<figure><img src="image_32.png" /><figcaption>**Figure 27.** Difference between pipeline output and model input for the NGC 3059 look-alike. As Figure 27, but for our NGC 3059 look-alike, reflecting a fainter galaxy with more extended source structure. This case does not show any notable bias with the 12 m+7 m data, but the 7 m only imaging shows a bias low. For the 7 m+TP imaging, a mild bias plus thermal noise represents a good model for the small offset of the pipeline results from the model. For the 7 m only data, the imaging struggles to recover the model. See Appendix C for more discussion.</figcaption></figure>

the 7 m only data. In our end-to-end tests, the PHANGS pipeline ACA-only imaging misses 20%–30% of the flux in the worst cases. We explore this issue with both simulations and real data in Appendix C.

## 8.4. Comments on Quality Assurance Results

Both the automated regression and the manual quality assurance tests played an important role in refining the PHANGS pipeline algorithms and catching several important bugs. In the final round of imaging using the latest pipeline, we still found a few cases where the imaging with the default parameters diverged or declared convergence too early (~4 out of ~250 total cases) in one or more planes. In these cases, we adjusted the pipeline parameters and reran the imaging. Usually, adjusting the convergence criteria or the primary beam cutoff improved the situation.

## 9. Summary

We have presented the PHANGS–ALMA data processing pipeline, explaining the key steps in the processing and our motivation for many of the key decisions. We do not review these here, but do highlight a few points that may be of general interest to those working on similar problems:

1. We note that issues related to regridding and interpolation can lead to patterns in the rms noise amplitude along the spectral dimension. The specific issue that we highlight is related to CASA, and we hope it will be addressable in future releases. However, the concern that data processing affects the spectral noise pattern and line spread function is general.

2. We present a robust two-stage approach to deconvolving spectral line observations. This approach employs a multiscale deconvolution down to an S/N threshold of around four. It then creates a mask based on bright signal
and uses a classic Högbom (1974) deconvolution approach to clean the bright emission “into the noise.” We have found this to run robustly and yield good results on a wide variety of nearby galaxy data.

3. We adopt a two-track approach to masking of spectral line data cubes. We create a “strict” mask with high confidence and a low false-positive rate, but potentially low completeness. This is appropriate for calculations that perform poorly in the presence of noise. We also create a high-completeness but noisier “broad” mask that will include many false positives but also encompass almost all emission in the cube. Leaving aside the specifics of their creation, we suggest that this two-track approach to masking is a good general approach.

4. We have found that a “matched-line width filtered peak temperature map” does an outstanding job of highlighting detailed structure in line data cubes. This is simply a conventional peak temperature (sometimes referred to as “moment 8”) map constructed from a cube that has been convolved spectrally with a matched-line width filter.

5. We have compared the imaging results for different arrays and vetted the performance of our pipeline using simulated observations with known input. These tests show that, after the inclusion of total power data, the pipeline does an excellent job of recovering known input. They also show that the 12 m+7 m imaging performs significantly better than 7 m only imaging in many cases, even after matching the resolution of the output images. The differences, which are explored in detail in the appendix, are a function of S/N and source structure.

The PHANGS–ALMA pipeline has so far been applied successfully to roughly 1000 individual measurement sets, and is publicly available on github.<fnref n="52" />

We gratefully acknowledge a prompt and constructive review by the anonymous referee during a difficult time. This work also benefited immensely from helpful discussions with Crystal Brogan, Jeffrey Mangum, and the North American ALMA Science Center and European Southern Observatory staff, including Dirk Petry. The computing and software infrastructure used to process PHANGS–ALMA and develop this pipeline at OSU was built and supported by David Will, who for years was the most supportive and welcoming person in a supportive and welcoming department. He will be sorely missed.

This work was carried out as part of the PHANGS collaboration. The work of A.K.L., J.S., and D.U. is partially supported by the National Science Foundation (NSF) under grants No. 1615105, 1615109, and 1653300, as well as by the National Aeronautics and Space Administration (NASA) under ADAP grants NNX16AF48G and NNX17AF39G. E.R. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number RGPIN-2017-03987, and computational support from Compute Canada. D.L., T.S., E.S., C.M.F., K.S., and T.G.W. acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 694343). C.H., A.H., and J.P. acknowledge support by the Programme National “Physique et Chimie du Milieu

Interstellaire” (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. A.H. acknowledges support by the Programme National Cosmology et Galaxies (PNCG) of CNRS/INSU with INP and IN2P3, co-funded by CEA and CNES. A.U. and A.G.-R. acknowledge support from the Spanish funding grants AYA2016-79006-P (MINECO/FEDER) and PID2019-108765GB-I00 (MICINN). A.U. acknowledges support from the Spanish funding grant PGC2018-094671-B-I00 (MCIU/AEI/FEDER). C.M.F. acknowledges support from the NSF under Award No. 1903946. M.C. and J.M.D.K. gratefully acknowledge funding from the German Research Foundation (DFG) through an Emmy Noether Research Group (grant No. KR4801/1-1). M. C., J.M.D.K., and J.J.K. gratefully acknowledge funding from the DFG Sachbeihilfe (grant No. KR4801/2-1). J.M.D.K. gratefully acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program via the ERC Starting Grant MUSTANG (grant agreement No. 714907). F.B., A.T.B., I.B., J.d.B., and J.P. acknowledge funding from the European Union’s Horizon 2020 research and innovation program (grant agreement No. 726384/EMPIRE). R.S.K. and S.C.O.G. acknowledge financial support from the DFG via the collaborative research center (SFB 881, Project-ID 138713538) “The Milky Way System” (subprojects A1, B1, B2, and B8). They also acknowledge subsidies from the Heidelberg Cluster of Excellence STRUCTURES in the framework of Germany’s Excellence Strategy (grant EXC-2181/1-390900948) and funding from the ERC via the ERC Synergy Grant ECOGAL (grant 855130). K.K. and F.S. gratefully acknowledge funding from the DFG in the form of an Emmy Noether Research Group (grant No. KR4598/2-1). E.W. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project-ID 138713538–SFB 881 (“The Milky Way System,” subproject P2). C.E. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) Sachbeihilfe, grant No. BI1546/3-1. A.S. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1903834.

This paper makes use of the following ALMA data, which have been processed as part of the PHANGS–ALMA CO(2–1) survey: ADS/JAO.ALMA#2012.1.00650.S, ADS/JAO.ALMA#2013.1.00803.S, ADS/JAO.ALMA#2013.1.01161.S, ADS/JAO.ALMA#2015.1.00121.S, ADS/JAO.ALMA#2015.1.00782.S, ADS/JAO.ALMA#2015.1.00925.S, ADS/JAO.ALMA#2015.1.00956.S, ADS/JAO.ALMA#2016.1.00386.S, ADS/JAO.ALMA#2017.1.00392.S, ADS/JAO.ALMA#2017.1.00766.S, ADS/JAO.ALMA#2017.1.00886.L, ADS/JAO.ALMA#2018.1.01321.S, ADS/JAO.ALMA#2018.1.01651.S, ADS/JAO.ALMA#2018.A.00062.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

*Software: ALMA Calibration Pipeline* (L. Davis et al. 2021, in preparation), *CASA* (McMullin et al. 2007), *numpy* (Oliphant 2006), *scipy* (Virtanen et al. 2020), *astropy* (Astropy Collaboration et al. 2013, 2018) IDL Astronomy User’s Library (Landsman et al. 1993), *cprops*

<footnote n="52">⁵² https://github.com/akleroy/phangs_imaging scripts</footnote>
(Rosolowsky & Leroy 2006), GILDAS Pety et al. (2005), R R Core Team (2015), PHANGS–ALMA Total Power Pipeline (Herrera et al. 2020), spectral-cube, radio-beam.

## Appendix A

### Contributions

The processing of the PHANGS–ALMA data and creation of the pipeline was a team effort, with major contributions from many people and input from the entire team. This paper also reflects major direct and indirect contributions from many people. We summarize some of the key contributions here.

**The PHANGS ALMA Data Reduction (ADR) Group:** The group has been led by J. Pety since the beginning of the PHANGS collaboration, and met weekly for most of the time since 2016. Key contributors to tests, discussions, and development over the course of the project include: M. Chevance, C. Faesi, C. Herrera, A. Hughes, A. Hygate, D. Liu, A. Leroy, T. Saito, E. Rosolowsky, E. Schinnerer, K. Sliwa, A. Schruba, and A. Usero.

**Interferometric and Postprocessing Pipeline:** The code was mostly developed by A. Leroy, D. Liu, E. Rosolowsky, and T. Saito, with code review at several stages by A. Schruba, and key input from J. Pety, E. Schinnerer, A. Schruba, and A. Usero. Additional tests related to many aspects of data processing were carried out by D. Liu and T. Saito. E. Koch and C. Wilson offered important input on algorithms. Tests of short-spacing correction algorithms were led by K. Sliwa during the pilot programs and then T. Saito during the Large Program and beyond. T. Saito led the research described in Appendix D of this paper. A. Leroy and T. Saito led the work described in Appendix C with major input from A. Hughes, J. Pety, E. Rosolowsky, and E. Schinnerer. The pipeline was deployed for PHANGS–ALMA by A. Leroy and T. Saito.

**Total Power Pipeline:** C. Herrera developed most of the total power pipeline, with major input from J. Pety and A. Usero, and code review by E. Rosolowsky. K. Sliwa played a key role in prototyping approaches to the total power processing using the pilot data. A. Usero developed and deployed the telluric ozone correction algorithm described in Section 5, and led investigation and communication of this issue in close collaboration with C. Faesi, C. Herrera, and J. Pety. A. Usero also led investigation of the calibration stability and gain in the total power data, described in Section 3.2 and Appendix B. A. Weiss, J. Pardo, and C. de Breuck also provided important input on this topic. A. Usero led investigation of the flux stability of the total power observations. The total power pipeline was deployed on PHANGS–ALMA by C. Faesi, C. Herrera, and A. Usero.

**Quality Assurance (Cubes):** A. Hughes developed the IDL version of the quality assurance software for cubes described in Section 8. D. Liu wrote the Python version. A. Hughes led regression testing and, with J. Pety, coordinated cube quality assurance efforts at several stages. A. Leroy and T. Saito developed and deployed the end-to-end tests described in Section 8.3. Many members of the team contributed careful review of data products, including: I. Beslic, M. Chevance, J. den Brok, C. Eibensteiner, C. Faesi, A. García-Rodríguez, C. Herrera, A. Hygate, M. Jimenez Donaire, J. Kim, A. Leroy, D. Liu, J. Pety, J. Puschnig, M. Querejeta, E. Rosolowsky, T. Saito, E. Schinnerer, A. Schruba, A. Sardone, J. Sun, A. Usero, D. Utomo, and T. Williams.

**Quality Assurance (Visibility Data):** T. Saito developed the u–v quality assurance procedures and software described in

Section 3.2. T. Saito and C. Herrera carried out most of the inspection using these tools. D. Liu carried out the analysis of the flux calibration scale described in Section 3.2.

**Infrastructure:** E. Rosolowsky created and maintained the PHANGS server and shared archive, which was crucial to distributing the work and results. D. Will created and maintained the computing and software environments used for building and executing the pipeline at OSU.

**Observatory and Community Support:** The Joint ALMA Observatory and North American ALMA Science Center offered extensive support. They were responsive and flexible regarding reobservations of total power data affected by the telluric ozone feature (Section 5), and responsive and helpful when issues related to imaging in CASA arose early in the project. We specifically acknowledge helpful communication with A. Remijan regarding imaging, C. Brogan regarding the noise behavior in Band 6, and J. Mangum regarding several aspects of data processing. More broadly, this work builds on the hard work of the CASA team, the ALMA pipeline team, and the ALMA observatory effort to provide excellent quality assurance. We acknowledge the hard work of the developers, the scientists who support and guide the effort, and the data analysts. Similarly, we build on the large work by the astropy and broader scientific Python community, and also acknowledge the astronomical IDL community, which laid the foundation for much of this work.

## Appendix B

### Internal Stability of the Calibration for the PHANGS–ALMA Total Power Data

The total power observations set the overall flux in our final data cubes. Our processing assumes that both the total power and interferometric data are correctly calibrated (Section 6.4 and Appendix D). The observatory calibration scheme anchors the amplitude calibration of the total power data to interferometric observations with the 7 m array, and so to the ALMA calibrator database. In principle, this should yield stable, high-quality calibration.

To check this, we assessed the internal consistency of the PHANGS–ALMA total power observations. Over the course of our ALMA Large Program, we observed the same targets repeatedly, and the individual observations are already deep enough that they detect most galaxies at high significance. This allows us to compare how the line brightness toward the same target varies when measured on different days. The magnitude of these variations gives us an upper limit to the stability of the ALMA total power flux calibration.

For this test, we selected a subset of six galaxies. Using the procedures described in Herrera et al. (2020) and Section 5, we generated a CO(2–1) line cube for every “execution block” (EB), each of which corresponds to an individual ~1 hr long observation. This resulted in 31 independent data cubes, with $N = 2–7$ cubes per galaxy. Each target galaxy was observed on 2–3 different dates, with the spread between observations spanning from 4 days to 11 months. Typically, two consecutive EBs were observed on any given day.

For each galaxy, we consider every possible pair of EBs. For each pair, we fitted a linear function with no intercept to the scatter plot of intensities measured at the same voxel position in the two data cubes. For the fit, we used a total-least-squares linear regression scheme, taking into account the noise level in both cubes. Because this exercise requires comparing detected
<figure><img src="image_33.png" /><figcaption>Figure 28. Assessment of the internal calibration of ALMA’s total power observations. Each histogram illustrates one of the four regression tests described in the text that we run on 74 × 2 EB pairs. The top and bottom panels show the two tests on line cubes and moment 0 maps, respectively. The blue filled histograms correspond to tests where all valid data are taken. The black histograms correspond to tests including only data where the nominal S/N in the ratio between the two measurements is >10. The orange dotted-dashed curve is a reference Gaussian distribution with 3% rms (0.013 dex).</figcaption></figure>

emission between the two EBs, we only consider velocities within the galaxy’s velocity range.

As a crosscheck, we repeated the exercise using the integrated intensity (moment 0) maps obtained by integrating over the galaxy’s velocity range. We also carried out fits both using all data and restricting to data with S/N > 10 in the ratio Y/X, where Y and X refer to the intensities or integrated intensities in the two data sets. We also repeated each comparison considering X|Y and Y|X, i.e., swapping which data set we treat as the reference variable, in order to prevent any biases from the way EBs are processed. Thus, we ended up with four different slope measurements: maps and cubes, each with and without an S/N cut. In total, we compared 74 × 2 EB pairs, and also considered each with Y|X and X|Y.

Figure 28 shows the distribution of fit slopes from each of our four tests. We expect a slope of unity (log₁₀ fit slope = 0) if the calibration is identical between the two EBs. Departures from this capture the variations in the relative calibration between the two EBs. We report results in log scale because it is natural to expect calibration uncertainties to be multiplicative.

The rms of the distribution of fit slopes shown in Figure 28 is 0.010–0.017 dex (≈2%–4%), regardless of how we calculate it: directly or by fitting the histograms with a Gaussian function. Although the histograms hint at some low-level wings, almost all the slope measurements deviate by less than ~7% (0.03 dex) from unity. We adopt a 3% rms scatter on the EB-to-EB scaling as a reasonable description of our results. We did not find any convincing indication that the slopes depend on the difference between the observing dates of the EB pairs. This suggests that the calibration uncertainties affecting different EBs are mutually uncorrelated.

We interpret this scatter as indicative of the stability of the ALMA total power calibration. It will not reflect underlying

uncertainties in the ALMA calibrator database, but most other uncertainties should be captured by this test. Assuming that calibration uncertainties affecting different EBs are uncorrelated, the uncertainty in individual EBs is about $\sqrt{2}$ times lower than the measured 0.03 dex ≈ 3% difference between two independent EBs.

The final total power cube for each galaxy typically results from averaging several EBs. If the calibration uncertainty is uncorrelated, this would reduce the uncertainty from 3% by an additional $\sqrt{N}$ factor, where N is the number of EBs. Thus, we conclude the internal calibration of the PHANGS–ALMA data is robust at the ~1% level. Given the link to the interferometric calibration scheme, this experiment also bolsters our confidence in adopting the observatory-provided calibration without rescaling when combining the total power and interferometric data.

A note on absolute calibration for PHANGS–ALMA “version 4”: As part of our quality assurance, we examined the stability of the total power antenna gain. This is the observatory-provided number used to translate from the “chopper wheel”-based Kelvin scale to an absolute flux scale. It is expressed in units of Jansky-per-Kelvin, or Jy K⁻¹. We found that the observatory-provided Jy K⁻¹ of individual observations varied systematically by ~7% based on delivery date. Consultation with the ALMA observatory revealed that this reflects delivery of some incorrect gain values during the time period 2017–2018. Surface improvements to the total power telescopes improved the gain, but there was some lag in reflecting these improvements within the delivered products. The correction for this effect is straightforward, but requires reprocessing the data from the original execution block stage, and so will not be reflected in PHANGS–ALMA’s initial public delivery, “version 4.” Taking into account the averaging of multiple blocks, we estimate that this effect implies a 2%–5% bias high for the overall flux scale of the data set for data delivered during 2018. The issue was not severe enough to disrupt the internal stability tests described here, and we expect it to be addressed in future releases.

## Appendix C

### Relative Performance of 7 m and 12 m+7 m Imaging

We image most of our targets using both the 7 m only and the combined 12 m+7 m data. In Section 8.3, we do the same with simulated galaxies in order to test the performance of the pipeline. These tests consistently show that the 7 m only imaging tends to deconvolve less flux than the 12 m+7 m imaging. The effect appears strongest for extended sources and at modest S/N.

We demonstrate this effect for both the real PHANGS–ALMA data and the simulation in Figures 29 and 30. The left panel in Figure 29 shows the ratio of cleaned flux in the 12 m +7 m imaging to that in the 7 m only imaging. That is, the y-axis shows the ratio of the summed fluxes of the model image. The x-axis shows a quantity that traces the typical S/N of reconstructed emission in the image. Specifically, we calculate the intensity-weighted mean intensity in the 7 m model via:

$$ \langle I_{\nu} \rangle = \frac{\sum_{\text{model}} I_{\nu}^2}{\sum_{\text{model}} I_{\nu}}, \qquad (C1) $$

where $I_ν$ is the intensity of a voxel in the model. Then, $\langle I_ν \rangle$ is just the weighted average intensity in the model, and so captures the typical brightness in the image. In Figures 29 and 30, we plot $\langle I_ν \rangle$ on the upper x-axis. The lower x-axis shows
<figure><img src="image_34.png" /><figcaption>**Figure 29.** *Deconvolved flux in different arrays.* (Left) The ratio of cleaned flux between the 12 m+7 m and 7 m only array images of the same galaxy (y-axis) as a function of the typical signal-to-noise ratio of deconvolved emission in the 7 m model image (x-axis; see text). (Right) The ratio of intensity at the peak of the 12 m +7 m model to intensity at the same location in the 7 m model, after convolving both to a matched 10'' resolution. Again, we plot this as a function of the approximate typical signal-to-noise in the 7 m model image. Blue points in both panels show PHANGS–ALMA targets. Red points show results for the two sets of simulations described in Section 8.3, with the bright, compact NGC 1097–based galaxy appearing as a star and the more extended NGC 3059–based galaxy as a hexagon. The 12 m+7 m imaging recovers more flux than the 7 m only imaging, and the difference depends on the typical signal-to-noise of the emission. Both the integrated flux and the peak flux show this effect, but the effect is much stronger with regards to the integrated flux.</figcaption></figure>

$\langle I_\nu \rangle / \sigma$, where $\sigma = 0.031$ Jy beam$^{-1}$ is a typical noise level across our full 7 m imaging data set. In both figures, we use blue points to plot each galaxy part imaged with both 12 m +7 m and with 7 m only. The simulations described in Section 8.3 appear as red points, with different shapes reflecting our two model distributions at different S/N levels.

*Imaging the 7 m only data deconvolves less flux than imaging the 12 m+7 m data:* The left panel of Figure 29 shows that, in both the simulations and the real data, the 12 m+7 m imaging consistently deconvolves more flux than the 7 m only imaging. The effect shows a clear anticorrelation with the typical S/N in the data, such that bright targets show a much better match between the two deconvolved images than fainter targets. For low-brightness sources, the 7 m model can contain as little as ~60% of the 12 m+7 m flux. Across the whole sample, the 7 m only imaging deconvolves a median 73% of the flux deconvolved by the 12 m+7 m imaging.

The red points in Figure 29 show that this effect occurs in the simulated data, too. The deconvolved fluxes in Table 6 also highlight this result. The simulations also show significant spread at fixed S/N, demonstrating that source structure plays a large role in deconvolution. The NGC 3059 look-alike galaxy has extended structure within individual channels and shows more severe discrepancies at a given S/N than the compact NGC 1097 look-alike. Similarly, the large spread in the real data at any given S/N level likely reflects differences in the source structure within individual channels. Consistent with this interpretation, the model for our compact simulation, NGC 1097, shows some of the best agreement between the 12 m+7 m and 7 m only data across the whole sample.

The right panel in Figure 29 shows that the effect is present, though with smaller magnitude, even at the peak of the map. Here, we plot the ratio of peak intensities in the two models after convolving both to 10'' resolution. On average, the 7 m only imaging achieves a peak intensity ~93% of that found

using the 12 m+7 m data at matched scales. Again, we observe an anticorrelation of the effect with S/N, but with significant source-to-source scatter.

The 7 m only imaging shows these shortcomings despite the fact that we clean the 7 m data to the 1$\sigma$ level during the single-scale clean (Section 4), and none of our by-hand attempts to improve the cleaning yielded systematically better results for the 7 m only data. Although we do require nearby 4$\sigma$ emission to conduct the single-scale clean, our by-eye assessment of the residuals does not reveal any systematic isolated <4$\sigma$ emission that could explain this behavior. Similarly, the 7 m images produced by our pipeline appear to compare favorably to the observatory-delivered products. In short, we have no reason to think that a simple algorithmic fix can address the issue, despite exploring several options. On the other hand, the 12 m+7 m data show excellent match to the input model in simulations and do not exceed the overall flux constraints set by the total power data. These 12 m+7 m images do, in fact, appear to represent our best images, and the combined arrays do a better job at flux recovery than the 7 m data alone.

Our best explanation for the issue is that the 12 m+7 m data have significantly better sensitivity on the relevant spatial scales to reconstruct emission from galaxies. Even at short $u-v$ separation distances, the 12 m only baselines add significant sensitivity and lead to a synthesized beam with fewer strong sidelobes. The 7 m data, on the other hand, have less sensitivity on scales matched to the emission and poorer $u-v$ coverage than the 12 m+7 m data. As a result, our deconvolution recovers less flux in the 7 m only image than the 12 m+7 m image.

While this qualitative explanation seems reasonable, we were surprised by the magnitude of the effect in the real data. Our current understanding is that, for realistic structures in nearby galaxies, the nonlinear nature of the deconvolution procedure interacts in a destructive way with the limited $u-v$ coverage and sensitivity of the 7 m array. This agrees qualitatively with
<figure><img src="image_35.png" /><figcaption>**Figure 30.** Sum and peak flux in different arrays with and without feathering. Similar to Figure 29, but now showing (top row) the ratio of the total summed flux in the 12 m+7 m image to that in the 7 m only image (top left) without feathering and (top right) with feathering. The bottom row shows the ratio of 12 m+7 m to 7 m intensities at the peak of the 12 m+7 m image after matching the resolution of the two images at 10". The bottom left image shows the case before feathering. The bottom right image shows the case after feathering. Again, the blue points show results for PHANGS-ALMA targets and red points show simulation results (Section 8.3). The 12 m+7 m imaging recovers more flux than the 7 m only imaging, with the two becoming more consistent as the signal-to-noise increases. After feathering, the two images are much more consistent for targets with reasonably high signal-to-noise, but still show some divergence in very low signal-to-noise cases. This effect appears much stronger in the integrated emission, but is present at a lower level in the peak intensity of the image. Both the simulations and real data show the effect, though it appears stronger in the real data due to the idealized nature of the simulations.</figcaption></figure>

previous investigations on similar topics, which show a strong nonlinearity in interferometric image reconstruction of complex sources when dealing with limited coverage and sensitivity (in particular, see Helfer et al. (2002)). The fact that the idealized simulations show results qualitatively similar to the data underscores that this is not an effect driven solely by calibration issues, limited knowledge of the ALMA primary beams, or some similar issue that would only affect the observations. These issues may still play important secondary roles, however. In particular, we expect that the combined impact of phase and amplitude noise might also lead to nonlinearities in the

sensitivity of the interferometer to any extended structures at low S/N (e.g., see Lay et al. (1994), for a discussion of the nature of amplitude noise). More careful analysis of low S/N simulations with phase noise might help this situation.

*In the real data, the images show the same effect:* The top left panel of Figure 30 shows the ratio of total flux in the 12 m +7 m image to that in the 7 m only image. The lower left panel shows the ratio of peak intensities between these two images at matched 10". In other words, the left column of Figure 30 shows the same results as Figure 29, but for the real data, with the residuals added back into the deconvolved model.
Including the residual emission improves the situation by a small amount for the real data. However, a significant overall offset between the total flux in the 12 m+7 m and 7 m images remains visible in the top left panel of Figure 30. The simulations show a much larger improvement when the residuals are included. We understand this to reflect that the residuals in the simulations are idealized relative to those in the real data. We expect this because our simulations neglect phase noise. The simulations also achieve better rotation synthesis, and so better $u-v$ coverage, than the real data because the simulations observe a long continuous 7 m block around transit while the real observations observe short blocks at random times. Still, the simulations continue to show a significant effect in the final images. The lower panel shows that effect also appears for the peaks of the image in the real data.

*Feathering largely corrects the issue, but not at the lowest S/N levels:* In PHANGS–ALMA, we always attempt to include total power observations. These serve to anchor the total flux in the images and also to provide short-spacing information in the final image. The right column of Figure 30 shows the ratios of flux (top) and peak intensity (bottom) between the 12 m+7 m and 7 m data after feathering.

The figures show that, in cases with mean intensity levels $\gtrsim 4\sigma$, the flux discrepancy almost vanishes after feathering. In the lower-significance cases, we expect that the overall S/N in the cube is so low that statistical uncertainties in, e.g., masking to calculate the total flux, may drive some of the visible scatter. The bottom right panel shows that the agreement in the peak intensity also becomes much better with feathering, implying that the short-spacing correction helps locally, not only for the global flux. Overall, feathering reduces discrepancies in the integrated flux to $\lesssim 5\%$.

*Synthesis:* These results clearly demonstrate that the deconvolution of 7 m only data suffers from significant shortcomings and that these persist into the final images for the real 7 m only data. Because the discrepancies are largely resolved by feathering, we expect our final data products, even those involving only the 7 m array, to be largely correct. However, 7 m only images of nearby galaxies should be viewed with caution. Even the feathered data seem likely to harbor second-order fidelity issues, though a detailed investigation beyond what we present in Section 8.3 will have to wait for future work.

This analysis highlights a somewhat unexpected point. It would have been easy to attribute the flux missed from the 7 m deconvolution to “spatial filtering” that can only be addressed by including short-spacing data. This does not appear to be the case. Instead, in galaxies with clumpy structure and strong velocity gradients, including sensitive 12 m data significantly improves our flux recovery.

## Appendix D
### Testing Short-spacing Correction Methods

Correcting interferometric data for missing short and zero spacings is a key part of reconstructing the true intensity distribution on the sky. Several SSC methods have been proposed, and there is not yet a clear consensus on the best approach. In this appendix, we test the suitability of three of these methods for PHANGS–ALMA. Our goal here is not a thorough assessment of each method, which would require a large amount of research; e.g., see ALMA memos 398 and 488 (Pety et al. 2001b; Tsutsumi et al. 2004). Instead, we test how

three popular methods work in a test case constructed to suffer from extreme spatial filtering.

To conduct this test, we use the CASA task `simobserve` to simulate interferometric and total power observations of artificial intensity distributions. We then image and combine these observations using different SSC techniques. We compare the recovered image to the known input image in order to evaluate the performance of each SSC technique.

We conduct these tests using a kind of “worst case” scenario for spatial filtering in a data set like PHANGS–ALMA. For our model input images, we adopt peak intensity (see Section 7) maps derived from the real PHANGS–ALMA data. We apply some clipping to isolate significant emission, but remove all velocity structure from the map. This leads to a model with widespread positive emission across each entire mosaic (e.g., as seen in the top left panels in Figures 31 and 32). This does not represent a truly realistic simulation of a galaxy. Our real targets show clumpy, sharp structure in individual velocity channels, while these models often show extended, relatively smooth structure on the scales accessed by the 7 m array used to carry out these tests. However, these models should present a case that can serve as a useful test of short-spacing correction algorithms. In that sense, this calculation complements the more realistic simulations in Section 8.3, in which the interferometric imaging recovers a larger fraction of the flux seen by the total power data.

*Simulations:* The simulations were set up as follows.

1. *Sample:* We run simulations considering 64 PHANGS–ALMA targets that had full 12 m+7 m+TP CO(2–1) imaging available and clear CO detections as of Fall 2019.

2. *Sky Model:* For each galaxy, we use the 12 m+7 m+TP peak CO(2–1) intensity map (Section 7) as the input sky model for `simobserve`. Before inputting them to the simulation, we clipped these images at a threshold corresponding to three times the rms noise in the map. By eye, this did a reasonable job of mostly including real structure emission associated with the galaxy. Pixels with values below this threshold had their values set to zero. After clipping, we convert the units of the maps to Jy beam$^{-1}$, appropriate for use with `simobserve`. We keep the sky coordinates the same as the true galaxy. For convenience, we set the source velocity to 0 km s$^{-1}$. This choice should have no impact on the imaging.

3. *Interferometric Simulations:* We use CASA 5.4.0 for the simulations, employing the task `simobserve` to construct the simulated measurement set and `tclean` for the subsequent imaging. We define our own hexagonally spaced mosaic grid to cover each input image. The spacing between neighboring pointings is set to 24", i.e., half-beam sampling for the 7 m array. For this exercise, galaxies observe with multiple independent mosaics in the real data set, e.g., NGC 2903 (Figure 11), were treated as a single image and not simulated in separate parts.

We simulate observations with the Cycle 5 ACA 7 m array configuration (aca cycle5.cfg$^{53}$), reflecting the fact that most PHANGS–ALMA 7 m observations were obtained during Cycle 5 in the context of our Large Program.

The integration time of each $u-v$ data point is set to

<footnote>$^{53}$ https://almascience.eso.org/tools/casa-simulator</footnote>
10 s. The total observing time is set to 4 hr, which represents a reasonable match to the typical PHANGS–ALMA 7 m observing time per target. The source transits at the midpoint of the simulated observations. The observations thus happen at the highest possible elevation for each source.

We did not add thermal or phase noise. Instead, we concentrate on evaluation of SSC methods in the case of ideal observations. Aside from simply creating scatter in the measurements, we expect that the main effect of adding thermal and phase noise would be to add uncertainty to the deconvolution procedure. Thus, we prefer to focus on only the short-spacing correction here.

4. *Interferometric imaging:* We image the simulated visibility data using `tclean`. As in the PHANGS–ALMA pipeline (see Section 4), we start with a multiscale deconvolution using `tclean`, setting the scale parameter set to [0, 2, 4] pixels, with the pixel scale set to $1''$. We clean until the peak residual is $\le 4$ times the noise determined from the input image before clipping. We then continue with a single-scale ("Högbom") `tclean`. This proceeds until the peak of the residuals $\le 1$ times the rms noise from the original image.

The imaging adopts Briggs weighting with `robust = 0.5`. We use `cyclefactor = 4`, `cell = 1''0`, `cycleniter = 100`, and `gain = 0.2` (resp. 0.1) for multiscale clean (resp. single-scale clean). We do use a clean mask, which we create by convolving the input image to the synthesized beam size and detecting the significant pixels in this smoothed image.

5. *Total power data for simulations:* We simulate ideal single-dish observations by convolving the input sky image with the beam of the total power telescopes, $28''/6$ at 230.5 GHz.

*Short-spacing Correction:* There are currently at least three popular methods for short-spacing correction for ALMA. CASA's `feather` routine represents the path recommended by many observatory guides and documentation. Alternatively, the `tp2vis` method offers the most advanced current implementation of joint deconvolution. A third path uses the input clean model to incorporate information on extended emission. Variations exist on each of these techniques, but broadly speaking, they span the range of current approaches in wide use. Before describing our results, we briefly describe each.

1. *Joint Deconvolution (tp2vis):* Koda et al. (2019) present and give a full description of the `tp2vis`. This method converts a total power map into visibilities via a “simple” deconvolution of the total power beam from the data in the Fourier plane. The data are then multiplied by the primary beam of the interferometric dish in the image plane—in this case, the 7 m antenna. Finally, the Fourier plane is fully sampled to produce a visibility table that reflects the total power data. The weight density of the total power visibilities is adjusted to match that of the interferometric visibilities. The total power visibilities are then merged with the interferometric ones using the CASA task `concat`. We use the same imaging scheme described above to image the combined interferometric and total power data set produced by `tp2vis`.

2. *Model-assisted CLEAN (tpmodel):* This method utilizes a user-defined image as an initial CLEAN model. This

has been used in various forms for several years (see, e.g., Dirienzo et al. 2015).

In our implementation, we pass the simulated total power image to `tclean` via the `startmodel` parameter. This initializes the CLEAN model, i.e., the deconvolved image, to the total power image. This input model is Fourier transformed and subtracted from the interferometric visibilities before the imaging proceeds. The imaging proceeds as normal, modifying the initial model until it achieves a good match to the interferometric data. Thus, this procedure essentially gives priority to the interferometer data and uses the total power as an additional guess to fill in missing information.

In practice, we first convert the units of the input total power image from Jy beam$^{-1}$ to Jy pixel$^{-1}$, because CASA tracks the CLEAN model in these units.

3. *Feathering (feather):* In feathering, the total power and interferometric images are combined in the Fourier domain after imaging and deconvolution (e.g., Bajaja & van Albada 1979; Cotton 2017). The main difference between `feather` and `tp2vis` is that, with `feather` data, combination happens after deconvolution, so `feather` does not represent “joint” deconvolution. The advantage of this approach is its simplicity and robustness. This combination approach is adopted in much of the CASA documentation and has been commonly used in MIRIAD as well, where a version is implemented as `immerge`.

In practice, we run `feather` following the default CASA approach, matching the CASA guides. We set `sdfactor = 1.0`, `effdishdiam = -1.0`, and `lowpassfiltersd = False`. As in the main PHANGS–ALMA pipeline processing, we apply the primary beam correction before feathering. We found that this leads to better recovery of the source structure near the edge of the mosaicked field of view.

For each target, we use all three methods to create a short-spacing corrected image. The `tp2vis` method produces images with a slightly larger synthesized beam size than the other two methods. Therefore, we convolve all of the short-spacing corrected images to $10''$, in order to allow a direct comparison of the methods.

*Evaluation of Results:* Figures 31 and 32 show the results from our experiment for two galaxies: NGC 0628 and NGC 4303. The figures show the convolved input images, the output of imaging using only the 7 m data with no SSC, and the results for each of the three SSC approaches. All panels have the same beam and intensity scale, to allow direct comparison.

The top rows of Figures 31 and 32 show examples of the input model and output imaging, both convolved to $10''$ resolution, or slightly coarser than the typical resolution of the 7 m array at 230 GHz. In both targets, the 7 m only image shows extended negative sidelobes, or “negative bowls,” in place of extended positive emission in the input image. This illustrates how our choice to collapse the emission to a single plane yields an image that appears positive essentially everywhere. In both galaxies, significant, positive emission pervades the map at the resolution of the 7 m array. As a result, the interferometric images visible in the top middle panel show much stronger spatial filtering than we observe in our actual PHANGS–ALMA data. This highlights the fact that the total
<figure><img src="image_36.png" /><figcaption>**Figure 31.** Results of short-spacing correction tests for NGC 0628. The top left panel shows our model image convolved to the comparison resolution of 10". We construct the model image from a clipped version of the peak intensity map of the real combined 12 m+7 m+TP PHANGS-ALMA CO(2-1) observations for this target. Because we drop all velocity information for this exercise and focus on analysis of relatively low-resolution 7 m observations, the model shows positive emission essentially everywhere, with very smooth structure. The top middle panel shows the result of simulated observations using this input model and only the ACA 7 m array with no total power information. Significant missing flux can be seen in the image, indicating strong spatial filtering by the interferometer. The bottom row shows short-spacing corrected simulated observations. Each panel shows a different SSC method, from left to right: joint deconvolution using tp2vis, CLEANing using the simulated total power data as a model (tpmodel), and Fourier plane combination after deconvolution (feather, our adopted method in the PHANGS-ALMA pipeline). All images have the same 10" beam, and the color scale is fixed across images in order to allow direct comparison. The white circle in the bottom left of each panel shows the beam.</figcaption></figure>

power information is crucial, though we again caution that we have created a scenario that made these effects severe.

To the eye, all the short-spacing corrected images appear fairly similar. This suggests that all three SSC methods generally do a good job of recovering the input sky model, with minor differences. However, when examined in detail, there are differences between the three results. In the rest of this appendix, we quantify the differences among the different SSC results, using three metrics.

We quantify the results for each SSC method using three measurements: the “image fidelity,” the fraction of the total model flux recovered, and the difference in peak intensity between the output and the model.

We calculate the image fidelity at each pixel defined, e.g., following ALMA memo 386 (Pety et al. 2001a), as:

$$ \text{fidelity} = \frac{|\text{input model}|}{|\text{input model} - \text{output image}|} \qquad (\text{D1}) $$

Thus, fidelity of 10 means that the difference between the image and the model is 9%, fidelity of 100 corresponds to a difference of ~1%, and fidelity of 1 corresponds to a 50%

difference. More generally, the higher the fidelity, the better the output image matches the model. In practice, we compute the median fidelity over the entire image in order to quantify the overall quality of each SSC method.

The top panel of Figure 33 shows the median image fidelity as a function of the size of the CO disk for the 64 PHANGS-ALMA targets in our sample. We pick CO disk size as our independent variable because we expect targets with more extended emission, i.e., a larger CO disk size, to show more spatial filtering and thus be more dependent on the SSC. We computed the size as the diameter that contains all the nonzero pixels in the model image.

As expected, the 7 m only images show extremely low median fidelity, 1.1 with rms scatter 0.1 across the sample. This corresponds to the output image differing by ~50% from the input image, on average. This is consistent with the visual appearance of strong spatial filtering seen when comparing the top left and top middle panels in Figures 31 and 32. The interferometer misses the large-scale structure that contributes much of the flux in the model.

All three of the SSC methods show much higher median fidelity than the interferometer data alone, with average values
<figure><img src="image_37.png" /><figcaption>Figure 32. Results of short-spacing correction tests for NGC 4303. Similar to Figure 31, but for NGC 4303.</figcaption></figure>

in the range 6.1–7.9). This implies that the reproduced images are consistent with the model within a ~10%–15% accuracy. They show high scatter from target to target, however. In general, small targets show lower fidelity, even after SSC correction, compared to large targets.

The middle panel of Figure 33 shows the difference in total flux between the output image and the model as a function of the CO disk size. We define:

$$ \text{total flux difference} = \frac{\text{sum of input model} - \text{sum of output image}}{\text{sum of input model}}. \quad (\text{D2}) $$

In this case, 0.0 corresponds to a perfect match between input and output images.

On average, the 7 m only images miss ~80% of the flux. The smallest sources show better flux recovery in these images, but for virtually every source with CO disk diameter ≳75", roughly 80% of the flux is missed. Recall that our test cases have discarded velocity information and so represent a worst case. In the actual PHANGS–ALMA data, the 7 m array recovers 50%–80% of the flux observed by the single dish (Figure 13) and some of the missed emission appears to be due to deconvolution effects rather than spatial filtering (Appendix C and Section 8.3).

The bottom panel in Figure 33 shows the difference in peak intensity between the output image and model. Again, we

define:

$$ \text{peak intensity difference} = \frac{\text{peak in input model} - \text{peak in output image}}{\text{peak in input model}}. \quad (\text{D3}) $$

This statistic captures the ability of the output image to capture the brightest emission in the image. On average, the 7 m only imaging recovers a peak flux 35% lower than in the model. Almost all 7 m images show a depressed peak flux. This shows that including total power data can be crucial even for studying compact sources. This will be especially true when, e.g., as is the case for galactic nuclei, these sources are surrounded by extended diffuse structures.

The peak fluxes of the images reconstructed by the three SSC methods agree with the model peak flux within ~10%. The recovered peak flux does not depend on CO disk size or other galaxy parameters (e.g., total flux, peak flux, and average flux).

Combining all three metrics, we can evaluate each of the SSC methods. Before noting a few shortcomings, we emphasize that all three methods represent a marked improvement over the imaging using only the 7 m data with no SSC.

**tpmodel**: Images reconstructed using the tpmodel method show median fidelity comparable to that of those reconstructed via feather. They show the best overall match to the data in peak intensity. However, the middle panel of Figure 33 shows that the tpmodel method does tend to
<figure><img src="image_38.png" /><figcaption>**Figure 33.** *Measurements of the effectiveness of short-spacing corrections.* These plots show results for simulated imaging of PHANGS–ALMA data using three short-spacing correction schemes (*tp2vis*, *tpmodel*, and *feather*) and imaging without any short-spacing correction (“7 m only”). Each point shows a result for one reconstruction algorithm applied to simulated images based on one PHANGS–ALMA galaxy. The color of each point indicates the algorithm used for short-spacing correction. The points are sorted by the diameter of CO emission from that galaxy. The top row shows median image fidelity (Equation (D1)). The middle row shows the fraction of flux missed in the output image compared to the input model; e.g., 0.0 means no missing flux, while 0.25 means 25% of the flux is missed in the output. The bottom row shows the fractional difference in peak intensity between the output image and the model; again, 0.25 indicates a 25% lower peak intensity in the output compared to the model. The dashed lines indicate the mean performance of each method for each metric. The legend reports the mean and standard deviation for each method and metric.</figcaption></figure>

recover slightly too much flux compared to the model. The total flux is overestimated by ~6% on average, and by as much as ~25% in the most extreme cases. This can be attributed to the fact that the total power data input as a model have a much larger beam size than does the CLEAN product, which creates an extended artifact surrounding strong peaks.<fnref n="54" /> Some groups have adopted iterative strategies to address this, e.g., using feathered data from a previous iteration of clean as a model (e.g., Bolatto et al. 2013; Leroy et al. 2015). We experimented with these methods and did not find a stable, general approach, but this might represent an interesting future direction.

*tp2vis*: Images reconstructed using *tp2vis* show a high median fidelity, but with a dispersion larger than those of the other two SSC methods. The middle panel also shows that, with *tp2vis*, one tends to underestimate the total flux in our simulations by ~22% on average, and by up to ~50% in the most extreme cases. We find that *tp2vis* does a good job of recovering the peak intensity, comparable to *feather* and slightly worse than the *tpmodel* approach.

We interpret the large scatter to mean that *tp2vis* may require some fine-tuning of parameters for each source. Given the computing requirements for one round of imaging, as well as the fact that *tp2vis* did not offer a clear improvement over the other algorithms, it was not realistic to apply this fine-tuning to the current round of PHANGS–ALMA imaging. This might represent a useful future direction.

*feather*: Images reconstructed using *feather* yield a high median fidelity, ~7.9, comparable to *tpmodel* and with a similar scatter. On average, *feather* recovers the total flux with accuracy similar to that of *tpmodel* and somewhat better than that of *tp2vis*. It shows lower scatter in total flux recovery than either of the other two methods. Feather tends to recover peak intensities ~7% too low, similar to *tp2vis* and slightly worse than *tpmodel*.

*Summary*: In summary, all three SSC methods represent a marked improvement over using only the 7 m data for these cases. They yield results consistent with one another at the ~10% level. For PHANGS–ALMA, we ultimately utilized *feather* because it is stable and simple with consistent performance across the sample. For ALMA, which has good

<footnote n="54">⁵⁴ https://github.com/teuben/dc2019/blob/master/talks/Kauffmann.pdf</footnote>
overall flux calibration and a consistent flux calibration scheme for both the interferometer and total power, feather has the additional advantage of not requiring additional human supervision or intervention.

On average, a feathered image in our experiment has a ~5% bias in recovering the total flux and a ~7% underestimate of the peak flux. The median deviation from the input image is ~12%, based on the image fidelity calculation. As emphasized above, these calculations significantly overstate the uncertainty, because we discard velocity information (Section 6). Still, they suggest a 5%-10% uncertainty associated with image reconstruction. This will be comparable to the uncertainty due to calibration uncertainty and thermal noise in many cases, and highlights the need for continued work on this topic.

## ORCID iDs

Adam K. Leroy https://orcid.org/0000-0002-2545-1700

Annie Hughes https://orcid.org/0000-0002-9181-1161

Daizhong Liu https://orcid.org/0000-0001-9773-7479

Jérôme Pety https://orcid.org/0000-0003-3061-6546

Erik Rosolowsky https://orcid.org/0000-0002-5204-2259

Toshiki Saito https://orcid.org/0000-0002-2501-9328

Eva Schinnerer https://orcid.org/0000-0002-3933-7677

Antonio Usero https://orcid.org/0000-0003-1242-505X

Christopher M. Faesi https://orcid.org/0000-0001-5310-467X

Cinthya N. Herrera https://orcid.org/0000-0001-6405-0785

Mélanie Chevance https://orcid.org/0000-0002-5635-5180

Alexander P. S. Hygate https://orcid.org/0000-0002-6488-471X

Amanda A. Kepley https://orcid.org/0000-0002-3227-4917

Eric W. Koch https://orcid.org/0000-0001-9605-780X

Miguel Querejeta https://orcid.org/0000-0002-0472-1011

Christine D. Wilson https://orcid.org/0000-0001-5817-0991

Gagandeep S. Anand https://orcid.org/0000-0002-5259-2314

Ashley Barnes https://orcid.org/0000-0003-0410-4504

Francesco Belfiore https://orcid.org/0000-0002-2545-5752

Ivana Bešlić https://orcid.org/0000-0003-0583-7363

Frank Bigiel https://orcid.org/0000-0003-0166-9745

Guillermo A. Blanc https://orcid.org/0000-0003-4218-3944

Alberto D. Bolatto https://orcid.org/0000-0002-5480-5686

Médéric Boquien https://orcid.org/0000-0003-0946-6176

Yixian Cao https://orcid.org/0000-0001-5301-1326

Rupali Chandar https://orcid.org/0000-0003-0085-4623

Jérémy Chastenet https://orcid.org/0000-0002-5235-5589

I-Da Chiang https://orcid.org/0000-0003-2551-7148

Enrico Congiu https://orcid.org/0000-0002-8549-4083

Daniel A. Dale https://orcid.org/0000-0002-5782-9093

Sinan Deger https://orcid.org/0000-0003-1943-723X

Jakob S. den Brok https://orcid.org/0000-0002-8760-6157

Cosima Eibensteiner https://orcid.org/0000-0002-1185-2810

Eric Emsellem https://orcid.org/0000-0002-6155-7166

Axel García-Rodríguez https://orcid.org/0000-0002-0697-0177

Simon C. O. Glover https://orcid.org/0000-0001-6708-1317

Kathryn Grasha https://orcid.org/0000-0002-3247-5321

Brent Groves https://orcid.org/0000-0002-9768-0246

Jonathan D. Henshaw https://orcid.org/0000-0001-9656-7682

María J. Jiménez Donaire https://orcid.org/0000-0002-9165-8080

Jaeyeon Kim https://orcid.org/0000-0002-0432-6847

Ralf S. Klessen https://orcid.org/0000-0002-0560-3172

Kathryn Kreckel https://orcid.org/0000-0001-6551-3091

J. M. Diederik Kruijssen https://orcid.org/0000-0002-8804-0212

Kirsten L. Larson https://orcid.org/0000-0003-3917-6460

Janice C. Lee https://orcid.org/0000-0002-2278-9407

Ness Mayker https://orcid.org/0000-0002-5993-6685

Rebecca McElroy https://orcid.org/0000-0003-2290-7060

Sharon E. Meidt https://orcid.org/0000-0002-6118-4048

Angus Mok https://orcid.org/0000-0001-7413-7534

Hsi-An Pan https://orcid.org/0000-0002-1370-6964

Johannes Puschnig https://orcid.org/0000-0003-1111-3951

Alessandro Razza https://orcid.org/0000-0001-7876-1713

Patricia Sánchez-Blázquez https://orcid.org/0000-0003-0651-0098

Karin M. Sandstrom https://orcid.org/0000-0002-4378-8534

Amy Sardone https://orcid.org/0000-0002-5783-145X

Jiayi Sun https://orcid.org/0000-0003-0378-4667

David A. Thilker https://orcid.org/0000-0002-8528-7340

Jordan A. Turner https://orcid.org/0000-0003-2261-5746

Dyas Utomo https://orcid.org/0000-0003-4161-2639

Elizabeth J. Watkins https://orcid.org/0000-0002-7365-5791

Thomas G. Williams https://orcid.org/0000-0002-0012-2142

## References

Anand, G. S., Lee, J. C., VanDyk, S. D., et al. 2021, MNRAS, 501, 3621

Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123

Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33

Bajaja, E., & van Albada, G. D. 1979, A&A, 75, 251

Bolatto, A. D., Leroy, A. K., Rosolowsky, E., Walter, F., & Blitz, L. 2008, ApJ, 686, 948

Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207

Chevance, M., Kruijssen, J. M. D., Hygate, A. P. S., et al. 2020, MNRAS, 493, 2872

Colombo, D., Meidt, S. E., Schinnerer, E., et al. 2014, ApJ, 784, 4

Cornwell, T. J. 2008, ISTSP, 2, 793

Cotton, W. D. 2017, PASP, 129, 094501

Dirienzo, W. J., Brogan, C., Indebetouw, R., et al. 2015, AJ, 150, 159

Helfer, T. T., Vogel, S. N., Lugten, J. B., & Teuben, P. J. 2002, PASP, 114, 350

Henshaw, J. D., Kruijssen, J. M. D., Longmore, S. N., et al. 2020, NatAs, 4, 1064

Herrera, C. N., Pety, J., Hughes, A., et al. 2020, A&A, 634, A121

Heyer, M., Krawczyk, C., Duval, J., & Jackson, J. M. 2009, ApJ, 699, 1092

Heyer, M. H., Carpenter, J. M., & Snell, R. L. 2001, ApJ, 551, 852

Högbom, J. A. 1974, A&AS, 15, 417

Hughes, A., Meidt, S. E., Colombo, D., et al. 2013, ApJ, 779, 46

Kepley, A. A., Tsutsumi, T., Brogan, C. L., et al. 2020, PASP, 132, 024505

Kerr, A. R., Pan, S.-K., Claude, S. M. X., et al. 2014, ITTST, 4, 201

Koch, E., Rosolowsky, E., & Leroy, A. K. 2018a, RNAAS, 2, 220

Koch, E. W., Rosolowsky, E. W., Lockman, F. J., et al. 2018b, MNRAS, 479, 2505

Koda, J., Teuben, P., Sawada, T., Plunkett, A., & Fomalont, E. 2019, PASP, 131, 054505

Landsman, W. B. 1993, in ASP Conf. Ser. 52, Astronomical Data Analysis Software and Systems II, ed. R. J. Hanisch, R. J. V. Brissenden, & J. Barnes (San Francisco, CA: ASP), 246

Lang, P., Meidt, S. E., Rosolowsky, E., et al. 2020, ApJ, 897, 122

Lay, O. P., Carlstrom, J. E., Hills, R. E., & Phillips, T. G. 1994, ApJL, 434, L75

Leroy, A. K., Bolatto, A., Bot, C., et al. 2009, ApJ, 702, 352

Leroy, A. K., Bolatto, A. D., Ostriker, E. C., et al. 2015, ApJ, 801, 25
Leroy, A. K., Hughes, A., Schruba, A., et al. 2016, ApJ, 831, 16

Leroy, A. K., Schinnerer, E., Hughes, A., et al. 2021, ApJS, submitted
(arXiv:2104.07739)

Makarov, D., Prugniel, P., Terekhova, N., Courtois, H., & Vauglin, I. 2014, A&A, 570, A13

Mangum, J. G., Emerson, D. T., & Greisen, E. W. 2007, A&A, 474, 679

McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in
ASP Conf. Ser. 376, Astronomical Data Analysis Software and Systems
XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell (San Francisco, CA: ASP), 127

McQuinn, K. B. W., Skillman, E. D., Dolphin, A. E., Berg, D., & Kennicutt, R. 2017, AJ, 154, 51

Oliphant, T. E. 2006, A Guide to NumPy, Vol. 1 (USA: Trelgol Publishing)

Pardo, J. R., Cernicharo, J., & Serabyn, E. 2001, ITAP, 49, 1683

Paturel, G., Petit, C., Prugniel, P., et al. 2003, A&A, 412, 45

Penzias, A. A., & Burrus, C. A. 1973, ARA&A, 11, 51

Pety, J. 2005, in SF2A-2005: Semaine del'Astrophysique Francaise, ed.
F. Casoli et al. (Les Ulis: EDP Sciences), 721

Pety, J., Gueth, F., & Guilloteau, S. 2001a, ALMA+ACA Simulation Tools, Alma Memo 386, IRAM

Pety, J., Gueth, F., & Guilloteau, S. 2001b, Impact of ACA on the Wide-Field Imaging Capabilities of ALMA, Alma Memo 398, IRAM

Pety, J., Schinnerer, E., Leroy, A. K., et al. 2013, ApJ, 779, 43

R Core Team 2015, R: A Language and Environment for Statistical Computing (Vienna: R Foundation for Statistical Computing)

Remijan, A. J., Markwick-Kemper, A. & ALMA Working Group on Spectral Line Frequencies 2007, AAS Meeting, 211, 132.11

Rosolowsky, E., Hughes, A., Leroy, A. K., et al. 2021, MNRAS, 502, 1218

Rosolowsky, E., & Leroy, A. 2006, PASP, 118, 590

Schinnerer, E., Hughes, A., Leroy, A., et al. 2019, ApJ, 887, 49

Schruba, A., Leroy, A. K., Walter, F., Sandstrom, K., & Rosolowsky, E. 2010, ApJ, 722, 1699

Shaya, E. J., Tully, R. B., Hoffman, Y., & Pomarède, D. 2017, ApJ, 850, 207

Stanimirovic, S., Staveley-Smith, L., Dickey, J. M., Sault, R. J., & Snowden, S. L. 1999, MNRAS, 302, 417

Sun, J., Leroy, A. K., Schinnerer, E., et al. 2020, ApJL, 901, L8

Sun, J., Leroy, A. K., Schruba, A., et al. 2018, ApJ, 860, 172

Teague, R., & Foreman-Mackey, D. 2018, RNAAS, 2, 173

Tsutsumi, T., Morita, K.-I., Hasegawa, T., & Pety, J. 2004, Wide-Field Imaging of ALMA with the Atacama Compact Array: Imaging Simulations, ALMA Memo 488

Tully, R. B., Courtois, H. M., & Sorce, J. G. 2016, AJ, 152, 50

Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, NatMe, 17, 261