). These observations were made with the IRAM 30 m telescope and have an angular resolution of 11 arcsec. As for Σ_H i, we convolve the images using a Gaussian kernel to the resolution of SPIRE350. We estimated |$\Sigma _{\rm {H_2}}$| using equation  4 of Leroy et al. (2009), considering a metallicity independent conversion factor X_CO (X_CO = N(H₂)/I_CO, where N(H|$\rm {_2}$|⁠) is the H|$\rm {_2}$| column density and I_CO is the line intensity) equal to 2 × 10²⁰ cm⁻²(K km s⁻¹)⁻¹ (the typical value for disc galaxies, see e.g. Bolatto, Wolfire & Leroy 2013), and a CO line ratio I_CO(2−1)/I_CO(1−0) = 0.8 (e.g. Leroy et al. 2009; Schruba et al. 2011; Casasola et al. 2015). We divide by a factor of 1.36 that is included in equation  4 of Leroy et al. (2009) to remove the helium contribution. In Section 3 we show that the results presented here remain true when considering a metallicity-dependent X_CO factor, using the X_CO−(12 + log O/H) relation of Genzel et al. (2011) and the spatially resolved metallicity measurements collected in DustPedia. The sensitivity limit, computed as the rms of our log|$\Sigma _{\rm H_2}$| maps at 500 pc resolution, is log|$\Sigma _{\rm H_2,\, lim}$| = 0.4 M_⊙ pc⁻². For the regions corresponding to a negative flux of ¹²CO(2 − 1), in the |$\Sigma _{\rm H_2,\, lim}$| map we replace the value with a randomly generated number between 0 and the sensitivity limit, so that |$\Sigma _{\rm H_2}$| can be computed as an upper limit. While this step does not influence our results concerning H₂, it allows us to extend the analysis also to the regions where H₂ is not detected. The right-hand panel of Fig. 1 shows the distribution of |$\Sigma _{\rm H_2}$| in NGC 0628. The H₂ is centrally concentrated, and mostly below the sensitivity limit for r > 0.5R₂₅. For the galaxies in our sample, the H₂ gas-to-stellar mass ratio (M|$_{\rm H_2}$|/M_⋆) within R₂₅ is almost constant around 11–14 per cent.

3 RESULTS

Before analysing the spatially resolved connection between star formation and gas components, we briefly comment on the integrated properties of the galaxies in our sample. It is worth underlying that, within R₂₅, three out of five galaxies have similar amount of neutral and molecular gas (M|$_{\rm H_2}$| and M_H i), within the uncertainties. This is consistent with the results of Casasola et al. (2020), as they find that, within R₂₅, galaxies with morphological type T = 4, 5, 6 have M|$_{\rm H_2}$|/M_H i = 0.91, 1, and 1.05, respectively. For NGC 5457 and NGC 5194, the average value associated with their morphological type does not describe well their gas properties. It is well know that NGC 5457 is likely to have experienced a recent event of gas accretion (Mihos et al. 2013; Vílchez et al. 2019) which can explain the H i rich outer disc and its high total H i mass. A high molecular gas mass fraction, as for NGC 5194, is likely the result of tidal stirring by a companion.

3.1 Dependency of the SFR on gas

With the data set in our hands, we first investigate the spatially resolved relations between the SFR and the different gas phases, by analysing how Σ_SFR relates to Σ_H i, |$\Sigma _{\rm H_2}$|⁠, and Σ_gas. This last quantity is computed as the sum of the neutral and molecular component for all the regions where the |$\Sigma _{\rm H_2}$| is above the sensitivity limit, while it is equal to |$\Sigma _{\rm H_I}$| otherwise, and it is thus a lower limit. The results of this exercise are shown in Fig. 2.

Figure 2.

Relations between Σ_SFR and Σ_H i (left-hand panel), |$\Sigma _{\rm H_2}$| (middle panel), and Σ_gas (for the total H i+H₂ gas, right-hand panel) colour coded as a function of the median value of Δ_MS in each bin. Only bins containing a minimum number of three cells are shown in the plot. The dashed contours encircle the areas of the plane containing from 10 per cent to 90 per cent of the data, at steps of 10 per cent. The sensitivity limits are represented by the dot–dashed black lines. The purple solid lines in the middle and right-hand panel represent the best fit to the data obtained fitting the points marked with crosses; the corresponding slope (N) and intercept (A) are written in the panels, together with the Spearman correlation coefficient r. In the central panel, the dotted lines mark constant molecular t_depl of 10⁸, 10⁹, and 10¹⁰ yr from top to bottom. In the right-hand panel, the dashed black line is the fit to local ULIRGs and SMGs taken from Daddi et al. (2010).

As expected, no significant correlation is found between Σ_SFR and Σ_H i (Spearman correlation coefficient r = 0.26), while tight correlations are present between Σ_SFR and |$\Sigma _{\rm H_2}$|⁠, and Σ_SFR and Σ_gas (r = 0.76), confirming several results in the literature (e.g. Bigiel et al. 2008; Kumari, Irwin & James 2020). In Fig. 2, we add the information on how regions located at different distance from the spatially resolved MS populate the logΣ_SFR − log|$\Sigma _{\rm H\,{\small I}/H_2/gas}$| plane. To do so, we divide the logΣ_SFR−log|$\Sigma _{\rm H\,{\small I}/H_2/gas}$| planes in bins colour coded according to the median value of Δ_MS in each bin. We observe that regions above the MS are found in correspondence to the highest Σ_H i, but span a wide range of |$\Sigma _{\rm H_2}$| values. Analogously, regions located below the MS are preferentially found at lower Σ_H i, while are characterized by |$\Sigma _{\rm H_2}$| spanning the whole range of possible values. For logΣ_SFR > −2, the trend between logΣ_H i and Δ_MS is less evident; this is due to the fact that we are not well sampling the region below the MS, as shown in fig. 5 of Paper I, and confirmed by the decrease of the scatter of the spatially resolved MS at the higher stellar surface densities. Analogously, the points with logΣ_SFR < −3 are mostly found on the MS or below it, thus hiding a possible trend at the lowest SFRs. When considering the total gas, we see that regions closer to the relation that describes local Ultra-Luminous IR Galaxies (ULIRGs) and sub-mm galaxies (dashed black lines, taken from Daddi et al. 2010) are the ones located above the relation. On the other hand, the general behaviour between the distance from the best-fitting relation and the distance from the MS is less regular than in the case of molecular gas. Indeed, the central panel of Fig. 2 suggests that the spatially resolved MS is intrinsically linked to the molecular gas–SFR relation, as MS regions (in white) fall very consistently along the logΣ_SFR–log|$\Sigma _{\rm H_2}$| relation. Regions that populate the upper (lower) envelope of the molecular KS law are also found in the upper (lower) envelope of the spatially resolved MS relation. This is qualitatively consistent with what found by Ellison et al. (2020b) when analysing the molecular gas–SFR relation exploiting ALMA and MaNGA data on kpc scales.

By fitting the average values of logΣ_SFR in bins of log|$\Sigma _{\rm H_2}$| and logΣ_gas (both above the sensitivity limit of log|$\Sigma _{\rm H_2}$|⁠), we find the following scaling relations (slopes N and intercepts A are also written in the corresponding panels):

$$\begin{eqnarray*} \log \Sigma _{\rm SFR} = 0.80(\pm 0.12)\times \log \Sigma _{\rm H_2}-2.97(\pm 0.85) \end{eqnarray*}$$

(2)

and

$$\begin{eqnarray*} \log \Sigma _{\rm SFR} = 1.21(\pm 0.18)\times \log \Sigma _{\rm gas}-3.74(\pm 1.15) \end{eqnarray*}$$

(3)

The two correlations have equal strength according to the Spearman coefficient, and their scatter is in both cases smaller than the one of the spatially resolved MS: 0.19 for the log|$\Sigma _{\rm H_2}$|–logΣ_SFR relation and 0.17 for the logΣ_gas–logΣ_SFR. The relation between logΣ_SFR and log|$\Sigma _{\rm H_2}$| is sub-linear, but becomes linear when the ODR fitting is applied. We retrieve a molecular t_depl that varies between 1.6 and 3 Gyr. These results are in agreement with the typicalt_depl in normal spiral galaxies (see e.g. Bigiel et al. 2008; Saintonge et al. 2011b; Leroy et al. 2013; Casasola et al. 2015). It is worth noticing that the slope of the spatially resolved KS relation obtained from the molecular and total gas are consistent, within errors, with the integrated relations (e.g. Genzel et al. 2010; Kennicutt & Evans 2012; Tacconi et al. 2013; de los Reyes & Kennicutt 2019; Freundlich et al. 2019), similar to what is found when comparing the spatially resolved and integrated MS relation. The scatter of the integrated relation is instead significantly higher (e.g. 0.28 in de los Reyes & Kennicutt 2019).

Finally, we underline here that the trends observed in Fig. 2 are not driven by one or few of the galaxies in our sample, but by and large are common to all five galaxies in our sample. Slope and intercept of the |$\log \Sigma _{\rm {H_2}}$|–log Σ_SFR and log Σ_gas–log Σ_SFR relations are summarized in Table 2.

Table 2.

Slope, intercept, and scatter of the following relations: molecular KS law, log Σ_gas–log Σ_SFR, MGMS, and log Σ_⋆–log Σ_gas. We list the best-fitting parameters for |$\log \Sigma _{\rm H_2}$| computed using a constant XCO factor and a metallicity dependent XCO obtained from estimates of the metallicity that use (1) the N2 index and (2) the O3N2 index.

Correlation	Slope			Intercept			Scatter
	Const αCO	O3N2	N2	Const αCO	O3N2	N2	Const αCO	O3N2	N2
|$\log \Sigma _{\rm H_2}$|–log ΣSFR	0.80 ± 0.12	0.83 ± 0.12	0.83 ± 0.11	−2.97 ± 0.87	−2.97 ± 0.93	−2.94 ± 0.94	0.19	0.20	0.19
log Σgas–log ΣSFR	1.21 ± 0.18	1.24 ± 0.16	1.25 ± 0.18	−3.74 ± 1.15	−3.74 ± 1.15	−3.73 ± 1.14	0.17	0.18	0.18
log Σ⋆–|$\log \Sigma _{\rm H_2}$|	0.91 ± 0.29	0.84 ± 0.29	0.87 ± 0.27	−6.15 ± 2.11	−5.66 ± 2.12	−5.93 ± 2.07	0.22	0.24	0.23
log Σ⋆–log Σgas	0.50 ± 0.14	0.49 ± 0.14	0.49 ± 0.13	−2.64 ± 0.97	−2.62 ± 1.08	−2.72 ± 1.05	0.24	0.25	0.25

3.2 Dependence of gas distribution on stellar mass

As the trends shown in Fig. 2 with Δ_MS are related to variations of the gas content with M_⋆, we show in Fig. 3 how the surface densities of neutral, molecular, and total gas vary as a function of Σ_⋆. The left-hand panel of Fig. 3 shows that a very weak anticorrelation is found between logΣ_⋆ and logΣ_H i. Indeed, when fitting the average values of log Σ_H i in bins of log Σ_⋆, the slope of the correlation is −0.11 ± 0.07. We stress that every galaxy shows a trend of decreasing Σ_H i towards the central regions, as in the central region the high pressure favours the H i to H₂ transition and most of the gas is in molecular form, but such a decrease can be more or less pronounced from galaxy to galaxy, and does not follow a universal behaviour. Starbursting regions are preferentially located at r > 0.5R₂₅, where the surface density of stars falls below 10⁷ M⊙ pc⁻², and are generally found along the spiral arms.

Figure 3.

Distributions of the regions in the log Σ_⋆–log Σ_H i plane (left-hand panel), log Σ_⋆–|$\log \Sigma _{\rm H_2}$| plane (central panel) and log Σ_⋆–log Σ_gas plane (right-hand panel). Each hexagonal bin the plane has been colour coded according to the average value of Δ_MS, as in Fig. 2. The purple solid lines are the best-fitting relations obtained by fitting the average values of log|$\Sigma _{\rm H\,{\small I},H_2,gas}$| in bins of log Σ_⋆, as marked with black crosses; the slope (N) and intercept (A) of the best fit are written in the panels, together with the Spearman correlation coefficient r. The green dashed line in the central panel is the MGMS of Lin et al. (2019), re-scaled to a Chabrier IMF.

The relation between log Σ_⋆ and |$\log \Sigma _{\rm H_2}$|⁠, shown in the central panel of Fig. 3, is consistently common to all five galaxies and gives birth to a very tight correlation, the MGMS (Lin et al. 2019). The MGMS (re-scaled to a Chabrier IMF) of Lin et al. (2019) is indicated with a green dashed line in the central panel of Fig. 3 and has a slope of 1.1. To obtain the slope of our MGMS relation, we fit the average values of |$\log \Sigma _{\rm H_2}$| in bins of log Σ_⋆, restricting the analysis to stellar surface densities where the average value of |$\log \Sigma _{\rm H_2}$| is above the sensitivity limit. We find

$$\begin{eqnarray*} \log \Sigma _{\rm H_2} = 0.91(\pm 0.29)\times \log \Sigma _{\star }-6.15(\pm 2.11). \end{eqnarray*}$$

(4)

This relation has a scatter of 0.22 dex, similar to that obtained for the MS (0.23 dex), and the Spearman coefficient is the same as for the |$\log \Sigma _{\rm {H_2/gas}}$|–log Σ_SFR relations. We find a slope that is consistent within the error with the one of Lin et al. (2019), i.e. 1.1. The different slopes can be ascribed to different fitting procedures; indeed, if we follow the ODR method, we also retrieve a super-linear slope. Regions with the largest sSFR are located in the upper envelope of this relation; in other words, cells located above the spatially resolved MS are also located above the log Σ_⋆–|$\log \Sigma _{\rm H_2}$| relation. This trend, outlined also in Ellison et al. (2020b), is here as significant as the one visible in Fig. 2 for the molecular KS relation.

A correlation is also apparent between log Σ_⋆ and log Σ_gas, that is the combination of the two behaviours seen in the left and central panel of Fig. 3. At low Σ_⋆ (log Σ_⋆ ≲ 7), the H i tends to dominate over H₂, and the scatter of the relation is larger, while it is slightly narrower at large Σ_⋆. This combined behaviour results in a slope of 0.50 ± 0.14 and an intercept of −2.64 ± 0.97, and a Spearman coefficient of 0.54. Slope and intercept of the log Σ_⋆–log Σ_gas and log Σ_⋆–|$\log \Sigma _{\rm H_2}$| relations are summarized in Table 2.

3.3 H i and H₂ in the Σ_⋆–Σ_SFR plane

To further analyse the link between the atomic, molecular, and total gas and the star formation properties of a region, we show in Fig. 4 how logΣ_H i and log|$\Sigma _{\rm H_2}$| vary across the logΣ_⋆–logΣ_SFR plane. In the two left-hand panels of Fig. 4, we show the logΣ_⋆–logΣ_SFR plane colour coded as a function of the average logΣ_H i (top) and log|$\Sigma _{\rm H_2}$| (bottom) values in each bin. The spatially resolved MS is indicated with the black solid line. To compute the average value of log|$\Sigma _{\rm H_2}$|⁠, we also used values below the sensitivity limit; therefore, it is important to emphasize that H₂ is detected only for |$\Sigma _{\rm H_2}$| above ∼3 M_⊙ pc⁻² that requires a Σ_⋆ higher than 10⁷ M_⊙ kpc⁻². On the other hand, H₂ column densities below this threshold value are hardly self-shielded and quite rare (e.g. Sternberg et al. 2014).

Figure 4.

H i and H₂ in the logΣ_⋆–logΣ_SFR plane. Top left-hand panel: logΣ_⋆–logΣ_SFR plane colour coded as a function of the average value of logΣ_H i in each bin. The black sold line marks the location of the spatially resolved MS relation. Top right-hand panel: Δ_MS, as a function of logΣ_H i. The average values of Δ_MS computed in bins of logΣ_H i are shown in green. Each bin is colour coded as a function of the number of cells that it contains. Bottom left-hand panel: logΣ_⋆–logΣ_SFR plane colour coded as a function of the average value of log|$\Sigma _{\rm H_2}$| in each bin. The black sold line marks the location of the spatially resolved MS relation. Bottom right-hand panel: Δ_MS, as a function of log|$\Sigma _{\rm H_2}$|⁠. The average values of Δ_MS computed in bins of log|$\Sigma _{\rm H_2}$| are shown in green. Each bin is colour coded as a function of the number of cells that it contains. In the right-hand panels, the grey shaded area marks the MS region.

Interestingly, along the MS relation the average value of logΣ_H i is fairly constant and equal to about 7 M_⊙ pc⁻² that corresponds to an H i column density of about 9 × 10²⁰ cm⁻². This indicates that for cells on the MS, the radiation field is strong enough to partially dissociate H₂, and large amounts of dust-rich H i gas prevent further H₂ dissociation (Sternberg et al. 2014). As expected, |$\Sigma _{\rm H_2}$| increases with increasing M_⋆, following the MGMS relation, suggesting that the gravity dominated by stars compresses and enhances the ISM volume density, thus favouring the formation of molecules. The upper envelope of the MS is populated by cells that, on average, have larger H i surface densities than counterparts located on the relation and below it. Focusing on H₂, we can see that no variations in log|$\Sigma _{\rm H_2}$| are visible perpendicular to the MS relation, while a weak trend on increasing log|$\Sigma _{\rm H_2}$| towards higher logΣ_SFR can be seen at fixed stellar surface density. For example, at logΣ_⋆ = 7.5 the average value of log|$\Sigma _{\rm H_2}$| on the MS is 0.8 M⊙ pc⁻², and increases to ∼1.35 M⊙ pc⁻² 0.8 dex above the relation. Following equation (2), this variation in log|$\Sigma _{\rm H_2}$| would correspond to a difference in logΣ_SFR of ∼0.5 dex, implying that the increase in H₂ seen at fixed stellar surface densities is not sufficient alone in setting large SFR. In the right-hand panels of Fig. 4, we show the distance from the spatially resolved MS plotted as a function of logΣ_H i (top) and log|$\Sigma _{\rm H_2}$| (bottom). As indicated qualitatively from Fig. 2, we observe a correlation between logΣ_H i and Δ_MS, for which regions located above the MS are characterized by the largest H i surface brightness, while regions below the MS correspond to cells with low logΣ_H i. We do not observe any correlation between log|$\Sigma _{\rm H_2}$| and Δ_MS. This is the combination of the two previous results: (1) the molecular KS relation is populated by regions on the MS and (2) the existence of the MGMS. This suggests that the absolute quantity of molecular gas in a region (or, equivalently its surface density) is not related to the sSFR of the region itself.

3.4 Dependence of the results on metallicity

A possible source of uncertainty in this work is the dependence of the conversion factor between CO and H₂ on gas-phase metallicity (α_CO). Indeed, several works have shown that α_CO varies strongly as a function of the metallicity (e.g. Bolatto et al. 2013), and strong metallicity gradients have been found in some of the galaxies in this sample, as well as in larger samples of local star-forming galaxies (Ho et al. 2014; Chiang et al. 2018; Vílchez et al. 2019), reaching a factor of 10 within the optical radius. From an integrated perspective, instead, Genzel et al. (2015) find that α_CO varies little within ±0.6 dex of the MS (thus for the large majority of the cells in this work). Nevertheless, such variations in metallicity need to be addressed properly in order to avoid biased interpretations of spatially resolved results. From the DustPedia archive, we download the table containing all the metallicity measurements available in literature (De Vis et al. 2019) and obtain in regions within R₂₅ of the five galaxies in our sample. For NGC 5457, there are 280 estimates of metallicity within the optical radius, while for NGC 6946 only 14 are available. In particular, we make use of the metallicities computed exploiting the N2 and O3N2 calibrations of Pettini & Pagel (2004).³ In particular, N2 is defined as |$\log ([{\rm N}\, {\rm{\small II}}_{6583A} / {\rm H}_{\,\alpha })$| and O3N2 as |$\log [([{\rm O}\, \rm {{\small III}}]_{5007A} / \rm H_{\beta }) / ([{\rm N}\, {\rm{\small II}}]_{6583A} / {\rm H}_{\alpha })]$|⁠. With the conversion relations of Kewley, Geller & Jansen (2004), we obtain the metallicities in the Denicoló, Terlevich & Terlevich (2002) calibration. For each galaxy, we then build a 1D metallicity profile by fitting the different measurements. We use the 1D metallicity profile to obtain a 2D map of the metallicity dependent α_CO factor exploiting the relation of Genzel et al. (2012), that is obtained by fitting the z ∼ 0 points of Leroy et al. (2011) with z > 1 ones collected in Genzel et al. (2012):

$$\begin{eqnarray*} \log \alpha _{\rm CO} = -1.3\times (12+\log \rm (O/H))_{\rm Denicolo02} + 12. \end{eqnarray*}$$

(5)

With the 2D map of log α_CO, we then estimate |$\Sigma _{\rm H_2}$|⁠. Fig. 5 shows a comparison of the molecular gas surface density computed considering a constant α_CO and the metallicity dependent one (in particular, the one obtained with the O3N2 calibration, but no significant differences are found when considering the N2 one). The highest scatter corresponds to small |$\Sigma _{\rm H_2}$|⁠, located in the outskirts of the optical disc, where the metallicity is, on average, smaller than in the centre. The source characterized by the largest scatter is NGC 5457, that is also the one with the strongest metallicity gradient (Vílchez et al. 2019). We note, nevertheless, that within 0.5 R₂₅ (i.e. in first approximation, the distance within which the estimate of |$\Sigma _{\rm H_2}$| is above the sensitivity limit), the maximum difference between the two estimates is around 0.2 dex.

Figure 5.

Comparison between the spatially resolved molecular gas mass computed with a constant α_CO factor and a metallicity dependent one (here for clarity we use the metallicity based on the O3N2 measurement; no significant differences are found when using the metallicity based on the N2 data). The points are colour coded as a function of their R/R₂₅ value. The green solid line marks the 1-to-1 relation.

We repeat the previously shown analysis considering |$\Sigma _{\rm H_2}$| estimated with the metallicity dependent α_CO. In Table  2, we report the slopes, intercepts, and scatter of the various relations discussed above: |$\log \Sigma _{\rm H_2}$|–log Σ_SFR, log Σ_gas–log Σ_SFR, log Σ_⋆–|$\log \Sigma _{\rm {H_2}}$|⁠, and log Σ_⋆–log Σ_gas. With respect to the case of constant α_CO, the slope of molecular KS relation slightly increases but not significantly given the errors on the estimates. The slope of the total gas KS law decreases to reach values closer to 1, but again this decrease is not significant when taking the errors into account. Similarly, the variations in slope and intercept of the log Σ_⋆–|$\log \Sigma _{\rm {H_2, gas}}$| relations do not vary significantly with respect to the values found in Section 3.2. The scatter of the four relations slightly increases. In particular, the scatter of the log Σ_⋆–|$\log \Sigma _{\rm {H_2, gas}}$| relations is comparable or larger than the one of the spatially resolved MS. This is expected, as we are adding several sources of uncertainty: the conversion between different metallicity calibrations, the correlation between α_CO and metallicity, as well as the fact that we are averaging the metallicity to obtain a 1D profile. In first approximation, this exercise reveals that the results in this paper are robust against variations of the α_CO factor as a function of metallicity, that is the main and most studied dependence of α_CO on physical/galaxy properties (e.g. gas temperature and abundance, optical depth, cloud structure, cosmic ray density, and UV radiation field, in addition to the metallicity). This happens because the central metallicities for the galaxies in our sample are similar, and the molecular gas maps are not deep enough to reach the outermost regions where the metallicity decrease with respect to the central value.

4 DISCUSSION

4.1 The origin of the main sequence and its scatter

The spatially resolved MS of galaxies constitutes the building block of the integrated MS relation of star-forming galaxies, so deeply analysed in literature to understand the star formation processes and the quenching mechanisms. When analysing the molecular gas component of nearby galaxies we find tighter relations than the MS itself, and that may be at the physical origin of it: the KS law (2) and the MGMS (4). By combining equations (2) and (4), we obtain a spatially resolved MS in the form

$$\begin{eqnarray*} \log \Sigma _{\rm SFR} = 0.73\times \log \Sigma _{\star }-7.89, \end{eqnarray*}$$

(6)

which, as expected, consistent with the spatially resolved MS relation characterizing our sample (log Σ_SFR = 0.76log Σ_⋆ − 8.15, see Section 2.1). We find that the |$\Sigma _{\rm H_2}$|–Σ_SFR relation is the tightest one of the three, with a scatter of 0.19 dex, followed by the Σ_⋆–|$\Sigma _{\rm H_2}$| relation, 0.22 dex, similar to the scatter of the spatially resolved MS (0.23 dex). Contrary to Lin et al. (2019), we find that the scatter of the spatially resolved MS is significantly smaller than the quadratic sum of the scatters of the Σ_⋆–|$\Sigma _{\rm H_2}$| and |$\Sigma _{\rm H_2}$|–Σ_SFR relations, indicating that the scatters of these relations are not independent. Indeed, regions located in the upper (lower) envelope of the molecular KS relation also populate the upper (lower) envelope of the MGMS. To further investigate the connection between the three relations (KS, MS, MGMS), we plot in the left-hand panel of Fig. 6 how regions with an estimate of |$\Sigma _{\rm H_2}$| above the sensitivity limit populate the 3D space made by log Σ_⋆, log Σ_SFR, and |$\log \Sigma _{\rm H_2}$| (four different projections of this space are shown in Fig. A1 in Appendix  A). The variables define a 3D relation, as found by Lin et al. (2019). This is expected, as we find no dependence of Δ_MS on |$\Sigma _{\rm H_2}$| (see Fig. 4). On the other hand, the analysis of Σ_H i in the log Σ_⋆–log Σ_SFR plane revealed that the spatially resolved MS scatter seems to be connected to the presence of neutral gas. Indeed, when analysing how regions populate the 3D space formed by log Σ_⋆, log Σ_SFR, and log Σ_H i, we find that they identify a plane, as shown in the right-hand panel of Fig. 6 (four different projections of this plane are shown in Fig. A2 in Appendix  A). The equation of the plane that minimizes the perpendicular distance of the points can be written as

$$\begin{eqnarray*} \log \Sigma _{\rm SFR} = 0.97\log \Sigma _{\star } + 1.99\log \Sigma _{\rm {H\,{\small I}}} - 11.11. \end{eqnarray*}$$

(7)

Figure 6.

Left-hand panel: Distribution of the regions having an estimate of |$\Sigma _{\rm H_2}$| above the sensitivity limit in the log Σ_⋆–log Σ_SFR –|$\log \Sigma _{\rm H_2}$| plane. Each point is colour coded as a function of |$\log \Sigma _{\rm H_2}$|⁠. Four projections of this space at different azimuthal angles are shown in Fig. A1. Right-hand panel: Distribution of the regions having an estimate of Σ_H i above the sensitivity limit in the log Σ_⋆–log Σ_SFR–log Σ_H i plane. Each point is colour coded as a function of log Σ_H i. The best-fitting plane is indicated by the green grid. Four projections of this plane, described by equation (7), at different azimuthal angles are shown in Fig. A2.

The relation expressed by equation (7) has a scatter of 0.14 dex, significantly smaller than the one of the spatially resolved MS relation. Interestingly, when the dependence of the SFR of H i surface densities is taken into account, the relation between log Σ_SFR and log Σ_⋆ becomes closer to linear. To better understand the origin of the relation expressed by equation (7), in Fig. 7 we show the log|$\Sigma _{\rm H_2}$|–logΣ_H i plane colour coded as a function of Δ_MS (left-hand panel) and r/R₂₅ (right-hand panel). From Fig. 7, we can appreciate that regions with Σ_H i higher than 10 M⊙ pc⁻² (that is the typical value for the H i to H2 transition, Bigiel et al. 2008; Leroy et al. 2008; Lee et al. 2012, 2014) correspond to the upper envelope of the spatially resolved MS and, on average, are preferentially located between 0.3 and 0.8 R₂₅. These regions span a wide range of log|$\Sigma _{\rm H_2}$| values: (1) up to log|$\Sigma _{\rm H_2}$| = 2 M_⊙ pc⁻² for 0.3R₂₅ < r <0.6 R₂₅ and (2) below the sensitivity limit for r >0.6 R₂₅. In the first case, the stellar surface density and average SFR are moderately high: high H i surface densities could be partially due to H₂ dissociation and are needed (together with dust) to prevent the further dissociation of the molecular gas by the intense radiation field. In the outer part of the optical disc, the SFRs are on average lower than in the inner disc, and so is the stellar surface density; nevertheless, the SFRs above the MS reach values that are comparable to SFRs on the MS in the inner part of the disc.

Figure 7.

The log|$\Sigma _{\rm H_2}$|–logΣ_H i plane, colour coded as a function of Δ_MS (left-hand panel) and R/R₂₅ (right-hand panel). Sensitivity limits are marked with dot–dashed lines.

Most likely, once the molecular gas gives birth to new stars, it is partly disrupted by the resulting intense UV radiation from hot massive stars. To illustrate this effect, in Fig. 8, we plot the |$\Sigma _{\rm H_2}$|/Σ_H i ratio as a function of Σ_gas. As expected, for higher Σ_gas this ratio increases: H₂ becomes progressively more dominant over H i as the chemical equilibrium shifts in favour of the molecular phase with increasing gas pressure. However, the correlation is quite broad, and the origin of the spread at fixed Σ_gas becomes evident once the cells are colour coded as a function of Δ_MS. Going from below to above the MS relation, |$\Sigma _{\rm H_2}$|/Σ_H i steadily decreases. We interpret this trend as evidence that stellar feedback (radiative and from supernova shocks) has the effect of partially dissociating the H₂ molecules in regions of intense star formation. The sheer size of this trend is worth emphasizing, as the H₂/H i ratio drops by about a factor of 100 when going from extreme sub-MS to super-MS (starbursting) cells. Such a wide range is indeed expected by theory, for a wide variation of the intensity of the UV radiation field (cf. fig. 7 in Sternberg et al. 2014, see also Tacconi, Genzel & Sternberg 2020).

Figure 8.

The |$\Sigma _{\rm H_2}$|/Σ_H i ratio as a function of Σ_gas. The cells have been colour coded as a function of the average Δ_MS.

We notice that a correlation between the H i abundance and the distance from the MS has been recently reported by Wang et al. (2020) when analysing integrated galaxy properties; that is, galaxies above the MS are more H i-rich than those below. They interpret this trend in terms of H i being an intermediate step (between the ionized and the molecular phase) in fuelling star formation in galaxies, but do not consider H i as a product of molecular dissociation. Our results instead indicate that H i is also a product of star formation and its surface density is extremely sensitive to the local UV radiation field.

4.2 Star formation efficiency versus gas fraction

The data set in our hands gives us the possibility to analyse the role of SFE and f_gas in setting the sSFR of a region, thus deciding its location with respect to the spatially resolved MS relation. As in literature, the gas fraction and SFE estimates may or may not include the contribution of neutral gas, depending on how the gas mass is measured, we define the molecular, atomic, and total SFE: SFE_mol = SFR/M|$_{\rm H_2}$|⁠, SFE_ato = SFR/M_H i, SFE_tot = SFR/(M_H i+M|$_{\rm H_2}$|⁠). Similarly, we define the molecular, atomic and total gas fractions as f_gas,mol = M|$_{\rm H_2}$|/(M|$_{\rm H_2}$|+M_H i+M_⋆), f_gas,ato = M_H i/(M|$_{\rm H_2}$|+M_H i+M_⋆) and f_gas,tot = (M_H i+M|$_{\rm H_2}$|⁠)/(M_H i+M|$_{\rm H_2}$|+M_⋆).

In Fig. 9, we show how the average SFE (top) and f_gas (bottom) vary in the logΣ_⋆–logΣ_SFR plane, separating the different phases. Qualitatively, we observe that SFE_mol varies strongly above and below the MS, for logΣ_⋆ <8 M_⊙ kpc⁻², while it is almost constant at higher stellar surface densities. These trends reflect the changes in f_gas,mol, that is characterized by strong variations above/below the MS only at higher stellar surface densities, leading to a constant SFE. We notice that regions above the MS at logΣ_⋆ <7 M_⊙ kpc⁻² have very low f_gas,mol, as they are located in the outer optical disc. SFE_ato (central top panel) is nearly constant above/below the MS, while it steadily increases along the MS relation for increasing stellar surface densities. The atomic gas fraction is subject to two distinct trends: it decreases along the MS relation, from low to high Σ_⋆, and tends to be higher above the MS. When considering the total gas, the variations of SFE_tot are less evident: SFE_tot increases slightly at fixed stellar surface densities, less significantly in the direction perpendicular to the MS relation, and it increases along the MS for logΣ_⋆ < 7.5 M_⊙ kpc⁻², to reach an almost constant value for logΣ_⋆ > 7.5 M_⊙ kpc⁻². Finally, we observe that f_gas,tot varies strongly when moving from the lower to the upper envelope of the MS, both perpendicular to the relation and at fixed logΣ_⋆. Regions with logΣ_⋆ < 7.0 M_⊙, that on average correspond to log|$\Sigma _{\rm H_2}$| below the sensitivity limit, have large gas fractions thanks to the contribution of the neutral gas.

Figure 9.

Molecular, atomic, and total SFE and f_gas in the logΣ_⋆–logΣ_SFR plane. The bins in the six panels are colour coded as a function of SFE_mol = SFR/M|$_{\rm H_2}$| in the top left-hand panel, SFE_ato = SFR/M_H i in the top central panel, SFE_tot = SFR/(M_H i+M|$_{\rm H_2}$|⁠) in the top right-hand panel, f_gas,mol = M|$_{\rm H_2}$|/(M_H i+M|$_{\rm H_2}$|+M_⋆) in the bottom left-hand panel, f_gas,ato = M_H i/(M_H i+M|$_{\rm H_2}$|+M_⋆) in the bottom central panel, and f_gas,tot = (M_H i+M|$_{\rm H_2}$|⁠)/(M_H i+M|$_{\rm H_2}$|+M_⋆) in the bottom right-hand panel. The spatially resolved MS is indicated with the green solid line.

The qualitative analysis carried on so far on Fig. 9 points to the role of both the SFE and f_gas in regulating the SFR of a region. From an integrated point of view, there is now convergence on the fact that an increase in SFR at fixed M_⋆ and cosmic epoch is due to a combination of increasing gas mass and decreasing depletion time (thus increasing SFE Saintonge et al. 2011b, 2012; Leroy et al. 2013; Huang & Kauffmann 2014). In the recent years, these studies could be carried out with larger and larger samples, using different sub-mm observations to trace gas, and exploring a wide range of cosmic epochs, 0 < z < 4.5, with the general consensus that an almost equal increase of gas fraction and SFE can explain an increase in sSFR at fixed redshift. Scoville et al. (2017) exploited sub-mm ALMA continuum observations of 700 COSMOS galaxies at 0.3 < z < 4 and estimated the gas mass from the dust mass. Several works in literature indicate that the dust mass is a tracer of the total gas mass (e.g. Leroy et al. 2011; Corbelli et al. 2012; Orellana et al. 2017; Casasola et al. 2020), but for 0.3 < z < 4 the total gas is dominated by the molecular fraction (e.g. Lagos et al. 2014). Genzel et al. (2015) and Tacconi et al. (2018) combine three different estimates of molecular gas mass (from FIR SED, ∼1 mm dust photometry and CO line flux) in the redshift range 0 < z < 4 and found that an increase in sSFR at fixed stellar mass and redshift is accompanied by an almost equal increase of SFE and f_gas. Recently, Ellison et al. (2020b), using molecular gas observations from the ALMaQUEST survey (median redshift ∼0.03) on kpc scales, find that variations of the SFE play a major role in setting the SFR at fixed stellar mass (and thus the scatter of the spatially resolved MS), with differences in f_gas,mol playing a secondary role. In Fig. 10, we compare our results to the trends found in Tacconi et al. (2018) and Ellison et al. (2020b). We define Δ_SFE as the distance of a region from the spatially resolved KS law at fixed molecular gas mass (central panel of Fig. 2), and |$\Delta _{\rm f_{\rm gas}}$| as the distance of a region from the spatially resolved MGMS (central panel of Fig. 3), as done in Ellison et al. (2020b). As the analysis of the connection between the scatter of these relations and Δ_MS in Sections 3.2 and 3.1 revealed that MS regions are located along the KS and MGMS relations, the definitions of Δ_SFE and |$\Delta _{\rm f_{\rm gas}}$| given above are consistent with those of Tacconi et al. (2018) that normalize t_depl and f_gas to their MS values. The panels show the variation between molecular and total SFE and gas fraction of a region with respect to the MS values (thus Δ_SFE and |$\Delta _{\rm f_{\rm gas}}$|⁠) as a function of Δ_MS. The top left-hand panel shows the Δ_SFE,mol–Δ_MS relation; the Pearson correlation coefficient is 0.56 and the best-fitting relation has a slope of 0.54 and a scatter of 0.18 dex, that is in excellent agreement with Tacconi et al. (2018, slope = 0.44) and Ellison et al. (2020b, slope = 0.5). We emphasize here that our work has a spatial resolution of 500 pc, thus reaching surface densities that are ∼1 dex smaller than Ellison et al. (2020b). A similar slope (0.48) is found when analysing |$\Delta _{\rm f_{\rm gas,mol}}$| as a function of Δ_MS, with a Pearson coefficient of 0.47 and a scatter of 0.23 dex. Our best-fitting relation is in excellent agreement with the one of Tacconi et al. (2018) (obtained from integrated quantities) that has a slope of 0.52. These results emphasize that when analysing the molecular gas phase, an increase in SFR at fixed M_⋆ and cosmic epoch is due to a combination of increasing gas mass and increasing (decreasing) SFE (t_depl). The situation painted by the molecular gas changes when the contribution of neutral gas is taken into account. In the left-hand panels of Fig. 10, we show the Δ_SFE,tot–Δ_MS (top) and the |$\Delta _{\rm f_{\rm gas,tot}}$|–Δ_MS (bottom) planes, thus considering both the neutral and molecular gas phases. Interestingly, we see that the relation between Δ_SFE,tot and Δ_MS is significantly weaker than in the molecular case, as we retrieve a Pearson coefficient of 0.30, a slope of 0.30, and a scatter of 0.28 dex. On the other hand, we observe a stronger correlation between Δ_MS and |$\Delta _{\rm f_{\rm gas,tot}}$| (Spearman ranking is 0.65), with a slope of 0.50 and a scatter of 0.19 dex. These results indicate the importance of the neutral gas phase in setting the scatter of the spatially resolved MS, as it partially traces molecular gas dissociated by the radiation field.

Figure 10.

Distributions of regions in the Δ_SFE,mol–Δ_MS plane (top left-hand panel), in the Δ_SFE,tot–Δ_MS plane (top right-hand panel), |$\Delta _{\rm f_{\rm gas,mol}}$| –Δ_MS plane (bottom left-hand panel), and |$\Delta _{\rm f_{\rm gas,tot}}$|–Δ_MS (bottom right-hand panel). The best-fitting relations of this work are shown as a black solid line. The best-fitting slope and the Pearson correlation coefficient are witting each panel. In the left-hand panels, we show relations of Tacconi et al. (2018) in purple, and the one of Ellison et al. (2020a) in orange.

Finally, the data set in our hands allows us to analyse the spatial variations of SFE and f_gas within the five galaxies of the sample. The spatially resolved maps of Δ_MS, Δ_SFE,tot, and |$\Delta _{\rm f_{\rm gas,tot}}$| for every galaxy can be found in Appendix  B (Figs B1 and B2). Here, we emphasize that while we do observe variations within galaxies and among them of the connection between Δ_MS and f_gas or SFE, on average the galaxy-by-galaxy analysis confirms that the gas fraction strongly correlates with Δ_MS.

5 CONCLUSIONS

In this manuscript, we exploit the combination of highly accurate measurements of Σ_⋆ and Σ_SFR at 500 pc resolution of five nearby, face-on spiral galaxies obtained following the procedure presented in Paper I, with observations of neutral and molecular gas. With this powerful data set, we study how the location of a region with respect to the spatially resolved main sequence (MS) is related to the gas in the different phases. We summarize here our main results:

• We find that log Σ_⋆, log Σ_SFR, and |$\log \Sigma _{\rm {H_2}}$| define a 3D relation (the left-hand panel of Fig.  6); the three projections are the Kennicutt–Schmidt (KS) law, the MS, and the molecular gas main sequence (MGMS). The KS law is the tightest relation, with a scatter of 0.19 dex, followed by the MGMS (0.22 dex) and the spatially resolved MS (0.23 dex). The existence of the MGMS at sub-kpc scales opens up the possibility to study molecular gas content from logΣ_SFR and logΣ_⋆ alone, which are generally easier to obtain and available for large samples.

• We study the distribution of the neutral and molecular gas in the logΣ_⋆–logΣ_SFR plane (Fig.  4) and we find that the surface density of molecular gas steadily increases along the MS relation, but is almost constant perpendicular to it. The surface density of neutral gas, instead, is almost constant along the MS, and increases (decreases) in its upper (lower) envelope. On average, regions located in the upper envelope of the spatially resolved MS have Σ_H i ≥ 10 M_⊙ pc⁻², that is the typical value for the H i to H₂ transition. The three variables log Σ_⋆, log Σ_SFR, and log Σ_H i are distributed along the plane log Σ_SFR = 0.97log Σ_⋆ + 1.99log Σ_H i − 11.11 that has a scatter of 0.14 dex (the right-hand panel of Fig.  6).

• When moving towards high Σ_SFR at fixed stellar surface densities, the molecular gas fraction and molecular SFE both increase. On the other hand, when we consider the total gas, thus also the contribution of the neutral component, we observe a steep increase of the gas fraction towards high SFRs, accompanied by a weak increase of the total SFE (Fig. 10).

Our results illustrate the intricate interplay between neutral and molecular gas, as it changes radially as a function of the distance from the centre of galaxies, as well as locally depending on the sSFR. We argue that molecular gas dissociation plays an important role in setting the observed trends of neutral and molecular gas surface densities around the MS relation (Fig. 8). Thus, high total gas surface densities favour the formation of molecular hydrogen clouds, which in turn promote star formation whose resulting UV radiation has the effect of dissociating the molecules, in a local baryon cycle that is a manifestation of the self-regulating nature of the star formation process. We shall return on these issues in a future paper, also expanding on their implications for our understanding of the star-formation process in high-redshift galaxies. These trends, obtained here for massive, disc-dominated spirals without a strong bar, will be analysed for galaxies with different morphologies (bulge dominated and spirals with strong bars) in another upcoming paper.

The continuity of trends above the MS, MGMS, and KS relations suggests that starburst regions do not result from a bi-modality in the star formation process, but rather from a steady variation of primarily the total gas fraction and partially the star formation efficiency. We speculate that this continuity could also explain the existence of high redshift starbursts, as the scatter of the spatially resolved MS is similar to the one of the integrated relation, and this last quantity is observed to be constant with redshift. It is widely believed that high-redshift galaxies are dominated by H₂ over H i, because their higher gas surface density favours the molecular phase. However, this finding suggests that the higher sSFR at high redshift may actually contrast this expectation, with intense stellar feedback leading to dissociation thus reducing the H₂/H i ratio. The next generation of radio telescopes like the _Square Kilometer Array (SKA), also ongoing surveys with MeerKAT, such as MIGHTEE (Jarvis et al. 2016) and LADUMA (Blyth et al. 2016), will directly measure the H i content in distant galaxies, thus unravelling its role in the star formation processes at earlier cosmic epochs.

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ACKNOWLEDGEMENTS

We thank the anonymous referee for constructive comments that improved the manuscript. LM is grateful to Sara Ellison and Bhaskar Agarwal for helpful discussion on the manuscript. LM acknowledges support from the BIRD 2018 research grant from the Università degli Studi di Padova. AE and GR are supported from the STARS@UniPD grant. GR acknowledges the support from grant PRIN MIUR 2017 – 20173ML3WW_001. GR and CM acknowledge funding from the INAF PRIN-SKA 2017 programme 1.05.01.88.04. We acknowledge funding from the INAF main stream 2018 programme ‘Gas-DustPedia: A definitive view of the ISM in the Local Universe’. This research made use of photutils, an astropy package for detection and photometry of astronomical sources (Bradley et al. 2019).

DATA AVAILABILITY

This research is based on observations made with the Galaxy Evolution Explorer, obtained from the MAST data archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NASA 5-26555. This work made use of HERACLES, ‘The HERACO-Line Extragalactic Survey’ (Leroy et al. 2009), and THINGS, ‘The H i Nearby Galaxy Survey’ (Walter et al. 2008). DustPedia is a collaborative focused research project supported by the European Union under the Seventh Framework Programme (2007–2013) call (proposal no. 606847). The participating institutions are Cardiff University, UK; National Observatory of Athens, Greece; Ghent University, Belgium; Université Paris Sud, France; National Institute for Astrophysics, Italy and CEA (Paris), France. We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr). The derived data underlying this article will be shared on reasonable request to the corresponding author.

Footnotes

1

The DustPedia data base is available at http://DustPedia.astro.noa.gr.

2

R₂₅ is defined as the length of the projected semimajor axis of a galaxy at the isophotal level 25 mag arcsec⁻² in the B band and it is taken from the HyperLEDA data base (Makarov et al. 2014).

3

We refer the reader to Casasola et al. (2020) and De Vis et al. (2019) for details of the metallicity calibration.

APPENDIX A: THE log Σ_⋆–log Σ_SFR–|$\log \Sigma _{\rm {H_2,H\,{\small I}}}$| 3D RELATION

As shown in Fig. 6, the three quantities log Σ_⋆, log Σ_SFR, and |$\log \Sigma _{\rm {H_2}}$| define a 3D relation. To better visualize this relation, in Fig. A1 we show four different projections of it, corresponding to azimuthal angles of 0^○, 60^○, 120^○, and 180^○. We stress here that we are plotting only the regions that have an estimate of |$\Sigma _{\rm {H_2}}$| above the sensitivity limit. In Fig. A2, we show, instead, the log Σ_⋆, log Σ_SFR, and log Σ_H i 3D plane at four different azimuthal angles, with the aim of better visualize the positioning of the cells along the 3D plane marked in green. We plot in Fig. A2 only the regions that have an estimate of Σ_H i above the sensitivity limit.

Figure A1.

Distribution of the regions with an estimate of |$\log \Sigma _{\rm {H_2}}$| above the sensitivity limit in the log Σ_⋆–log Σ_SFR–|$\log \Sigma _{\rm {H_2}}$| 3D space. For different projections of the plane are shown, corresponding to different azimuthal angles: 0^○ (top left), 60^○ (top right), 120^○ (bottom left), and 180 ^○ (bottom right). The point are colour coded as a function of log Σ_H i.

Figure A2.

Distribution of the regions with an estimate of log Σ_H i above the sensitivity limit in the log Σ_⋆–log Σ_SFR–|$\log \Sigma _{\rm {H_I}}$| 3D space. For different projections of the plane are shown, corresponding to different azimuthal angles: 0^○ (top left), 125^○ (top right), 175^○ (bottom left), and 220 ^○ (bottom right). The points are colour coded as a function of |$\log \Sigma _{\rm {H_2}}$|⁠.

APPENDIX B: Δ_MS, SFE, AND GAS CONTENT WITHIN GALAXIES

In this section, we discuss the distributions of Δ_MS, |$\Delta _{\rm f_{\rm gas,tot}}$|⁠, and Δ_SFE,tot within the five galaxies in our sample, shown in Figs B1 and B2. We recall here that Δ_SFE,tot and |$\Delta _{\rm f_{\rm gas,tot}}$| are computed as the distance of the region from the global total gas–SFR relation (the right-hand panel of Fig. 2) and from the global total gas–mass relation (the right-hand panel of Fig. 3), and are thus a measure of the SFE and gas content with respect to the value on the best-fitted relation at a given gas or stellar surface density (e.g. regions with |$\Delta _{\rm f_{\rm gas,tot}}\gt $| 0 have higher gas content than the average).

Figure B1.

Δ_MS (left), |$\Delta _{\rm f_{\rm gas,tot}}$| (centre), and Δ_SFE,tot (right) maps of (from top to bottom) NGC 0628, NGC 3184, NGC 5194, and NGC 5457. The highlighted regions are discussed more in detail in the text.

Figure B2.

Δ_MS (left), |$\Delta _{\rm f_{\rm gas,tot}}$| (centre), and Δ_SFE,tot (right) maps of NGC 6946. The highlighted regions are discussed more in detail in the text.

It is clear that the Δ_SFE,tot and the |$\Delta _{\rm f_{\rm gas,tot}}$| in the inner regions will be anticorrelated because the regions where the bulk of molecular hydrogen is not spatially coincident with the regions where the FUV star formation tracer peaks. This is due to the time-delay between the formation of molecular clouds and the exposed phase of star formation (Corbelli et al. 2017). In the inner regions of spiral galaxies, the spiral pattern rotates slower than the stars and hence molecular clouds form out of compressed gas along the inner part of the arm. These are the regions with higher gas fraction than the average. The young stars become visible after dispersing the original gas and, moving faster than the arm, they appear shifted with respect to the newly formed molecular complexes. These are regions with low gas content but numerous visible young stars, hence appear with a star formation efficiency above the average. For the outer regions, at or beyond corotation, the situation should reverse with respect to the arm but the anticorrelation between Δ_SFE,tot and the |$\Delta _{\rm f_{\rm gas,tot}}$| should still hold. Here, the low surface density of molecules and the presence of external perturbations make the study more challenging: tidal perturbations, gas stripping, and infall have a strong impact and this reflects on Δ_MS that can vary substantially from one region to the next, being star-forming regions more coarsely spaced in the outer discs. Below we describe a few selected regions in each galaxy more in detail:

• The central region of NGC 0628, i.e. the bulge, is located below the MS and has low gas content, while Δ_SFE,tot varies of ±0.3 dex around zero. Regions located in the upper envelope of the MS relation are located mostly along the spiral arms. We observe regions where |$\Delta _{\rm MS}\, \sim 0$| (A, B, and C) or Δ_MS ∼ 1 (D), or Δ_MS ∼ −1 (E), all with low gas fractions and high or average SFE.

• NGC 3184 also has a central region characterized by mostly negative Δ_MS and |$\Delta _{\rm f_{\rm gas,tot}}$|⁠, while Δ_SFE,tot is, for the majority of cells, positive. In the spiral arms, we observe regions where the SFR is significantly higher than the MS value (B and C) that correspond to gas fractions above the average, and varying SFE. We identify three blobs (A, D, and E) with negative |$\Delta _{\rm f_{\rm gas,tot}}$| and Δ_MS varying slightly around the MS value (as in A and E) or Δ_MS < 0 (as in D).

• NGC 5194 is characterized by a central region that has SFR values mostly above the MS. Positive values of Δ_MS are located mainly along the spiral arms that are also well traced by an excess of total gas compared to the average. The regions A, B, C, and D are all above the MS relation, but they show different properties: while the majority of pixels within C and D are have |$\Delta _{\rm f_{\rm gas,tot}}\gt 0$| and Δ_SFE,tot ∼ 0, A and B show clumps of Δ_SFE,tot well above 0 and |$\Delta _{\rm f_{\rm gas,tot}}$| varying between negative and positive values.

• NGC 5457 is characterized by two strong spiral arms with several blobs that have an SFR higher than the MS value (regions A, B, C, D, E). Within these regions, we observe gas fractions that are almost always higher than the MS values, while Δ_SFE,tot varies more strongly between positive and negative values. Region F, for which the majority of cells are well below the MS relation, has Δ_SFE,tot ∼ 1, but |$\Delta _{\rm f_{\rm gas,tot}}\sim$| −1.

• NGC 6946 has a central region characterized by SFR higher than MS values, high gas content and SFE lower than the average (region B). Regions A, C, and D are also characterized by values of Δ_MS close to 1, but different SFE. While regions A and D have close to normal gas content and SFE above the average, the more central regions B and C have a high gas content but a low SFE.

In general, we conclude that in the innermost and outer regions the decrease or enhancement of the local gas content follows closely that of the star formation rate along the MS. For the innermost region and the spiral arms, the enhancement or decrease of the SFE is opposite to that of the local gas content. But there are exceptions to this behaviour. Given the possible temporal and spatial lag between molecular and FUV peaks (Kruijssen et al. 2019), the relation between Δ_SFE,tot and Δ_MS for individual galaxies is more complex and requires dedicated analysis.