SuperCAM CO( 3 − 2 ) APEX survey at 6 pc resolution in the Small Magellanic Clouds

Context. The Small Magellanic Cloud (SMC) is an ideal laboratory to study the properties of star-forming regions due to its low metallicity, which a ff ects the molecular gas abundance. However, a small number


Introduction
The Small Magellanic Cloud (SMC), the nearest low metallicity galaxy to the Milky Way (∼ 60 kpc, Hilditch et al. 2005), with a low metal abundance (Z ≈ 0.2 Z ⊙ , Russell & Dopita 1992) and high Gas-to-Dust ratio (GDR ∼ 2000, Roman-Duval et al. 2017), has presented a challenge in the study of the molecular component of the interstellar medium (ISM) and its association with star-forming regions.The low dust content prevents protection from the high ultra-violet (UV) radiation field allowing a strong dissociation of most of the molecular gas at low A V , specifically carbon monoxide (CO), the common tracer of H 2 gas.
Theoretical models (Wolfire et al. 2010;Seifried et al. 2020) show that due to the strong H 2 self-shielding, the H 2 molecule starts to form in low hydrogen nuclei density (n H = 10 − 10 3 cm −3 ) regions where A V takes values from 0.2 to 1.5 mag.These molecular H 2 regions, also containing neutral (C) and ionized carbon (C + ) but without CO gas, are frequently embedded within strong photodissociation regions (PDRs) well traced by the [CII] emission at 158 µm (see also Requena-Torres et al. 2016;Pineda In the Magellanic Bridge (MB), Muller et al. (2014) made a study of the CO(3 − 2)/CO (1 − 0) in several clouds at 22 ′′ resolution.A much higher CO(3 − 2)/CO(1 − 0) ratio of ∼ 2.5 was found towards the cloud MB-B, which is associated with recent or current star formation.However, this high ratio is not seen in other sites of the Magellanic Bridge, like the clouds MB-A and MB-C, which show CO(3 − 2)/CO(1 − 0) ratio ≲ 1.Such clouds may be remnants of a past period of star formation.
In this paper, we present a CO (3−2) survey of the main body of the SMC (SMC-Bar) performed with SuperCAM attached to the APEX telescope at 6 pc resolution.In combination with the CO(2 − 1) survey of the SMC (Saldaño et al. 2023) we have determined the CO(3 − 2)-to-CO(2 − 1) ratio of the SMC and studied this ratio for clouds located in different environments within the galaxy.In addition, we have derived and analyzed the physical properties of the CO(3 − 1) clouds and studied their scaling relations.Our results will impact the study of external galaxies where CO  emission is being used to determine the mass and properties of the molecular gas.In the following section (Sec.2), we detail the reduction of the SuperCAM data and we show the complementary data used for the analysis.In Sect.3, we show the methodology used to estimate the CO(3 − 2)-to-CO(2 − 1) ratio in different parts of the SMC, and in Sect.4, we explain the cloud identification by the CPROPS algorithm.In Sect.5, the main results are shown, while in Sect.6 the discussion of the main results are presented.Finally, In Sect.7, we present the conclusion and final remarks.

CO(3 − 2) Observations
The SMC survey was performed using the SuperCAM multipixel focal plane array of superconducting mixers attached to the 12m Atacama Pathfinder EXperiment (APEX2 ) (Güsten et al. 2006)  SuperCAM consists of a 64-pixel 345 GHz heterodyne imaging spectrometer designed to operate in the astrophysically important 870 µm atmospheric window (Walker et al. 2005).This camera was built by the Steward Observatory Radio Astronomy Laboratory (SORAL 3 ), a project belonging to the University of Arizona, and is by far the largest such array used to perform very large surveys of the sky.For instance, it was used to map a 2.7 square degree area of the Orion molecular cloud complex (Stanke et al. 2022).For more technical details of the array receiver see Groppi et al. (2010) and Kloosterman et al. (2012).
The SMC was mapped in multiple overlapping regions of size ∼ 20 ′ × 10 ′ using the on-the-fly (OTF) mode.These maps were later combined to improve the signal-to-noise ratio (S/N) of different regions of the galaxy.This process generated three large maps, SMC-SWBAR, SMC-MID, and SMC-N, that cover most of the SMC-BAR as is shown in Figure 1.In the figure, the white contours show the observed SuperCAM area superimposed on the 24 µm emission image.The figure also shows the areas of CO(2-1) mapping (Saldaño et al. 2023).The reduction of the OTF maps, as well as the combination of all of them, were made using an automatic procedure following a set of GILDAS/CLASS and Python algorithms developed by the SO-RAL team, which include the baseline fitting to each spectrum in the cubes using a linear polynomial fit.As a reference for the baseline fitting, we used the NANTEN CO(1 − 0) data cube (Mizuno et al. 2001;Mizuno 2009).
The antenna temperature, T A , was transformed to brightness temperature of the main beam (T mb = T A /η mb ) using the telescope beam efficiency η mb = 0.38.The final reduction produced CO(3−2) cubes with a spatial resolution of HPBW = 20" (∼ 6 pc at the SMC distance) and a spectral resolution of 0.233 km s −1 .To further increase the signal-to-noise ratio of the cubes, we resampled the velocity axis to a spectral resolution of 0.4 km s −1 .The median intensity rms of the mapped region is ∼ 1 K.The final SMC-SWBAR, SMC-MID cubes have sizes of To obtain the final SMC-Bar CO(3-2) cube, we performed a mosaicing with the SMC-SWBAR, SMC-MID and SMC-N cubes.We show the integrated CO(3 − 2) emission of the SMC-Bar in Fig. 2. The integration was performed within the velocity range of the clouds with S/N > 3. We included an artificial homogeneous background noise in the map to enhance the ap-pearance of the detected clouds.In Appendix A, we show the rms map of the CO(3 − 2) emission.

Complementary Data
We used the APEX SMC CO(2 − 1) survey reported by Saldaño et al. (2023).The APEX CO(2 − 1) survey has a spatial and spectral resolution of 30 ′′ (∼ 9 pc at the SMC distance) and ∆V = 0.25 km s −1 , respectively, and covers a subset of regions in the SMC, namely SW-Bar, NE-Bar, N66 and DarkPK, which are shown in Figure 1 by yellow boxes.The CO(2 − 1) rms intensity of the regions vary between ∼ 0.1 − 0.3 K.
We also used the Infrared Array Camera (IRAC) 8 µm image and the Multiband Imaging Photometer (MIPS) 24, 70, and 160 µm images from the Spitzer Survey "Surveying the Agents of Galaxy Evolution" (SAGE; Gordon et al. 2011)).We also included for the analysis the HERITAGE Herschel data in three bands from 100 to 250 µm from Gordon et al. (2014) and the Hα image from the "Magellanic Cloud Emission-Line Survey" (MCELS, Winkler et al. 2015).

The CO(3 − 2)-to-CO(2 − 1) ratio
We are interested in quantifying the R 32 = [CO(3 − 2)/CO(2 − 1)] ratio in the SMC.This ratio can be determined only towards the common areas in both transitions as the CO(2-1) maps do not cover completely the CO(3-2) map, namely SW-Bar, DarkPK, N66, and NE-Bar regions as shown in Fig. 1.The SW-bar and N66 CO(3 − 2) maps show high S/N ratios so we determined R 32 using a pixel-by-pixel method.The first step in this procedure was to convolve the CO(3 − 2) data cubes to the CO(2 − 1) spatial resolution of 30 ′′ by using a Gaussian beam of ∼ 22 ′′ .After convolution, both the CO(3 − 2) and CO(2 − 1) data cubes were resampled to a common spatial grid.Then, we integrated the data cubes in both transitions using the moment masking method (Dame 2011) and we used the following criteria for this method.We smoothed the data cube to a beam of 2 times the original spatial resolution and in 4 times the channel width to build the masked cube and masked the emission below 5σ rms in temperature.This mask is used to integrate the data cubes only within spectral CO lines that we consider as true brightness temperatures, avoiding spurious and unrealistic (e.g., spikes) emissions.These unrealistic emissions occur mainly in the SuperCAM data cubes that have pronounced non-uniform noise distributions (see Figure A.1). Finally, we calculated R 32 pixel-by-pixel using the integrated CO(3 − 2) and CO(2 − 1) maps using pixels that have S/N > 3 in intensity.
Due to the non-uniform and much higher noise of the CO(3− 2) maps towards the DarkPK and NE-Bar, we used a different method to determine R 32 in these two regions.Instead of a pixelby-pixel approach, we used the CO integrated spectrum towards the strongest clouds in the two transitions identified in each region to obtain R 32 (see Figs. 3 and 4).We extracted the CO(3−2) and CO(2 − 1) integrated spectra at the peak of the cloud from the convolved cubes at 30 ′′ resolution.The integrated emissions (I CO ) in both transitions were calculated using the zeroth-order moment method between the total width of the CO lines, and finally, R 32 is calculated as the ratio between both integrated intensities.

Cloud Identification
In addition to determining the R 32 ratio, we also identified the individual molecular clouds in CO(3 − 2) at 6 pc resolution.For  The original cubes (with ∆V = 0.23 km s −1 ) were re-sampled to a spectral resolution of 0.4 km s −1 to increase the signal-to-noise ratio.b The median T rms is calculated in 0.4 km s −1 spectral resolution.
the identification, we used the CPROPS algorithm (Rosolowsky & Leroy 2006) in the three SuperCAM CO(3 − 2) maps using the following criteria in the algorithm: clouds with sizes larger than the spatial resolution (20"), FWHM greater than 3 channels in velocity (> 1.2 km s −1 ) and 2 sigma above the noise level.So we fixed the CPROPS input parameters: MINAREA= 1 and MINCHAN= 3. The THRESHOLD input parameter (the cut in intensity to define "islands", see Rosolowsky & Leroy 2006) was fixed to 2. The EDGE input parameter was first set to 1.5 to 1.0 to extend the wing of the "islands".For EDGE = 1.5, only some tens clouds were identified with S/N > 3 in all three cubes.We changed to EDGE = 1, which extends the wing of the "islands" and we found many more but weaker clouds, some of which could be false CO emissions (e.g., spikes).To discriminate between these weaker true and false clouds, we extracted the spectrum of the cloud integrating on the area of the cloud as defined by its size and selected only those clouds that have an integrated spectral line with a velocity width larger than 3 adjacent channels (≃ 1.2 km s −1 ) and temperatures ≳ 3×rms in the channels.We considered the clouds identified by these criteria as confirmed clouds.
The properties of the CO(3 − 2) clouds such as the radius (R in pc), velocity dispersion (σ υ in km s −1 ), CO flux (F CO in K km s −1 ) given by CPROPS by mean of the moment method in the position-position-velocity data cube are summarized in Ta-ble 2. In col. 1, we listed the identification (ID) number of the clouds with high S/N (≳ 5).In col. 2 and 3, the Right Ascension and Declination in J(2000) are indicated.In col. 4 to 10, we listed the radius (R), the local-standard of rest velocity (V lsr ), the velocity dispersion (σ υ ), the peak temperature (T peak ), the integrated CO(3 − 2) intensity (I CO  ), the CO(3 − 2) luminosity (L CO  ), and the virial mass (M vir ).The ID numbers in Table 2 refer to their number on the online version table, which includes all clouds with S/N > 3. The CO cloud parameters are corrected by sensitivity bias and resolution bias, which is originated by the non-zero noise of CO emission and by the instrumental convolutions (finite spatial and spectral resolutions, see Rosolowsky & Leroy 2006).For the calculation of the radius R, CPROPS uses the Solomon et al. (1987) definition for spherical clouds assuming a factor of 1.91 to convert the second moments of the emission along the major and minor axes of clouds (σ r ) to R. For unresolved clouds along the minor axis, we obtained the radii following Saldaño et al. (2023) calculation.The deconvolved σ υ is calculated from equation (10) from Rosolowsky & Leroy (2006), and the FWHM of the spectral line is given by √ 8 ln (2) σ υ .
The CO flux of the clouds is converted to luminosity by mean: Article number, page 5 of 14 where F CO (0K) is the flux measured at infinite sensitivity, and d is the distance of the galaxy in parsec of 60 kpc.Another important parameter used to analyze the stability of molecular clouds is the virial mass, given by the formula (Solomon et al. 1987): where σ υ and R are the corrected velocity dispersion and radius in parsec, respectively.For this last equation, a self-gravitating sphere with density profile ρ ∝ r −1 was assumed.The external forces, like magnetic fields and external pressure, are discarded.
The uncertainties in the properties and derived parameters are estimated by CPROPS with the bootstrapping technique.For the case of the unresolved clouds in which the sizes were recalculated, we estimated the error in the radius and virial mass calculation using the error propagation.

CO(3 − 2) emission in the SMC-Bar
The distribution of the CO(3 − 2) emission in the SMC-Bar is shown in Fig. 2. The emission is found in many isolated clouds dispersed all over the SMC-Bar.Only two major strong emission concentrations are seen, one located in the SW-bar and the other in the northern N66 region.
In Figs 3 and 4, we show the CO(3 − 2) and CO(2 − 1) integrated emission maps for the SW-Bar, DarkPk, N66 and NE-Bar (see labels in Fig. 1).The integrated maps have the same spatial resolution of 30 ′′ .For the SW-Bar, the velocity range where the CO emissions were found is 100 − 150 km s −1 , and for the DarkPk is between 130 − 165 km s −1 .In the northern regions, N66 and NE-Bar, the velocity range of the CO emission is 140 − 170 km s −1 and 150 − 200 km s −1 , respectively.
We found that most of the clouds in the SW-Bar and N66 regions are detected in both J = 3−2 and J = 2−1 transitions and only a few clouds show weak or even no CO(3−2) emission.For example, in N66, the plume-like component to the northeast and the bar structure to the southwest are well seen in the CO(3 − 2) as in the CO(2 − 1) map.On the contrary, in the DarkPK, there are only four positions, labeled as A, B, C, and D in the bottom panels of Fig. 3, where CO(3 − 2) emission is detected.In the NE-Bar region, being the CO(3 − 2) map much nosier than in the other regions of the SMC, we also detected four clouds, labeled as A, B, C, and D in the bottom panel of Fig. 4.

The CO(3 − 2)-to-CO(2 − 1) ratio in the SMC
We determined R 32 in the SMC using different approaches for each of the regions mapped.
For the SW-Bar and N66 we used the pixel-by-pixel integrated emissions (I CO ) of CO(3 − 2) and CO(2 − 1).In Fig. 5, we plotted the correlation of both integrated emissions for each region.This correlation shows a linear trend in the log-log scale for the stronger emission (low uncertainty), i.e., that with lower than 20% uncertainties in both transitions and therefore not noise-dominated.Assuming that I CO (3−2) is proportional to I CO(2−1) , and representing this by y = a x model, where the slope a gives the integrated CO spectral line ratio (R 32 ), we found that the best fit of Fig. 5a has a slope of a = 0.65 ± 0.05 for the SW-Bar, while for N66 in Fig. 5b, we found a slightly higher slope of a = 0.7 ± 0.1.If we assumed a power-low model (y = α x β ), we found that the power-index is β = 0.94±0.10 and α = 0.74±0.10for SW-Bar, while for N66 the best fit has a power index of β = 0.9 ± 0.2 and α = 0.9 ± 0.2.The two model fits are shown in Fig. 5a and 5b.The scatter of the two correlations increases for the weaker integrated emission, i.e., for uncertainties higher than 20% (high uncertainty), an effect that could be accounted to the lower S/N ratio of CO(3 − 2) compared to that of CO(2 − 1).We adopt the linear fit slope for the R 32 ratio.
As an alternative method to determine a median ratio R 32 in SW-Bar and N66, we made histograms from the R 32 maps (Fig. 6).These histograms are shown in Fig. 7 and were made with the pixel values of the R 32 maps with uncertainties lower than 30%.This limit was estimated to be consistent with the integrated CO emission of low uncertainty (< 20%) in both transitions used in Fig. 5.We found that the median of R 32 for SW-Bar and N66 is 0.65 and 0.8, respectively, both with a standard deviation of 0.3.
For the DarkPK and NE-Bar, we only estimated R 32 using the spectral lines taken from the peak positions indicated in Figs 3 and 4. We show these spectral lines in Fig 8 .In the DarkPK, we found that R 32 ≃ 1 − 2 in the position A, B, C, and D, with ∼ 20 − 50% of uncertainties.While in NE-Bar, we found a R 32 of 0.35 ± 0.04, 0.7 ± 0.2, 0.6 ± 0.2, and 0.9 ± 0.4 for the A, B, C, and D positions, respectively.

SMC CO(3 − 2) Clouds
We have identified 225 CO clouds in the SMC with S/N ratio > 3. Out of this total sample, 201 are well-resolved clouds with R ≥ 1.5 pc.Increasing the S/N ratio ≳ to 5 then 20 clouds are found with only 17 that have resolved sizes.These 17 clouds are the brightest, well-resolved CO clouds in the J = 3−2 transitions at 6 pc resolution that we found in the SMC.The parameters of these clouds are listed in Table 2 4 .
We used all the CO(3 − 2) clouds identified by CPROPS to show the scaling relations between their properties, i.e., sizelinewidth, Luminosity-size, luminosity-velocity dispersion, and virial mass-luminosity.In Figure 9, we plotted the scaling relations for the CO(3 − 2) clouds with S/N ratio ≳ 5 in black dots and the CO(3 − 2) clouds with S/N ratio between 3 and 5 in white dots.However, we only performed linear fits in the log-log scales to these scaling relations using the brightest, well-resolved clouds (S/N ≳ 5), as the parameters of clouds with low S/N ratios tend to be more uncertain (Rosolowsky & Leroy 2006) and will highly affect the linear fit in the scaling relation (see Wong et al. 2011).We followed the procedure indicated in Saldaño et al. (2023) and found the following relationships: log M vir = (0.9 ± 0.5) In each of the five panels of Figure 9, we included the best fit obtained.For comparison, we plotted in blue the distribution of the CO(2 − 1) clouds which contains more than 90% of the Best fit: y = (0.9 ± 0.2)x (0.9 ± 0.2) M vir (hh:mm:ss.s)(dd:mm:ss) (pc) Note: I CO(3-2) and L CO  are in unit of 10 2 K km s −1 and 10 2 K km s −1 pc 2 , respectively.This table only lists those clouds with S/N ≳ 5. Acomplete version of the table, with the 225 clouds identified with S/N > 3, can be found in the online version. Te ID numbers in col. 1 follow the order of the complete table.
CO(2 − 1) clouds with S/N > 5 (Saldaño et al. 2023).This dot density map is plotted in steps of 0.8, 0.4, 0.5, and 0.3 dex per unit area in panels (a) to (d), respectively.We included in the panels the inner Milky Way relationship (Solomon et al 1986).(Saldaño et al. 2023).In all the panels, the best fits for the brightest CO(3 − 2) clouds are indicated by dot-dashed lines.The Solomon et al. (1987) relation is indicated by dotted lines.In panel (e), the dashed horizontal line indicates the median sizes by a factor of 1.9 ± 1.0 and over-luminous for similar velocity dispersion by a factor of 1.7 ± 1.6.The luminosity-virial mass relation (panel d) shows that for luminosities larger than L CO ∼ 3 − 4 × 10 3 , the CO(3 − 2) tend to have larger virial masses than their Milky-Way counterpart at similar luminosity, while for clouds less luminous the virial masses show a larger dispersion in their value.Thus, the scaling relations of the CO(3 − 2) are similar (within the error) to the CO(2 − 1) clouds scaling relations found by Saldaño et al. (2023).
Assuming virial conditions for the CO(3 − 2) clouds, we can estimate the CO-to-H 2 conversion factor (α CO (3−2) ) as the ratio between the virial mass and CO luminosity.In panel (e) of Fig. 9, we plot the conversion factor as a function of the luminosity.We did not find an evident correlation between the CO luminosity and α CO(3−2) (Spearman's ρ = −0.02).The distribution of the conversion factor of the CO(3 − 2) bright clouds has a median value of 11.7 +5 −4 M ⊙ (K km s −1 pc 2 ) −1 .Including those clouds with S/N ratio between 3 and 5, then the median conversion factor is 12.6 +10 −7 M ⊙ (K km s −1 pc 2 ) −1 .

Discussion
6.1.The R 32 in the SMC We found a median R 32 of 0.65 and an average R 32 of 0.7 for the SMC-Bar, with a standard deviation of 0.3.These values are similar to R 32 ≃ 0.6 − 0.8, found in low-metallicity galaxies with metallicities ranging between 0.1 − 0.5 Z ⊙ (Hunt et al. 2017) and somehow higher than the mean ratio R 32 ≃ 0.5 found in the local group of low-mass dwarf galaxies (Leroy et al. 2022).
Depending on the environment of the observed region in the SMC, we found variations of the R 32 values.For example, we estimated a median value of 0.65 in the SW-Bar which is similar to the value in the quiescent SMCB1#1 cloud located in the southwest part of the SMC obtained by Bolatto et al. (2005), although measured at a coarser 109 ′′ (32 pc) resolution than ours at 30 ′′ (9 pc).However, we found that more evolved and active star formation regions (N22, SWBarN, SWBarS, associated to multiple HII regions, see Jameson et al. 2018) have median R 32 = 0.7 − 0.9, higher than the quiescent cloud (see Fig. B.1).This is also the case for N66, the brightest HII region of the SMC, which shows a median R 32 = 0.8 value.
Inspecting the distribution of the R 32 values in the clouds, we found a high dispersion of R 32 in SW-Bar and in N66, between 0.2 and 2.0 (see Fig. 7) which may be an indication of a dependence of R 32 on environmental local conditions (Peñaloza et al. 2018). Figs. B.1 and B.2 show that the highest values of R 32 are associated with strong emission at 8 µm and Hα, while lower values than 0.65 are found in regions that are either in the line-of-sight of the weakest HII regions or not associated to any HII region.Peñaloza et al. (2018) modeled the ISM evolution affected by the interstellar radiation field (ISRF) and found changes in the CO line ratios depending on the environmental conditions.They showed that R 32 can increase by a factor up to ∼ 1.5 − 2.0 as the ISRF increases two orders of magnitudes, which would be consistent with our findings.
In the DarkPK, the four points (A, B, C, and D) where we estimated R 32 (see Figs. 4 and 8) give R 32 = 1 − 2. Such high ratios were not expected, as the DarkPK has no signs of active star formation.This region is dominated by the ISRF and has a low range of visual extinction, A V < 1 (Jameson et al. 2018).In this region, the far-ultraviolet photons from evolved stellar sources controlling the gas heating and chemistry would be dissociating more rapidly the CO(2 − 1) in the external part of the H 2 envelopes than the CO(3 − 2) located in the innermost part of the molecular cloud.In this scenario, there would be a CO(2 − 1) deficiency increasing R 32 above the median value.In the NE-Bar region, the integrated CO spectral line ratio towards cloud A is R 32 = 0.35 ± 0.04, while R 32 towards cloud B, C, and D is R 32 ≥ 0.6.The cloud B is on the low R 32 range found and it is not associated neither with strong 8 µm emission nor HII regions, meanwhile, clouds B, C, and D, are on the high R 32 range, and are associated to the strongest peak emission at 8 µm and Hα (see Fig. B.2).

Environment dependence of R 32 in the SMC
In order to explore the dependence of R 32 with observational properties, we made correlations with CO emission, far IR (FIR) color, and total IR (TIR) surface brightness which trace star formation activity.We used the intensity of CO(2−1) and CO (3−2) shown in our study, the Herschel bands (100 − 250 µm) from HERITAGE (Gordon et al. 2014), and the Spitzer MIPS 24, 70 and 160 µm from SMC-SAGE (Gordon et al. 2011).We convolved the images to the HERITAGE Herschel maps to have a common resolution and spatial grid maps.In this analysis, the parameters estimated by the integrated maps of both SW-bar and N66 CO data cubes were used jointly and are referred to as SMC-Bar in the plots.
We show the correlation of R 32 with the local integrated intensity of CO(3 − 2) and CO(2 − 1) in the panels (a) and (b) of Fig. 10, respectively.We found a very weak correlation of R 32 with CO(3 − 2), with a Spearman's correlation ρ S = 0.4.At high brightness temperature in the CO J = 3 − 2 transition, reliable values of R 32 (lower uncertainty than ∼ 25%) tend to have values higher than the median value.However, in low brightness temperature regions, R 32 shows a higher dispersion giving a hint of values lower than the median.On the contrary, R 32 do not correlate with CO(2 − 1) (Spearman's correlation is ρ S = −0.1).
The correlation of R 32 with the FIR color [70/160] of the Spitzer bands is shown in panel (c) of Fig. 10, with a Spearman's coefficient of ρ S = 0.5.The R 32 increases for higher values of the FIR color.For environments with FIR colors [70/160] larger than 0.8, most of the R 32 have values above the median of 0.65 determined for the SMC-Bar.This correlation is similar to finding in nearby disk galaxies (den Brok et al. 2021), based on the integrated spectral line CO(2−1) to CO(1−0) ratio (R 21 ) instead.As the FIR color trace dust temperature and also interstellar radiation field (ISRF) strength, R 32 in the SMC-Bar is found higher in active star-forming regions, where the ISRF, dust temperature, and the density of the gas should be higher.
Finally, we correlated R 32 with the TIR surface brightness in the SMC-Bar as shown in panel (d) of Fig. 10.To determine the TIR surface brightness we have followed the same method described in Jameson et al. (2018), where the Spitzer MIPS 24 and 70 µm bands are combined to the Herschel 100, 160, and 250 µm bands by using the equation S TIR = c i S i .S TIR is the TIR surface brightness, and S i is the brightness in the given Spitzer and Herschel bands i.Both are in the unit of W kpc −2 and c i is the calibration coefficient from combined brightness provided by Galametz et al. (2013).We found a moderate correlation between R 32 and the TIR surface brightness (Spearman's coefficient ρ S ≃ 0.4).R 32 tends to be lower than the median value for low TIR surface brightness, while R 32 tends to increase above the median value for higher TIR surface brightness.The TIR surface brightness scales with the molecular gas surface density, where we expect that the star formation activity may be embedded.Our finding indicates that R 32 in the SMC-Bar tends to be higher in very active, and dense star-forming regions.
These correlations could be useful to consider when using R 32 as a diagnostic for environmental properties in external galaxies.To improve these correlations, higher sensitivity observations are needed as these will allow us to increase the range in the observed properties.Moreover, the coarser resolution of the Spitzer and Herschel data used does not allow us to study the smaller structures resolved in this work since the ISM properties are averaged over larger areas.
Considering these caveats, our results indicate that values of R 32 typically ∼ 0.7 − 1.0, in general, were found toward active star-forming regions.These regions are usually excited by HII regions and/or shock emission.While lower R 32 ratios (≲ 0.6) were found in more quiescent regions.This behavior is consistent with those found in other galaxies and in semi-analytic studies of the ISM, in which R 32 (including ratios in other transitions) increase in more active star-forming regions and/or denser and hotter gas, poorly shielded by dust (Peñaloza et al. 2018;Celis Peña et al. 2019;den Brok et al. 2021;Leroy et al. 2022).

Scaling Relation in the SMC
We identified 225 CO clouds in the J = 3 − 2 transition at 6 pc resolution, and we determined their main properties, such as R, σ υ , L CO , M vir .However, we analyzed the scaling relationships for 17 high S/N (≳ 5) ratio clouds due to the limited sensitivity of our CO(3 − 2) survey.Despite the low number of clouds at high S/N ratios, our results are consistent with the study of the scaling relations in the SMC obtained at different spatial resolutions, from 1 to 100 pc (Bolatto et al. 2008;Saldaño et al. 2018Saldaño et al. , 2023;;Kalari et al. 2020;Ohno et al. 2023).It seems that independent of the J-transitions and the cloud identification algorithm used, the cloud properties in the scaling relationships would be intrinsic to the SMC.
For example, in the size-linewidth relation (Fig. 9a), we found that the CO(3 − 2) clouds are below the Milky-Way clouds of similar size by a factor of 1.3.In the CO(2 − 1) survey of the SMC, Saldaño et al. (2023) indicate that such departure is by a factor of ∼ 2, and they explained that it might be due to the CO cloudlets in the SMC, which can not trace the total turbulence of larger H 2 envelopes (see Bolatto et al. 2008).They also discard a deficit of turbulent kinetic energy in CO clouds to explain such departure in the size-linewidth relation since these clouds would be gravitationally bounded.Ohno et al. (2023) showed similar results in their CO(2 − 1) survey at 2 pc resolution in the SMC, finding a departure factor of 1.5 below the Milky-Way trend.These authors ascribe this departure to lower column densities (by a factor of 2) than those in the Milky Way clouds of similar size.
Finally, we found that α CO(3−2) of our SMC clouds showed a flattened trend with L CO(3−2) (Fig. 9e) between 10 2 − 10 4 K km s −1 pc 2 .We determined a median value of 11.7 +5   (Gordon et al. 2011), and in panel (d), R 32 as a function of the TIR surface brightness from Spitzer and Herschel bands (Gordon et al. 2011(Gordon et al. , 2014)).The red and black dashed lines in all panels indicate the median value of R 23 and the best fit, respectively.The Spearman's correlations (ρ S ) and the best-fit equations (in log-log scale) are located in the right bottom corners.  in the same regions, we found that α CO(3−2) at 9 pc resolution is 14.5 +8 −7 M ⊙ (K km s −1 pc 2 ) −1 , a bit higher than that estimated at 6 pc.Despite the uncertainties in the determination of conversion factors, α CO(3−2) tend to be higher than α CO(2−1) by a factor of ∼ 1.4, which agrees with our estimation of 1/R 32 ∼ 1.5.This result is expected for CO clouds that tend to have lower luminosities at higher J-transitions, while the virial mass would not change considerably.

Conclusions
The main conclusion of the SuperCAM CO  survey can be summarized as follows: telescope, located in Llano de Chajnantor, near San Pedro de Atacama, Northern Chile.The galaxy was mapped in the CO(3−2) line during the period the visiting instrument Su-perCAM was deployed.The observations were done on two dates, 2014 December 08, and 2015 May 16, 2015 (PI.M. Rubio, Project C-095.F-9707B, C-094.F-9306A, PI. A. Bolatto O-094.F-9306A).

1 Fig. 2 .
Fig. 2. CO(3 − 2) integrated map of the SMC-BAR observed by SuperCAM.The integration was done within the velocity range of clouds with high S/N ratios (> 3).We included an artificial homogeneous background noise in the map to enhance the appearance of the detected clouds.The real background noise is shown in Fig. A.1.

Fig. 3 .Fig. 4 .
Fig. 3. Integrated CO emission in the SW-Bar and DarkPK.All maps were obtained with the moment-masked method.The left panels correspond to the transition J = 3 − 2, while the right panels show the CO emission in the transition J = 2 − 1.The spatial resolution of 30 ′′ is indicated in the bottom right corner of all maps.The upper panels were used to determine R 32 pixel-by-pixel.In the DarkPK regions, the boxes A, B, C, and D indicate the positions that showed reliable CO emission in both transitions to estimate R 32 .

Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .
Fig. 5. Relationship between I CO(3−2) and I CO(2−1) for SW-Bar and N66.The integrated emission in both transitions has S/N > 3. The green dots (indicated as low uncertainty) correspond to integrated emission with relative uncertainties < 20% in both transitions.The white dots indicate integrated emissions with higher relative uncertainties.The solid and dashed red lines show the best fits of the low uncertainty data assuming a linear and a power-law model, respectively.

Fig. 9 .
Fig. 9. Scaling relations of the CO(3 − 2) clouds parameters in the SMC: panel a) the size-linewidth relation (σ υ − R), panel b) the luminosity-size relation (R − L CO ), panel c) the luminosity-linewidth relation (σ υ − L CO ), panel d) the luminosity-virial mass relation (L CO − M vir ), and panel e) the CO-to-H 2 conversion factor-luminosity relation (α CO − L CO ).The black dots correspond to clouds with S/N ratio ≳ 5, while the gray dots correspond to clouds with S/N between 3 and 5.For comparison, we plot the distribution of the CO(2 − 1) clouds in a blue color palette scale showing the concentration of the CO(2 − 1) clouds(Saldaño et al. 2023).In all the panels, the best fits for the brightest CO(3 − 2) clouds are indicated by dot-dashed lines.The Solomon et al. (1987) relation is indicated by dotted lines.In panel (e), the dashed horizontal line indicates the median α CO(3−2) of 12.6 +20 −7 M ⊙ (K km s −1 pc 2 ) −1 .

Fig. 10 .
Fig. 10.Environment dependence of R 32 .The ratio (with uncertainty lower than ∼ 25%) is correlated with the local intensity of CO(3 − 2) and CO(2 − 1) in panels (a) and (b), respectively.In panel (c), R 32 as a function of the far-infrared color of the Spitzer MIPS bands(Gordon et al. 2011), and in panel (d), R 32 as a function of the TIR surface brightness from Spitzer and Herschel bands(Gordon et al. 2011(Gordon et al. , 2014)).The red and black dashed lines in all panels indicate the median value of R 23 and the best fit, respectively.The Spearman's correlations (ρ S ) and the best-fit equations (in log-log scale) are located in the right bottom corners.

Table 2 .
Physical parameters of CO(3 − 2) clouds in the SMC