Siena Galaxy Atlas 2020

1.1. Scientific Context

1.2. The Need for a New Large-galaxy Atlas

With the historical context in mind, several recent developments motivate a renewed effort to assemble a uniform data set of large angular-diameter galaxies. First, three new ground-based optical imaging surveys jointly called the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys (hereafter, the Legacy Surveys) have delivered deep imaging in g, r, and z over ≈20,000 deg² of the extragalactic (i.e., low Galactic extinction) sky (Dey et al. 2019; D. J. Schlegel et al. 2023, in preparation). These data provide exquisite photometric and astrometric precision and reach 1–2 mag deeper than either SDSS or Pan-STARRS1 (Chambers et al. 2016). In addition, the development of the state-of-the-art image modeling code The Tractor provides a computationally tractable means of working with multiband, multipass, variable-seeing imaging, enabling dedicated studies of large angular-diameter galaxies (Lang et al. 2016; D. Lang et al. 2023, in preparation).

Second, in 2021 May, the DESI Survey began a 5 year program (2021–2026) to obtain precise spectroscopic redshifts for an unprecedented sample of more than 40 million galaxies and 10 million stars over the ≈14,000 deg² Legacy Surveys footprint accessible from the 4 m Mayall Telescope at Kitt Peak National Observatory (KPNO; DESI Collaboration et al. 2016a, 2016b; Abareshi et al. 2022). As part of this effort, the DESI Bright Galaxy Survey (BGS) is obtaining spectra and redshifts for a statistically complete sample of >10 million galaxies brighter than r = 20.175 (Hahn et al. 2023). A high-quality photometric catalog of the largest angular-diameter galaxies over the DESI footprint is needed to ensure the BGS has high completeness and does not suffer from the photometric shredding and spectroscopic incompleteness of the SDSS at bright magnitudes (Wake et al. 2017).

To address these and other needs, we present the 2020 version of the Siena Galaxy Atlas (SGA), SGA-2020, an optical and infrared imaging atlas of nearly 4 × 10⁵ galaxies approximately limited to an angular diameter of 25'' at the 26 mag arcsec⁻² isophote for galaxies brighter than r ≈ 18 over the 20,000 deg² footprint of the DESI Legacy Imaging Surveys Data Release 9 (LS/DR9; Dey et al. 2019; D. J. Schlegel et al. 2023, in preparation; see Figure 1). The SGA-2020 delivers precise coordinates, multiwavelength mosaics, azimuthally averaged optical surface-brightness and color profiles, model images and photometry, and additional metadata for the full sample. ¹⁰ Notably, for many of the largest (e.g., NGC/IC/Messier) galaxies in the sky, especially outside the SDSS imaging footprint, the SGA-2020 delivers the first reliable measurements of the optical positions, shapes, and sizes of large galaxies since the RC3 was published more than 30 yr ago.

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By combining existing (archival) spectroscopic redshifts with forthcoming DESI spectroscopy, the SGA-2020 will spur a renewed effort to tackle several outstanding problems in extragalactic astrophysics, particularly the interplay between galaxy formation and dark matter halo assembly. It will also support studies of time-domain and multimessenger astronomical events, which are often hampered by incomplete or heterogeneous catalogs of large, nearby galaxies, which are most likely to host the electromagnetic counterparts of gravitational wave events (Gehrels et al. 2016; Abbott et al. 2020) and other classes of transients. Moreover, within the ≈14,000 deg² DESI footprint, the SGA-2020 is ensuring high photometric completeness for the BGS, and is facilitating high-impact ancillary science through a variety of secondary targeting programs (DESI Collaboration et al. 2023a; Myers et al. 2023). For example, the DESI Peculiar Velocity Survey will place precise new constraints on the growth rate of large-scale structure by measuring the Tully–Fisher and fundamental-plane scaling relations (Tully & Fisher 1977; Djorgovski & Davis 1987) from SGA-2020 targets at z < 0.15 (Saulder et al. 2023). And finally, the SGA-2020 will help engage the broader public with visually striking color mosaics of large, well-resolved, nearby galaxies, enabling a myriad of educational and public-outreach activities.

We organize the remainder of the paper in the following way: In Section 2, we define the SGA-2020 parent sample and describe the procedure we use to define the final sample of galaxies and their associated (angular) group membership. In Section 3, we describe our photometric analysis, including how we construct the custom multiwavelength mosaics, model the two-dimensional images of each galaxy, and measure their azimuthally averaged surface-brightness and color profiles. Of particular interest for some readers may be Section 3.3, where we validate our surface-brightness profiles and summarize the principal SGA-2020 data products. In Section 4, we quantify the completeness of the SGA and review how it improves upon existing large-galaxy catalogs, and in Section 5, we highlight some of the exciting potential scientific applications of the SGA-2020. Finally, Section 6 summarizes the main results of this paper and outlines some of the improvements we intend to include in the next version of the SGA.

Note that, unless otherwise indicated, all magnitudes are on the AB magnitude system (Oke & Schild 1970) and have not been corrected for foreground Galactic extinction. We report all fluxes in units of "nanomaggies," where 1 nanomaggie is the (linear) flux density of an object with an AB magnitude of 22.5. ¹¹

2.1. Building the Parent Sample

Many of the largest, highest-surface-brightness galaxies in the sky have been famously known for a long time and are part of many of the legacy (photographic-plate) large-galaxy catalogs discussed in Section 1 (e.g., RC3). More recently, fainter, lower surface-brightness (but still "large," spatially resolved) galaxies have been cataloged by modern, wide-area optical and near-infrared imaging surveys like the SDSS, 2MASS (Skrutskie et al. 2006), and Pan-STARRS1 (Chambers et al. 2016). For the first version of the SGA, we opt to build upon this body of previous work by beginning from these and other catalogs of "known" large angular-diameter galaxies (but see the discussion in Section 6).

Fortunately, several user-oriented databases exist, which curate the positions, sizes, magnitudes, redshifts, and other information on millions of extragalactic sources cataloged by different surveys, including SIMBAD (Wenger et al. 2000), the NASA Extragalactic Database (NED; Helou et al. 1991), and HyperLeda (Makarov et al. 2014). After some experimentation, we opt to construct the initial SGA-2020 parent sample using the HyperLeda ¹² extragalactic database. HyperLeda includes extensive metadata on nearly all known large angular-diameter galaxies, building on the heritage of the RC3 and earlier large-galaxy atlases. In addition, an effort has been made by the HyperLeda team to homogenize the angular diameters, magnitudes, and other observed properties of the galaxies that have been ingested into the database from a wide range of different surveys and catalogs (Paturel et al. 1997; Makarov et al. 2014). This procedure imposes some uniformity on our parent sample, although we show in Section 3.3 the significant value of computing the geometry (diameter, position angle, and ellipticity) and photometry of galaxies consistently and using modern (deep, wide-area) optical imaging.

With these ideas in mind, we query the HyperLeda extragalactic database for galaxies with angular diameter D_L(25) > 12'' ($0\buildrel{\,\prime}\over{.} 2$), where D_L(25) is the major-axis diameter of the galaxy at the 25 mag arcsec⁻² surface-brightness isophote in the optical (typically the Johnson–Morgan B band; see Appendix A for additional details). Our query results in an initial parent sample of 1,436,176 galaxies.

Using visual inspection and a variety of quantitative and qualitative tests, we cull this initial sample by applying the following additional cuts: first, we remove the Large and Small Magellanic Clouds and the Sagittarius Dwarf Galaxy from the sample by imposing a maximum angular diameter of ${D}_{{\rm{L}}}(25)\lt 180^{\prime}$. These galaxies span such a large projected angular size on the sky (many degrees) that their inclusion is outside the scope of the SGA (but see Jarrett et al. 2019). After removing these objects, the largest angular-diameter galaxies that remain are NGC 0224 = M31 and NGC 0598 = M33 whose D_L(25) diameters are $178^{\prime}$ and $62^{\prime}$, respectively.

Furthermore, we limit the sample on the lower end to D_L(25) > 20'', which removes roughly 900,000 galaxies (approximately 65% of the initial sample). We implement this cut because we find that the fraction of sources with incorrect (usually overestimated) diameters in HyperLeda increases rapidly below this limit. Moreover, we find that galaxies smaller than D_L(25) ≈ 20'' are well modeled by Tractor as part of the standard photometric pipeline used in LS/DR9 (Dey et al. 2019; D. J. Schlegel et al. 2023, in preparation).

Next, we remove approximately 3800 galaxies with no magnitude estimate in HyperLeda (as selected by our query; see Appendix A), which we find to be largely spurious, as well as approximately 6500 objects with significantly overestimated diameters (or spurious sources), which we identify via visual inspection. Many of these cases are groupings of small galaxies or stars along a line, which have been misinterpreted by previous fitting algorithms as a single edge-on galaxy. In addition, we remove approximately 1700 galaxies whose primary galaxy identifier (in HyperLeda) is from either SDSS or 2MASS and whose central coordinates place it inside the elliptical aperture of another (non-SDSS and non-2MASS) galaxy with D_L(25) diameter greater than 30''. We find that in the majority of cases these objects have grossly overestimated diameters, presumably due to shredding by the 2MASS and SDSS photometric pipelines. Figure 2 displays a gallery of some of the most common types of sources we reject from our initial parent sample using these cuts.

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Now, to improve the completeness of the parent sample, we supplement the initial HyperLeda catalog with sources drawn from three additional catalogs, making sure to carefully handle duplicate entries. First, we add a subset of the Local Group dwarf galaxies from McConnachie (2012). From the original sample of 93 galaxies in McConnachie (2012), we remove 47 that have such a low surface brightness and are so well resolved that including them is beyond the scope of the current version of the SGA. ¹³ For reference, the median surface brightness of these 47 systems is μ_V = 28.8 mag arcsec⁻², well below the surface-brightness completeness limit of the SGA-2020 (see Section 3.3). Furthermore, we remove the Fornax and Sculptor dwarf galaxies, which are higher surface brightness (μ_V = 25.1–25.5 mag arcsec⁻²) but very well resolved into stars and star clusters and too challenging to include in this initial version of the SGA.

Next, we add 190 galaxies from the RC3 and OpenNGC ¹⁴ catalogs which are missing from our initial HyperLeda sample. Surprisingly, many of these systems are large and have high average surface brightness; however, we suspect that an issue with our database query (see Appendix A) may have inadvertently excluded these sources from our initial catalog. And finally, we use the Legacy Surveys Data Release 8 (DR8) photometric catalogs to identify 2890 additional large-diameter galaxies in the Legacy Surveys footprint. ¹⁵ Specifically, after applying a variety of catalog-level quality cuts and extensive visual inspection, we include in our parent sample all objects (not already in our sample) from DR8 with half-light radii r₅₀ > 14'' based on their Tractor model fits.

Our final parent sample contains 531,677 galaxies approximately limited to D_L(25) > 20'' and spanning a wide range of magnitude and surface brightness. In Figure 3, we show the celestial distribution of this sample, and in Figure 4, we show the range of apparent b_t -band magnitude ¹⁶ and angular diameter spanned by the parent sample. We discuss the completeness of the sample in Section 4.

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2.2. Projected Group Catalog

3.1. Imaging Data

3.2. Multiwavelength Mosaics and Surface-brightness Profiles

At this point in the analysis, we have multiband optical and infrared imaging covering roughly half the sky (Section 3.1) and an input parent catalog of central coordinates and system diameters for more than half a million sources (Section 2.2). The next steps are to build custom multiwavelength mosaics centered on each of these positions (Section 3.2.1); model all the sources in the field using The Tractor (Section 3.2.2); and measure elliptical aperture photometry and azimuthally averaged surface-brightness profiles (Section 3.2.3).

Before proceeding, we briefly summarize the principal software products we use, as well as the relationship between them. First, given an astrometrically and photometrically calibrated image, inverse variance image, and knowledge of the point-spread function (PSF), The Tractor ²¹ uses the PSF and a family of two-dimensional galaxy models to forward-model the observed pixel-level data (Lang et al. 2016; Dey et al. 2019; D. Lang et al. 2023, in preparation). One of the principal advantages of The Tractor is that it handles multiband, multi-CCD, variable-PSF imaging in a statistically rigorous way, which is especially important when dealing with the full range of optical and infrared (WISE) data from the Legacy Surveys. In order to handle the imaging data, the Legacy Surveys team has developed legacypipe, ²² a photometric pipeline that wraps The Tractor as its fitting engine and conveniently handles many tasks related to this imaging data set (Dey et al. 2019). Finally, for the SGA project specifically, we have developed the SGA ²³ and legacyhalos ²⁴ software products, which rely on some of the lower-level legacypipe functionality (with Message Passing Interface parallelization) but also include code to carry out the nonparametric photometric analysis, which is one of the cornerstone data products of the SGA-2020 (see Section 3.3).

3.2.1. Mosaics

Given the diameter of each system and its central coordinates (group_ra, group_dec, and group_diameter; see Section 2.2), we first determine if LS/DR9 imaging exists in all three grz bands over at least 90% of the area. If not, we remove that system from further analysis (including, unfortunately, NGC 0224 = M31, where we only have MzLS z-band imaging). Then, for the remaining objects, we generate g-, r-, and z-band mosaics with a size that depends on the group size: for groups with group_diameter < 14', we generate a mosaic of diameter 3 × group_diameter; for groups with 14' < group_diameter < 30' ​, we generate a mosaic of diameter 2 × group_diameter; and for NGC 0598 = M33, whose group_diameter is $\gt 30^{\prime}$, we use a mosaic diameter of 1.4 × group_diameter. We also choose the input imaging according to the following criteria: we use the DECam imaging (from DECaLS and DES) for all of the SGC, and for the North Galactic Cap when group_dec < 32375; and the BASS plus MzLS imaging otherwise (see Section 4.1.3 of Myers et al. 2023).

Our analysis begins with reduced and calibrated CCD-level 90Prime, Mosaic-3, and DECam imaging. These reduced data are generated using the NOIRLab Community Pipeline (CP) dedicated to each instrument (e.g., Valdes et al. 2014), together with several custom data-reduction steps developed by the Legacy Surveys team. We refer the reader to Dey et al. (2019) and D. J. Schlegel et al. (2023, in preparation) for a detailed description of these data-reduction procedures. Briefly, we use Pan-STARRS1 PSF photometry (Chambers et al. 2016; Finkbeiner et al. 2016) transformed to the natural filter system of each instrument for photometric calibration ²⁵ and Gaia Data Release 2 (Gaia Collaboration et al. 2018) stellar positions for astrometry. ²⁶ The average photometric precision for bright (but unsaturated) stars is better than ±10 mmag in grz over the full footprint, and the astrometric precision is approximately ±0030 for DECam and Mosaic-3 and ±012 mas for 90Prime (Dey et al. 2019).

Accurate large-galaxy photometry depends crucially on robust and unbiased background-subtraction. For the SGA-2020, we utilize the same background-subtracted images used for LS/DR9. As we discuss below and in Section 3.3, however, the sky-subtracted data do contain systematic errors, which we intend to mitigate in future versions of the SGA (see the discussion in Section 6).

First, the CP carefully masks astrophysical sources and then subtracts the large-scale sky-pattern across the field of view from each exposure using a low-order spline model derived from robust statistics measured on the individual CCDs. We note that the 90Prime, Mosaic-3, and DECam CCDs are approximately $30^{\prime} \times 30^{\prime}$, 175 × 175, and $9^{\prime} \times 18^{\prime}$, respectively, so the angular scale of this background model is much larger than all but the largest galaxies in the SGA-2020. Next, the CP subtracts the camera reflection pattern (or pupil ghost) from the DECam and Mosaic-3 data and the fringe pattern from the Mosaic-3 z-band and 90Prime r-band data. Telescope reflections from very bright stars are not removed. Next, the CP aggressively subtracts the high-frequency pattern noise (caused by a drifting amplifier bias level) present in the Mosaic-3 imaging. The pattern fitting was designed to preserve counts in smaller galaxies and stars but, unfortunately, has a significant effect on the low-surface-brightness outer envelopes of the galaxies in our sample. This pattern-noise subtraction affects all the MzLS imaging and causes galaxies to appear too green in the grz color mosaics (see Appendix C). For DECam, we also subtract a residual g-, r-, and z-band sky pattern and a z-band fringe pattern from the data using median-scaled templates derived from multiple exposures (in a given bandpass) within one or more nights. ²⁷ Finally, we remove the spatially varying sky-background on the smallest scales by dividing each CCD into 512 pixel boxes, computing the robust median, and using spline interpolation to build the final background map. During this step, we mask pixels that lie within the elliptical aperture of any galaxy in the SGA-2020 parent catalog (from Section 2.1), as well as Gaia stars and other sources detected in each image.

Finally, with all the reduced data in-hand, we build the full-field mosaic for each galaxy (or galaxy group) as the inverse-variance weighted sum of all the available imaging (in each bandpass) projected onto a tangent plane using Lanczos-3 (sinc) resampling. For the grz imaging, we adopt a constant pixel scale of 0262 pixel⁻¹, and for the unWISE mosaics, we use 275 pixel⁻¹. The left panels of Figures 5 and 6 show, as examples, the grz color mosaics for the isolated galaxy NGC 5016 and PGC 193192, a member of the PGC 193199 Group, respectively.

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3.2.2.  Tractor Modeling and Masking

We use The Tractor to model all the sources in a given mosaic, including the large angular-diameter galaxies of interest. Note that all source detection and model fitting with The Tractor takes place on these coadded images (triggered by invoking the --fit-on-coadds option in legacypipe), unlike for the standard DR9 processing in which all model fitting is done using the unresampled CCD images jointly (see Dey et al. 2019; D. J. Schlegel et al. 2023, in preparation).

One issue is that The Tractor tends to fit the high-surface-brightness central regions of large galaxies at the expense of their outer envelopes, creating undesirable systematic residuals in their outer parts. This problem occurs despite the larger variance—smaller inverse variance—in the central parts from source Poisson noise. Therefore, before fitting, we multiply the optical inverse variance mosaics (I) by a factor of $\sqrt{I/{I}_{50}}$, where I₅₀ is the median inverse variance of the whole mosaic. This scaling tends to reduce I in the central part of the galaxy and increase it in its outer regions, generally leading to better modeling results.

In addition, we increase the threshold for detecting and deblending sources by specifying --saddle-fraction 0.2 and --saddle-min 4.0 (the default values are 0.1 and 2.0, respectively). The saddle-fraction parameter controls the fractional peak height for identifying new sources around existing sources, and saddle-min is the minimum required saddle-point depth (in units of the standard deviation of pixel values above the noise) from existing sources down to new sources. We find these options necessary in order to prevent excessive shredding and overfitting of the resolved galactic structure in individual galaxies (e.g., H ii regions). Finally, The Tractor detects sources, creates a segmentation map, and then uses the mean PSF of the coadd to compute the two-dimensional, maximum-likelihood model of each source (fitting all three grz bands simultaneously) from among the following possibilities: PSF, REX, EXP, DEV, or SER. ²⁸ For reference, we construct the PSF of the coadd as the inverse-variance weighted average PSF of the individual pixelized PSFs contributing to the coadd, which is sufficient given that the galaxies we are interested in, D_L(25) ≳ 20'', are significantly larger than the optical image quality, PSF_FWHM ≈ 1''–2''.

The middle left panels of Figures 5 and 6 show The Tractor model image stack for NGC 5016 and the PGC 193199 Group, respectively. Overall, the model is an excellent description of the data, particularly for the small, compact sources in the field. However, note how The Tractor fits the (resolved) spiral arms in NGC 5016 as elongated blue "galaxies," and the extended outer envelopes of the early-type galaxy models in the PGC 193199 Group compared to the data. Despite these issues, The Tractor models of the large galaxies in our sample are extremely useful and complementary to the nonparametric photometric measurements we carry out in Section 3.2.3.

Using The Tractor models, we next build an image mask, which we use in Section 3.2.3. First, we read the maskbits ²⁹ bit-mask image produced as part of the pipeline, but only retain the BRIGHT, MEDIUM, CLUSTER, ALLMASK_G, ALLMASK_R, and ALLMASK_Z bits. Hereafter, we refer to this mask as the starmask. Next, we build a residual mask, which accounts for statistically significant differences between the data and the Tractor models. In detail, we flag all pixels that deviate by more than 5σ (in any bandpass) from the absolute value of the Gaussian-smoothed residual image, which we construct by subtracting the model image from the data and smoothing with a 2 pixel Gaussian kernel. This step obviously masks all sources, including the large galaxies of interest, but we restore those pixels in the next step. In addition, we iteratively dilate the mask two times and mask the pixels along the border of the mosaic with a border equal to 2% the size of the mosaic.

Then, we iterate on each galaxy in the group from brightest to faintest based on The Tractor r-band flux and carry out the following steps: (1) For each galaxy, we construct the model image from all Tractor sources in the field except the galaxy of interest and subtract this model image from the data. (2) We measure the mean elliptical geometry of the galaxy (center, ellipticity, position angle, and approximate semimajor axis length) based on the second moment of the light distribution (hereafter, the ellipse moments) using a modified version of Michele Cappellari's mge.find_galaxy ³⁰ algorithm (Cappellari 2002). When computing the ellipse moments, we first median-filter the image with a 3 pixel boxcar to smooth out any small-scale galactic structure, and we only use pixels with μ_r < 27 mag arcsec⁻². (3) Finally, we combine the residual mask with the starmask (using Boolean logic), but we unmask pixels belonging to the galaxy based on the ellipse moments geometry using 1.5 times the estimated semimajor axis of the galaxy.

Occasionally, the preceding algorithm fails in fields containing more than one galaxy if the central coordinates of one of the galaxies are masked by a previous (brighter) system. We consider a source to be impacted if any pixel in a 5 × 5 pixel box centered on The Tractor position of the galaxy is masked. In this case, we iteratively shrink the elliptical mask of any of the previous galaxies until the central position of the galaxy currently being analyzed is unmasked. We emphasize that this algorithm is not perfect, particularly in very crowded galactic fields like the center of the Coma Cluster, but we intend to improve it in future versions of the SGA. Another occasional failure mode is if the flux-weighted position of the galaxy based on the ellipse moments differs by The Tractor position by more than 10 pixels, which can happen in crowded fields and near bright stars and unmasked image artifacts; in this case, we revert to using The Tractor coordinates and model geometry.

The bottom left panels of Figures 5 and 6 show the final masked r-band image for NGC 5016 and PGC 193192, respectively.

3.2.3. Surface-brightness Profiles

With the multiwavelength mosaics and per-galaxy image masks in-hand, we next measure the surface-brightness profiles and photometric curves of growth for each galaxy in the sample using the standard ellipse-fitting and aperture photometry techniques in photutils ³¹ (Bradley 2023). We assume a fixed elliptical geometry as a function of semimajor axis using the ellipse moments measured in Section 3.2.2, and robustly determine the surface brightness along each elliptical path from the light-weighted central pixel to 2 times the estimated semimajor axis of the galaxy in a 1 pixel (0262) interval. In detail, we measure the surface brightness (and the uncertainty) using two σ clipping iterations, a 3σ clipping threshold, and median-area integration. ³²

From the r-band surface-brightness profile, we also robustly measure the size of the galaxy at nine equally spaced surface-brightness thresholds between μ_r = 22 and 26 mag arcsec⁻². We perform these measurements by fitting a linear model to the surface-brightness profile converted to mag arcsec⁻² versus r^1/4 (which would be a straight line for a de Vaucouleurs galaxy profile), but only consider measurements that are within ±1 mag arcsec⁻² of the desired surface-brightness threshold. To estimate the uncertainty in the resulting radius, we generate 30 Monte Carlo realizations of the surface-brightness profile and use the standard deviation of the resulting distribution of radii.

We also measure the curve of growth in each bandpass using the tools in photutils.aperture. Briefly, we integrate the image and variance image in each bandpass using elliptical apertures from the center of the galaxy to 2 times its estimated semimajor axis (based on the ellipse moments), again with a 1 pixel (0262) interval. ³³ We fit the resulting curve of growth, m(r), using the following empirical model:

$$\begin{eqnarray}&&m(r)={m}_{\mathrm{tot}}+{m}_{0}{\mathrm{log}}_{e}\left[1+{\alpha }_{1}{\left(\displaystyle \frac{r}{{r}_{0}}\right)}^{-{\alpha }_{2}}\right],\end{eqnarray} \tag{ 1 }$$

where m_tot, m₀, α₁, α₂, and r₀ are constant parameters of the model, and r is the semimajor axis in arcseconds. In our analysis, we take the radius scale factor r₀ = 10'' to be fixed (which makes α₁ dimensionless). Note that, in the limit r → ∞ , m_tot is the total, integrated magnitude. Using this model, we infer the half-light semimajor axis length, r₅₀, analytically from the best-fitting model parameters:

$$\begin{eqnarray}&&{r}_{50}={r}_{0}{\left\{\displaystyle \frac{1}{{\alpha }_{1}}\left[\exp \left(-\displaystyle \frac{{\mathrm{log}}_{10}(0.5)}{0.4{m}_{0}}\right)-1\right]\right\}}^{-1/{\alpha }_{2}},\end{eqnarray} \tag{ 2 }$$

where r₅₀ is measured in arcseconds, and m₀ is in magnitudes.

3.3. Summary and Validation of SGA-2020 Data Products

The final SGA-2020 sample consists of 383,620 galaxies in the ≈20,000 deg² LS/DR9 imaging footprint. The final catalog contains precise coordinates; multiwavelength mosaics; model images and photometry from The Tractor; azimuthally averaged optical surface-brightness profiles; aperture photometry and radii; and extensive metadata for all galaxies in this sample. In this section, we briefly highlight some of these measurements; for a comprehensive description of the SGA-2020 data products and how they can be accessed, see Appendix B.

Figure 7 shows the celestial positions of the galaxies in the SGA-2020 in an equal-area Mollweide projection. The curved black line represents the Galactic plane, which divides the sample into the North Galactic Cap and SGC imaging regions of the LS/DR9 footprint (see Dey et al. 2019). The total area subtended by the sample is 19,721 deg², covering nearly 50% of the sky.

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In Figure 8, we highlight a handful of the measured SGA-2020 properties, as well as the relationships between them. In a multivariate corner plot (Foreman-Mackey 2016), we show r_R(26), the r-band magnitude within R(26), where R(26) is the semimajor axis at the 26 mag arcsec⁻² isophote; $\langle {\mu }_{r,R(26)}\rangle \equiv {r}_{R(26)}+2.5{\mathrm{log}}_{10}\,[\pi {R}^{2}(26)]$, the average r-band surface brightness within R(26); ϕ is the galaxy position angle (measured counterclockwise from north to east); and ≡ 1 − b/a, the galaxy ellipticity, where b/a is the minor-to-major axis ratio. Note the expected strong correlation between R(26) and r_R(26), and the anticorrelation between and 〈μ〉_r,R(26), which is due to the light in more edge-on galaxies being attenuated more by the larger column of internal dust attenuation (famously known as the Holmberg "transparency test"; Holmberg 1958; Giovanelli et al. 1994).

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In Figure 9, we compare some of the new geometrical measurements in the SGA-2020 against the measurements collated in HyperLeda. In panel (a), we plot Δdecl. versus ΔR.A., the difference in equatorial coordinates. The overall agreement in positions is very good; the median, mean, and ±1σ scatter are 03, 04, and ±05, respectively, although the coordinates of individual (especially irregular and low-surface-brightness) galaxies differ by up to tens of arcseconds. In Figure 10, we show a randomly selected set of 20 galaxies where the central coordinates in the SGA-2020 and HyperLeda differ by more than 3''. Although reasonable algorithms may disagree about the central positions of some galaxies due to dust lanes or the lack of a prominant central bulge (e.g., NGC 4948 = IC 4156 and ESO293-034), it is clear that the coordinates in the SGA-2020 for most of the examples highlighted in Figure 10 are more accurate in measuring the centroid of galaxies with bright cores and the center of light for more diffuse systems, even for very large, well-known galaxies like NGC 4636 = UGC 07878, and NGC 3521 = UGC 06150.

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Next, in Figure 9(b), we plot D_L(25) (defined in Section 2.1) versus D(25), the SGA-2020 major-axis diameter measured at the 25 mag arcsec⁻² isophote. Not unexpectedly, we find a strong correlation between the two quantities, although D(25) is ≈20% larger, on average, than D_L(25), presumably due to the deeper optical imaging used in the SGA-2020. Finally, in Figures 9(c) and (d), we plot the correlation between position angle, ϕ, and ellipticity, , respectively, between HyperLeda and the SGA-2020. For more than 95% of the sample, the agreement between the two ϕ and measurements are excellent.

In order to validate our measurements further, in Figure 11, we compare the SGA-2020 coordinates and mean geometrical measurements against the WISE Extended Source Catalog of the 100 Largest Galaxies (hereafter, WXSC-100; Jarrett et al. 2019). ³⁴ Of the 104 galaxies in the WXSC-100 sample, 59 are in the SGA-2020. Note that WISE imaging is less affected by dust extinction and more sensitive to the underlying spatial distribution of the older stellar population compared to our optical imaging, so we do expect some differences in these measurements.

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Focusing on Figure 11(a) first, we find good overall agreement in the central coordinates: the median, mean, and ±1σ scatter in the coordinate differences are 076, 23, and ±24, respectively, notably smaller than the ≈6'' FWHM WISE W1 PSF (Wright et al. 2010). However, there are some notable outliers, the three largest of which (NGC 0247, NGC 2403, and NGC 4395) have been annotated in the figure. Examining the optical and infrared mosaics of these and other sources in this comparison sample, we find that the differences are due to a combination of a lack of a distinct bright center and, for a handful of cases, errors in the SGA-2020. For example, both NGC 2403 and NGC 0247 are late-type spirals (Hubble type 6 or SABc; see de Vaucouleurs et al. 1991) without a clear, bright nucleus, so the differences are arguably defensible. On the other hand, for NGC 4395 and a handful of other objects, the SGA-2020 central coordinates are likely incorrect (by up to ≈7'') relative to those published in the WSXC-100 (see Section 6 for additional discussion).

Turning next to Figure 11(b), we compare D(26) in the SGA-2020 to 2 × R_W1 in the WXSC-100; 2 times the radius of the galaxy measured down to an isophotal level of μ_W1,AB ≈ 25.7 mag arcsec⁻². We find the two sizes to be reasonably well correlated, despite the differences in imaging effective wavelength, albeit divided into two broad sequences. The sizes of the spirals (Hubble types 2 to 3—Sab to Sb) and later generally follow the one-to-one relation (median difference of −0.004 dex) with a scatter of 0.11 dex (±30%), while the earlier-type, spheroidal galaxies (Hubbles types −5 to 1—E to Sa) are offset to larger sizes in the WXSC-100 by −0.25 dex (≈70%) with a scatter of 0.16 dex (±50%). As discussed by Jarrett et al. (2019), the WISE W1 band is very sensitive to light from evolved stars down to low surface-brightness levels (particularly due to its large pixels, 275), so it is not surprising for the WSXC-100 (infrared) diameters to be notably larger than the (optical, r-band) D(26) diameters in the SGA-2020. Moreover, the extended, low-surface-brightness envelopes of massive spheroidal galaxies are especially prone to oversubtraction (e.g., Blanton et al. 2011; Bernardi et al. 2013), which may also be contributing to the systematically smaller sizes of the early-type galaxies in the SGA-2020 relative to the WSXC-100 (see also Section 6).

Finally, in Figures 11(c) and (d), we compare the position angles and ellipticities reported in the SGA-2020 and WXSC-100 catalogs, respectively, and find very good agreement: the mean differences are ϕ_SGA − ϕ_WXSC = 083 ± 77, and _SGA − _WXSC = 0.017 ± 0.12.

Quantifying the completeness of the SGA-2020 is difficult because the parent sample is largely defined by HyperLeda (see Section 2.1), which aggregates data from many different surveys—each with their own potentially complicated selection function—from the ultraviolet to the radio. This heterogeneity can be clearly seen in Figure 7 as variations in the sample surface density on both large and small angular scales and between the North Galactic Cap and SGC. Indeed, as we discuss in Section 6, one of the primary goals of the next version of the SGA is to redefine the parent sample using the Legacy Surveys imaging itself, in order to begin with a more uniform and quantifiable selection function over the full area. Nevertheless, we can still assess the SGA's completeness by comparing against existing catalogs that include large angular-diameter galaxies.

We choose to characterize the completeness of the SGA-2020 by comparing against HECATE (version 1.1; Kovlakas et al. 2021). ³⁵ HECATE is an all-sky value-added catalog of ≈200,000 galaxies at z < 0.047 (≲200 Mpc), which contains a breadth of both observed and derived (physical) galaxy properties. Although HECATE also uses HyperLeda to define its parent sample, the comparison is still valuable because the analysis carried out by Kovlakas et al. (2021) is independent of ours, and it includes additional completeness checks against NED and against the local B-band luminosity function.

First, from the parent HECATE sample of 204,733 galaxies, we identify 154,093 objects (75%) to be within the LS/DR9 imaging footprint using the LS/DR9 random catalogs, which contain a wealth of information about the imaging data (bandpass coverage, depth, PSF size, etc.) at random positions over the footprint (Myers et al. 2023). ³⁶ Specifically, we merge together five random catalogs to achieve an effective source density of 12,500 deg⁻², and conservatively retain all HECATE objects whose center lies within $2^{\prime}$ of one of these points. Next, we remove 2844 galaxies without any size information in HECATE; visually inspecting a random subset of these reveals that they are predominantly small objects, D(25) ≪ 30'', well under the SGA-2020 angular diameter limit (Figure 4). Finally, from the remaining 151,249 objects, we match 95,800 (63%) of them to an object in the SGA-2020 using the HyperLeda PGC number (Paturel et al. 1989; Makarov et al. 2014), which both HECATE and the SGA-2020 record (where it is defined). We choose to use the PGC designation because the differences in coordinates can be significant, such that a single matching radius results in a nonnegligible number of false-positives. For example, among the PGC-matched samples, the mean difference in coordinates is 050 ± 092, but with a tail that extends out to 80'' for IC 2574, a well-known $18\buildrel{\,\prime}\over{.} 7$-diameter late-type (SABm) galaxy with no well-defined center. In fact, 126 PGC-matched galaxies have coordinate differences larger than 10'', 90% of which have $D(26)\gt 1^{\prime}$. Nevertheless, with these caveats in mind, we can still match an additional 178 objects using a 3'' matching radius, resulting in a final matched sample of 95,978 galaxies.

In Figure 12, we plot b_t -band magnitude versus 2 × R₁ for the 154,093 HECATE galaxies, which overlap the LS/DR9 footprint, where R₁ is the semimajor axis length reported in HECATE. The dashed red histogram (corresponding to the right-hand axis) shows the raw fraction of matching HECATE-SGA galaxies as a function of galaxy size, in uniform 0.2 dex wide bins of angular diameter between ≈2'' and $\approx 15\buildrel{\,\prime}\over{.} 8$. The small numbers written above each bin of the histogram report the number of HECATE galaxies in that bin. In addition, the horizontal gray line indicates, for reference, a matching fraction of 100%.

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Taken at face value, the (raw) matching fractions shown in Figure 12 are surprisingly poor. For example, these results suggest that the SGA-2020 is missing 3%–5% of galaxies with angular diameters between $2\buildrel{\,\prime}\over{.} 5$ and $10^{\prime}$ and a whopping 20% of the galaxies between $10^{\prime}$ and $16^{\prime}$. In total, we find 2.94% (367/12,487) of the HECATE galaxies with $2\times {R}_{1}\gt 1^{\prime}$ to be missing from the SGA-2020. To explore this purported incompleteness, we visually inspect the LS/DR9 imaging at the position of the 367 "missing" galaxies and find the following results: 20 objects are Local Group dwarf galaxies, which are intentionally excluded from the SGA-2020 (see Section 2.1); 44 objects fall on the edge of the imaging footprint or other serendipitous (but unfortunate) gaps in three-band (grz) coverage; 64 galaxies are real, but the angular diameters reported in HECATE are overestimated, sometimes by a significant factor; 78 are part of a larger galaxy (e.g., H ii regions) and other kinds of photometric shreds; and 24 are entirely spurious. The solid purple histogram in Figure 12 shows the corrected fraction of HECATE-SGA matches after accounting for these errors. In the end, we find that just 137 out of 12,257 (1.12%) HECATE galaxies with $2\times {R}_{1}\gt 1^{\prime}$ are real and genuinely missing from the SGA-2020.

Although the fraction of missing galaxies is relatively low, since both the SGA-2020 and HECATE ultimately originate (in large part) from HyperLeda, it is surprising that any objects are missing from the SGA-2020, especially ones with angular diameters larger than 1'. Although we do not know why these objects do not appear in our parent HyperLeda catalog, we suspect that an issue with the database query may be ultimately responsible (see Appendix A). In any case, we intend to ensure that these and other missing objects serendipitously identified by the SGA team through visual inspection are included in the next version, as we discuss in Section 6.

What about the completeness of the SGA-2020 among smaller angular-diameter galaxies, $25^{\prime\prime} \lesssim 2\times {R}_{1}\lt 1^{\prime}$? According to Figure 12, the completeness remains relatively high, above ≈90%. However, our analysis of the $\gt 1^{\prime}$-diameter galaxies reveals that more than half of the HECATE objects missing from the SGA-2020 either have incorrect (or overestimated) diameters, or are spurious, and we have checked that these and other effects increase steeply with decreasing angular diameter (see, for example, Figure 2). Therefore, we conclude that the SGA-2020 completeness is likely ≳95% for galaxies with angular diameters between ≈25'' and $1^{\prime}$.

None of this discussion, of course, addresses the surface-brightness incompleteness of the sample, since both HECATE and the SGA-2020 inherit whatever incompletenesses and heterogeneities are present in HyperLeda, which aggregates data from many different surveys. For example, regions of the sky that have been imaged by the SDSS (Strauss et al. 2002; Blanton et al. 2011) or DES (Dark Energy Survey Collaboration et al. 2016; Abbott et al. 2021) have uniform, deep optical imaging (μ_r,50 < 24.5 and μ_r < 25.6 mag arcsec⁻² in the SDSS and DES, respectively, where μ_r,50 is the r-band half-light surface brightness, and the DES surface brightness is measured in a 195 diameter aperture), but these surveys cover just 34% (SDSS; 14,000 deg²) and 12% (DES; 5000 deg²) of the sky. Other optical and near-infrared surveys like 2MASS (Jarrett et al. 2000; Skrutskie et al. 2006) and Pan-STARRS1 (PS1; Chambers et al. 2016) cover all or nearly all of the sky (100% and 75% for 2MASS and PS1, respectively); however, 2MASS is relatively shallow compared to these other surveys (μ_r ≈ 22.7 mag arcsec⁻² assuming a median r − K_s ≈ 2.7 color for low-redshift galaxies; Jarrett et al. 2019) while the photometry of bright, large angular-diameter galaxies in PS1 is known to be problematic (Magnier et al. 2020; Makarov et al. 2022). In other words, it is difficult to fully assess the incompleteness of the SGA-2020 given the variations in the completeness of the surveys that contribute to HyperLeda.

Nevertheless, we can still make some quantitative statements using the results shown in Figure 8 and the comparisons with HECATE, above. Based on the correlation between the mean surface brightness, 〈μ_r,R(26)〉, and the apparent brightness within the 26 mag arcsec⁻² isophote, r_R(26), we conclude that the SGA-2020 is approximately 95% complete for galaxies with R(26) ≳ 25'', r_R(26) ≲ 18, and 〈μ_r,R(26)〉 ≲ 26 mag arcsec⁻²; in addition, the SGA-2020 is more than 99% complete for galaxies larger than $1^{\prime}$ and brighter than r_R(26) ≲ 16 down to the same surface-brightness limit.

As discussed in the Introduction, atlases of large angular-diameter galaxies have played a pivotal role in observational cosmology and in our modern understanding of galaxy astrophysics and the galaxy–halo connection. By delivering a carefully constructed catalog of known "large" galaxies with new deep optical and infrared imaging from the DESI Legacy Imaging Surveys, we anticipate the SGA-2020 to play a commensurately high-impact role in a wide range of observational studies of large, nearby, well-resolved galaxies.

The growing spectroscopic data set from DESI is an especially powerful complement to the SGA-2020. As discussed in Section 1.2, DESI is targeting the SGA-2020 sample over 14,000 deg² (70% of the LS/DR9 footprint) as part of the flux-limited (r < 20.175) BGS (Hahn et al. 2023). ³⁷ In addition to providing precise spectroscopic redshifts, the spectral coverage (3600–9800 Å), instrumental resolution (${ \mathcal R }\approx 2000\mbox{--}5000$), and spectrophotometric precision (±2%) of the DESI spectra (Abareshi et al. 2022; Guy et al. 2023) will yield important insights into the physical conditions and stellar populations of the central regions of these systems (for recent reviews, see Conroy 2013; Kewley et al. 2019; Sánchez 2020, and references therein).

Figure 13 illustrates the tremendous scale of the DESI data set. Although the majority of galaxies in the SGA-2020 have previously measured redshifts in HyperLeda (264,865 galaxies, or approximately 70% of the sample), these redshifts come from a wide range of different surveys spanning many decades. By the end of its 5 year Main Survey (2021–2026), DESI will produce a homogeneous, high-precision spectrophotometric data set for more than 300,000 SGA-2020 targets over 14,000 deg² as part of a larger sample of approximately 14 million BGS targets and more than 25 million fainter extragalactic targets (DESI Collaboration et al. 2023b; Myers et al. 2023). Indeed, in its 2023 June Early Data Release (EDR), DESI has already delivered high-quality spectroscopy for nearly 7700 SGA-2020 targets, which were observed during the DESI Survey Validation period (DESI Collaboration et al. 2023a). ³⁸

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In addition to these Main Survey observations, one of the especially exciting and synergistic secondary DESI programs is the Peculiar Velocity survey (Saulder et al. 2023). ³⁹ This program aims to use the fundamental plane and Tully–Fisher relations as direct distance indicators in order to map the peculiar-velocity field at z < 0.15; this map will be used to place new, stringent constraints on the cosmological parameters and the growth of large-scale structure (e.g., Strauss & Willick 1995). As part of this effort, galaxies in the SGA-2020 are being targeted not only in their bright nucleus but also at various positions along their major axis and other "off-center" positions (Saulder et al. 2023; K. A. Douglass et al. 2023, in preparation). Together with the central spectra, these data will help constrain the total (dynamical) masses and physical conditions in a sample of tens of thousands of SGA-2020 galaxies.

The SGA-2020 also has the potential to support the growing number of time-domain and multimessenger astronomical discoveries, wherein the observations of transient astrophysical events are detected by one or more messenger particles (electromagnetic radiation, neutrinos, cosmic rays, and gravitational waves; e.g., Neronov 2021). In the case of gravitational wave events, for example, identifying the host galaxy and, ideally, the electromagnetic counterparts of these events is extremely challenging due to the significant positional error ellipse of gravitational wave observations, ≳100 deg² (Gehrels et al. 2016; Abbott et al. 2020). Statistically complete catalogs of large, nearby galaxies with accurate coordinates, size information, and multiband photometry like the SGA-2020 are needed to help identify the most likely source of gravitational wave events (e.g., Gehrels et al. 2016; Ducoin et al. 2020; Kovlakas et al. 2021).

Finally, we highlight one other area where the SGA-2020 is playing an important ancillarly role. The SGA-2020 is being used as a foreground angular mask for all the DESI dark-time cosmological tracers: luminous red galaxies (LRGs; Zhou et al. 2023); emission-line galaxies (ELGs; Raichoor et al. 2023); and quasars (QSOs; Chaussidon et al. 2023). Like bright stars, large angular-diameter galaxies can bias the small-scale clustering signal in cosmological analyses because photometric pipelines tend to shred structurally resolved galaxies into many smaller sources. Similarly, the same angular mask can be used as an external input when building photometric catalogs from other imaging data; for example, an early version of the SGA-2020 was used to maximize the purity of the 3–5 μm unWISE photometric catalog of 2 billion infrared sources (Schlafly et al. 2019). In other words, by providing a high-quality geometric mask, the SGA-2020 is helping these and other observational programs fulfill their scientific promise.

We present the 2020 version of the SGA, SGA-2020, a multiwavelength optical and infrared imaging atlas of 383,620 large angular-diameter galaxies covering ≈20,000 deg². ⁴⁰ The SGA-2020 contains precise coordinates; optical (grz) and WISE/W1 through W4 (3.4–22 μm) infrared mosaics; model images and photometry based on the state-of-the-art image modeling code, The Tractor; azimuthally averaged grz surface-brightness and color profiles; elliptical curves of growth and half-light radii; and extensive ancillary information for the full sample. The complete SGA-2020 can be accessed through the dedicated web portal, https://sga.legacysurvey.org.

Our measurements of the central coordinates, isophotal diameters, ellipticities, and position angles show overall good agreement with published measurements collated in the HyperLeda extragalactic database and in the WISE Extended Source Catalog of the 100 Largest Galaxies (WXSC-100; Jarrett et al. 2019). Disagreements in these quantities between the SGA-2020 and HyperLeda are generally due to erroneous measurements in HyperLeda; however, the comparison with WXSC-100 identifies small but notable (≈few arcsecond) errors in the SGA-2020 coordinates for some of the largest ($\gt 5^{\prime}$) galaxies in the sample.

We evaluate the completeness of the SGA-2020 by comparing against the HECATE all-sky, value-added galaxy catalog (Kovlakas et al. 2021). We find that the SGA-2020 is missing approximately 1% of known galaxies larger than 1' and ≈5% of galaxies between 25'' and 1'; however, we compute these statistics only after determining (through visual inspection) that nearly 30% of the sources larger than 1' in HECATE that are missing from the SGA-2020 are either spurious or photometric shreds. Overall, we estimate that the SGA-2020 is more than 95% complete for galaxies larger than R(26) ≈ 25'' and r < 18 measured at the 26 mag arcsec⁻² isophote in the r band.

We discuss some of the potential scientific applications of the SGA-2020 and highlight the ongoing amassing of high-quality optical spectrophotometry from the DESI (DESI Collaboration et al. 2023b) survey. Approximately 70% of the SGA-2020 sample lies within the 14,000 deg² DESI footprint and is being targeted as part of the BGS (Hahn et al. 2023). To date, 7700 DESI spectra of SGA-2020 galaxies are publicly available as part of the DESI EDR (DESI Collaboration et al. 2023a), representing less than 3% of the final sample. In addition, the DESI Peculiar Velocity secondary program (Saulder et al. 2023) is obtaining tens of thousands of major-axis, minor-axis, and other off-center spectra of SGA-2020 galaxies in order to constrain the peculiar-velocity field at z < 0.15, further enhancing the scientific impact of the SGA-2020. Finally, we highlight the potential impact of the SGA-2020 for identifying the electromagnetic counterparts of time-domain and multimessenger astronomical events.

We conclude by discussing some of the planned improvements of the SGA. Future versions will focus on four broad areas, listed here in no particular order:

• 1.  
  Completeness. As discussed in Section 4, the SGA-2020 inherits the heterogeneity and incompleteness of the parent HyperLeda sample. To mitigate these issues, we intend to build a new parent sample of candidate large angular-diameter galaxies by detecting them from the Legacy Surveys imaging data themselves using a combination of traditional source-detection techniques (e.g., convolution kernels optimized for detecting large galaxies) and one or more state-of-the-art deep-learning techniques (e.g., Stein et al. 2022; Zaritsky et al. 2023). By inserting artificially generated galaxies of varying size, integrated flux, and surface brightness into the data, we intend to quantify the completeness limits of the sample as a function of these observational quantities.
• 2.  
  Centroiding and masking. Another area of improvement is how the SGA pipeline handles mergers and other systems with two or more close companions (e.g., in dense cluster environments like the Coma Cluster), as well as galaxies near bright stars. Evaluating and optimizing the performance of the pipeline in these circumstances will be part of a larger visual inspection effort (e.g., Walmsley et al. 2022) to ensure that the central coordinates of the largest galaxies in the SGA-2020 are accurate (or at least defensible, in the case of galaxies with irregular morphologies) compared with previous independent measurements (e.g., see the discussion in Section 3.3).
• 3.  
  Background subtraction. As discussed in Section 3.2.1, aggressive subtraction of the Mosaic-3 pattern-noise significantly impacts the z-band photometry of the SGA-2020 galaxies in the northern (BASS+MzLS) portion of the footprint, decl. ≳ 32°, including some of the most famous and largest angular-diameter galaxies in the sample like NGC 5194 = M51a and NGC 5457 = M101. Moreover, we show in Section 3.3 that the outer envelopes of the early-type, spheroidal galaxies in the atlas have likely been oversubtracted, thereby biasing their surface-brightness profiles and inferred isophotal diameters. We intend to address both these issues in a future version of the SGA (see, for example, Li et al. 2022 for a new sky-subtraction technique, which addresses the latter issue).
• 4.  
  Extensions in footprint and wavelength. Since the SGA-2020 was finalized, thousands of square degrees of additional DECam imaging have been acquired; we intend to use these data to extend the SGA footprint. ⁴¹ In addition, in the next version of the SGA, we intend to (1) include DECam i-band imaging, which is available for more than 15,000 deg² of area; (2) regenerate the unWISE coadds but also add ultraviolet (1528 and 2271 Å) coadds from the GALEX (Martin et al. 2005; Morrissey et al. 2005), where GALEX data are available; and (3) measure the surface-brightness profiles in all the available bandpasses from 0.15 to 22 μm. These additional measurements will further increase the scientific impact and long-term legacy value of the SGA.

Finally, future version of the SGA will also include ancillary spectroscopic redshifts and spectrophotometric measurements from DESI and, eventually, a wide range of physical properties (stellar masses, star formation rates, etc.) derived using state-of-the-art spectral energy distribution modeling (e.g., Leja et al. 2017).

We gratefully acknowledge specific contributions and thoughtful feedback from Michael Blanton, Yao-Yuan Mao, and Kevin Napier, and from former Siena College undergraduate students Alissa Ronca and Luis Villa, who contributed to an early version of the SGA web-application. In addition, we thank Mara Salvato and the anonymous referee for helpful comments on the manuscript.

J.M. gratefully acknowledges funding support from the U.S. Department of Energy, Office of Science, Office of High Energy Physics under award No. DE-SC0020086 and from the National Science Foundation under grant AST-1616414. A.D.M. was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under award No. DE-SC0019022. A.D., S.J., and B.A.W.'s research activities are supported by the NSF's NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

We acknowledge the use of the HyperLeda database, and we are especially grateful for the time and expertise contributed by Dmitry Makarov to this project. This research has also made extensive use of the NASA/IPAC Extragalactic Database (NED), which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology; NASA's Astrophysics Data System; and the arXiv preprint server.

The Legacy Surveys consist of three individual and complementary projects: the Dark Energy Camera Legacy Survey (DECaLS; Proposal ID #2014B-0404; PIs: David Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Prop. ID #2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy Survey (MzLS; Prop. ID #2016A-0453; PI: Arjun Dey). DECaLS, BASS, and MzLS together include data obtained, respectively, at the Blanco telescope, Cerro Tololo Inter-American Observatory, NSF's NOIRLab; the Bok telescope, Steward Observatory, University of Arizona; and the Mayall telescope, Kitt Peak National Observatory, NOIRLab. The Legacy Surveys project is honored to be permitted to conduct astronomical research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation.

NOIRLab is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciencies de l'Espai (IEEC/CSIC), the Institut de Fisica d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig Maximilians Universitat Munchen and the associated Excellence Cluster Universe, the University of Michigan, NSF's NOIRLab, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A&M University.

BASS is a key project of the Telescope Access Program (TAP), which has been funded by the National Astronomical Observatories of China, the Chinese Academy of Sciences (the Strategic Priority Research Program "The Emergence of Cosmological Structures" grant No. XDB09000000), and the Special Fund for Astronomy from the Ministry of Finance. The BASS is also supported by the External Cooperation Program of Chinese Academy of Sciences (grant No. 114A11KYSB20160057), and Chinese National Natural Science Foundation (grant No. 11433005).

The Legacy Survey team makes use of data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by the National Aeronautics and Space Administration.

The Legacy Surveys imaging of the DESI footprint is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under contract No. DE-AC02-05CH1123, by the National Energy Research Scientific Computing Center, a Department of Energy Office of Science User Facility under the same contract; and by the U.S. National Science Foundation, Division of Astronomical Sciences under contract No. AST-0950945 to NOAO.

Software: Astropy (Astropy Collaboration et al. 2013, 2018, 2022), corner.py (Foreman-Mackey 2016), healpy (Zonca et al. 2019), NumPy (Harris et al. 2020), Matplotlib (Hunter 2007), Photutils (Bradley 2023), PyDL (Weaver et al. 2019), scipy (Virtanen et al. 2020), seaborn (Waskom 2021).

In Section 2.1, we present our procedure for building the SGA-2020 parent sample, which begins with a HyperLeda database query. For the purposes of reproducibility, this appendix documents the exact query we execute on the 2018 November 14 version of the HyperLeda database, which results in a catalog of 1,436,176 galaxies:

• WITH
• "R50" AS
• (
• SELECT pgc, avg(lax) AS lax, avg(sax) AS sax
• FROM rawdia
• WHERE quality=0 and dcode=5 and band between 4400 and 4499 GROUP BY pgc
• ),
• "IR" AS
• (
• SELECT pgc, avg(lax) AS lax, avg(sax) AS sax
• FROM rawdia
• WHERE quality=0 and iref in (27129) and dcode=7 and band=0 GROUP BY pgc
• )
• SELECT
• m.pgc, m.objname, m.objtype, m.al2000, m.de2000, m.type,
• m.bar, m.ring, m.multiple, m.compactness, m.t, m.logd25,
• m.logr25, m.pa, m.bt, m.it, m.kt, m.v, m.modbest,
• "R50".lax, "R50".sax, "IR".lax, "IR".sax,
• FROM
• m000 AS m
• LEFT JOIN "R50" USING (pgc)
• LEFT JOIN "IR" USING (pgc)
• WHERE
• objtype='G' and (m.logd25>0.2 or "R50".lax>0.2 or "IR".lax>0.2)

In this appendix, we define the data model for the SGA-2020 data products and describe how all the data can be accessed. All the input imaging data used to construct the SGA-2020, including the 6 year unWISE image stacks, are publicly accessible through https://www.legacysurvey.org. The SGA-2020 data themselves can be retrieved through the SGA-2020 Data Portal at https://sga.legacysurvey.org. This portal provides a searchable database for retrieving data and visualizations for individual galaxies, as well as bulk-download access to the full data set. For example, the following link will navigate directly to the beautiful face-on spiral (Hubble type SABc) NGC 2532: https://sga.legacysurvey.org/group/NGC2532. In addition, the data can be accessed (and cross-referenced against a growing number of additional data sets, including DESI) through NSF's NOIRLab Astro Data Lab at https://datalab.noirlab.edu/sga.php. Finally, one can interactively explore the sample in the Legacy Surveys imaging footprint via the SGA layer of the Legacy Surveys Viewer; for example, the following link will navigate to the position of NGC 2532 in the North Galactic Cap: https://legacysurvey.org/viewer?ra=122.5638&dec=33.9568&layer=ls-dr9&zoom=13&sga.

Most users will be interested in the SGA-2020.fits file, a multiextension FITS catalog, which contains detailed information for all 383,620 galaxies in the SGA-2020. Table 1 summarizes the contents of this file, and Table 2 contains a detailed description of the ELLIPSE header and/or data unit (HDU). In addition, Table 3 defines the ELLIPSEBIT bit-masks, which record issues associated with the ellipse fitting and surface-brightness profile modeling, if any.

Furthermore, for each galaxy group in the atlas (i.e., each row in the SGA-2020.fits catalog where GROUP_PRIMARY is True), we generate the set of files summarized in Table 4 (see also Section 3.2), which include the individual multiwavelength mosaics, Tractor catalogs, surface-brightness profiles, and other key data products. These files are organized into the directory structure RASLICE/GROUP_NAME, where GROUP_NAME is the name of the galaxy group (see Section 2.2), and RASLICE, which ranges between 000 and 359, is the 1° wide slice of the sky that the object belongs to. Specifically, in Python,

• RASLICE=":03d".format(GROUP_RA)

Finally, Table 5 documents the data model of the ellipse-fitting and surface-brightness-profile results for each individual galaxy in the SGA-2020.

Table 5. Ellipse-fitting Data Model

Column Name	Units	Description
SGA_ID	⋯	See Table 2.
GALAXY	⋯	See Table 2.
RA	degree	See Table 2.
DEC	degree	See Table 2.
PGC	⋯	See Table 2.
PA_LEDA	degree	See Table 2.
BA_LEDA	⋯	See Table 2.
D25_LEDA	arcminute	See Table 2.
BANDS	⋯	List of bandpasses fitted (here, always grz).
REFBAND	⋯	Reference band (here, always r).
REFPIXSCALE	arcsec pixel−1	Pixel scale in REFBAND.
SUCCESS	⋯	Flag indicating ellipse-fitting success or failure.
FITGEOMETRY	⋯	Flag indicating whether the ellipse geometry was allowed to vary with semimajor axis (here, always False).
INPUT_ELLIPSE	⋯	Flag indicating whether ellipse parameters were passed from an external file (here, always False).
LARGESHIFT	⋯	Flag indicating that the light-weighted center (from ellipse moments) is different from The Tractor position by more than 10 pixels in either dimension, in which case we adopt The Tractor model position.
RA_X0	degree	R.A. (J2000) at pixel position X0.
DEC_Y0	degree	Decl. (J2000) at pixel position Y0.
X0	pixel	Light-weighted position along the x-axis (from ellipse moments).
Y0	pixel	Light-weighted position along the y-axis (from ellipse moments).
EPS	⋯	Ellipticity, ≡ 1 − b/a, where b/a is the semiminor to semimajor axis ratio BA in Table 1.
PA	degree	Galaxy position angle (astronomical convention, measured east of north); equivalent to PA in Table 1.
THETA	degree	Galaxy position angle (physics convention, measured north of west) given by 270-PA mod 180.
MAJORAXIS	pixel	Light-weighted length of the semimajor axis (from ellipse moments).
MAXSMA	pixel	Maximum semimajor axis length used for the ellipse-fitting and curve-of-growth measurements (typically taken to be 2 × MAJORAXIS).
INTEGRMODE a	⋯	Integration mode (here, always median).
SCLIP a	⋯	σ clipping threshold (here, always 3).
NCLIP a	⋯	σ clipping iterations (here, always 2).
PSFSIZE_〈grz〉	arcsec	Mean FWHM of the point-spread function over the full mosaic (derived from the PSFSIZE_〈grz〉 columns in The Tractor catalogs).
PSFDEPTH_〈grz〉	AB mag	Mean 5σ point-source depth over the full mosaic (derived from the PSFDEPTH_〈grz〉 columns in The Tractor catalogs).
MW_TRANSMISSION_〈grz〉	⋯	Galactic transmission fraction (taken from the corresponding Tractor catalog at the central coordinates of the galaxy).
REFBAND_WIDTH	pixel	Width of the optical mosaics in REFBAND.
REFBAND_HEIGHT	pixel	Height of the optical mosaics in REFBAND.
〈grz〉_SMA	pixel	Ellipse semimajor axis position.
〈grz〉_INTENS	nanomaggies arcsec−2	Linear surface brightness at 〈grz〉_SMA.
〈grz〉_INTENS_ERR	nanomaggies arcsec−2	1σ uncertainty in 〈grz〉_INTENS.
〈grz〉_EPS	⋯	Ellipse ellipticity; here, fixed at EPS.
〈grz〉_EPS_ERR	⋯	1σ uncertainty in 〈grz〉_EPS.
〈grz〉_PA	degree	Ellipse position angle; here, fixed at PA.
〈grz〉_PA_ERR	degree	1σ uncertainty in 〈grz〉_PA.
〈grz〉_X0	pixel	Ellipse x-axis pixel coordinate; here, fixed at X0.
〈grz〉_X0_ERR	pixel	1σ uncertainty in 〈grz〉_X0.
〈grz〉_Y0	pixel	Ellipse y-axis pixel coordinate; here, fixed at Y0.
〈grz〉_Y0_ERR	pixel	1σ uncertainty in 〈grz〉_Y0.
〈grz〉_A3 b	⋯	Third-order harmonic coefficient; not used.
〈grz〉_A3_ERR b	⋯	1σ uncertainty in 〈grz〉_A3.
〈grz〉_A4 b	⋯	Fourth-order harmonic coefficient; not used.
〈grz〉_A4_ERR b	⋯	1σ uncertainty in 〈grz〉_A4.
〈grz〉_rms b	nanomaggies arcsec−2	Rms surface brightness along the elliptical path.
〈grz〉_PIX_STDDEV b	nanomaggies	Pixel standard deviation estimate.
〈grz〉_STOP_CODE b	⋯	Fitting stop code.
〈grz〉_NDATA b	⋯	Number of data points used for the fit.
〈grz〉_NFLAG b	⋯	Number of points rejected during the fit.
〈grz〉_NITER b	⋯	Number of fitting iterations.
〈grz〉_COG_SMA	pixel	Do not use; see Appendix C.
〈grz〉_COG_MAG	AB mag	Do not use; see Appendix C.
〈grz〉_COG_MAGERR	AB mag	Do not use; see Appendix C.
〈grz〉_COG_PARAMS_MTOT	AB mag	Do not use; see Appendix C.
〈grz〉_COG_PARAMS_M0	AB mag	Do not use; see Appendix C.
〈grz〉_COG_PARAMS_ALPHA1	⋯	Do not use; see Appendix C.
〈grz〉_COG_PARAMS_ALPHA2	⋯	Do not use; see Appendix C.
〈grz〉_COG_PARAMS_CHI2	⋯	Do not use; see Appendix C.
RADIUS_SB〈sblevel〉	arcsec	Do not use; see Appendix C.
RADIUS_SB〈sblevel〉_ERR	arcsec	Do not use; see Appendix C.
〈grz〉_MAG_SB〈sblevel〉	AB mag	Do not use; see Appendix C.
〈grz〉_MAG_SB〈sblevel〉_ERR	AB mag	Do not use; see Appendix C.

Notes. Ellipse-fitting results and surface-brightness profiles for a single galaxy in the SGA-2020; specifically, this table documents the data model for the GROUP_NAME-largegalaxy-SGA_ID-ellipse.fits file listed in Table 4. In this table, 〈grz〉 denotes the g-, r-, or z-band filter, and 〈sblevel〉 represents the 22, 22.5, 23, 23.5, 24, 24.5, 25, 25.5, and 26 mag arcsec⁻² isophote.

^a See the photutils.isophote.Ellipse.fit_image method documentation. ^b See the photutils.isophote.Isophote and photutils.isophote.IsophoteList method documentation.

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Not surprisingly, a catalog of the size and complexity of the SGA-2020 has imperfections, most of which were identified after the fitting was finalized. In this appendix, we document the currently known issues, all of which we intend to address in future versions of the SGA. For additional details and the most up-to-date documentation regarding these and other issues, we refer the interested reader to the following URL: https://github.com/moustakas/SGA/issues?q=is%3Aopen+is%3Aissue+label%3A%22SGA-2020+Issue%22.

In terms of the data reduction, the most significant known issue impacting the SGA-2020 is the pattern-noise subtraction from the Mosaic-3 imaging, which distorts the z-band surface-brightness profiles and colors of galaxies in the (northern) BASS+MzLS portion of the footprint (see Section 3.2.1 for details). In addition, SGA users have reported that in some cases the WISE W1 and W2 background signal has been oversubtracted. We hypothesize that this oversubtraction arises because the unWISE background is modeled as the median flux after subtracting all the point sources in a $1^{\prime} \times 1^{\prime}$ grid (Schlafly et al. 2019), which would potentially impact all galaxies in the sample larger than approximately 1'.

Some issues also impact the availability and accuracy of the optical photometry in the SGA-2020. The most significant problem is that the elliptical aperture photometry (and the corresponding curves of growth) reported in the individual GROUP_NAME-largegalaxy-SGA_ID-ellipse.fits files (see Table 4) were impacted by a catastrophic bug, which rendered these measurements unusable. The data model for this file is documented in Table 5, and the impacted columns are flagged with the text "Do not use; see Appendix C." Fortunately, however, we were able to recover the curves of growth from the surface-brightness profiles themselves, which were not affected by this bug; we record those measurements in the ELLIPSE HDU of the merged SGA-2020.fits file (as documented in Table 2).

Moreover, ellipse fitting was skipped, failed, or rejected for a few different reasons, which are encoded in the ELLIPSEBIT column; this column appears in Table 2 and is documented in Table 3. First, a total of 8415 galaxies were not ellipse-fit because they were deemed to be too small (ELLIPSEBIT = 2¹ or ELLIPSEBIT = 2²) via their best-fitting Tractor model and half-light radius (shape_r); specifically, the objects modeled by The Tractor as type=REX with shape_r < 2'' or type={EXP,DEV,SER} with shape_r < 5'' were not ellipse-fit. ⁴² Second, ellipse fitting did not complete (ELLIPSEBIT = 2⁴) for 27 galaxies in the following seven groups: IC 1613, NGC 0055 Group, NGC 0253 Group, NGC 0300 Group, NGC 0598 Group, NGC 3031 Group, and NGC 5457. The central galaxies in these groups rank among the largest in the sample (18 ' < GROUP_DIAMETER < 62'), so modeling these systems posed some especially acute computational challenges. Third, the ellipse-fitting results for 52 galaxies were rejected (ELLIPSEBIT = 2⁵) because they were found via visual inspection to be incorrect or unreliable, usually due to incomplete or imperfect masking of nearby bright stars or other galaxies. Finally, ellipse fitting was not carried out (or silently failed) on 6161 galaxies where the pipeline did not indicate a problem, and therefore, ELLIPSEBIT=0 for these systems even though there are no measured surface-brightness profiles.

In no particular order, some of the additional currently known issues include the following:

• 1.  
  A small number of objects without imaging in all three grz bandpasses made it into final sample, despite the requirement of three-band optical imaging discussed in Section 3.2. ⁴³
• 2.  
  A small fraction of objects have compromised surface-brightness profiles due to their proximity to bright stars ⁴⁴ or because of poor deblending of multiple sources (typically due to incompleteness in the parent HyperLeda catalog). ⁴⁵
• 3.  
  The central coordinates for a small number of the largest ($\gt 5^{\prime}$) galaxies in the SGA-2020 are incorrect by up to a few arcseconds, as discussed in Section 3.3.
• 4.  
  In a handful of spheroidal galaxies with large ellipticity ( > 0.5 or b/a < 0.5), our masking algorithm (see Section 3.2.2) is too aggressive and inadvertently masks some of the outer-envelope light of the galaxy along the minor axis. ⁴⁶