Ultra-Diffuse Galaxies (UDGs) with Hyper Suprime-Cam I: Revised Catalog of Coma Cluster UDGs

This is the first in a series of papers on the properties of ultra-diffuse galaxies (UDGs) in clusters of galaxies. We present an updated catalog of UDGs in the Coma cluster using \textit{g}- and \textit{r}-band images obtained with Hyper Suprime-Cam (HSC) of the Subaru telescope. We develop a method to find UDGs even in the presence of contaminating objects, such as halos and background galaxies. This study expands upon our previous works that covered about half the area of the Coma cluster. The HSC observations covered the whole Coma cluster up to the virial radius and beyond (an area twice larger than the previous studies) and doubled the numbers of UDGs ($r_{\rm eff, r} \geq 1.5$ kpc) and sub-UDGs ($1.0 \leq r_{\rm eff, r}<1.5$ kpc) to 774 and 729 respectively. The new UDGs show internal properties consistent with those of the previous studies (e.g., S\'ersic index of approximately 1), and are distributed across the cluster, with a concentration around the cluster center. The whole cluster coverage clearly revealed an excess of their distribution toward the east to south-west direction along the cluster center, where Coma connects to the large scale structure, and where a known substructure exists (the NGC4839 subgroup). The alignment of the UDG distribution along the large scale structure around Coma supports the interpretation that most of them lie at the distance of the Coma cluster and the NGC4839 subgroup.


INTRODUCTION
Ultra-diffuse galaxies (UDGs) are extremely large low surface brightness (LSB) galaxies, with effective radii comparable to the Milky Way's, but with stellar masses as low as ∼ 10 −2 to 10 −3 the Milky Way's (comparable to dwarf galaxies). While LSB galaxies (e.g., Impey et al. 1988;Sandage & Binggeli 1984;Dalcanton et al. 1997) have been studied for a long time, only a few of them were known to be extremely large LSB galaxies (i.e. UDGs; see Yagi et al. 2016 Appendix B for a comprehensive literature search for UDGs). Their large abundance has been revealed only recently, which has underlined their importance as a population. Some dwarf galaxy studies found relatively large dwarfs, but not many are as large as UDGs (e.g., Thompson & Gregory 1993;Jerjen et al. 2000;Conselice et al. 2002Conselice et al. , 2003Mieske et al. 2007;de Rijcke et al. 2009;Penny et al. 2009Penny et al. , 2011. Previous catalogs occasionally listed the relatively bright centers of UDGs, but identifying their full extents by detecting their diffuse, extended envelopes is often very difficult. Since the discovery of the 47 in the Coma cluster in van Dokkum et al. (2015), UDGs have been found to be prolific within many clusters. Coma alone was found to have ∼ 10 3 UDGs in R-band imaging (Koda et al. 2015;Yagi et al. 2016;Zaritsky et al. 2019). Similar studies have since reported UDGs in other clusters (van der Burg et al. 2016), including the Virgo (Lim et al. 2020), Hydra (Iodice et al. 2020), Perseus (Gannon et al. 2022), and Fornax clusters, (Venhola et al. 2017) as well arXiv:2307.07141v1 [astro-ph.GA] 14 Jul 2023 as in the field (Leisman et al. 2017;Jones et al. 2018;Greco et al. 2018b;Zaritsky et al. 2019; Barbosa et al. 2020;Marleau et al. 2021).
Despite their ubiquity, the nature of such extremely large LSB galaxies remains elusive, and several UDG formation scenarios have been proposed. van Dokkum et al. (2015) initially suggested that UDGs may be "failed" galaxies, residing in dark matter halos comparable to the Milky Way (∼ 10 12 M ), but with truncated star-formation histories. Followup measurements of a representative UDG, DF44, have placed the mass somewhat lower at ∼ 10 11 M (van Dokkum et al. 2019; Saifollahi et al. 2021). Another possibility is that UDGs are dwarf galaxies, which have relatively inflated stellar distribution to more conventional dwarfs. Amorisco & Loeb (2016) suggested that UDGs may form as intrinsically diffuse structures in dwarf-mass halos with large angular momenta. Alternatively, the stellar distribution of a dwarf-like progenitor may have been inflated through either internal processes such as stellar feedback (Di Cintio et al. 2017;Chan et al. 2018), or external processes such as tidal interactions (Carleton et al. 2019;Jiang et al. 2019;Sales et al. 2020;Jones et al. 2021) and mergers (Conselice 2018;Bennet et al. 2018;Wright et al. 2021).
Their environment can be an important factor. Compared to cluster UDGs, UDGs in the field tend to be bluer, more HI-rich, and more irregularly shaped (Greco et al. 2018a;Rong et al. 2020a; Barbosa et al. 2020;Kadowaki et al. 2021;Tanoglidis et al. 2021). The denser cluster environment may also play a key role in producing quiescent UDGs. Cluster UDGs may initially form as diffuse galaxies in the same manner as the bluer field UDGs, but have undergone additional quenching by the cluster environment (Penny et al. 2011;Jiang et al. 2019;Prole et al. 2019;Grishin et al. 2021;Junais et al. 2022). Even within a single galaxy cluster itself, the immediate environment, such as galaxy density, varies and may alter the properties of UDG populations as a function of cluster radii, substructure, and local inhomogeneities. Janssens et al. (2019), for instance, found that UDGs are asymmetrically distributed around clusters, being deficient in regions of high mass density as traced by gravitational lensing. Furthermore, the UDG distributions appear anticorrelated with the distributions of ultra-compact dwarf (UCD) galaxies, leading them to hypothesize that UCDs are the remnants of destroyed UDGs with surviving compact centers. Thus, the distribution of UDGs relative to the surrounding overdensities and the large scale structure can yield information on how they form and evolve, as different formation mech-anisms will leave different imprints on the population distributions and structural parameters.
A complete population study of UDG in a local cluster requires satisfying 3 key points: a large field of view, sufficient point source/surface brightness sensitivities, and high spatial resolution to resolve point sources on top of the UDGs. A large field of view is necessary to cover a wide environmental range, e.g., both the entire cluster and its surroundings. By definition, UDGs are very low surface brightness objects, so a high sensitivity in surface brightness is needed to both detect and accurately analyze them. An additional complication comes from source confusion: over the large extents of UDGs, there are often foreground and background objects, i.e., stars and background galaxies, as well as their own globular clusters. These objects are compact and typically show higher surface brightnesses (or fluxes within the point spread function) than the UDGs, which hinder the detection and analysis of the UDG. Thus, a high spatial resolution is needed to resolve the sources of confusion and remove them from the UDG.
Identification of LSB objects is inherently difficult, due to the deep depths required to detect them, as well as contamination from other, higher surface brightness objects with LSB tails. In response to these challenges, a number of techniques have been developed to overcome them. One approach is "thresholding", where clusters of pixels above some threshold level can be associated and identified. For instance, Bennet et al. (2017) spatiallyrebinned CFHT images at a target size scale and selected all pixels at some significance above the background to search for diffuse dwarf galaxies around M101. The advantages of this method are that it is relatively simple to implement, and it does not require any prior information on the target object other than the target size. A disadvantage of this is the false positive rate due to background galaxies and the halos around foreground stars. Some assumptions on the properties of the contaminants, such as proximity to bright objects, may be used to improve the detection efficiency. In order to remove the outskirts of bright objects, which can mimic UDGs when detecting large LSB objects, Greco et al. (2018b) detected objects at both high and low significance levels. A low significance detection (LSB objects) that shares a certain amount of their area with a high significance detection (high surface brightness object) is associated to the high significance detection as its faint outskirt, and rejected as a UDG. In wide low-resolution observations, where blending is a significant source of contamination, independent high-resolution imaging can be used to model all emission from blended objects in order to be subtracted (van Dokkum et al. 2020). Improv-ing the signal-to-noise ratio can also be done to improve detection efficiency. Zaritsky et al. (2019), searching for UDGs in DESI images, used the technique of wavelet transformations to spatially filter the images. Wavelet transformations are similar to smoothing in that they improve the S/N of objects at the size of the kernel, while suppressing the contribution from features at different scales. This allows for UDGs at different kernel sizes to be selectively detected at higher contrast. These technical developments for detection of LSB galaxies are becoming even more important, in view of the upcoming Legacy Survey of Space and Time (LSST) at the Vera Rubin observatory (Ivezić et al. 2019).
In this paper, we revisit UDGs in the Coma cluster. We use new deep g-and r -band images obtained with Hyper Suprime-Cam (HSC hereafter), and cover the whole Coma cluster out to its virial radius (an area twice larger than previous studies). This catalog is built on r -band based detection, as we expect r -band to trace the mass distribution better than g-band. In order to mitigate the issue of confusion, we develop a procedure to remove contaminants in multiple stages. One of the original selection criteria of UDGs, i.e., the effective radius of r eff,r ≥ 1.5 kpc, was from an instrumental limitation (van Dokkum et al. 2015), not from an intrinsic property of UDGs. Hence, we catalog all objects with r eff,r ≥ 1.0 kpc as UDGs, and call smaller ones (r eff,r ≤ 1.5 kpc) as "sub-UDGs". With our larger search area in 2 bands, we roughly double the numbers of UDGs and add color information for all detected objects. With its high resolution and depth, and by covering the entire cluster out to the virial radius and beyond with HSC, our data is suited for obtaining a more spatially-complete UDG population in the cluster in order to analyze their radial and azimuthal distribution.
The paper is organized as follows. In Section 2, we outline our terminology and definiton of UDGs. In Section 3, we discuss our observations of the Coma cluster with HSC. In Section 4, we describe our automated procedure for identifying UDGs, removing background contaminants (small objects) before running a UDG detection algorithm. In Section 5, we present this catalog and some of their statistical properties. We conclude with a summary in Section 6.
Throughout this paper, we use the following notations: the apparent magnitude m [mag], effective radius r eff [kpc], central and mean surface brightness within r eff , µ 0 and µ eff [mag·arcsec −2 ], Sérsic index n, axis ratio q, and position angle P A [degree]. When a band needs to be specified, we will use a subscript, e.g., r eff,g or r eff,r for g-and r-band, respectively. We omit the units for simplicity unless otherwise specified. The AB magnitude system is used throughout this paper. We adopted cosmological parameters of (h 0 , Ω M , Ω λ ) = (0.697, 0.282, 0.718) (Hinshaw et al. 2013) and a distance modulus for the Coma cluster of (m − M) 0 = 35.05 (Kavelaars et al. 2000). These parameters correspond to a luminosity distance of 102 Mpc, and 0.473 kpc·arcsec −1 with an angular diameter distance of 98 Mpc.

DEFINITIONS OF UDGS AND TERMINOLOGY
UDGs are large LSB galaxies near the limitation of detection threshold. As such, their exact definition inevitably depends on the limitation of instruments and measurements. An often-used definition is r eff,g ≥ 1.5 and µ 0,g ≥ 24. This µ 0 is not directly from data, but is from the Sérsic model assuming an index of n = 1. The equivalent mean surface brightness is µ g eff ≥ 25.1. These are not initially intended as the selection criteria, but are the parameter ranges that enclose the first set of 47 UDGs with the CFHT photometry (van Dokkum et al. 2015).
In the literature, different studies use different criteria due to the instrumental limitations (Yagi et al. 2016;van der Burg et al. 2017;Greco et al. 2018b;Janssens et al. 2019;Gannon et al. 2022) or astrophysical motivations (i.e. physical properties of the objects; Zaritsky et al. 2019;Lim et al. 2020). Additionally, there are large uncertainties in parameter determination due to existing software and/or to a choice of approach in data reduction and analysis (see Section 5.1). Objects that satisfy a set of criteria in one measurement may not satisfy the same criteria in the other measurement (see Section 5.1). For these reasons, our previous study with Subaru adjusted the thresholds leniently, e.g., r eff from SExtractor (Bertin & Arnouts 1996) (Peng et al. 2002) to be > 0.7, instead of > 1.5, to include all the Dragonfly UDGs in the Subaru measurements (Koda et al. 2015;Yagi et al. 2016). Otherwise, our measurements would have rejected some of the Dragonfly UDGs (see more examples in Sections 5.1.1-5.1.3). We also note that the Dragonfly UDGs with SExtractor's r eff < 1.5 turned out to have r eff ≥ 1.5 with GALFIT (Peng et al. 2002(Peng et al. , 2010 in Yagi et al. (2016). This paper updates our previous Subaru study and largely inherits its approach with some adjustments based on the progress made since then. Our previous study used R-band of the Subaru Prime Focus Camera (Suprime-Cam), instead of g-band, for detection and identification (Koda et al. 2015;Yagi et al. 2016). In this study, we adapt r -band of Hyper Suprime-Cam (HSC), because the majority of UDGs known so far are red, and the r -band should reflect their stellar masses better than g-band. In addition, a g-band identification is more susceptible to some bias: e.g., star-forming and non-star-forming UDGs with the same g-band luminosity can have very different r -band luminosities and stellar masses.
Following the Yagi et al. (2016)'s spirit for an inclusive catalog and to absorb the uncertainty mentioned above, we select objects with a threshold of 1. r eff,r > 1.0 2. µ r eff ≥ 24 at a redshift of z = 0, in HSC r-band. When necessary, we separate the ones with r eff =1.0-1.5 as "sub-UDGs" -this is not for making a subclass of UDGs, but only for a convenience in discussions in this paper. From this inclusive catalog, readers can select their own objects with their own criteria.

HYPER SUPRIME-CAM IMAGING OF COMA CLUSTER
The Coma cluster was observed in g-and r -bands using Hyper Suprime-Cam (HSC) on the Subaru telescope in March 2016 and in March and June 2017. HSC has 104 CCD detectors, providing a roughly circular field of view with a diameter of ∼ 1.5 • and a scale of 0 .168 (Furusawa et al. 2018;Kawanomoto et al. 2018;Komiyama et al. 2018;Miyazaki et al. 2018). The coverage consists of 7 pointings of the camera in a hexagonal pattern (see Figure 1) combined into a single ≈ 15 deg 2 tract that spans the large cluster up to its virial radius of 3 Mpc (≈ 1.8 • ) (Kubo et al. 2007). Typical integration times in r -and g-bands are about 48 and 136 minutes in total per pointing, respectively, with the dithering pattern optimized so that gaps between CCDs should not overlap. Each dither integration (called "visit") was started with the rotator angle of 0 degree, so that the flat pattern near the edge of the field-of-view is consistent among the integrations. The typical seeing throughout the observing runs were ∼ 1 . For easier data handling, the tract is divided into square patches of 12' on a side (4200 × 4200 pixels) in size, with 17" (100 pixels) of overlap between adjacent patches. We search for UDGs on a patch-by-patch basis, and we search 294 patches in total.
The galactic extinction in r -band across the coverage varies between ∼ 0.015 and ∼ 0.03 mag according to NASA/IPAC Extragalactic Database (NED) 1 , which is based on Schlegel et al. (1998) and Schlafly & Finkbeiner (2011). We assume that the variation of the extinction is negligible within each patch, and use the value at the center for all UDGs contained in the patch. Hereafter, the magnitudes and the SB are corrected for the galactic extinction.
The data were reduced using the HSC pipeline hscPipe version 4.0.1 (Bosch et al. 2018), which is built on a software in development for the Legacy Survey of Space and Time (LSST) project (Ivezic et al. 2008;Jurić et al. 2017), and an additional package for sky-subtraction provided by the HSC Helpdesk. Astrometric and photometric calibrations were done using the Sloan Digital Sky Survey (SDSS)-III DR9 catalog (Ahn et al. 2012) distributed with the HSC pipeline, which is recalibrated by the HSC software team for photometric zero points against those of the Panoramic Survey Telescope & Rapid Response System 1 (Magnier et al. 2013;Schlafly et al. 2012;Tonry et al. 2012). The background sky was subtracted with a grid of a 512 pixel size (∼ 87 ). This angular size is larger than the anticipated size of UDGs (r eff,r ≈ 1.5 kpc ∼ 3 .2 at the distance of Coma) and the one used in the previous studies ∼ 51 (Koda et al. 2015;Yagi et al. 2016). We take the fully reduced, photometrically and astrometrically calibrated, sky-subtracted images from each visit, and make median-stacked images using imcio2 (Yagi et al. 2002) to reduce the presence of bright artifacts from single exposures.
The HSC pipeline measures the photometric zero point with 24-pixel aperture and derives the amount of aperture correction. The scatters in aperture correction among the visits are only 1.2% in r-band and 0.8% in gband. Hence, we applied constant aperture corrections, -0.026 mag for r -band and -0.025 mag for g-band, to all patches.

IDENTIFICATION OF UDGS
Historically, LSB objects tended to be overlooked because of the inherent difficulty in detecting extended objects only a few percent brighter than the background sky. Several faint background objects are often on top of UDGs and are a major source of confusion. We therefore need to develop a UDG identification procedure to resolve these issues. We conduct the search on image patches, hereafter "patches" (Section 3), and extensively use SExtractor version 2.19.5 (Bertin & Arnouts 1996) and GALFIT version 3.0.5 (Peng et al. 2002(Peng et al. , 2010. For some of the steps below, we use small cutout images, hereafter "cutouts", with a size of 53."9 × 53."9 (321 × 321 pixels) around the barycenters of the UDGs, as measured by SExtractor after removing contaminants in a separate "cleaning" stage. The broad outline is as follows, with more detailed descriptions presented in the following subsections:

Removing bright objects and compact objects.
When compact objects are on top of a UDG, SExtractor tends to split the UDG and assign the pieces to the compact objects as their diffuse tails. Therefore, we first clean the patches by removing the compact objects with SExtractor and the unsharp masking technique (Section 4.1). At this stage, only the bright cores of the compact objects are removed, while their diffuse tails remain in the images.
2. Generating crude candidate catalog. We run SExtractor on the cleaned r -band patches and select UDGs based on the SExtractor parameters. Here we generate a blanket candidate catalog that, in the parameter space, includes all objects in the volume larger than the part where UDGs are expected to occupy (Section 4.2). This procedure leaves false detections, mostly the blends of and contamination by the tails of the cleaned compact objects.
3. Removing blended objects. We identify false detections due to the blending and contamination of the compact objects on a small cutout of raw (uncleaned) image for each UDG. We again utilize SExtractor to (over)split the UDG into pieces and to see if the pieces are associated with compact objects. We remove the UDGs from the catalog when they are blended or heavily contaminated by the compact objects (Section 4.3).
4. Refinement of initial parameters and catalog selection. We use GALFIT to refine the structural parameters of the UDGs with a 2-dimensional Sérsic function. In order to avoid background contamination, we use the cleaning algorithm from Step 1 (Section 4.1) to generate a mask for compact objects. We then visually inspect each cutout, remove any clear false positive including stellar halos and tidal tails, and perform any necessary adjustments to the mask. After removing false positives, we finalize the catalog selection, selecting all objects that satisfy the definition of a UDG by measured GALFIT parameters (Section 4.4).

5.
Final parameter refinement. Finally, we refine the fits by taking into account the possibility of a nuclear component. To evaluate the possibility, we re-fit the candidates, this time including a PSF function. The magnitude of any possible PSF is unknown, so we search the space of initial guesses in PSF magnitude (m psf ). We compare the fits with the single Sérsic and Sérsic + PSF in terms of the contrast between the Sérsic and PSF aperture fluxes at the center and Bayesian information criterion, and determine whether the single Sérsic or Sérsic + PSF fit result is appropriate (Section 4.6).

Removing Bright Objects And Compact Objects
Because of their large extents and low brightnesses, the search for UDGs with SExtractor encounters two major problems: oversplitting and blending. Multiple compact objects in the foreground and background often overlap with UDGs. When SExtractor detects those objects on UDGs, it tends to split the diffuse extended light of the UDGs into multiple pieces and associate them to the foreground/background objects (oversplitting). In addition, UDGs located next to bright stars or galaxies can be confused with the tails of those brighter neighbors (blending). SExtractor is equipped with two control parameters to tackle these problems, DE-BLEND MINCONT and DEBLEND NTHRESH, but we found it impossible to optimize them to rescue UDGs simultaneously against the splitting and blending. Therefore, we leave the two parameters at default settings and take a different approach.
Our approach is to remove the contaminating objects before running SExtractor for UDG detections. We aim to detect and remove as many contaminants as possible without disturbing the portions of the images containing UDGs. One method is to use separate SExtractor runs, each optimized to detect a type of contaminant separately (Rix et al. 2004;Barden et al. 2012; Step-by-step demonstration of our cleaning procedure for one UDG. (top) From left to right: none (original raw image), high brightness objects, smaller objects in isolation, and smaller objects on top of the UDG. (bottom) The removed objects. Prescott et al. 2012;Greco et al. 2018b). We exploit the fact that UDGs are by definition both large and faint, and hence, detect and remove all objects that are either too small or too bright. This cleaning consists of SExtractor runs on the patches, each of which is tailored to find different types of contaminants: objects with brightness too high to be UDGs, and objects too small to be UDGs. We identify these types of objects with SExtractor by adjusting the control parameters (described below). For each type, SExtractor outputs the CHECKIMAGE image that contains only the detected objects. These images are subtracted from the original image. Figure 2 shows the procedure in sequence.
We first identify and remove objects brighter than UDGs from the patches (see Figure 2b). In SExtractor, the bright objects can be detected by setting a higher detection threshold (23 mag·arcsec −2 ) without limits on size. The halos of bright objects will remain in the image and will be removed at catalog level in Section 4.2. The masking fraction due to bright objects in each patch is typically 5%, but it can be as high as 10% within ∼0.2 degrees of the cluster center.
The second type of contaminant, objects smaller than UDGs, can be split into 2 cases: smaller objects in isolation (i.e., outside the UDGs; Figure 2c), as well as ones on top of UDGs ( Figure 2d). These two cases have to be treated separately in practice. The smaller objects in isolation can be detected by setting a maximum area threshold (DETECT MAXAREA) of 400 pixels (11.29 arcsec 2 ) at a detection threshold of 27.5 mag·arcsec −2 (∼ 1.5σ detection threshold across all patches). Note for comparison, a UDG ends up having a typical area on the order of 2000 pixels (56.4 arcsec 2 ). To find the smaller objects on top of UDGs, we use the unsharp masking technique. In this technique, we smooth the original r -band patch by a convolution with a Gaussian kernel (FWHM = 2."6), and subtract this smoothed copy from the original. The size of the kernel was determined by trial and error to prevent oversplitting. What remains are the features with sizes on the order of, or smaller than, the smoothing kernel. Thus, the UDGs are mostly removed, and the overlapping compact objects are still left in the patch. We run SExtractor on this unsharp masked patch with the maximum area threshold (DE-TECT MAXAREA) set at 400 pixels (11.29 arcsec 2 ). The masking fraction due to compact objects in each patch is typically 8%.
Some contaminants still remain in the cleaned image ( Figure 2d). A more stringent threshold can remove many of the remaining contaminants, but it can also damage the UDG-part of the image significantly. In practice, the remaining contaminants are relatively minor and do not hinder the detection and analysis of UDGs.
These operations remove the peaks of contaminating objects, preventing oversplitting ( Figure 3). However, the faint outskirts of the removed objects still remain in the image. The remnants include halos of bright objects and blended tails of clusters of small objects (Figures 4a and b respectively). SExtractor detects the blended stellar clusters as large and faint objects, which mimic UDGs in the eyes of SExtractor. These must be removed by other means in the following steps.

Generating Crude Candidate Catalog
The previous step removes most of the contaminating objects, including the ones on top of UDGs, which prevents the oversplitting of the UDGs by SExtractor. However, these cleaned patches still have the halos of the removed bright objects (Figure 3d (purple)), which still results in false detections by SExtractor. We choose to remove the halos after making an initial catalog of UDGs with SExtractor, instead of attempting to remove them from the image before making the catalog.
For each patch, we run SExtractor in the dual imaging mode to detect UDGs and to measure their parameters: we detect on the cleaned patches, and run analysis on the corresponding uncleaned patches. In the detection image, SExtractor may identify the halo of removed bright objects as a UDG, but the measurement in the analysis image includes the removed bright peaks. Hence, the object will has a high surface brightness and will be rejected via a surface brightness cut below.
With the SExtractor outputs, we make parameter cuts to filter out non-UDGs. We tune the cutoffs in the parameter space to include as many UDGs from the Yagi et al. (2016) catalog as possible. We select preliminary UDGs by the following parameter cuts in the r -band: 1. The FLAGS value is less than 32.
3. The apparent magnitude (M AG AU T O) is brighter than 26.
4. The half light radius (F LU X RADIU S with F LU X F RAC = 0.5) is greater than 1.375 arcsec (approximately 0.65 kpc). This is smaller than the definition of a UDG (r eff ≥ 1.5 kpc), and will be refined once more accurate parameters for the objects are obtained later in Section 4.4.
5. The full width half maximum (F W HM ) is greater than 2.65 arcsec (approximately 1.25 kpc).
6. The isophotal area (ISOAREA IM AGE) above the analysis threshold (27.5) is greater than 840 pixels (23.71 arcsec 2 ). This corresponds to a circular area of radius 1.3 kpc.
7. The mean surface brightness within the effective radius (M U M EAN M ODEL) is between 23.44 and 28.88. The bright end of this cut is brighter than the cut we will ultimately use for the catalog ( µ r eff ≥ 24), and will be refined once more accurate parameters for the objects are obtained later in Section 4.4.
8. The difference between the surface brightnesses at the effective radius (M U EF F M ODEL) and µ r eff is less than 1.44.
Criteria 1 and 2 help remove spurious detections. Criterion 3 also removes noises with the faintest magnitude cut (m r < 26).
Criteria 4 and 5 may appear somewhat redundant, but we found this combination work for our purpose after trials and error. Figure 5 shows all UDGs detected by SExtractor in blue, while yellow and red markers show the objects in our final UDGs catalog. These two criteria clearly eliminates two distinct, abundant populations of non-UDGs.
Criterion 6 is a measure of the size of the galaxy, independent of the shape of the object or model used to fit it.
Criterion 7 removes spurious detections below the detection limit in surface brightness ( µ r eff ≥ 28.88 mag·arcsec −2 ), and also removes bright objects ( µ r eff ≤ 23.44). The bright limit is set relatively less stringent as to keep the UDGs catalog inclusive (any marginal objects will be removed later).
Criterion 8 removes the objects with extremely steep surface brightness profiles. Assuming a Sérsic profile, this corresponds to a constraint of the Sérsic index n 4.
These cuts leave a catalog of detected candidates of 8950 objects. To reiterate, this is a crude catalog, which intentionally contains many entries that do not qualify as UDGs.

Identifying Blended Objects
We searched for UDGs in the cleaned patches (Section 4.1) and generated the UDG catalog (Section 4.2). The cleaning process is developed to avoid the oversplitting problem when compact objects are on top of UDGs. Once the compact objects are cleaned, SExtractor can find UDGs as single objects, but it now causes an over-blending problem when multiple small objects are  clustered; their halos, after the cleaning (peak subtractions), can appear connected and are identified as a single object (Figure 4b). In this step, we re-analyze the cutouts of individual UDGs and remove the contamination. We again utilize SExtractor.
This time, we aim to distinguish clustered compact objects from UDGs. We investigate cutouts from the uncleaned original patches, in which compact objects are not removed. We let SExtractor split a UDG into small pieces in a cutout (as in Figure 3b). We check the properties of each piece to see if it consists only of compact objects, or if there is an excess of background emission in addition to the compact objects. We identify pieces consisting of only compact objects as those that satisfy two criteria; CLASS STAR ≥ 0.1 and ISOAREA smaller than 350 pixels (9.87 arcsec 2 ). The area of pieces consisting of only compact objects is subtracted from the total area of the UDG. If the remaining area is still greater than or equal to 350 pixels, we keep it in the UDG catalog.
Some objects are located between adjacent patches and have 2 (or more) entries. We identify those du-plicates based on their coordinates and average their images into a single entry. This leaves 5581 objects.

Initial Parameter Refinement And Catalog Selection
We use GALFIT to identify UDGs with refined parameter measurements in m, r eff , n, q, and P A. After the selection in r -band, we run GALFIT to derive the g-band parameters.

Local Sky-subtraction and Sérsic Modeling
First, we re-subtract the local sky from a cutout because a small error in the sky determination impacts on the properties of faint UDGs. The sky is estimated as "2.5×median -1.5×mean" of the cutout flux (Da Costa 1992). This flux excludes the circular region within a 10 radius from the center of the UDG to avoid the light of the UDG. The center of the UDG is redefined with the SExtractor measured center after cleaning. To exclude the contaminants, we employ the mask made in Section 4.1, but with a modification of expanding the masked regions by 3 pixels outward to include the halos and tails around the masked objects. Figure 6b shows an example of the mask for a sample UDG.
We then fit a single-component 2-d Sérsic profile to each UDG cutout and extract their structural properties. An initial guess for each GALFIT parameter is made based on the SExtractor outputs. The PSF image is generated from running PSFEX version 3.22.1 2 (Bertin 2013) on the patch the cutout is taken from. We use a constant sigma image, assuming the dominant source of noise is sky-based. Figures 6c and d also show the resulting GALFIT model and residual for a sample UDG. The g-band Sérsic index is also held fixed at the r -band value.

Artifact Removal
This GALFIT run gives solutions for most UDGs, but not for 920 of 5581 cases. Of the 920 objects, 629 turned out to be either artifacts or spurious detections (see Figure 7) and do not have convergent GALFIT solutions. These 629 were identified and removed manually through visual inspection. In principle, this process can also be automated, but the number of the nonconvergent cases is relatively small, and the spurious detections are obvious in the cutouts, and we chose to remove them manually. Each cutout was examined, and removed if its morphology was in the following categories ( Figure 7): The remaining cases did not converge to a solution, mainly due to an incomplete masking of the contaminants. In such cases, the mask is manually dilated to remove the contaminants where possible. This step leaves 4952 objects.
Note again that our notations are the effective radius r eff [kpc], the central and mean surface brightness within r eff , µ 0 and µ eff [mag·arcsec −2 ], the Sérsic index n, axis ratio as q, and position angle P A [degree].
Criterion 1: as mentioned in Section 2, our UDGs include "UDGs" with the common threshold of r eff ≥ 1.5, and "sub-UDGs" with r eff = 1.0-1.5. The latter are included to mitigate the large error in r eff and to avoid missing true UDGs by this error. Figure 8 shows sample UDGs organized by r eff,r for comparison.
Criterion 2: following Yagi et al. (2016), we adopt µ eff ≥ 24.0. We take this as a definition at z = 0, and the cosmological dimming changes the threshold to 24.1 for Coma (z = 0.023).
Here, we neglect the band difference between HSC r and Suprime-Cam R in Yagi et al. (2016). Using the SDSS spectra of galaxies around the Coma cluster within a radius of 2 • and in 0.015 < z < 0.035, we derive the conversion equation (see Yagi et al. 2013): For a median color of (g − r) HSC ∼ 0.55 among the UDGs (Section 5.4), R = r − 0.07. Yagi et al. (2016) did not take into account the cosmological dimming. Hence, our inclusion of the dimming correction and neglect of the color conversion more or less compensate, and the two studies use roughly the same threshold.  Comparisons of this threshold to those of the other studies require some conversions. We adopt the µ eff instead of µ 0 because µ r eff is less sensitive to the Sérsic index n. Many studies used µ 0 of the Sérsic model, not of a UDG image, under an assumption of n = 1, and in this case, µ eff = µ 0 + 1.124. ( UDGs are roughly on a red sequence in the Coma cluster (Koda et al. 2015;Yagi et al. 2016). With the HSC color, they have (g−r ) HSC ∼ 0.55 ± 0.20 (see also Section 5.4). The cosmological dimming correction may or may not be applied, depending on the studies. Given these, the often-used threshold of µ 0,g = 24.0 in g-band translates to µ r eff = 24.4-24.8 in r-band (plus the cosmological dimming term when it is applied). Hence, our threshold of ≥ 24.1 at z = 0.023 is about 0.3 brighter than the often-used threshold. Figure 9 shows examples of UDGs organized by µ r eff .
Criterion 3: The color cut is imposed to remove background objects, the objects too red for galaxies in the Coma cluster. Among the objects redder than g−r = 1, 54 have SDSS spectra, and all of them are at higher redshifts (z ≥ 0.421).
We measure the colors from the images themselves within a fixed aperture. The aperture color is measured using the g-and r -band fluxes of the images within a 2 kpc radius (2 × r eff,r of our smallest UDGs), excluding masked regions and the inner 1 to avoid any potential nuclei.
By trial and error, we found that systematic errors stemming from the masking of contaminants and the sky-subtraction play significant roles in the fit (discussed in Section 5.1.1). In addition, the errors reported by GALFIT appear optimistic for the quality of the fits. For example, we take the 12 UDGs in Figure 9 (arranged from brightest to faintest µ r eff and examine the χ 2 values in the parameter space of r eff,r , n r , and r. In this multidimensional space, an error surface (e.g., the surface of χ 2 −χ 2 min = 1) forms a manifold, and Figure 10 shows its two projections: (a) one derived with r eff,r and r held constant in each fit and the rest of the parameters (Sérsic index, center position, axis ratio, position angle) free to be optimized, and (b) the other with r eff,r and n r fixed and the rest free. The sampling step is 1/41 of the widths. In Figure 10a, the χ 2 − χ 2 min = 1 contours extend over the widths of about (0.03, 0.05, 0.2, 0.5) kpc and (0.02, 0.03, 0.10, 0.15) mag from the higher (the left column) to lower (right) µ r eff . In Figure 10b, the contours extend over about (0.02, 0.03, 0.16, 0.22) in n r . The red crosses in each panel show the errors from GALFIT, which are smaller than the sizes of the χ 2 − χ 2 min = 1 contours. Correlations among the errors in r eff,r , n r , and r are evident, especially for the fainter UDGs.

Removal of Redshift Outlier
To remove objects which are already known to be outside the Coma cluster, we searched NED for spectro-  scopic redshifts within a 3" radius of the 1504 UDG candidates. We found redshift measurements for 38 objects. With the adopted Coma cluster redshift range of z=[0.015, 0.035], one of the 38 objects is at a lower redshift of z=0.0064 (SDSS DR7), and none are beyond z > 0.035.
This leaves 1503 objects with r eff,r ≥ 1.0 kpc and 774 with > 1.5 kpc. While our selection is based on the measurements in r-band, 535 of the 1503 satisfy the traditional definition of r eff,g = 1.5 kpc and µ 0,g ≥ 24.0 mag/arcsec 2 in g-band. Figure 10. Change in χ 2 from the best fit solution, χ 2 min , for the sample of UDGs in Figure 9. From the three-dimensional parameter space of r eff,r , mr, and nr, we show two projections: (a) r eff,r and mr, and (b) r eff,r and nr. The χ 2 values are optimized in the other parameters for each fixed pair (nr, r eff,r ) and (mr, r eff,r ). The χ 2 − χ 2 min = 1 contour is shown in yellow, while the error output from GALFIT is shown in red. Blank regions are where no convergent solution was found. As in Figure 9, columns are arranged according to µr eff : from left to right, µr eff fainter than 24, 25, 26, and 27 mag·arcsec −2 . The plot ranges span (∆n, ∆r eff,r , ∆mr) = (0.1, 0.1 kpc, 0.1 mag) for the left 2 columns, and (0.5, 1.0 kpc, 0.5 mag) for the right 2 columns.

Final Parameter Refinement
While several of our UDGs are fit by a single Sérsic profile that produces a flat GALFIT residual image, this is not always the case. In particular, several UDGs appear to be nucleated (Yagi et al. 2016). To account for these cases and determine the nucleation fraction for this catalog, we refit each UDG with a Sérsic + PSF composite model, using the result from the single Sérsic fit as the initial guess. The PSF component is also positioned initially at the center of the single Sérsic fit. We ran GALFIT multiple times with a range of initial guesses for the PSF magnitude (m psf ), from 17 to 27 in steps of 0.25. The fits are made with no parameters fixed, and both the Sérsic and PSF positions may drift independently from the initial guess and from each other. We pick the result with the lowest χ 2 . In cases where no convergent Sérsic + PSF fit was found, the UDG is considered non-nucleated.
We set two criteria for classifying nucleated UDGs (i.e., choosing the Sérsic + PSF results over the sin-gle Sérsic ones). First, the Sérsic and PSF components must be centered within one arcsecond of each other. Second, we compare the fit quality of the best Sérsic + PSF fit to the single Sérsic fit. To objectively compare the two models, and to take into account the difference in the number of free parameters, we use the Bayesian information criterion (BIC) (Schwarz 1978), where N = n dof + n param is the number of pixels used in the fit. The fit with the lowest BIC is considered a better fit result. With this comparison, 309 galaxies are classified as nucleated, 183 of which are UDGs with r eff ≥ 1.5 and 126 are sub-UDGs with r eff = 1.0-1.5.

Note on Contamination by Galactic Cirrus
Zaritsky et al. (2021) checked probable cirrus contamination in the SMUDGes catalog by checking cirrus emission in WISE 12 µm (≥ 0.1 MJy/sr) (Meisner & Finkbeiner 2014) and Planck τ 353 (≥ 0.05) images (Planck Collaboration et al. 2014;Green 2018). They found that only 1.8% of their UDGs were misclassified cirrus. Applying the same method to our UDGs, we did not find any UDG to be contaminated by cirrus emission. We note that our visual inspection during the UDG selection did not identify irregular shapes expected for cirrus emission.

CATALOG
The catalog of best-fit parameters from GALFIT in both g-and r -band, along with their aperture colors, is given in Table 1 (the table in its entirety, including fit errors from GALFIT is available in machine-readable form). The right ascension, declination, m, r eff , n, q, P A were taken from the output of GALFIT. The P A is defined such that P A = 0 when the major axis lies along the north, increasing counterclockwise. The gband positions and Sérsic indices are set by the corresponding r -band fit values. Other parameters are fit independently in g-and r -bands. For cases where the UDG is nucleated, m psf is also listed. Figure 11 shows the distribution of UDGs in this catalog compared to 3 other UDG catalogs in the same area (van Dokkum et al. 2015;Yagi et al. 2016;Zaritsky et al. 2019). We calculate both µ eff and µ 0 from the GALFIT parameters as: µ eff = m + 2.5 log 10 2πqr 2 eff , µ 0 = µ eff + 2.5 log 10 n b 2n Γ(2n) where 2γ(2n, b) = Γ(2n). Γ and γ are the complete and incomplete gamma functions respectively (Graham & Driver 2005). In the following subsections, we will compare our new catalog with other catalogs in the literature. In particular, we empirically evaluate errors in our own measurements in comparison with the previous Subaru catalog (Section 5.1.1). In summary, we estimate the random errors to be (0.15 mag, 0.16 kpc, 0.13) in (m, r eff , n). The systematic errors, likely due to errors in sky subtraction, can be (0.04 mag, 0.05 kpc, 0.09).

Previous catalogs of Coma UDGs
We compare the parameters in this and previous catalogs. As we will see, the measurements of UDGs are inherently difficult and suffer significantly from random and systematic errors due to different sensitivities, resolutions, and artifacts. Therefore, the selection criteria have to be optimized to realistically reflect each data quality. This is part of the motivation for having a tolerance in our catalog (see Sections 2 and 4.4.3) and including sub-UDGs.

Comparison with Yagi et al.(2016)
Yagi et al. (2016) used R-band Suprime-Cam images to find 854 UDGs in a smaller, approximately 1.7 • × 2.7 • area around the center and the western half of the cluster, supplemented with B -band information from Yamanoi et al. (2012) for 232 UDGs in a sub-region within the R-band area. Compared to these Suprime-Cam UDGs ("SC-UDGs"), we have approximately doubled the searched area to a roughly 2 • radius around the cluster center, and added color information to all UDGs. The number of objects has nearly doubled from 854 SC-UDGs (in the limited area) to 1503 (across the full cluster), 774 of which have r eff,r ≥ 1.5.
Within the Suprime-Cam search area, there are 1059 UDGs, 674 of which are in Yagi et al. (2016), and the remaining 385 are new UDGs. By looking back the intermediate steps in Yagi et al. (2016), ∼75% of the 385 new UDGs were detected in their SExtractor run, but rejected by their selection criterion of FWHM> 4 with SExtractor. Figure 12 shows that the FWHMs from Suprime-Cam are smaller than those from the new HSC. The remaining ∼25% of the 385 were not detected by their SExtractor run mainly due to blending and bleeding. With the cleaning algorithm, we are able to detect them properly.
Of all the 854 SC-UDGs, 674 are retained in the new catalog. The remaining 180 are rejected, most of which are now measured to be smaller than the size cutoffs in our analysis.   The most likely cause of this offset is an oversubtraction of the sky in the Suprime-Cam study due to the difficulty of determining the extents of UDGs' faint outskirts. In fact, the offset diminishes if we reevaluate the sky levels as "2.5×median -1.5×mean" in the cutout images of Suprime-Cam (the same method we used for the new data; see Section 4.4.1).
This level of discrepancies among measurements may not be avoidable when the objects are as faint as UDGs. A representative set of 9 objects that deviate by 3σ from the solid lines in Figure 13 is shown in Figure 14a. Figures 14b and c show the residual images when subtracting a Sérsic profile with the best fit r -band parameters found in this work, and with the R-band parameters from Yagi et al. (2016) respectively. We use equation (1) for the color conversion. The differences between most of the residuals are subtle, despite the fit values being outliers in the correlation plot.
More extreme outliers from the correlations may stem from a difference in the masking of contaminants. In Figure 15, we compare the masks between this work and Yagi et al. (2016) for one of the outlier UDGs in Figure 14. The new masking technique presented in Section 4.1 identifies and masks point sources on top of and around the UDG efficiently (the impacts of insufficient masking on top of UDGs is discussed again in Section 5.2). As shown in Figure 10, fainter UDGs have wider error bars, and their parameters are more difficult to constrain. This is reflected by the increase in scatter towards fainter m in Figure 13a. While the Suprime-Cam and new HSC catalogs are mostly consistent, these discrepancies demonstrate the difficulty of the UDG fit. The UDGs are intrinsically faint, which limits the accuracy of any catalog, including the one presented in this paper.
The comparisons of the two measurements with the similar data offer an opportunity to estimate errors in the UDG measurements (see Figure 13). As discussed above, the differences between the two arise from several sources of errors: including, but likely not limited to, (a) the different data realizations, (b) different sky subtractions, (c) different masks, and (d) fitting errors with GALFIT. It is difficult to separate them completely, but we can have a sense. The scatters between the two measurements likely indicate random errors, due to the combination of (a) and (d). These random errors are (0.15 mag, 0.16 kpc, 0.13) in (m, r eff , n), where we used only the 90% data around the center of each parameter distribution to exclude outliers, which are due to (c). We take these random errors as the errors in our current measurements, but if the errors in the two measurements contribute equally, we should divide the random error values by √ 2. Errors due to (c) occur only occasionally, but when they occur, they are large. It is difficult to characterize these errors by one number, but from Figure 13, the most extreme deviations are ∼ 3 mag, 2.5 kpc, and 1.5 in n. The systematic shifts between the two measurements are one realization of the systematic error due to (b). The amounts are (0.21 mag, 0.06 kpc, 0.09).

Comparison with van Dokkum et al. (2015)
All 47 UDGs detected with the Dragonfly telescope ("DF-UDGs") from van Dokkum et al. (2015) are detected in this catalog 3 . Yagi et al. (2016) intentionally adjusted the selection criteria to include DF-UDGs as a fiducial set.
As discussed in Sections 4.1 and 4.3, the confusion of foreground and background objects is a major obstacle in identification of UDGs at the distance of the Coma cluster. This study found a much larger number of UDG mainly due to the higher resolution being able to separate contaminants from the galaxies. For GAL-FIT fitting, van Dokkum et al. (2015) used CFHT gand r -band images, and assumed a pure exponential (n = 1) profile fitting to increase the stability of the fit. We leave n as a free parameter for all galaxies, due to the high surface brightness sensitivity. The r eff are in agreement without systematic offsets despite the difference in band (g-band and r -band), but as a reminder, the g-band Sérsic index is held fixed to the r -band value.
2 of the 47 DF-UDGs do not have r eff,r ≥ 1.5, and are sub-UDGs. These 2 DF-UDGs have an r eff,g of exactly 1.5 in van Dokkum et al. (2015), so these are marginal cases whose sizes hover about the cutoff depending on band, fit quality, and sky estimation. Such marginal cases are the impetus for using a lower r eff selection cut. The remaining 45 DF-UDGs have r eff,r ≥ 1.5, so the majority of the DF-UDGs are on the larger half of this catalog.
It is not straightforward to assess the completeness of the van Dokkum et al. (2015) study with respect to the new catalog. van Dokkum et al. (2015) did not attempt completeness, which already explains the large difference in the numbers of detections. While the selection criterion of (a) r eff ≥ 1.5 and (b) µ 0 ≥ 24 are often referred to van Dokkum et al. (2015), their selection was not based on these criteria, but on a set of others tuned for SExtractor outputs on the images of 6" resolution. Our detections are made on a substantially different basis in image quality (e.g., 1" vs 6" PSF size and sensitivity), band for detection (e.g., r vs g+r combined), and software for measurement (GALFIT vs SExtractor). As the best effort, however, we adopt (a), (b), and two additional criteria that mimic van Dokkum et al. (2015)'s: (c) 20 ≤ m g ≤ 23, and (d) low central concentration |m g − m aperture | ≤ 1.8 with 3 -radius aperture magnitude m aperture in g-band. By applying (a)-(d) to our catalog, we yield 687 objects. Of these, 33 are also found in van Dokkum et al. (2015).  et al. (2015) converted the CFHT to SDSS photometry. Overall, the two are consistent. The small offsets in µ 0 are expected from the band difference between SDSS and HSC (∼ 0.1 mag). Given that, the offsets are smaller than the scatters. The r eff are also consistent, and the large standard deviation of 0.87 is larger than the systematic offsets of 0.22. We note that between this work and van Dokkum et al. (2015), there is a negligi- Figure 13. Comparison of r -band values to corresponding R-band values in Yagi et al. (2016). UDGs in this work are plotted as blue dots, while the 65 SC-UDGs that were removed by the GALFIT r eff,r selection criterion are shown as orange crosses. For m, the dashed line is equation (1), assuming the median color g-r = 0.55.   Zaritsky et al. (2019), the first result of the SMUDGes survey, covers a much wider area beyond the Coma cluster (approximately 300 square degrees, which is 20 times larger than our area), but with shallower depth. 99 SMUDGes UDGs are present in our field coverage, with 98 having corresponding entries in our catalog. SMUDGes includes only objects with r eff ≥ 2.5 in the g-band. The object (SMDG 1306050+273627), rejected in our work, is shown in Figure 17. Our selection procedure rejected this object as a blended star cluster. Of the 98 SMUDGes UDGs, 51 do not fulfill their own selection criteria with our measured parameters. 47 of them have r eff,g ≤ 2.5, and 7 have µ 0,g < 24.0. Pinning down the exact cause of the offsets is difficult without their data. However, we found that adding a constant positive background can reduce the offsets. Adding a constant sky of 28.5 mag·arcsec −2 to the UDG cutouts makes the offsets of all the parameters smaller than the scatters in Figure 16. Since we found the same course of errors between the Suprime-Cam and HSC studies with the same telescope (Section 5.1.1), it would not be a surprise if the sky-subtraction is again an issue here.
The other possibilities include differences in the masks of compact objects and in the treatment of the Sérsic index in fitting. Zaritsky et al. (2019) used wavelet transformations, as opposed to the unsharp masking (Sections 4.1 and 5.2). They also fixed n = 1, while we set it free. Our fitting found that the average Sérsic index of the 98 SMUDGes UDGs is 0.86, and the difference from n = 1 could alter the sizes and µ 0 (see equation 4).
If we apply the selection criteria of SMUDGes (r eff,g ≥ 2.5 and µ 0,g ≥ 24.0) to our measurements of the new catalog, we find 126 objects. Of these, only 47 are found in SMUDGes (Zaritsky et al. 2019), and the rest 79 are not. Figure 18 shows the µ eff and µ 0 distributions of the 126 UDGs, separating the 47 matched and 79 unmatched UDGs with Zaritsky et al. (2019). Approximately half of the 79 unmatched UDGs are fainter than the 47 matched UDGs.
If we estimate the combined errors of SMUDGes and ours by comparing the two measurements as we did in Section 5.1.1, the random errors are (0.22 mag, 0.53 kpc) in (m, and r eff ). The systematic errors are (0.38 mag, 0.60 kpc) and are likely due to the errors in sky subtraction. It is difficult to separate the error sources between the two measurements, however, these errors are larger than those found in the comparisons of the two Subaru measurements (Section 5.1.1).   Zaritsky et al. (2022) More recently, SMUDGes has substantially extended the coverage to ∼ 15,000 square degrees (Zaritsky et al. 2022). The procedure for UDG detection and measurements was improved from Zaritsky et al. (2019). For example, Zaritsky et al. (2022) measured all parameters with n free, while Zaritsky et al. (2019) measured most parameters with n = 1 fixed, except magnitude (m) which were determined without n fixed. Zaritsky et al. (2022) found 88 SMUDGes UDGs in the Coma cluster area that we covered, of which only 58 were in Zaritsky et al. (2019). On average, their new r eff are smaller by 0.24 kpc, and the new m are fainter by 0.20 mag than the old ones. The measured n are ∼ 0.8 rather than 1, which may cause the difference in r eff . However m is measured with n free in both studies, and hence, the difference in m suggests an existence of an additional systematic difference independent of n. One possibility, among others, could be sky-subtraction (see Section 5.1.1).

Comparison with
Of the 88 new SMUDGes UDGs, 86 have a corresponding entry in our catalog. The remaining two are SMDG1304338+264623 and SMDG1252075+272654. The former is at z= 0.0064, not in the Coma cluster redshift (removed in Section 4.5). The latter is rejected due to contamination by an optical ghost in our image. Their selection criteria include r eff > 2.5 kpc. Of the 86, 57 have r eff > 2.5 kpc in our catalog as well.
The parameters in the new SMUDGes catalog are more consistent with ours. Figures 16i-l compare this work and Zaritsky et al. (2022). For the objects with r eff > 2.5 kpc in both catalogs, the differences in (µ 0 , m, r eff , n) are (0.01, -0.11, 0.47, 0.07) in average and (0.07, -0.04, 0.24, 0.00) in median. These differences were calculated as their average/median values minus ours, and we used their values after their model-based bias correction. The differences are small except for r eff . We note that the difference between Zaritsky et al. (2019) and Zaritsky et al. (2022) were even larger, and by comparing the averages, the former were 0.60 kpc larger than the latter.

Effect of small objects on parameters
As discussed in Section 4.1, the deep imaging in this work can detect and mask compact objects on top of the UDG via unsharp masking. Since shallower studies cannot apply such a mask, we quantify the effect of masking by running GALFIT without this compact objects mask in the r -band cutouts. Figure 19 compares the best-fit GALFIT parameters with and without the compact objects mask. Other types of contaminants, bright objects and isolated small objects outside the UDGs, are masked in both cases, as they can be identified in shallower or lower-resolution studies. The presence of compact objects on top of the UDG causes infrequent, but significant, impacts on the GALFIT parameters (e.g., the extreme outliers in Section 5.1.1). In a few cases, the presence of compact objects skews the best-fit parameters to much brighter and larger profiles. Among the 1503 UDGs in our catalog, 88 would appear brighter by 0.5 mag and 153 would have r eff larger by 0.5 kpc without the compact object masks, than their counterparts fitted with the masks. Figure 20 shows the histograms of r -band µ 0 , r eff , n, and q in the r -band. We show the results for Figure 19. Comparison of best-fit GALFIT r -band (a) m, (b) r eff , and (c) n, when compact objects on top of the UDG are masked or not masked. The blacked dashed lines have unit slope. Some of the parameters derived without the compact object masks deviate from the line, and they tend to be skewed towards brighter and larger fits.

r-band Structural parameters
UDG candidates of all sizes, including sub-UDGs with 1.0 ≤ r eff,r < 1.5, and UDGs with r eff,r ≥ 1.5. The average Sérsic index, n r ,for both UDGs and sub-UDGs is between 1.0 and 1.1, similar to dwarf elliptical galaxies, which have comparable stellar mass but are less diffuse. The average axis ratio, q r , is between 0.72 and 0.74 for both UDGs and sub-UDGs. The skew to large q r is not consistent with a population of randomly oriented thin-disk galaxies in a statistical sense, but the ISOAREA cut in Section 4.2 may bias our detection against low axis ratios. The relative lack of round (q r ≥ 0.9) UDGs compared to the peak favors the interpretation that UDGs are randomly oriented, oblate-triaxial shapes (Rong et al. 2020b;Kado-Fong et al. 2021). Figure 21 shows a r e -M r plot of the UDGs, with normal galaxies around the Coma cluster from the SDSS DR17 data (Abdurro'uf et al. 2022) also plotted as a reference 4 . Black dashed lines show constant effective surface brightness assuming an exponential profile (n = 1). The majority of the UDGs trend towards a region similar to dwarf galaxies (the orange shaded region in Figure 21) (M r ≥ -15, r eff,r ≤ 1.5, and n r ≈ 1.0, Boselli & Gavazzi 2014), which suggests UDGs and dwarf galaxies are related, and not distinct populations.

g -r Color
Figure 23 plots the GALFIT measured structural parameters in r -band versus the corresponding value in g-band. The structural parameters between the g-and r -bands are tightly correlated. For fits with equal Sérsic indices between bands, this suggests that most UDGs 4 The SDSS mr are converted to the equivalent in HSC using equation (5) in the following section  GALFIT r eff,r vs. mr for UDGs using a distance modulus of 35.05 (red crosses for r eff,r ≥ 1.5, blue crosses for 1.0 ≤ r eff,r < 1.5). For comparison, we plot the r eff,r (ex-pRad R) vs. mr of SDSS DR17 galaxies (black dots) near the cluster redshift (0.01 ≤ z ≤ 0.04) in a 3 • radius region around the cluster center are plotted for comparison. The cyan and orange shaded regions show the typical distributions for elliptical and dwarf galaxies, respectively.
have uniform color profiles. We show the aperture colormagnitude diagram of the UDGs in Figure 22 along with SDSS galaxies within a redshift range 0.018 ≤ z ≤ 0.028 and a 4 • × 4 • around the Coma cluster center. We also estimate the SDSS red sequence by linearly fitting the peak of the SDSS g -r distribution vs m r per 1 mag bin in the range 13 ≤ m r ≤ 18, where the red sequence is well-populated. Using the conversion equations derived with a set of spectra from Furusawa et al. (2000) and transmission curves from Doi et al. (2010), the SDSS colors are converted to HSC colors as The UDGs are clustered around the SDSS red sequence extrapolated to fainter magnitudes, indicating they are a quiescent and passively-evolving population. Figure 22 shows very small deviations of the UDGs (∼ 0.1 in g-r) from the red-sequence fit (solid line), although in Koda et al. (2015), the UDGs are right on the red-sequence in the B-R vs R plane. At this point, it is difficult to conclude if the deviations are real. To confirm such small deviations, we need to analyze the data consistently for the reference sample that defines the red-sequence. Currently, the reference sample is from SDSS, and their parameters are measured in a different scheme and in different bands from ours. Note in Koda et al. (2015), the colors and magnitudes of both their UDGs and reference sample are taken from Yamanoi et al. (2012), and hence, are based on the same data and analysis. In addition, in the range of the UDGs, the solid line is an extrapolation by almost 4 mag from the fitted range. A slight change in its slope could potentially put both the SDSS galaxies and the UDGs on the same line.
When measuring the g-band parameters, the n g of each UDG was fixed to the corresponding value in rband. Leaving both n g and n r free during the fit instead does not substantially change the correlation, but adds additional scatter (see Figure 24). The Sérsic indices, despite being fit independently, are correlated between g-and r -band. Outliers of the Sérsic index correlation plot also become outliers in the r eff correlation plot relative to the line of unity (n g = n r ), which may be due to the degeneracy between r eff and Sérsic index in fitting ( Figure 10).

Nucleated UDGs
As mentioned in Section 4.6, 309 UDGs and sub-UDGs are classified as nucleated, 183 of which are UDGs with r eff ≥ 1.5 and 126 are sub-UDGs with r eff = 1.0-1.5. Our total nucleation fraction (f n ), including the  sub-UDGs, is therefore 21%. This fraction is approximately half the value reported of 52% in Yagi et al. (2016), which also used BIC to determine which UDGs are nucleated. The main difference between the two catalogs is that our m psf are rarely fainter than 26, whereas Yagi et al. (2016) list m psf as faint as 27.79 for nucleated UDGs in Suprime-Cam. Figure 25 shows 4 sample UDGs, which were classified as nucleated in Yagi et al. (2016), but are re-classified as non-nucleated in this work. If the nucleated UDGs in Yagi et al. (2016) were limited to m psf ≤ 26 as well, the f n would be closer to our value, at 21%.
The effective cutoff in m psf is tied to the BIC classification and the estimated noise level of the image. To  illustrate this, we increased the noise in each cutout by adding artificial noise equal to the on-sky noise and re-fit the UDG before redetermining whether they are nucleated or not. In Figure 26, we plot the magnitude of the PSF component vs the magnitude of the Sérsic component for all convergent Sérsic + PSF fit results, separated by whether the UDG is nucleated or not. When artificial noise is added, the upper limit on m psf decreases from 26 to 25. This shows that the nucleated/nonnucleated classification is affected by signal-to-noise. In Yagi et al. (2016), an incorrectly low background noise was used, which resulted in picking up faint and insignificant PSF components. The differences in the skysubtraction and masking, discussed in Section 5.1.1, also contribute to the classification, but their effects are relatively minor and reduce the nucleation fraction by about 5%.  Figure 27a shows the nucleation fraction as a function of absolute magnitude M r for our UDGs. We note that in the literature, the brightest and most massive dwarf galaxies can reach f n close to 1, decreasing with fainter luminosities (den Brok et al. 2014;Muñoz et al. 2015;Hoyer et al. 2021). In our analysis, the decrease in f n with fainter M r is the result of the bias with the method of nucleation classification we have chosen. We use the BIC to determine whether a UDG is nucleated or not, and this appears to impose a limit on m psf that depends on the signal-to-noise ratio. As our m psf are limited to values brighter than 26, and m r is mildly correlated with m psf in Figure 26, f n apparently decreases at fainter M r . However, it is also possible that nucleation fraction may be correlated with luminosity generally, due to more massive galaxies having a deeper potential and thus a better ability to pile material in their central regions (Sánchez-Janssen et al. 2019; Zanatta et al. 2021).
In Figure 27b, we show f n as a function of projected cluster radius for m r ≤ 20. As discussed above, our f n does not include nuclei fainter than m psf = 26.0, so we exclude UDGs fainter than 20 to avoid incompleteness from this limit in m psf based on the behavior in Figure  26. We find the nucleation fraction of Coma UDGs is approximately constant across the entire cluster. This is in contrast with the literature, where quiescent nu-cleated galaxies that contain nuclear star clusters appear to be preferentially located in denser environments, such as the centers of clusters (Baldassare et al. 2014;Lim et al. 2018;Ordenes-Briceño et al. 2018;Sánchez-Janssen et al. 2019;Zanatta et al. 2021). The lack of radial trend in nucleated UDGs, as opposed to clear trends in other galaxy populations, may have an implication on their formation history. Figure 27. Nucleation fraction fn as a function of a) Mr and b) projected radius with respect to the Coma cluster center. The latter is restricted to mr ≤ 20 (Mr ≤ −15.05) to avoid incompleteness from the limit in m psf . The error bars assume Poissonian noise. Figure 28 is another presentation of the UDG distribution (from Figure 11). We show the kernel density estimator of the UDGs positions using a Gaussian kernel in Figure 28. The kernel bandwidth is 0. • 297, estimated through Scott's rule. There is a clear elongation to the distribution. To better quantify the anisotropy, we take a circular histogram by binning along clustercentric angle by a 10 • increment (see Figure 29) centered at the Coma cluster center (α J2000 , δ J2000 ) = (12:59:42.8, +27:58:14). There are 2 peaks in two directions (230 • and 70 • ), which coincide with the direction of the Coma filaments (Fontanelli 1984) connecting the cluster to the large scale structure. The southwestern (230 • ) peak is in the direction of the NGC4839 subgroup and may connect to the southwestern filament (Akamatsu et al. 2013) going to A1367, while the northeastern peak (70 • ) is in the direction of a filament going to A2199. Malavasi et al. (2020) report a potential third filament towards the north, but there is no noticeable corresponding excess in our sample of UDGs.

Spatial Distribution
The alignment of the UDGs distribution along the large scale structure around Coma reassures the interpretation that most of them, from the center to the outskirts, lie at the distance of the Coma cluster. Conversely, this means UDGs should trace out the  large scale structure, and be fairly common in filaments (Román & Trujillo 2017a,b). Figure 30 shows the projected radial surface density of all 1503 UDGs, and the subset of 774 UDGs with r eff,r ≥ 1.5. The two profiles are similar, with the former being approximately double the latter at all projected radii. In combination with Figure 29, we see that sub-UDGs (r eff = 1-1.5) share the same spatial distribution as the UDGs (r eff ≥ 1.5). At approximately 0.5 Mpc there is an inflection point in the projected radial surface density plot. If the UDGs followed the distribu- Figure 30. Surface density of all UDG candidates in the catalog (blue) and UDG candidates excluding sub-UDGs (red) in 0.25 Mpc projected radius bins. As a reference, the black dashed line shows the theoretical density if the UDGs were distributed as a uniform sphere.
tion of a uniform sphere, the projected surface density would be concave up everywhere, so there are less detected UDGs in the very central region than a spherical distribution predicts. UDG may be destroyed by tidal forces below a certain radius (van Dokkum et al. 2015). However, the lack of central UDGs could also be due to either the diffuse light in the cluster center affecting the background subtraction and making the detection more difficult, or obscuration by bright galaxies (Adami et al. 2006).

CONCLUSION
We present an updated catalog of UDGs in the Coma cluster in g-and r -band. We have outlined an automated procedure to detect and measure UDGs in the presence of contaminants. This procedure uses multiple SExtractor runs to remove specific types of contaminants in images before searching for UDGs. Our main results are the following: • We develop a cleaning algorithm to resolve the problem of foreground and background object interfering with the detection of UDGs. We search for UDGs across the whole Coma cluster out to the virial radius, approximately 3 Mpc from the cluster center, and the surrounding area beyond the virial radius. Our larger coverage has increased the number of UDGs to 1503. Among them, 774 have r eff,r ≥ 1.5. We also measure the colors of all the UDGs.
• The new UDGs show internal properties consistent with those of the previous studies (e.g., Sérsic index of ∼1), and are distributed across the cluster, with a concentration around the cluster center. With the addition of g-r color, we see that the r eff and µ eff between g-and r -bands are tightly correlated, while their colors place them around the red sequence of Coma. They are seen to be a passively-evolving population, around the red sequence of Coma.
• The whole cluster coverage reveals that the spatial distribution of UDGs aligns with the large-scale structure. This supports the interpretation that most of our UDGs are cluster members. The excess toward the south-west direction from the cluster center also coincides with the location of the NGC4839 subgroup, so many UDGs in this direction are likely to be associated with this infalling group.
This work was built upon and expanded our previous study (Yagi et al. 2016). All, or parts, of our method could be combined with other potential approaches, e.g., NoiseChisel (Akhlaghi & Ichikawa 2015) and others, for potentially better detection of extended LSB objects. While testing the other suggested approaches is beyond the scope of this work, we expect further improvement on the detection and measurement method, and hence on studies of extended LSB objects, in particular in view of the upcoming Vera Rubin survey.