Cloud-Scale Molecular Gas Properties of the Antennae Merger: A Comparative Study with PHANGS-ALMA Galaxies and NGC 3256

We present observations of the central 9 kpc of the Antennae merger (NGC 4038/9) at 55 pc resolution in the CO 2-1 line obtained with the Atacama Large Millimeter/submillimeter Array (ALMA). We use a pixel-based analysis to compare the gas properties in the Antennae to those in 70 nearby spiral galaxies from the PHANGS-ALMA survey, as well as the merger and nearest luminous infrared galaxy NGC 3256. Compared to PHANGS galaxies at matched spatial resolution, the molecular gas in the Antennae exhibits some of the highest surface densities, velocity dispersions, peak brightness temperatures, and turbulent pressures. However, the virial parameters in the Antennae are consistent with many of the PHANGS galaxies. NGC 3256 has similar gas surface densities but higher nuclear velocity dispersions than the Antennae, as well as higher system-wide peak brightness temperatures and virial parameters. NGC 3256 is at a later stage in the merging process than the Antennae, which may result in more intense merger-driven gas flows that could drive up the turbulence in the gas. The high virial parameters in NGC 3256 may indicate that this increased turbulence is suppressing future star formation as NGC 3256 moves out of the starburst phase. In comparison, the relatively normal virial parameters in the Antennae may imply that it is about to undergo a new burst of star formation.


INTRODUCTION
From the spatial correlation of molecular gas and recent star formation seen in galaxies throughout the universe, we know that stars form from molecular gas.The efficiency with which molecular gas is converted into stars has been observed to be fairly similar at subkiloparsec scales across many nearby spiral galaxies (Leroy et al. 2008).However, the global star formation efficiency (SFE) (calculated from the star formation rate (SFR) and molecular gas mass (M mol ) via SFE = SFR/M mol ) for the most actively star-forming galaxies deviates from what is observed in more normal spiral galaxies (e.g.Kennicutt & de los Reyes 2021).Observations of these different star-forming regimes, done at comparable angular resolutions and sensitivities and using the same tracer, will allow us to understand what causes this difference in star formation efficiency.
Both global and kiloparsec-scale observations of spiral galaxies and starbursts have revealed the difference in SFEs but not the cause (e.g. de los Reyes & Kennicutt 2019; Wilson et al. 2019; Kennicutt & de los Reyes 2021), so observations of the molecular gas at smaller scales are the natural next step.Many nearby spiral galaxies have been observed in molecular gas at scales around 100 pc and even smaller (e.g.Schinnerer et al. 2013;Leroy et al. 2021b), but the relative rarity of and distance to starbursting galaxies have precluded similar observations.Brunetti et al. (2021) and Brunetti & Wilson (2022) presented the highest spatial-resolution observations (∼100 pc) of molecular gas in NGC 3256, a luminous infrared galaxy (LIRG) and actively star-forming merger.Comparisons to the Physics at High Angular resolution in Nearby GalaxieS with ALMA (PHANGS-ALMA) homogeneous survey of 70 nearby spiral galaxies (Sun et al. 2020;Leroy et al. 2021b) at matched resolution revealed that the molecular gas in the merger reaches some of the highest mass surface densities, velocity dispersions, peak brightness temperatures, virial parameters, and internal turbulent pressures seen in the sample.However, a single merger that happens to be the nearest LIRG cannot be expected to be representative of all merging and starbursting systems.To extend the sample of mergers, we have observed NGC 4038/9 (Arp 244, "the Antennae") at ∼100 pc spatial resolution to add it to these comparisons of molecular gas properties.At a distance of 22 Mpc (Schweizer et al. 2008), NGC 4038/9 is the nearest gas-rich major merger (Stanford et al. 1990;Wilson et al. 2000;Gao et al. 2001a;Wilson et al. 2003;Brandl et al. 2009; Ueda et al. 2012;Schirm et al. 2014;Bigiel et al. 2015) with ∼2 × 10 10 M ⊙ of molecular gas in the central region.Based on a significant body of numerical work on reproducing the morphology and kinematics of the interaction, the system is currently either just before or just after the second pericentre passage (e.g.Toomre & Toomre 1972;Barnes 1988;Mihos et al. 1993;Karl et al. 2010;Teyssier et al. 2010;Privon et al. 2013;Renaud et al. 2015).Its central region hosts two progenitor nuclei separated by about 7 kpc.Given these orbital details, NGC 4038/9 is likely at an earlier merger stage than NGC 3256, and so offers a chance to probe how the molecular gas properties depend on the phase of the merger.
The total SFR of the Antennae is between 11 M ⊙ yr −1 (separately estimated from far-ultraviolet probing ∼1 to 100 Myr and 24 µm probing ∼1 to 400 Myr) and 20 M ⊙ yr −1 (from H probing ∼1 to 10 Myr; Chandar et al. 2017).Although not technically a LIRG from its infrared luminosity, the higher of these SFR estimates would give the Antennae a similar SFR to LIRGs.Separated from the nuclei is the starbursting "overlap region" which alone exhibits a SFR of about 4 M ⊙ yr −1 over the last ≲100 Myr estimated from mid-through farinfrared observations (Brandl et al. 2009;Klaas et al. 2010;Bemis & Wilson 2019).The remainder of the central part of the merger has an infrared-estimated SFR totaling about 2.6 M ⊙ yr −1 (Bemis & Wilson 2019).
NGC 4038/9 hosts an estimated population of at least 10 4 young massive star clusters, with masses in some cases exceeding 10 6 M ⊙ (Whitmore et al. 2010;Chandar et al. 2015;Mok et al. 2020).Several stellar populations of different ages have also been identified throughout the system with a young starburst population in the overlap region (∼3 to 10 Myr; Mengel et al. 2001Mengel et al. , 2005;;Whitmore et al. 2010) and older post-starburst populations in the nuclei (∼65 Myr; Mengel et al. 2001).Exploring the molecular-gas properties of this system will provide the details on what conditions are necessary to form the most massive star clusters (e.g.He et al. 2022).Our understanding of nearby mergers like NGC 4038/9 should also fill in the small-scale information on how star and cluster formation occurred at high redshift, where mergers were much more common (e.g.Romano et al. 2021) and when the progenitors of globular clusters formed.
In this paper we present Atacama Large Millimeter/Submillimeter Array (ALMA) observations of the central ∼9 kpc of NGC 4038/9 in the carbon monoxide (CO) =2-1 line at linear scales of 55 pc, corresponding to giant molecular cloud (GMC)-scales, and use them to probe the molecular gas properties across the diverse interstellar medium (ISM) of NGC 4038/9.These observations have comparable sensitivity and resolution but are a significant improvement in area coverage (see Figure 1), and image fidelity (covering the full range of spatial scales) over earlier ALMA observations of the Antennae (Whitmore et al. 2014;Sun et al. 2018).Section 2 describes the new observations, along with our calibration and imaging procedure for the CO (2-1) data.In Section 3 we describe the pixel-based method used to measure the molecular gas properties in NGC 4038/9 at a range of spatial resolutions.In Section 4, we compare NGC 4038/9 to the PHANGS-ALMA results presented by Sun et al. (2018Sun et al. ( , 2020) ) and the LIRG NGC 3256 presented in Brunetti et al. (2021), and we discuss the implications in Section 5. Finally, in Section 6 we summarize the results and conclusions of this work.

Observations
Mosaicked ALMA observations of the central ∼9 kpc of NGC 4038/9 covering the entire disks of the two merging galaxies were obtained in Cycle 6 (see Table A1 for details of the observations).The main 12 m-array was used in both a compact and extended configuration.The Morita Atacama Compact Array (ACA) was included for sensitivity to larger-scale emission, and the total power (TP) array was also included to capture the largest-scale emission.Band 3 and 6 observations were carried out with spectral setups designed to cover the =1-0 and =2-1 rotational transitions of 12 CO, the =1-0 transitions of C 17 O and the cyanide radical (CN), and the =2-1 transitions of 13 CO and C 18 O.Sufficient bandwidth was covered to also allow detection of continuum emission in both bands.The spectral resolution of the 12 CO (2-1) spectral window is 1.953 MHz, or approximately 2.54 km s −1 .The native beam size is 0.51 ′′ (55 pc) and the rms noise at this resolution is 0.24 K.The calibration accuracy of ALMA at these frequencies is 5%.This paper focuses on the 12 CO =2-1 line; the continuum data products have been presented in He et al. (2022).The remaining CO spectral lines are presented in He et al. 2024 (submitted).

Calibration and imaging
Calibration of all interferometric data was carried out by observatory staff as part of data quality assurance using the ALMA pipeline for Common Astronomy Software Applications (casa) (McMullin et al. 2007); casa and pipeline versions used for calibration are summarized in Table A1.After downloading the raw data from the archive, we used the same versions to reapply the calibration prior to our imaging.We inspected the diagnostic plots in the observatory weblogs to search for problematic data that were not properly calibrated or left unflagged by the ALMA pipeline.Nothing was identified that was serious enough to warrant changes to the calibration or additional flagging.
Given the complex morphology of molecular line emission expected in the Antennae at the resolution of our observations, and the number of lines to be imaged, we requested access to an early version of the PHANGS-ALMA imaging pipeline 1 for casa (Leroy et al. 2021a).Starting from the version-one code (at commit 5ef53d3), we made modifications for imaging the additional array combinations and spectral lines included in our observations of NGC 4038/9 2 .These modifications include implementation of different angular sizes of the model components during multi-scale cleaning, for which we use point sources, 0.5, 1, 2.5, 5, and 10 arcsec.All spectral-line cleaning was carried out using the newest casa version available at the time (5.6.1-8) to run the PHANGS-ALMA imaging pipeline.The observations from the two 12 m-array configurations and the ACA were all imaged and cleaned together.Cleaned cubes were also visually inspected for artefacts related to calibration and cleaning errors before combining with the TP data.
TP data processing was carried out with the PHANGS-ALMA TP calibration and imaging pipeline for casa in casa version 4.7.2 (see Table A1 for more details).This version of casa was the newest version that the TP pipeline had been tested with at the time.Herrera et al. (2020) describe the full details of the pipeline procedure.We used a modified version that does not perform any spectral bin- 1 The procedure followed by the imaging pipeline has not changed dramatically between version one and the version described in detail by Leroy et al. (2021a). 2 Details of these modifications are given in Appendix A. Our modified version of the imaging pipeline will be shared on reasonable request to the corresponding author, with a fully annotated Git change history.ning and all continuum subtraction was carried out using order-one polynomial (linear) fits to the continuum levels.
The interferometric and TP cubes were combined using the PHANGS-ALMA imaging pipeline to produce the complete measurements of the spectral line emission in NGC 4038/9 (again using casa version 5.6.1-8).Interferometric cubes corrected for the primary beam response were first made by dividing by the primary beam cubes, and the corrected cubes were convolved to have circular synthesized beams.The interferometric cubes were padded with masked pixels to cover at least the entire TP field of view (FoV), and the TP cubes were regridded on to the same astrometric and spectral grid as the interferometric cubes.Using the feather task in casa, the TP cubes were combined with both main array configurations plus the ACA.The feathered cubes still contain the primary beam response applied to the interferometric data (and the inherent response in the TP data), so another copy of the cubes was made which was multiplied by the interferometric primary beam response to produce flat-noise cubes for future use in identifying individual clouds using algorithms such as pycprops (Rosolowsky et al. 2021).
Several versions of the interferometric cube were made when the synthesized beam was made circular, with FWHM physical sizes of 55, 80, 90, 120, and 150 pc.These beam sizes facilitate direct comparisons to the analyses at 55, 80, and 120 pc by Sun et al. (2018) and Brunetti et al. (2021), as well as at 90 and 150 pc by Sun et al. (2020) and Brunetti & Wilson (2022).The cube with 55 pc resolution (0.51 arcsec) has an rms noise of approximately 0.25 K. Following Sun et al. (2018) and Brunetti et al. (2021), after feathering the TP data with the convolved interferometric cubes, each cube was spatially regridded such that the pixels were half the synthesized beam FWHM on a side to roughly Nyquist sample the beams.Moment maps calculated from the CO (2-1) data cube as described in Brunetti et al. (2021) are shown in Figure 1.

Measuring molecular gas properties
Maps of total molecular gas mass surface density (Σ mol ), velocity dispersion (  ), and peak brightness temperature ( B,max ) were calculated in the same way as in Brunetti et al. (2021).The only difference was that we adopted a single Milky-Way like conversion factor of  CO(2−1) = 4.35/0.70= 6.25 M ⊙ pc −2 (K km s −1 ) −1 for all measurements from NGC 4038/9, following Sun et al. (2018), where 0.70 is the commonly used value for the 12 CO =2-1 / =1-0 line ratio (cf.Leroy et al. 2022).Using the same conversion factor as Sun et al. (2018) means any differences in the estimated mass surface densities originate from different integrated intensities.The conversion factor in NGC 4038/9 is not yet well constrained (see Section 5 for further discussion) but previous investigation has estimated it may be similar to the typical Milky Way value (Wilson et al. 2003).This conversion factor includes a contribution from helium and other heavy elements.
From our measurements of Σ mol and   we also estimate the virial parameter and internal turbulent pressure in each pixel, following Sun et al. (2020), with and where  beam is the FWHM of the synthesized beam.These are equivalent to equations 13 and 15 from Sun et al. (2018) that were used by Brunetti et al. (2021).As described in Sun et al. (2018), these equations assume that a single cloud roughly fills each synthesized beam along with the equation for the virial parameter assuming a cloud density profile that goes as () ∝  −1 .Maps of molecular gas properties at 55 pc resolution are shown in Figure 2; maps at 150 pc resolution are shown in Figure A1.We provide the binned data used in this paper for both NGC 4038/9 and NGC 3256 as two separate machine-readable tables (see Table B1 and B2 for format).Note that we use square pixels, following Sun et al. (2018) and Brunetti et al. (2021), but Sun et al. (2020) resample their maps to have hexagonal pixels that match the beam size before measuring the gas properties.

Separating measurements by region
To examine the impact that the location within NGC 4038/9 has on the molecular gas properties, we separate our measurements into sub-samples that are close to the nuclei and farther away.Following Sun et al. (2018) and Brunetti et al. (2021), all pixels that are less than 1 kpc from either nucleus (shown as gray circles with radii of 1 kpc in Figures 2 and A1) are included in the nuclear pixel sample, and the remaining pixels make up the non-nuclear sample.Since the CO (3-2) observations of NGC 4038/9 from Whitmore et al. (2014) analysed by Sun et al. (2018) only covered the overlap region, we also separate pixels in our CO (2-1) data into another sub-sample that lies in the same on-sky footprint as the CO (3-2) observations for direct comparisons between the two datasets (gray polygons in Figures 2 and A1).Note that Sun et al. (2020) separate their aperture measurements into central and disc regions within each galaxy based on distinct structures identified in near-infrared images (the full description of this methodology is given by Querejeta et al. 2021) rather than by a 1 kpc radius as we do in this work3 .

Morphology of the CO emission at 55 pc resolution
The CO emission of the Antennae shown in Figure 1 has a very complex structure.As seen in earlier work (Stanford et al. 1990;Wilson et al. 2000;Ueda et al. 2012), the regions of highest integrated intensity in the moment 0 map are found in the northern nucleus (NGC 4038), the southern nucleus (NGC 4039), and the overlap region.These regions with high integrated intensities also typically show large line widths in the moment 2 map and high brightness temperatures and pressures (Figure 2).Both nuclei show rather distorted morphologies, especially NGC 4039, with filaments at different pitch angles emerging from each nucleus.
The velocity field shown in the moment 1 map is particularly striking in appearance, with sudden shifts in velocity on the scale of a few resolutions elements visible in many parts of the map.The western arm (to the west of NGC 4038) shows a consistent velocity gradient reminiscent of the velocity field of a rotating disk, but this interpretation is hard to reconcile with the quite redshifted emission from the nucleus of NGC 4038 itself.The emission in the central 40 arcsec of NGC 4039 also suggests large-scale rotation, but this organized structure breaks up in the central 5-10 arcsec, where several shifts from red-to blue-shifted emission are seen.There are a variety of filamentary structures visible in the integrated intensity map, including the long filament to the east of NGC 4039 highlighted in Espada et al. (2012), and also a variety of other similar structures particularly to the south of the NGC 4038 nucleus.While these structures typically exhibit narrow line widths in the moment 2 map, some of them show a nearly constant radial velocity in the moment 1 map while others shows signs of a gradient in radial velocity along their length.

RESULTS
In this section, we compare the molecular gas properties of NGC 4038/9 with spiral galaxies from the PHANGS-ALMA survey as well as with the merger and nearest LIRG NGC 3256.In Section 4.1 we present the mean values for gas mass surface density, velocity dispersion, and peak brightness temperature along with two derived quantities, the virial parameter and the turbulent pressure.In this analysis, we distinguish between the central nuclear regions and the rest of the disk.In Section 4.2, we examine the correlations between velocity dispersion and mass surface density in the various galaxies and regions.

Distribution of cloud-scale molecular gas properties
Qualitative comparisons between NGC 4038/9, NGC 3256, and the PHANGS-ALMA galaxies presented by Sun et al. (2018) at 120 pc resolution are shown as mass-weighted medians (symbols) and inner 68 th percentiles (errorbars) in Figure 3. Galaxies are split between nuclear (triangles) and non-nuclear (circles) sub-samples, with the Whitmore et al. ( 2014) overlap region FoV also included for NGC 4038/9 (stars).Figure 4 shows the mass-weighted distributions of the various sub-samples from NGC 4038/9 and NGC 3256 smoothed with Gaussian kernel density estimators (KDEs, e.g.Sun et al. 2018)  4 .
There is considerable overlap in all cloud-scale properties between the nuclear and non-nuclear sub-samples from NGC 4038/9.NGC 4038/9 exhibits higher mass surface densities measured in CO (2-1) relative to all the PHANGS-ALMA galaxies 5 in Figure 3.The nuclear and non-nuclear surface density samples from NGC 4038/9 and NGC 3256 are similar.Mass surface density distributions from the central regions of PHANGS-ALMA galaxies overlap the most with NGC 4038/9, but the disc region distributions from several galaxies also overlap with NGC 4038/9.However when comparing nuclei to nuclei and non-nuclei to non-nuclei, the samples from NGC 4038/9 are wider, have slightly higher medians, and extend to higher surface densities at all resolutions.The greater sample spread and maximum surface densities stand out especially in Figure 4.
The results of comparing NGC 4038/9 to the PHANGS-ALMA galaxies in velocity dispersion, peak brightness temperature, and internal turbulent pressure are similar to those seen in mass surface density, with the central regions of the PHANGS-ALMA galaxies overlapping the most with NGC 4038/9.NGC 4038/9 exhibits some of the highest values, although the centres of NGC 3256 and sometimes NGC 3627 often reach significantly higher values.NGC 4038/9 appears most consistent with the PHANGS-ALMA galaxies in virial parameter, with the relatively low median and very large sample width meaning it overlaps at least partially with all PHANGS-ALMA galaxies.The higher mass surface densities and slightly lower velocity dispersions measured in CO (3-2) in NGC 4038/9 lead to virial parameter samples from the CO (3-2) measurements that are much lower than in CO (2-1) via Equation 1.However, Equation 2 results in the CO (3-2) sample of internal turbulent pressures being only 4 Measurements at 120 pc resolution are shown but comparisons at 80 pc and 55 pc resolution were also made with generally the same results as seen in Figures 3 and 4. 5 We note that the surface density values derived from the CO (3-2) measurements for NGC 4038/9 from Sun et al. (2018) exceed the CO (2-1) values.This difference is likely due to the assumed value for the CO =3-2 / =1-0 line ratio being smaller than the value observed in He et al. 2024 (submitted).   .Mass-weighted Gaussian KDEs of the 120 pc resolution measurements from the entire FoVs of NGC 4038/9 and NGC 3256 in the solid orange and black lines, respectively.The samples from NGC 4038/9 are also separated into regions near the nuclei (dotted), farther than 1 kpc from the nuclei (dashed), and within the Whitmore et al. (2014) overlap region FoV (dash-dotted).The blue-shaded regions show where the whole-FoV sample from NGC 4038/9 is above the sample from NGC 3256.Gaussian KDE bandwidths for the whole FoV samples were automatically chosen using the scipy implementation of Scott's Rule (Scott 1992), and the other regions from NGC 4038/9 use the same bandwidth as that of the whole FoV.slightly higher than in CO (2-1).Peak brightness temperatures are also similar between the two spectral line samples.
In properties other than mass surface density, the medians from NGC 4038/9 are often lower than those measured in NGC 3256.The two mergers appear most consistent in their non-nuclear samples of velocity dispersion and pressure, though the sample from NGC 4038/9 is wider, extending both above and below the sample from NGC 3256.The comparison of virial parameters in NGC 4038/9 and NGC 3256 is quite different from the other gas properties.The median virial parameter in NGC 4038/9 is less than half that in NGC 3256.The nuclear median from NGC 4038/9 also appears lower than that of the non-nuclear pixels, contrary to NGC 3256 but similar to what is seen in the centres and discs of the PHANGS-ALMA galaxies.However, the spread of the samples from both NGC 4038/9 and NGC 3256 does result in considerable overlap in the virial parameter between the two mergers.
The same comparisons of physical properties are made in Figure 5 but the samples from NGC 4038/9 are now shown with the full PHANGS-ALMA sample analysed by Sun et al. (2020) at 150 pc resolution6 .Note that we made the separation of pixels into regions in the PHANGS-ALMA galaxies in the same manner as for NGC 4038/9, not using the centre and disc designations from Sun et al. (2020).We chose this approach to reduce variability in the comparison with NGC 4038/9 potentially brought on by differences in how pixels are assigned to the different regions.Using the simple 1 kpc radius also has the benefit of often increasing the number of pixels within the centres of galaxies, resulting in less stochastic inner 68 th percentiles for the less massive and/or more distant galaxies.However, given the size-stellar mass relation of galaxies, the fraction of a galaxy included in the central region will increase as stellar mass decreases.For example, across the stellar mass range (1.2 × 10 9 to 8.3 × 10 10 M ⊙ ) of the PHANGS-ALMA galaxies shown in Figure 5, a range of stellar radii of about 6 to 30 kpc is expected (Trujillo et al. 2020;Sánchez Almeida 2020).This effect will likely result in the percentiles from the centres of low stellar mass galaxies being underestimated since contaminating disc pixels will make up a larger fraction of pixels in their central 1 kpc.
Trends in the medians and inner 68 th percentiles with resolution are not very strong in NGC 4038/9 so the GMC measurements for the Antennae in Figure 5 do not appear very different compared to Figure 3.The general trends between NGC 4038/9 and PHANGS-ALMA disc galaxies observed in Figure 3 appear in the comparisons in Figure 5 as well.The centres of PHANGS-ALMA galaxies are the most similar to NGC 4038/9, regardless of spatial scale, with greater similarities at higher stellar masses.NGC 4038/9 exhibits some of the highest mass surface densities, velocity dispersions, peak brightness temperatures, and internal turbulent pressures compared to the PHANGS-ALMA galaxies.Virial parameters measured in NGC 4038/9 are much more similar to typical values measured in PHANGS-ALMA galaxies.Finally, for each property shown in Figure 5, there are usually at least a few PHANGS-ALMA galaxies that are more extreme in one or more aspects than NGC 4038/9.PDFs are made from Gaussian KDEs, with bandwidths automatically chosen using the scipy implementation of Scott's Rule (Scott 1992).

Correlations between velocity dispersion and mass surface density
Figure 6 shows velocity dispersion vs. mass surface density PDFs of all significant pixels from NGC 4038/9, NGC 3256, and apertures from all galaxies presented by Sun et al. (2020).KDEs show measurements made at 150 pc resolution in NGC 4038/9 and PHANGS-ALMA and 120 pc resolution in NGC 32567 .The shift of most of the mass to both higher surface densities and velocity dispersions in NGC 4038/9 and NGC 3256 is visible, but the lower values from the merger samples overlap with the higher values from the PHANGS-ALMA galaxies.The apertures from the centres of (primarily barred) PHANGS-ALMA galaxies populate a very similar part of the parameter space to NGC 4038/9 and NGC 3256 (see Figure 2 from Sun et al. 2020 for the separation of PHANGS-ALMA samples by region and whether a galaxy contains a bar).These central values make a dispersion-surface density trend that is slightly offset to higher velocity dispersion for a given surface density from the rest of the PHANGS-ALMA sample.The dispersion-surface density trends in the merger samples are more consistent with this offset PHANGS-ALMA trend.There may also be evidence for the merger sample trends broadening at high surface densities, extending to higher velocity dispersions at a given surface density than the PHANGS-ALMA sample.This broadening in velocity dispersion would also produce a larger range of virial parameter at high surface densities (see Equation 1).However, the sensitivity limit in this parameter space roughly follows the upper-left edge of the contours (see Figure 1 from Sun et al. 2020), so that we do not have enough sensitivity to detect low surface density regions with large velocity dispersions.This effect is likely truncating the extent of the scatter in velocity dispersion seen along the trends for NGC 4038/9 and NGC 3256 at lower surface densities.To explore if the trends in the mergers truly broaden only at high surface densities or are possibly broader than the PHANGS-ALMA trend at all surface densities would require observations with a sensitivity a factor of two to four times better than the current dataset.
Figure 7 shows the same contours for NGC 3256 and the PHANGS-ALMA galaxies, but now the sample from NGC 4038/9 is split into pixels within 1 kpc of either nucleus and those beyond.As already seen in Figures 3 and 5, pixels near the nuclei of NGC 4038/9 exhibit higher surface densities and velocity dispersions.The twodimensional view also emphasizes the split between regions is not perfect as there is considerable overlap between the two sub-samples in NGC 4038/9.The nuclear regions of NGC 4038/9 are generally most consistent with the centres of (mostly barred) PHANGS-ALMA galaxies, while the non-nuclear region extends over nearly the complete range limits of the full PHANGS-ALMA sample (both discs and centres), likely due to the presence of the high surface density overlap region within the non-nuclear region of NGC 4038/9.A similar separation of samples by nuclear and non-nuclear regions is seen in NGC 3256 (see figure 7 from Brunetti et al. 2021).We also note that the trend of velocity dispersion with surface density appears stronger in the non-nuclear sample from NGC 4038/9 than the nuclear sample, such that a majority of the mass in the nuclear sample actually appears with nearly constant velocity dispersion with surface density.This feature may indicate our choice of CO-to-H 2 conversion factor is not appropriate for regions near the nuclei of NGC 4038/9, and we discuss this possibility further in Section 5.  Sun et al. (2018Sun et al. ( , 2020)), which did not use mass weighting.

Comparison of the two mergers
NGC 4038/9 and NGC 3256 are in different merger stages and the two systems also show significant differences in their molecular gas conditions.Such differences are indeed predicted by merger simulations.Previous numerical work on replicating the morphology and kinematics of NGC 4038/9 seems to point towards it being sometime around second pericentre passage (Toomre & Toomre 1972;Barnes 1988;Mihos et al. 1993;Karl et al. 2010;Privon et al. 2013;Renaud et al. 2015), with the large gas content suggesting that it may eventually enter the ULIRG phase (e.g., Gao et al. 2001b).NGC 3256 is a late-stage merger, likely entering the point of coalescence, due to its disturbed morphology and closely separated nuclei that share a common envelope (Stierwalt et al. 2013).In their simulations of galaxy mergers, Moreno et al. (2019) show that after first pericentre passage, the SFR of the merging galaxy relative to an isolated control galaxy increases by a factor of about five for about 25 Myr before settling to a more moderate enhancement of a factor of about two.After second pericentre passage and during coalescence, a second dramatic enhancement, with the SFR ∼10 to 30 times higher than the control galaxy, persists for about 500 Myr before more gradually decreasing.A comparison of the SFR estimate of NGC 4038/9 (ranging from 11 to 20 M ⊙ yr −1 ) and NGC 3256 (50 M ⊙ yr −1 ) to the simulated SFR enhancements fits their inferred merger stages.He et al. (2023) used these same simulations to investigate how the properties of the molecular clouds evolve during the merger.They find that clouds in the merger have higher virial parameters than in simulations of isolated galaxies and that the increase in virial parameter coincides with the increase in the global star formation rate.
Our observations of higher molecular gas surface densities in NGC 4038/9 than NGC 3256 (see e.g. Figure 4) but lower SFR may also fit into the evolution of dense gas in the simulations presented by Moreno et al. (2019) and investigated further in He et al. (2023).After the first pericentre passage and until just after the second passage, the mass of cold dense gas ( > 10 cm −3 ,  < 300 K) in their fiducial merger simulation is enhanced to almost twice that in their isolated galaxy control (their figure 7).The dense gas mass then becomes depleted relative to the isolated galaxy before rebounding to about the same mass just before coalescence, and then slowly depleting to below the mass in the isolated galaxy.We may be catching NGC 4038/9 close enough to its second encounter that the molecular gas mass is still maximally enhanced whereas NGC 3256 is showing signs of the subsequent reduction of molecular gas.
To explain the higher SFR in NGC 3256 compared to NGC 4038/9 despite their comparable ranges of molecular gas surface density we turn to the behaviour of the densest gas in the simulations.While Moreno et al. (2019) found the total mass of molecular gas decreased after second passage, the mass in cold ultra-dense gas ( > 1000 cm −3 ,  < 300 K) increased by a factor of about 1008 .The fraction of cold dense gas in the ultra-dense regime increased from about 0.1 per cent to around 30 per cent, leading to the dramatic increase in the SFR after second passage.Thus, it could be that the total mass of very dense gas is significantly higher in NGC 3256 than in NGC 4038/9, which could lead to an increase in the overall star formation rate.
While the velocity dispersions in the non-nuclear regions of NGC 4038/9 and NGC 3256 are quite similar, the nuclear velocity dispersions in NGC 3256 are significantly higher than in NGC 4038/9 (Figure 3).Higher velocity dispersions near the nuclei of NGC 3256 may also be driven by the different merger stages and possibly influenced by the presence of outflows (Sakamoto et al. 2013).Star formation is predicted to produce at most about 10 km s −1 of turbulent velocity dispersion (Shetty & Ostriker 2012; Krumholz et al. 2018), with gas flows required to power larger velocity dispersions (Krumholz et al. 2018).The later merger stage of NGC 3256, resulting in more morphological disruption and likely more significant tidal flows of gas towards the nuclei, could result in the larger velocity dispersions compared to NGC 4038/9.
Combining higher surface densities with similar velocity dispersions (in the non-nuclear regions) in NGC 4038/9 as compared to NGC 3256 results in lower virial parameters for some of the gas in NGC 4038/9.While we might expect the higher SFR in NGC 3256 to imply lower virial parameters than in NGC 4038/9, we may be seeing the combination of enhanced turbulence and ultra-dense gas in NGC 3256 making the gas appear unbound at the scales probed.Perhaps in the more violent coalescence stages only the densest (and therefore smaller volume) portions of the molecular gas in NGC 3256 will even approach being gravitationally bound.In contrast, weaker tidal flows in NGC 4038/9 (cf.Ueda et al. 2017) may not have transformed its ISM away from appearing largely near virial equilibrium or collapse like many of the PHANGS-ALMA galaxies.The ISM in NGC 4038/9 still being in a transitional stage may explain the wide range of virial parameters compared to PHANGS-ALMA and the non-nuclear regions of NGC 3256.
It could also be that the methods to measure SFR observationally (which measure the average SFR over 10-100 Myr, Kennicutt & Evans 2012) lag behind the properties of the molecular gas (which are measured "instantaneously").The dynamical state of the molecular gas in NGC 3256 may now be unfavorable for widespread star formation but our SFR indicators rely on a currently existing population of stars that are the result of past gas conditions.We must also caution that the virial parameters shown in Figures 3 through 5 do not account for pressure confinement contributing to binding the observed molecular gas.Brunetti et al. (2021) roughly estimate that stellar surface densities and cloud-cloud collisions between GMCs could provide enough external pressure to balance the internal pressure for some of the gas in NGC 3256.
If the CO emission is optically thick in both NGC 4038/9 and NGC 3256 then the peak brightness temperature would be roughly equal to the kinetic temperature of the molecular gas.The higher peak brightness temperatures we measure in NGC 3256 would then indicate that the kinetic temperature of the gas is also higher than in NGC 4038/9.Given the higher SFR in NGC 3256 is producing more stars to heat the molecular gas, it is not surprising that the molecular gas appears hotter in NGC 3256 than NGC 4038/9.A radiative transfer analysis of NGC 3256 spanning several CO transitions as well as optically thin and thick isotopologues would be necessary to further investigate differences in the temperatures and densities of the molecular gas in the two mergers at GMC scales.
As mentioned in Section 4.1, the changes in the median molecular gas properties with resolution in NGC 4038/9 are typically small relative to PHANGS-ALMA measured by Sun et al. (2018Sun et al. ( , 2020)).Even weaker trends in median molecular gas properties were measured in NGC 3256 by Brunetti et al. (2021).Starting with a beam that is roughly the size of a typical GMC and then increasing the beam size, the measured surface density and peak brightness temperature would tend to decrease as a result of beam dilution.Conversely, if the starting beam is smaller than the typical GMC size, then increasing the beam size would likely not result in very much change in the measured surface density.The cloud-finding analysis by Brunetti & Wilson (2022) resulted in cloud radii slightly larger in NGC 3256 than PHANGS-ALMA galaxies, pointing towards NGC 3256 being in the second scenario described.The weak trends measured in NGC 4038/9 imply it is also in the second scenario and that the typical size of GMCs may again be larger than those in PHANGS-ALMA galaxies.The clouds in NGC 4038/9 may not be as large as in NGC 3256 since we measured slightly stronger trends in NGC 4038/9.An interesting investigation would be to calculate the "clumping factor" defined by Leroy et al. (2013) for NGC 4038/9 and NGC 3256 and compare to those calculated by Sun et al. (2022) for the PHANGS-ALMA galaxies.If the mergers exhibit lower clumping factors than the PHANGS-ALMA galaxies, then a shortcut for estimating the clumping and typical GMC size could be to calculate the changes in molecular gas property medians over a fairly modest change in resolution.

CO-to-H 2 conversion factor considerations
Since the CO-to-H 2 conversion factor influences many of the molecular gas properties presented here, we now discuss the appropriateness of our choice to use a single value (the Milky Way value) throughout NGC 4038/9.A single conversion factor has the benefit that changes to the factor result in shifting the sample of quantities all together.However, it is likely an oversimplification to assume all regions within NGC 4038/9 truly have the same conversion factor.For example, in their merger simulations, Renaud et al. (2019a) find that the CO-to-H 2 conversion factor has a significant time variation.They conclude that the conversion factor fluctuations are produced by both feedback energy and velocity dispersion.In their analysis of a simulation of an Antennae-like merger, Renaud et al. (2019b) find that the conversion factor has strong spatial variations as well.
There may be a signature in our data of the conversion factor in NGC 4038/9 changing in the gas closer to the nuclei.While a trend between the velocity dispersion and surface density in NGC 4038/9 is obvious up to about 10 3 M ⊙ pc −2 , for surface densities above this value there is a flattening of the trend that is most easily seen in the nuclei in Figure 7 (top panel).Since this flattening is strongest in the nuclear sub-sample from NGC 4038/9, and is not seen in any of the sub-samples from Sun et al. ( 2020) (who adopt a radially variable conversion factor), our choice of a single conversion factor for NGC 4038/9 may be the cause 9 .Larger velocity dispersions and hotter gas, like the medians from NGC 4038/9 in Figure 3 imply, can drive the conversion factor down (Bolatto et al. 2013).If the conversion factor does decrease towards the nuclei in NGC 4038/9 then the nuclear surface densities would need to be shifted to the left in Figure 7.An interesting consequence of this interpretation is that for pixels with surface densities roughly below about 10 3 M ⊙ pc −2 , the conversion factor may not vary as much as it will in the nuclear regions.
As for the choice of the Milky Way value itself, this choice helps in simplifying comparisons with other work like Sun et al. (2018) and Galactic studies.For example, a single conversion factor across NGC 4038/9 and the PHANGS-ALMA galaxies from Sun et al. (2018) means that Figure 3 indicates that the surface brightness of CO emission is systematically higher in NGC 4038/9.However, there is evidence that the Milky Way conversion factor may not be far off for the bulk of the CO emission in NGC 4038/9, even given the typical differences between spiral galaxies and starbursts/mergers (Narayanan et al. 2011(Narayanan et al. , 2012;;Renaud et al. 2019a,b).Wilson et al. (2003) estimated  CO(1−0) ≈6.5 M ⊙ pc −2 (K km s −1 ) −1 in NGC 4038/9 from virial mass estimates of resolved super giant molecular complexes, or a factor of ≈1.5 larger than the Milky Way value we use here.Schirm et al. (2014) performed non-local thermodynamic equilibrium radiative transfer modeling of NGC 4038/9 with the radex code on eight transitions of CO and two transitions of [CI].To make their mass estimate consistent with that of Brandl et al. (2009) they had to assume a starburst-like CO abundance and arrived at a conversion factor of  CO(1−0) ≈7 M ⊙ pc −2 (K km s −1 ) −1 , consistent with Wilson et al. (2003).Scaling this conversion factor to CO (2-1), with the same  21 we adopted, gives a value of  CO(2−1) ≈ 10 M ⊙ pc −2 (K km s −1 ) −1 .Given the observed spread in the conversion factor within starbursts of factors of ∼3 to 4 (Bolatto et al. 2013), we have opted to simplify comparisons to previous works by simply using the Milky Way value.We will address the question of what conversion factor is appropriate for NGC 4038/9 by combining all CO data in the present observations with additional ALMA observations of several transitions of optically thin and thick CO isotopologues, at similar spatial resolution to the observations presented here (He et al. 2024, submitted).

CONCLUSIONS
We have presented GMC-scale observations of the central 9 kpc of NGC 4038/9 in CO (2-1).Maps of molecular gas mass surface density, velocity dispersion, peak brightness temperature, virial parameter, and internal turbulent pressure have been derived from these data at a range of spatial resolutions from 55 to 150 pc.Comparisons of the pixel-by-pixel distributions of these gas properties from NGC 4038/9 have been made at matched spatial resolution to the PHANGS-ALMA sample of 70 nearby spiral galaxies (Sun et al. 2018(Sun et al. , 2020)), the overlap region of NGC 4038/9 observed in CO (3-2) (Whitmore et al. 2014;Sun et al. 2018), and the merger and nearest luminous infrared galaxy NGC 3256 (Brunetti et al. 2021).
Relative to the PHANGS-ALMA galaxies, NGC 4038/9 has some of the highest molecular gas surface densities, velocity dispersions, peak brightness temperatures, and turbulent pressures.These gas properties measured in the discs of the PHANGS-ALMA galaxies 9 An alternative interpretation is that the gas in the nuclei is far from selfgravitating, in which case no correlation between velocity dispersion and surface density would be expected.
are often significantly lower than those measured in NGC 4038/9.The centres of the PHANGS-ALMA galaxies with the highest stellar masses do show some overlap with the gas properties in NGC 4038/9.Virial parameters measured in NGC 4038/9, while spanning a large range, are much more similar to the PHANGS-ALMA galaxies than any other gas property.Differences by region within NGC 4038/9 (nuclei vs. non-nuclear) are similar to those seen within PHANGS-ALMA galaxies, with the most extreme gas properties near the nuclei.
Gas surface densities are similar between NGC 4038/9 and NGC 3256, though the highest values are measured in NGC 4038/9.On the other hand, velocity dispersions near the nuclei of NGC 3256 and peak brightness temperatures throughout the system are significantly higher than in NGC 4038/9.Higher peak brightness temperatures may be indicative of higher kinetic temperatures caused by the higher star formation rate in NGC 3256.Some of the higher velocity dispersions in the nuclei of NGC 3256 may be due to contamination from the jet in the southern nucleus and/or the outflow in the northern nucleus (Sakamoto et al. 2013;Brunetti et al. 2021).However, the later merger stage of NGC 3256 compared to NGC 4038/9 may also be producing more intense merger-driven flows into the nucleus of NGC 3256 that could produce more turbulence and result in larger line widths.The wider but systematically lower range of virial parameters in NGC 4038/9 compared to NGC 3256 could also be a consequence of the differing merger stages.NGC 3256 may be leaving the starburst phase as coalescence of the progenitor galaxies increases the turbulence and suppresses further star formation, but NGC 4038/9 may be caught in the transition between bursts of enhanced star formation.
Next steps will focus on comparisons of several CO isotopologues and transitions across the entire region observed in this work (He et al. 2024, submitted).=2-1 transitions of 13 CO and C 18 O as well as the =1-0 transition of 12 CO were also observed in this project and will allow for exact matching of  coverage as well as spatial and spectral resolutions.Additional observations have been obtained with ALMA, mapping the same field of view with the same array combinations in 12 CO (3-2) and 13 CO (1-0), extending the area probed by these transitions at cloud scales.With three transitions of 12 CO and two transitions of 13 CO a radiative transfer analysis can constrain the densities and temperatures of the molecular gas in NGC 4038/9, and help to estimate the CO-to-H 2 conversion factor at cloud scales (He et al. 2024, submitted).
In summary, these two nearby galaxy mergers show significantly higher molecular gas surface densities, velocity dispersions, peak brightness temperatures, and turbulent pressures on giant molecular cloud scales compared to spiral galaxies from the PHANGS-ALMA survey.However, there are also significant differences between the two mergers that may be linked to the phase of the merger.For example, the larger velocity dispersion and higher gas temperature of NGC 3256 may be linked to enhanced feedback from star formation in its more advanced merger phase compared to NGC 4038/9.In contrast, there may be a current up-tick in the star formation rate in NGC 4038/9, highlighting time variability as an important factor in understanding galaxy mergers observationally as well as theoretically (Moreno et al. 2019;He et al. 2023).Additional studies on molecular cloud scales of nearby starburst mergers as well as the pre-and postmerger stages will be important for placing these results in a wider context and ultimately informing our understanding of the high star formation rates seen in galaxies at high redshift.had to switch to setting "chanchunks" to −1 in tclean since our highest resolution cubes could not fit in memory all at once.To further improve memory management and processing speed, we removed additional image padding in right ascension and declination during imaging and instead added padding of the interferometric cubes before feathering to ensure the angular coverage was at least as large as the TP cubes.The final change related to the cube size was adding a check during writing masks to disk that would do the writing in batches of channels to avoid memory issues for our largest cubes that were about 16 GB in size.Since the pre-imaging regridding would not guarantee exactly the same spectral channels would be filled with data across all arrays, we added a call to the split task to remove one channel at each end of the imaging spectral windows (SPWs) to avoid blank channels being included in the cube for cleaning.Finally, substantial effort was also spent on properly capturing all casa logging output and redirecting it to output files.This message capturing was missing in version one and made it difficult to ensure each step was performed correctly as well as verifying adjustments to the code for the Antennae observations.Table A1 gives a summary of the observations and the calibration method used for each individual observation.Figure A1 show the resulting maps processed at 150 pc resolution for comparison to Figure 2 at 55 pc resolution.

APPENDIX B: DATA TABLES
We provide the binned data used in this paper for both NGC 4038/9 and NGC 3256 as two separate machine-readable tables (see Table B1 and B2 for format).In these tables, each row reports our measurements for one pixel in one galaxy; pixel values at different physical resolutions are reported sequentially.The contents of the rows are as follows: (i) The resolution (beam FWHM) of the dataset in parsecs.(ii) the right ascension and declination of the pixel in degrees.(iii) The logarithmic value of the molecular gas surface density, Σ mol in M ⊙ pc 2 ; the velocity dispersion,  v in km s −1 ; the peak brightness temperature,  B in K; the virial parameter,  vir ; and the logarithmic value of the turbulent pressure,  turb , in K km s −1 .
(iv) The projected distances of the pixel from each of the two nuclei, in kpc.
Table B1 also indicates whether or not a pixel lies in the overlap region.Table B2 indicates whether or not a pixel lies in the north or south portion of the jet or the west exclusion zone; see Brunetti et al. (2021) for details.
This paper has been typeset from a T E X/L A T E X file prepared by the author.

Figure 1 .
Figure 1.CO (2-1) moment maps of NGC 4038/9 at 55 pc resolution.Top left: integrated intensity (moment 0); top right: velocity field (moment 1); bottom: velocity dispersion (moment 2).Pixels are half of the beam FWHM on a side.The squares in the bottom right corner of each panel contain a circle with diameter equal to the beam FWHM (0.51 ′′ ).A scale bar indicating 1 kpc at the distance of NGC 4038/9 is also shown in the bottom right corner of each panel.

Figure 2 .
Figure 2. Maps of molecular-gas properties in NGC 4038/9 at 55 pc resolution, calculated from CO (2-1) moment maps.The top row shows, from left to right, mass surface density, velocity dispersion, and peak brightness temperature.The bottom row shows the virial parameter on the left and the internal turbulent pressure on the right.Pixels are half of the beam FWHM on a side.Given the range of measured virial parameters, we chose a relatively low upper clipping value of  vir = 10 to show pixels that are likely unbound (yellow) while still showing some of the structure for pixels that may be bound by external material (orange) and pixels that are likely marginally bound (black/blue).The gray circles indicate the regions within 1 kpc radii of the nuclei, denoting the nuclear and non-nuclear regions discussed in later sections.The gray polygons in the lower left indicate the overlap-region FoV observed in CO (3-2) by Whitmore et al. (2014) and analysed bySun et al. (2018).Pixels in these polygons make up our overlap region sub-sample.The squares in the bottom right corner of each panel contain a circle with diameter equal to the beam FWHM (0.51 ′′ ).A scale bar indicating 1 kpc at the distance of NGC 4038/9 is also shown in the bottom right corner of each panel.A CO-to-H 2 conversion factor of 6.25 M ⊙ pc −2 (K km s −1 ) −1 was used to convert integrated intensities to mass surface densities, which also affects the estimates of the virial parameter and internal turbulent pressure (see Equations 1 and 2).

)Figure 3 .
Figure 3. Comparisons of mass-weighted pixel sample percentiles at 120 pc resolution from NGC 4038/9,NGC 3256, and Sun et al. (2018)  for mass surface density, velocity dispersion, peak brightness temperature, virial parameter, and internal turbulent pressure.Medians are shown as symbols and the inner 68 th percentiles as error bars.Samples are split between centre (triangle) and non-centre/disc (circle) pixels.NGC 4038/9 also has pixel samples from theWhitmore et al. (2014) overlap region FoV, shown as stars.Percentiles from our CO (2-1) observations of NGC 4038/9 are in orange, from the CO (3-2) observations in blue, NGC 3256 is in black, and the remainder of the galaxies analysed bySun et al. (2018) are in brown.Galaxies fromSun et al. (2018) are ordered along the  axis with stellar mass increasing from left to right.Stellar masses are fromSun et al. (2020), where available, and fromSun et al. (2018) otherwise (i.e.M 31, M 33, and M 51).
Figure 4. Mass-weighted Gaussian KDEs of the 120 pc resolution measurements from the entire FoVs of NGC 4038/9 and NGC 3256 in the solid orange and black lines, respectively.The samples from NGC 4038/9 are also separated into regions near the nuclei (dotted), farther than 1 kpc from the nuclei (dashed), and within theWhitmore et al. (2014) overlap region FoV (dash-dotted).The blue-shaded regions show where the whole-FoV sample from NGC 4038/9 is above the sample from NGC 3256.Gaussian KDE bandwidths for the whole FoV samples were automatically chosen using the scipy implementation of Scott's Rule(Scott 1992), and the other regions from NGC 4038/9 use the same bandwidth as that of the whole FoV.

Figures 6 Figure 5 .
Figures 6 and 7 show mass-weighted probability density functions (PDFs) of the velocity dispersion versus mass surface density.All

Figure 6 .
Figure6.Mass-weighted Gaussian KDEs velocity dispersion vs. mass surface density measured in all significant pixels or hexagonal apertures from NGC 4038/9 (orange filled contours), NGC 3256 (black dotted contours), and all PHANGS-ALMA galaxies presented bySun et al. (2020) (brown contours).Contours enclose 99.5, 90, 50, and 20 per cent of the mass from each data set.Measurements shown are made at 150 pc resolution in NGC 4038/9 and PHANGS-ALMA and 120 pc resolution in NGC 3256.Note that the mass weighting used in this figure results in a different distribution of contours compared to those presented inSun et al. (2018Sun et al. ( , 2020)), which did not use mass weighting.

Figure 7 .
Figure 7. Same as Figure 6 but now the sample from NGC 4038/9 is separated into pixels within 1 kpc of the nuclei (red) and those beyond (blue).Contours from NGC 3256 and PHANGS-ALMA are the same as in Figure 6 and are identical in the top and bottom panels of this figure.