On the Properties of Spectroscopically Confirmed Ultra-diffuse Galaxies across Environments

Ultra-diffuse galaxies (UDGs) are simply defined as spatially extended (typically requiring that the effective radius, r_e , be ≥ 1.5 kpc), low surface brightness galaxies (typically requiring that the optical central surface brightness, μ_g (0), be ≥24 mag arcsec⁻²). Such galaxies have been recognized for over 40 yr (Disney 1976; Sandage & Binggeli 1984; Vigroux et al. 1986; Impey et al. 1988; Bothun et al. 1991; McGaugh et al. 1995; Schwartzenberg et al. 1995; Dalcanton et al. 1997; Sprayberry et al. 1997; Conselice et al. 2003; Penny & Conselice 2008). Work has continued since their discovery towards trying to understand how these galaxies fit into an evolutionary picture (e.g., Conselice et al. 2003; Sabatini et al. 2005; Penny et al. 2009, 2011, 2014). Improvements in imaging technology and data reduction techniques (e.g., Mihos et al. 2005, 2013; Slater et al. 2009; Abraham & van Dokkum 2014; van Dokkum et al. 2014; Zaritsky et al. 2019; Infante-Sainz et al. 2020) have recently reinvigorated the field with the discovery of large numbers of such galaxies in galaxy clusters and groups (van Dokkum et al. 2015a; Koda et al. 2015; Mihos et al. 2015; Yagi et al. 2016; van der Burg et al. 2016; Mihos et al. 2017; Román & Trujillo 2017a; Greco et al. 2018; Danieli et al. 2019; Tanoglidis et al. 2021).

Our understanding of this class of galaxy is hampered by the lack of distance measurements and the broad selection criteria for UDGs, which lead to heterogeneous samples (Martin et al. 2016; Merritt et al. 2016; Martínez-Delgado et al. 2016; Román & Trujillo 2017a; van der Burg et al. 2017; Leisman et al. 2017; Prole et al. 2019; Torrealba et al. 2019). Distances are required to constrain the local environment and determine physical parameters, including the size of UDGs, which correlates with the enclosed mass (see the Appendix). UDG mass measurements are necessary to disentangle the myriad of proposed UDG formation and evolutionary models. While previous studies have found evidence that the majority of UDGs are low-mass galaxies (Amorisco & Loeb 2016; Sifón et al. 2018), which suggests a substantial overlap between UDGs and low-mass cluster galaxies identified in Conselice et al. (2003), UDGs exhibit a wide range of properties. For example, internal dynamics measurements for DF44 show a halo mass of 1.6 × 10¹¹ M_⊙ (van Dokkum et al. 2019b), which is comparable to the halo mass of the Large Magellanic Cloud (1.4 × 10¹¹ M_⊙; Erkal et al. 2019). Although internal dynamical measurements for UDGs remain rare, the inferred halo masses for UDGs with r_e > 3 kpc are typically ≳10¹¹ M_⊙ (the Appendix). Such findings suggest that a fraction of UDGs live in relatively massive dark matter halos (M > 10¹¹ M_⊙). The origins of this subset of UDGs may well be very different from that of their less massive counterparts, which include cluster dwarf ellipticals (dEs) and dwarf spheroidals (dSphs) studied extensively by Sandage & Binggeli (1984), Conselice et al. (2003), Penny et al. (2009).The SMUDGes Survey catalogs this subset of potentially large (and therefore massive) UDGs (Zaritsky et al. 2019).

Two inferences drawn from recent results where investigators were able to estimate the total mass for small, select samples of UDGs drive the current flurry of interest in UDGs. First, at least some UDGs appear to be examples of galaxies with highly inefficient star formation, or “failed galaxies” (van Dokkum et al. 2015a). The extremely large effective radii (>4 kpc) of some UDGs and their survival against the tidal forces present in the dense cluster environment together suggest that these may reside within large dark matter halos. Given their low stellar luminosities, these galaxies may be up to a hundred times less efficient at forming stars than an L^* galaxy. Because this result was first obtained for galaxies in the Coma galaxy cluster (van Dokkum et al. 2015a; Koda et al. 2015) and there is evidence for bluer galaxies outside of clusters (Román & Trujillo 2017a, 2017b), it was broadly speculated that UDGs were “failed” galaxies due to environmental processes that removed the gas early and effectively (e.g., van Dokkum et al. 2015a; Román & Trujillo 2017b). Given the extreme properties of UDGs, the environmental differences among UDGs might be even greater than those among high surface brightness galaxies. However, the situation may be more complicated than this simple scenario suggests because, although environmental color differences have been found (Román & Trujillo 2017a; Greco et al. 2018; Tanoglidis et al. 2021), low star formation efficiencies are observed even for H i bearing field UDGs (Leisman et al. 2017).

Second, at least some UDGs appear to be the most massive examples of galaxies that are dark matter dominated even within their optical radii. As such, UDGs provide a probe of dark matter halo profiles that are minimally disturbed by baryonic processes. Dynamical measurements of the mass of UDGs can be determined using either the unresolved stellar light (van Dokkum et al. 2016) or globular clusters (Beasley et al. 2016a). These early efforts led to estimates of a mass-to-light (M/L)_g ratio of ∼50–100 within the effective radius for DF44 in the Coma cluster and VCC 1287 in the Virgo Cluster, respectively. To estimate masses for a significantly larger sample of UDGs, others apply scaling relations, either between the host galaxy’s globular cluster populations and dynamical mass (Blakeslee et al. 1997; Peng et al. 2008; Spitler & Forbes 2009; Harris et al. 2013, 2017) or between the structural parameters and mass (Zaritsky 2017; Lee et al. 2020). Although less reliable than the direct dynamical measurements, these studies agree that UDGs span a wide range of masses, with most UDGs likely to be comparable in mass to standard dwarf galaxies (e.g., Amorisco et al. 2018), but also that there is a population extending to higher total masses (>10¹¹ M_⊙; Zaritsky 2017; Forbes et al. 2020; Lee et al. 2020).

As mass measurements have improved, some of the early estimates for the most iconic UDGs have been revised downward, potentially undercutting both of the reasons for why UDGs may be of interest. For example, higher fidelity stellar kinematic measurements and globular cluster counts now result in estimates of (M/L)_I ∼ 26 M_⊙/L_⊙ within the effective radius for DF44 (van Dokkum et al. 2019b) and a total mass in the neighborhood of 10¹¹ M_⊙ rather than the original estimates that placed it closer to 10¹² M_⊙ (van Dokkum et al. 2019b; Saifollahi et al. 2021). Even so, DF44 and other similarly sized UDGs are extraordinary. Compare them with another galaxy of total mass ∼10¹¹ M_⊙, the Large Magellanic Cloud (Erkal et al. 2019; Eskew et al. 2012; van Dokkum et al. 2019b). The mass-to-light ratio within the half-light radius of the Large Magellanic Cloud (LMC) is only 4.6 (calculated using r_1/2 from Drlica-Wagner et al. 2020, the enclosed i-band luminosity from Eskew & Zaritsky 2011, and the H i rotation curve of Kim et al. 1998) in comparison to for DF44 in solar units (van Dokkum et al. 2019b).

Our goals for this study are twofold. First, we search for more examples of physically large, and presumably massive, UDGs. Second, we extend the study of spectroscopically confirmed UDGs to the field environment. With this work we aim to (1) establish the characteristics of physically large UDGs, and (2) determine whether such systems exist outside the cluster environment.

To study the physical characteristics of massive UDGs in a field environment, we need to conduct an extensive, spectroscopic follow-up survey of candidates. However, due to the low surface brightnesses of even the largest UDGs, for which the spectrograph slit can capture more light, obtaining spectroscopy is expensive. On 8 and 10 m class telescopes, integration times range between 3600–5400 s for the largest UDGs (Kadowaki et al. 2017; van Dokkum et al. 2015b). As such, most spectroscopic surveys have utilized multiobject spectroscopy, targeting regions of high UDG surface density, galaxy clusters (Alabi et al. 2018; Ruiz-Lara et al. 2018; Chilingarian et al. 2019). While this technique allows for aggregations of spectra in a few observations, these surveys favor the “typical” UDG with a smaller radius and thus a smaller halo mass. Therefore, while there has been a significant increase in the number of spectroscopically confirmed UDGs in the literature, confirmed field UDGs are still rare. We instead use single-object spectroscopy of UDG candidates that are potentially of the same large class as DF44 in the region surrounding the Coma cluster. We do this with the aim of investigating the properties of large UDGs over a contiguous region that spans environment classes. In Section 2 we present our observations and combine those with data available in the literature. In Section 3 we present our results, including the comparison of properties across environment.

Our sample of low surface brightness candidate UDGs comes primarily from the first SMUDGes catalog (Zaritsky et al. 2019), which was constructed using image processing techniques specifically designed to detect diffuse galaxies in survey images from the Legacy Survey (Dey et al. 2019). That initial effort was carried out on the region encompassing the Coma galaxy cluster, where they could compare results to those from previous, independent UDG searches. To summarize, their technique employs a cleaning algorithm to eliminate image artifacts, point sources, and high surface brightness astronomical objects. After flattening these cleaned images, they apply wavelet filtering with varying kernel sizes to detect UDG candidates. Selection on size and central surface brightness based on model fitting using GALFIT (Peng et al. 2002, 2010) produces a candidate list that is further vetted through visual examination and a neural network classifier. Refinements to the image processing, parameter estimation, rejection of contamination, and completeness and uncertainty estimation are all in progress and may result in minor changes to the first SMUDGes catalog (D. Zaritsky et al. 2021, in preparation).

We augment the published SMUDGes catalog by similarly processing a few small regions of the Legacy Survey that lie far from the Coma cluster to provide targets when Coma was unavailable during our assigned telescope time. We refer to these areas and the candidates we identified there as “off-Coma.” These all have an R.A. < 12^h . Spectroscopic observations of candidates in the off-Coma region yielded a few candidates with redshifts, but the bulk of our data come from the area covered by the original SMUDGes catalog, which we refer to as covering the “Coma region.”

We targeted candidates that are of large angular extent and lie beyond the Coma splashback radius. We impose the first of the two criteria because we seek physically large UDGs as indications suggest that they are hosted in more massive dark matter halos (see the Appendix). Under the assumption that most of the candidates lie either within Coma or the surrounding large-scale structure, those that have a larger angular extent are also those that have a larger physical extent. Of course, some contamination by physically smaller, nearby objects is expected. We impose the second of the two criteria because there is a growing sample of published redshifts for UDGs within the Coma cluster and because we seek to find field versions of the passive, large, massive UDGs that are found within Coma. Due to practical concerns (R.A. distribution, weather), the observed sample is somewhat heterogeneous and in no way complete in terms of angular size, environment, or surface brightness.

We observed our selected sample of UDG candidates with the Multi-Object Double Spectrograph (MODS; Pogge et al. 2010) in binocular mode on the Large Binocular Telescope on three separate observing runs occurring on the nights of 2017 February 25–26, 2018 January 17–18, and 2019 April 4–5 (UTC). MODS1 experienced a glycol leak at the end of the 2017 February 25th (UTC) observing night, and was subsequently decommissioned for the remainder of the run. MODS2 remained functional throughout the 2017 February run. Due to the flat surface brightness profiles of UDGs and their angular extent, we used a custom 24 wide long slit, twice the width of the previously available widest slit, to increase the integrated light at the expense of spectral resolution. We positioned the long slit on our objects to maximize the integrated light from the galaxy, while primarily being constrained by the locations of guide stars. When possible, we tried to minimize contamination from bright, nearby stars. We observed each target for 40 to 100 minutes in a series of dithered 20 or 30 minute exposures (see Table 1 for total exposure times), combining data from both spectrographs when possible. The total observing time for each object was dictated by both the surface brightness of the object and observing conditions. We used the G400L grating (400 lines mm⁻¹ blazed at 44 centered on 4000 Å with a resolution of 1850) in the blue channel (3200–5800 Å) and the G670L grating (250 lines mm⁻¹ blazed at 43 centered on 7600 Å with a resolution of 2300) in the red channel (5800–10,000 Å). Because the red channel data suffer from higher sky backgrounds, we only use the blue channel data to measure redshifts.

In a series of steps, we prepared the data for analysis. We used the modsCCDRed package in the MODS data reduction pipeline (Pogge et al. 2010) to fix bad pixels, subtract the bias level, correct for overscan and readout artifacts, and to flat field images. Next, we used the Laplacian Cosmic Ray Identification (L.A. Cosmic; van Dokkum 2001) software suite to remove cosmic rays from the calibration and science images. We identified calibration lamp lines in our calibration spectra and calculated wavelength solutions for each observing run using the IDENTIFY, REIDENTIFY, and FITCOORDS tasks in IRAF ⁴ We refined our wavelength calibration using observed systematic zero-point deviations in prominent Hg i and [O ii] night sky lines (λ = 4046.56, 4358.35, 5460.74, and 5577.34 Å) in MODS1 (2017) and MODS2 (2017 and 2018) blue-channel wavelength solutions. No refinement was required for MODS1 and MODS2 wavelength solutions for the 2019 data. We corrected for zero-point calibration offsets by applying the measured offset of 2.25 Å and 1 Å for the 2017 MODS1 and MODS2 blue-channel wavelength solution, respectively, and 0.53 Å for MODS2 blue channel in 2018. This correction sufficiently improved the precision of the wavelength solution to within 0.16 Å. Even if one suspects, given the magnitude of the imposed zero-point velocity corrections, that the systematic wavelength calibration uncertainty is ∼2 Å, this level of error translates to a velocity uncertainty of ∼130 km s⁻¹, which does not affect any of our analysis. We applied the corrected wavelength solutions to our science images using the IRAF task TRANSFORM. We performed sky subtraction on all science frames using the BACKGROUND task, with the lower (low_rej) and upper (high_re) rejection bounds set to 2σ and fitting order interactively set to between 8 and 15. We then stacked all of the exposures of each object using the IMSHIFT and LSCOMBINE IRAF tasks. We could not always use the continuum from the UDG to align the individual exposures before stacking due to the low signal-to-noise ratio (S/N) of the spatially extended low surface brightness profile. In those cases where the alignment was troublesome, we used stars that happened to lie in our long slit. The long slit also enabled us to use over 80% of the slit length to obtain a high S/N sky spectrum for subtraction. We performed a second sky subtraction pass once the images were stacked to remove any residual sky light or artifacts, using the same rejection parameters and a low fitting order (order = 3–4). Finally, we extracted the 1D stacked spectra for each object using the APALL IRAF task.

We repeatedly encountered scattered light in the MODS spectrograph that evolves on similar timescales as our exposure lengths. The light originates from bright (m_r < 12) stars within 2° of our targets. This scattered starlight dominates the continuum spectra of UDG candidates and sometimes happens to fall coincident on the detector to the UDG. To combat this problem, we eventually evolved our observing strategy to reject targets with scattered light present in the acquisition image taken immediately prior to the spectral observations. Furthermore, we excluded any individual exposures with large areas of elevated counts, which we interpreted as a signature of scattered light, from the image stack.

We determined the redshift of our UDG candidates by cross-correlating the spectra of our targets with an A-type stellar template. We chose this particular template because of the prominence of Balmer lines in UDG spectra (Kadowaki et al. 2017). We also tested a later-type stellar template, but in no case where the A-type template failed did the later-type template result in an identified redshift. In the cross-correlation, we excluded a list of narrow wavelength ranges that correspond to bright sky lines and laser light contamination in MODS (the latter is used to enable flexure compensation while observing). We measured the redshift of each object using the XCSAO and the EMSAO IRAF tasks in the RVSAO add-on package, setting the acceptable recessional velocity range between −5000 and 30,000 km s⁻¹. We visually examined each fit. Of the targets listed in Table 1, only 14 out of 23 yielded acceptable redshifts. UDG redshift estimation with these low S/N data is somewhat uncertain and catastrophic failures are possible. While we only present those in which we have confidence, it is certainly possible that in a small number of cases we have been fooled by an unlucky coincidence of noise.

While the continuum was present in the 2D spectra of all 23 observed objects, most of those that did not yield redshifts were dominated by noise despite the long exposure times. In a handful of cases, we observed no discernible emission or absorption lines despite a reasonably strong continuum. In the remainder of cases, despite our efforts we were foiled by low levels of scattered light.

We present the parameters of our sample galaxies, including the physical parameters that can be calculated once distances are known, and details of the observations in a series of tables. To calculate physical quantities, we adopt a ΛCDM cosmology with Ω_M = 0.31, Ω_Λ = 0.69, and H₀ = 67 km s⁻¹ Mpc⁻¹ (Planck Collaboration et al. 2020). In Tables 2, 3, and 4, we provide the g-band central surface brightness (μ_g (0)), effective radius (r_e), g-band absolute magnitude (M_g ), recessional velocity (cz), and environmental classifications (discussed below) for the set of UDG candidates in the Coma region and in our off-Coma region. The tables are divided according to the provenance of both the spectroscopic redshift and the candidates. In Table 2 we present data for SMUDGes candidates for which we obtained redshifts with the LBT, as described here and by Kadowaki et al. (2017). In Table 3 we present the data for SMUDGes candidates in the Coma region for which redshifts come from other sources. Finally, in Table 4 we present the data for UDG candidates in the Coma region that are not in the SMUDGes catalog and for which the redshifts come from other sources.

We report all redshifts in Tables 2, 3, and 4 in the cosmic microwave background (CMB) rest frame. Specifically, we used the radial_velocity_correction method in Astropy's SkyCoord module to correct for heliocentric velocities of objects in Table 1 and Kadowaki et al. (2017). While van Dokkum et al. (2015b), Gu et al. (2018), Ruiz-Lara et al. (2018), and Chilingarian et al. (2019) do not explicitly state the adopted frame, we assumed that the reported velocities are heliocentric on the basis of some intercomparison among published results. Velocities from all other literature sources explicitly state that they are corrected to the heliocentric reference frame. We adopted an apex of ℓ_apex = 26414, b_apex = + 4826, and V_apex = 371.0 km s⁻¹ (Fixsen et al. 1996) to compute the CMB rest-frame velocities for all galaxies. Additionally, we used only the whole galaxy “W” velocity measurements from Ruiz-Lara et al. (2018). In the cases where multiple literature sources report velocity measurements for the same galaxy, we first computed the heliocentric, weighted mean velocity and its standard error with variance weighting before converting the velocity into the CMB rest frame.

We report the redshift uncertainties when possible. We note that the spectroscopic redshift uncertainties for some literature sources were unavailable. When available, we propagated the redshift uncertainties through our determination of the overall uncertainties for r_e , M_NUV, M_g , M_r , and M_z , with optical uncertainties provided by GALFIT. The average uncertainty in r_e is ∼0.1 kpc, although it trends larger at higher redshifts. Six candidates at roughly the distance of Coma have uncertainties greater than 0.25 kpc, while two candidates in the background to Coma have the largest r_e uncertainties of 0.5 and 1 kpc. Uncertainties in the magnitudes are from 0.05 to 0.1 for each band, with the uncertainty decreasing at higher redshifts because of the lower relative uncertainty in the distance. All six objects with magnitude uncertainties greater than 0.2 occur in candidates with recessional velocities less than 1600 km s⁻¹. Uncertainties at these levels do not affect the broad conclusions we discuss below. Instead, uncertainties are dominated by sample size, statistical considerations, and selection biases.

A few details are important. We report the extinction-corrected photometry in Tables 2, 3, and 4. We measured the structural parameters and the optical, grz-band photometry for all sources, even those not originally in the SMUDGes catalog, using the standard SMUDGes pipeline described by Zaritsky et al. (2019). One major change to the photometry pipeline allowed for floating Sérsic indices n. Compared to the previous version, which strictly fixed n to 1 for exponential profiles, the floating n pipeline yields more accurate photometry. We used NED’s Galactic Extinction Calculator ⁵ to correct for extinction, using the extinction map from Schafly & Finbeiner (2011). As such, all of the candidates are on the same photometric system and analyzed in the same manner.

Similarly, we redid the NUV photometry from the Galaxy Evolution Explorer (GALEX; Martin et al. 2005) data obtained via MAST ⁶ both because some of the candidates we consider here are not in the original SMUDGes catalog and because our new fitting has changed the measured r_e in those that were included in the original work. We followed the measurement procedure presented by Singh et al. (2019) and considered only those with flux S/N estimates >3 to be detected. Among the 68 candidates, four (SMDG1237294+204442, SMDG1306148+275941, SMDG1313189+312452, and SMDG1315427+311846) have previously reported NUV detections (Singh et al. 2019) and we recovered three of those as well. We did not recover SMDG1306148+275941, which also happens to be the only object in our catalog with a prior FUV detection, but it lies only slightly below our S/N > 3 criterion. Two of the candidates lack GALEX data (SMDG1231329+232917 and SMDG1253152+274115). In total, we detected 20 of our candidate UDGs in the NUV band. Ten of these candidate UDGs (SMDG1313189+312452, SMDG1221577+281436, SMDG1226040+241802, SMDG1230359+273310, SMDG1241425+273352, SMDG1248019+261235, SMDG1255415+191239, SMDG1302418+215952, SMDG1312223+312320, and SMDG1315427+311846) were detected in 100 s AIS images; six (SMDG1103517+284118, SMDG1240017+261920, SMDG1239050+323015, SMDG1300263+272735, SMDG1220188+280132, and SMDG1225185+270858) were detected in guest investigator programs; and an additional four (SMDG0914401+283036, SMDG1237294+204442, SMDG1245277+181801, and SMDG1225277+282903) were detected in 1500 s MIS images. We present the NUV magnitudes or our upper limits in Tables 2 to 4.

In the subset of candidates with LBT spectroscopy, we observe bright [O ii] and [O iii] emission lines only in the spectra of SMDG1301304+282228 (DF08) and the off-Coma UDG SMDG0914401+283036. In the latter, the optical flux likely originates from two distinct regions of the galaxy that can be seen as bright patches in Figure 1. We also report an NUV flux detection for this source, consistent with the interpretation of the emission line flux as indicative of ongoing star formation. SMDG1301304+282228 (DF08) is a bit more puzzling in that we have only an NUV flux limit and it falls on the optical red sequence (Figure 2 from Singh et al. 2019), both of which would suggest that it is passive. DF08 serves as a cautionary tale that no single star formation indicator can definitively identify objects with low levels of active or recent star formation. Low levels of star formation may very well be occurring even in objects with NUV limits and red optical colors.

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Before proceeding to present our results, we discuss one subtlety in our UDG criteria. Given observational uncertainties in μ_g (0) and r_e , it was unclear whether we should exclude objects that were within their measurement uncertainties of our class-defining thresholds of μ_g (0) ≥ 24 mag arcsec⁻² and r_e ≥ 1.5 kpc. We opted to also consider as UDGs those galaxies that do not strictly satisfy the criteria but are within 2σ of the surface brightness and size thresholds. These modified criteria can also be thought of as effectively lowering the size and surface brightness cuts for our sample to r_e ≥ 1.4 kpc and μ_g (0) ≥ 23.8 mag arcsec⁻². This choice leads to an overall modest increase of nine additional UDGs to our sample, up to a total of 44 confirmed UDGs (SMDG1221086+292921, SMDG1302166+285717, SMDG1306148+275941, SMDG1315427+311846, 1255567+273017, 1259041+281422, 1259042+281507, 1259299+274302, and 1259372+274815). Although we have modestly relaxed the defining criteria of a UDG, we do not account for measurement uncertainties when we refer to large (≥3.5 kpc) UDGs.

Once distances are established, many of the UDG candidates fail the physical size criterion for the UDG class. Subsequently, we refer to candidates that pass the size criterion as UDGs and to those that fail as non-UDGs. Given that the physically largest UDGs are rare, a spectroscopic selection favoring candidates of large angular size, which is the case in our work, will naturally favor nearer, smaller galaxies. Of the 19 candidates for which we present LBT redshifts in Table 2, four have cz_CMB < 1000 km s⁻¹ and an additional five have cz_CMB < 2000 km s⁻¹. Among all of the candidates we present in the three tables, 12 have cz_CMB < 1000 km s⁻¹. Due to peculiar velocities, we cannot reliably compute the distances of UDGs candidates with small recessional velocities. We will not consider further the characteristics of galaxies with cz_CMB < 1000 km s⁻¹, except to say that all but one (SMDG1255415+191239), on the basis of a distance derived strictly from their recessional velocity, would fail the UDG physical size requirement. We refer to these galaxies as “unconstrained.” Four out of the seven UDG candidates with 1000 < cz_CMB < 2000 km s⁻¹ also fall below the size requirement and are therefore non-UDGs. In summary, we have five galaxies (50%) that we consider to be UDGs in this sample that have cz_CMB < 4000 km s⁻¹.

Further characterizing our basic spectroscopic findings, we find that among candidates in our SMUDGes catalog for which we obtained LBT spectroscopic redshifts (19 targets), 15 are in the Coma region and four are in the off-Coma region. The Coma region can be roughly described as an area of projected radius of ∼19 Mpc (11°) from the cluster center [α = 12^h59^m487; δ = (J2000)]. For our full sample of UDG candidates with spectroscopic redshifts, 68 in total, we exclude the 12 with cz_CMB < 1000 km s⁻¹, leaving us with 56 viable candidates. Among these, 44 (79%) are UDGs by the relaxed surface brightness and size criteria we adopt, with all but one (SMDG0914401+283036) in the Coma region, and 12 are non-UDGs (21%).

3.1. Environment Classification

3.2. The Spatial Distribution of UDGs

In Figure 2, we mark the positions of Coma region, spectroscopically confirmed UDGs in relation to the large-scale structure in a redshift wedge plot with the physical projected separation, , along the x-axis and the proper distance, D_proper, along the y-axis. Most of the UDGs in our sample lie within the cluster or the filamentary structure associated with the Coma cluster. Qualitatively, at least, the distribution of UDGs follows that of the high surface brightness on large scales. The larger UDGs appear to avoid the center of Coma, but we attribute this result, at least in part, to the selection of the sample. Confirmed UDGs within Coma come primarily from multiobject spectroscopic studies, which by construction mostly target typical UDGs, while UDGs outside of Coma come primarily from our own work that emphasized larger, rarer UDGs. This difference in the construction of the sample of UDGs inside and outside of Coma will, unfortunately, play a role in various aspects of our analysis and discussion.

As expected, there is tendency for UDGs in environments designated as locally dense to lie within the Coma cluster and as sparse to lie outside of it. However, there are exceptions, with a few UDGs in locally dense environments located outside of Coma. Such exceptions are potentially important test cases that can help us determine the relative importance of local versus global environment on the properties of UDGs.

In Figure 3, we present the phase-space distribution of UDGs relative to that of high surface brightness galaxies in and around the Coma cluster and compare their local environments. Eighteen of 24 Coma UDGs (75%) reside in what we classify as locally dense environments. Among those UDGs, the ones that we classify as residing in locally sparse environments tend to scatter farther in recessional velocity from the Coma mean velocity (σ_cz = 1304 ± 210 km s⁻¹) than those that we classify as residing in locally dense environments (σ_cz = 892 ± 231 km s⁻¹), with only a 1.5% random chance of such a difference. We speculate that the Coma UDG sample classified as residing in locally sparse environments is partly contaminated by foreground or background. Beyond the splashback radius, only two of 10 Coma region UDGs (20%) within ±2500 km s⁻¹ of the Coma cluster mean recessional velocity reside in a dense environment. In conclusion, our two measures of environment highlight mostly the same galaxies as being in either high- or low-density environments. There are a few exceptions, but because of this nearly complete overlap we do not expect to reach vastly different conclusions depending on which measure of environment we choose to use. This resulting similarity in environment designations may just be a feature of the current sample, which is dominated by the Coma cluster. Future samples, where we have more systems in dense local environments that are not also in a dense global environment, may enable us to identify differences related to classes of dense environments. Such comparisons have been illuminating in the study of high surface brightness galaxies (Lewis et al. 2002; Gómez et al. 2003).

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3.3. The Physical Size Distribution of UDGs

Due to the observed correlation between the half-light radius and the derived enclosed mass (Figure A1), finding the most massive UDGs requires searching among the largest UDGs. For this purpose, we consider UDGs with an effective radius ≥3.5 kpc as potentially interesting. For example, DF44 (circularized r_e = 3.9 kpc) has an estimated halo mass of ∼10¹¹ M_⊙ (van Dokkum et al. 2019b; Saifollahi et al. 2021).

These physically large systems are highlighted in Figures 2 and 3 with bold, black outlined markers. We again urge caution in interpreting the distribution of these systems across the structure in Figure 3 because different selection preferences exist among the spectroscopic studies. Namely, UDG redshift surveys using multiobject spectrographs target the core of the cluster to utilize the multiplexing capability. These surveys will include whatever candidates are in the field of view, large or small, while a long-slit spectroscopic survey such as ours, but also that of van Dokkum et al. (2015b), will tend to focus on the larger, more physically interesting targets. Indeed, for this study we preferentially targeted systems with a large angular extent across the various environments within the survey area. Nevertheless, physically large systems are found both inside and outside the cluster and in dense and sparse regions. As far as our environment designations can resolve, we do not find an environmental effect on the size of the largest UDGs.

As such, we now combine all of our UDGs and compare the size distribution of SDSS galaxies and UDGs in Figure 4. We have normalized the distributions for comparison and find that galaxies with r_e ≥ 6 kpc are exceedingly rare (six out of 1950 among the SDSS galaxies in this region and only two, SMDG1302166+285717 and SMDG1315427+311846, in our UDG sample). Although it is difficult to interpret any difference in the shapes of the two size distributions because of the biases described previously, the UDG size distribution is not strikingly different than that of the SDSS galaxies.

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Of the 44 UDGs in our sample, 16 have effective radii ≥3.5 kpc, including two exceptionally large ones that we just mentioned with r_e > 6 kpc (SMDG1315427+311846 with r_e = 6.5 kpc and SMDG1302166 + 285717 with r_e = 9.9 kpc). The largest of these also has the smallest measured axis ratio (b/a = 0.37) in our sample, which we suspect indicates that it is a tidal tail or tidally distorted galaxy rather than a UDG. Upon further examination, we find that it lies near a luminous early-type galaxy (positioned slightly beyond the region shown in Figure 1) that shares roughly the same redshift and that it is elongated in the direction toward this companion galaxy. We will discuss the distribution of b/a in our sample further in Section 3.5, but here we conclude that this source is unlikely to be a bona fide UDG.

Using COLOSSUS (Diemer 2018) and the Tinker et al. (2008) mass function, we estimate that halos of galaxies with r_e > 6.0 kpc (which we estimate to correspond roughly to a halo mass of 10^12.1 M_⊙ (see the Appendix) and up to a maximum r_e of 10.0 kpc (10^12.5 M_⊙)) comprise of 4% of all galaxies larger than our cutoff of 1.5 kpc (with an estimated corresponding mass of 10^10.8 M_⊙). Given that our sample has 44 UDGs, finding one or two UDGs of such size is consistent with this expectation. Given our preference for spectroscopically observing candidates of large angular extent, and the prevalence for the SMUDGes candidates in this area of sky to lie at roughly the Coma distance, we conclude from our results that UDG candidates with r_e significantly larger than 6 kpc should be rare and viewed with some skepticism.

3.4. Relationships among UDG Structural and Photometric Parameters

In this section we examine whether relationships exist among UDG structural and photometric parameters (i.e., surface brightness, luminosity, color index, effective radius, axis ratio, and Sérsic index). In Figures 5 and 6, we present the data in graphical form, with UDGs distinguished according to global and local environments, respectively. The contour plots represent the probability density of every unique pair of parameters and this is calculated using multivariate, kernel density estimation (KDE). The diagonal histograms feature the distribution of each parameter and its probability density.

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We employ hypothesis testing to determine statistically significant feature correlations in UDGs. In addition, we identify features with underlying differences in their means and distributions in sparse and dense environments. Specifically, for each pair of features analyzed in Figures 5 and 6, we assess the statistical significance of a possible correlation using the Spearman’s rank correlation test, the differences in the means using the independent sample Student’s t-test, and in the distributions themselves using the Kolmogorov–Smirnov test. Because the probability of false positives increases when multiple inferences are made, we adopt the Bonferroni correction to compensate by requiring a higher confidence of rejection. To be specific, if we require a 5% chance or less of reproducing the measured correlation in order to reject the hypothesis that the data are uncorrelated among a single set of parameters, we now set the requirement to α/m, where α = 5% is the original significance level and m = 35 is the total number of pairwise comparisons plus the number of comparisons made between feature mean and distribution shapes of UDGs. We report only the statistically significant (≥95% confidence level) correlations and distribution differences under this heightened requirement.

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So defined, we find statistically significant results in a limited number of tests. These break down into a few categories. First, the somewhat trivial cases include the correlation between size, r_e , and luminosity, M_g . Also in this category are relationships between the projected radial separation from the Coma cluster and environmental density. Second are the cases that we suspect arise due to the different cluster and field selection. As we discussed previously, it is somewhat difficult to compare structural properties of UDGs inside and outside of the Coma cluster with this sample. This category contains the significant inverse correlation between separation from Coma and absolute magnitude. Finally, the third category consists of those trends that warrant further investigation and interpretation. In this category, we find evidence for correlations between (1) central surface brightness, μ_g (0), and Sérsic index, n; (2) g − r and separation from the Coma cluster; and (3) for distinctions in the g − r distributions with either cluster membership or environmental density.

3.4.1.  μ_g (0) versus n

We observe a negative correlation between a UDG’s central surface brightness and its Sérsic index (Pearson correlation coefficient of −0.59, which has a chance of arising randomly of 7 × 10⁻⁵ in this sample). Fainter galaxies have lower n. Higher signal-to-noise ratio imaging is needed to determine whether there are two physical components playing off each other or whether there is a real range in the overall structure of a single component. Overall, UDGs exhibit close to exponential surface profiles, with an average n ∼ 1. The largest n value in the sample presented here is 1.8 for SMDG1302166+285717 (DF03).

The trend we find between μ_g (0) and n is consistent with that found among UDGs drawn from eight galaxy clusters by Mancera Piña et al. (2019) and from Coma in both the Dragonfly (van Dokkum et al. 2015a) and the Subaru (Yagi et al. 2016) samples. Furthermore, such a trend has also been found among dwarf elliptical galaxies (dEs) in the Coma cluster by Graham & Guzmán (2003), who attributed it to the combination of what they interpret to be two more fundamental scaling relations: one between the magnitude M_B and central surface brightness and the other between M_B and Sérsic index. While we do not find significant evidence for these two trends in our UDG data, when we look back at previous studies, we do find correlations between magnitude and n and, in particular, between magnitude and surface brightness in both the Yagi et al. (2016) and Mancera Piña et al. (2019) samples, providing some support for the Graham & Guzmán (2003) postulate regarding the interplay of these three relations.

3.4.2.  g − r versus Environment

We observe a strong environmental dependence on the UDG g − r color. In Figure 7, we highlight the local environmental dependence of color within the Coma region phase-space diagram, with red UDGs predominantly residing in dense environments. From the perspective of the global environment, red UDGs are primarily cluster members. Given the strong correlation between our global and local environmental measures because we are so dominated by the Coma cluster, it is difficult to ascertain if there is a further dependence of star formation on local environment as has been shown to be the case for high surface brightness galaxies (Lewis et al. 2002; Gómez et al. 2003). However, as seen for the high surface brightness galaxies in those studies, the trend in diminished star formation for UDGs also appears to extend beyond the cluster’s region of direct physical influence, whether that is interpreted to be the virial or splashback radius.

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There is a potential concern that the color difference we identify between cluster and field (or high- and low-density environments) could be the result of heterogeneous spectroscopic selection and variable incompleteness in the absorption line spectroscopy of redder UDGs. To address this concern, we examine results solely from our LBT sample. For this sample, the target selection is color independent across environment and, although it may be easier for us to measure a redshift for a bluer galaxy than for a redder one, we expect any possible color-dependent bias is also independent of environment. Despite the far smaller total sample size, we find a statistically significant rank correlation between UDG color and projected separation from the cluster center (a Spearman test rejects the null hypothesis with 96.7% confidence). The reality of the color trend with environment is further supported by the result that all seven of our UDGs with GALEX detections, which are unbiased relative to Coma, are outside of the Coma cluster.

To probe further, we plot the color–magnitude diagram for UDGs in Figure 8 and compare to the location of the early-type red sequence galaxies. We define the location of the early-type red sequence by linearly extrapolating the mean g − r colors and their 2σ lower limit for elliptical galaxies (Schombert 2016) in five luminosity bins (2.0, 1.0, 0.5, 0.2, and 0.1L_*). We convert the luminosities to the r-band absolute magnitudes using the measured luminosity function of SDSS DR6 galaxies in the r-band (Montero-Dorta & Prada 2009), which has a characteristic magnitude of . While the adoption of z-band absolute magnitude would better correlate with mass, we opt for the adoption of the r-band due to the high sky brightness in the z-band, which would yield less accurate photometry. Using z-band absolute magnitudes does not alter our conclusions from this analysis. We consider all galaxies with g − r colors greater than the extrapolated 2σ red sequence lower limit to be red. Given the similarity of the environmental behavior observed so far when environment is defined either globally or locally, we now merge the two designations. For this discussion and Figure 8, we consider a UDG to be in a dense environment if it lies in either in the cluster environment or a locally dense one. From this extrapolated relation, we determine that all but one red UDG (SMDG1251014+274753) reside in high-density environments.

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We extend this discussion by considering UV observations. Singh et al. (2019) present UV photometry of the Zaritsky et al. (2019) catalog, providing limits in most cases but detections of 16 UDGs. Their analysis was conducted assuming that most of the sources are at the distance of the Coma cluster and now we evaluate whether that is likely to be the case. Unfortunately, among their detections we only match four with spectroscopic redshifts (SMDG1237294+204442, SMDG1306148+275941, SMDG1313189+312452, and SMDG1315427+311846). We note that we do not replicate the NUV detection for SMDG1313189+312452 as the S/N = 2.7 falls just below our detection threshold. Only one of these is consistent with lying at the distance of Coma and clearly satisfies the UDG criteria. Among those not detected in the UV, which is all of the other SMUDGes sources in Tables 2 and 3, the fraction at the distance of Coma is 57% (17/30). However, as we have noted before, our spectroscopic selection biases us toward the foreground and so we cannot directly apply this result to the entire sample of candidates. Fortunately, most of the results presented by Singh et al. (2019) are distance independent.

To close this section, we discuss three interesting red (g − r ≥ 0.5) UDGs from Figure 7. These are (1) the large triangle projected within the splashback radius but relatively offset from the Coma mean recessional velocity (SMDG1302166+285717; DF03), (2) the “red” UDG at ∼3.5 Mpc and 6000 km s⁻¹ (SMDG1251014+274753), and (3) the “orange” UDG at ∼10 Mpc and almost at the Coma recessional velocity (SMDG1240530+321655). The first of these is identified as lying in a dense local environment and we have already discussed this one as being a likely tidal tail or distorted object (Section 3.3), so we disregard this galaxy. The second one is sufficiently close to the estimated splashback radius that, given uncertainties, perhaps could have already made a pass through the Coma environment. So although this UDG is potentially an example of a passive UDG that is in a low-density environment, it is not definitively so. The third UDG is this sample’s best example of a quiescent field UDG. Its g − r color places it just slightly below the red sequence region identified in Figure 8, so perhaps it is not a truly passive galaxy. As such, we have found two interesting examples of potential passive field UDGs but no definitive ones and the majority of field UDGs are clearly either currently or recently star forming given their optical blue colors, and in many cases corresponding NUV detection.

3.5. UDG Axis Ratios

Given our findings that, aside from their colors, field and cluster UDGs are quite similar, if there is only a single UDG formation channel then it must be environment independent. Among the models proposed for the origin of UDGs, a subset are environment independent. One such model stipulates that UDGs are galaxies that reside in high angular momentum dark matter halos (Amorisco & Loeb 2016), while another suggests that baryonic matter in these galaxies retains a larger fraction of the their halo’s angular momentum (Posti et al. 2018). In either case, we expect a trend between the axis ratio, b/a, and effective radius, r_e , for UDGs of fixed stellar mass (see Dalcanton et al. 1997).

Venhola et al. (2017) investigated whether such a trend exists for UDGs and low surface brightness dwarf galaxies in the Coma and Fornax clusters. Their study, without considering the stellar masses of the UDGs, found a statistically significant anticorrelation, as expected in these models, between b/a and r_e for UDGs in the Fornax cluster but not for those in the Coma cluster.

Mancera Piña et al. (2019) extended this type of analysis across eight clusters, including 247 UDGs projected within R₂₀₀ of their respective host galaxy cluster and 195 UDGs lying in regions beyond this projected distance. When considering all of their galaxies, binned by stellar mass, they find weak evidence for an anticorrelation between b/a and r_e for UDGs lying within R₂₀₀. They find no such trend for UDGs beyond R₂₀₀. Mancera Piña et al. (2019) conjectured that the UDGs may become more elongated after interacting within their host cluster, complicating any interpretation relating b/a to the UDG’s angular momentum.

We revisit this topic with our sample. Because we established that r_e correlates strongly with the luminosity of the UDG, we must correct for this trend prior to comparing r_e values among our UDGs. Our concern is that because there is a mass (and luminosity) difference as a function of clustercentric radius due to the selection of the samples, a real relation between b/a and size might artificially suggest a false relation between b/a and clustercentric radius (i.e., an environmental reason for changes in b/a). As such, we focus our investigation on whether UDGs that deviate from the mean r_e for galaxies of their mass have unusual b/a. In particular, do UDGs with unusually large values of r_e , which might be due to tidal effects, also have unusually low values of b/a? To standardize r_e , we adopt a functional form such that M_r and are linear, because M_r is linear with for a Sérsic profile. We first measure the empirical relation between r_e and M_r using least-squares regression and find

We then define the standardized effective radius, , as the ratio between the measured r_e and the expected value for the corresponding M_r .

We analyze UDGs in high- and low-density environments separately because of the environmental differences observed by Mancera Piña et al. (2019). In Figure 9, we present the relation between b/a and . Although there is a large scatter among UDGs in both environments, we find a hint of an anticorrelation between b/a and for UDGs in high-density environments (chance of random occurrence is only 0.032). We find that there is no significant correlation for UDGs in low-density environments (chance of random occurrence is 0.25). These results are in agreement with those found by Mancera Piña et al. (2019).

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We caution that it is premature to use these results to bolster or refute certain models that make predictions for the trends in b/a (i.e., Amorisco & Loeb 2016; Posti et al. 2018). The scatter in Figure 9 is large and our data limited. There may also be results imposed by the sample selection. For example, consider that selecting galaxies with a highly limited range of central surface brightness imprints a relationship between galaxy flux and projected size. If we select for constant flux (or luminosity or stellar mass assuming all galaxies are at the same distance), axis ratios will need to decrease with increasing major axis, approximated by the effective radius, to maintain a constant projected area. Alternatively, rounder objects of the same effective radius will have a larger total flux. Although the UDG central surface brightness range in photometric samples is ∼2 magnitudes, the range in the spectroscopic studies is much more limited due to practical observing constraints. In another example of potential complications, the spectroscopic sample is likely to be affected by nonuniform b/a selection criteria among studies, such as the rejection of UDGs with smaller axis ratios in one or another study on the basis that these candidates might more likely be interlopers. Finally, because blue UDG candidates are typically clumpy and red ones are typically smooth (Karunakaran et al. 2020), fitting smooth GALFIT models may result in different systematics. For example, Karunakaran et al. (2020) argue that the application of smooth GALFIT models to clumpy star-forming UDGs systematically underestimates the axial ratio because the fit parameters are being pulled by the clumps instead of the underlying, fainter light from the smoother, older population. While their hypothesis needs to be tested with simulations, the sense of differences between cluster and noncluster UDG axial ratios in Figure 9 is consistent with that systematic effect. All of these issues must be satisfactorily resolved before venturing to use b/a to evaluate theoretical models.

Independent of UDG formation models, the results shown in Figure 9 suggest a distinction in the axis ratio properties of UDGs in dense and sparse environments. As such, the geometry of UDGs might provide insightful clues to their likely formation and evolutionary pathways beyond the expectation drawn from models involving angular momenta. To examine further the effects of the environment on the evolution of these enigmatic galaxies, we present the UDG axis ratio distribution inside and outside the Coma cluster. We find a relatively flat distribution of projected axial ratios from 0.4 to 1 for cluster UDGs, as shown in Figure 10. The absence of galaxies with b/a < 0.4 is at least partially due to SMUDGes selection criteria (Zaritsky et al. 2019). This flat distribution is consistent with findings from larger studies of cluster UDGs (Koda et al. 2015; Burkert 2017) and dwarf elliptical galaxies (Lisker et al. 2009; Chen et al. 2010).

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We measure a mean projected axis ratio that is consistent between our cluster and noncluster UDG populations (0.73 and 0.69, respectively) and with previous studies of similar populations. The mean axis ratio of Coma cluster UDGs from the Yagi et al. (2016) catalog varies between 0.69 to 0.72, depending on the selection criteria used for each study (Koda et al. 2015; Yagi et al. 2016; Burkert 2017). The low surface brightness galaxy population in Chen et al. (2010) has a mean axis ratio of 0.73 ± 0.18. We perform the Student’s t-test to compare the mean of our noncluster population with that of the cluster population from the Yagi et al. (2016) catalog with effective radius and surface brightness cuts to match those used in our study (r_e ≥ 1.4 kpc and μ_g (0) ≥ 23.8). We find no significant difference between these samples. Despite the lack of statistical evidence for differences, there are hints of potential differences in the distribution of values for field and cluster UDGs. First, we do not find the same absence of round UDGs (b/a = 0.9–1.0) as found by Burkert (2017), which had supported their conclusion that Coma cluster UDGs favor a prolate geometry. Second, the distribution of apparent axial ratios for our cluster and noncluster populations are visually quite different (Figure 10). However, when we conduct the Kolmogorov–Smirnov and Anderson–Darling tests to assess this possibility, the differences do not rise to a sufficiently high confidence level, presumably because of the small sample sizes involved. We conclude that there are potentially interesting signatures that need to be explored with larger samples.

3.6. Effects of Local Peculiar Velocity

From our spectroscopic follow-up campaign of SMUDGes candidate UDGs, we reach a set of milestones and conclusions.

1. 1.  
   We confirm two key observational challenges in the study of UDGs. First, even a significant exposure time (∼1 hour) on 10 m class telescopes often fails to yield a redshift for a candidate UDG (in our case for nearly half of our targets). Because this failure can, at least in part, depend on the lack of strong absorption lines, there is the possibility that final spectroscopic samples are biased in terms of age, metallicity, or star formation history. Second, field samples of UDG candidates can be significantly contaminated by non-UDGs. In our case, the percentage of non-UDGs, once we establish physical sizes, was ∼40%.
2. 2.  
   Despite these difficulties, after combining our results with those in the literature for UDGs in the Coma cluster, we compiled a sample of 44 spectroscopically confirmed UDGs with which to explore the nature of UDGs in and around the Coma cluster.
3. 3.  
   Outside of the Coma cluster, the confirmed UDGs divide roughly evenly between those lying within the large-scale structure surrounding Coma and those completely unassociated with Coma. We classify all of these as field galaxies for our discussion. All but five of these (15 of 20) are in what we categorize as sparse environments (i.e., not projected within 300 kpc of a massive galaxy (M_g < 19.0) with a relative velocity difference <500 km s⁻¹).
4. 4.  
   Large UDGs (r_e > 3.5 kpc) are found both in the cluster and field environment. We find no measurable dependence of size on environment, but the cluster and field samples are selected differently, which complicates any interpretation of the current sample.
5. 5.  
   We conclude that the largest UDG in our sample (SMDG1302166+285717, r_e = 9.9 kpc) is likely to be the result of tides (either a tidal filament or tidally distorted) due to its unusually large size, its extreme axis ratio, its association with a nearby massive galaxy, and its orientation toward that same galaxy.
6. 6.  
   Excluding that one galaxy, we find that the distribution of UDG sizes is similar to that of SDSS galaxies, with r_e > 6 kpc galaxies being exceedingly rare. This result coincides well with our estimated halo mass for such a UDG of ∼10¹² M_⊙. Galaxies of this mass or greater should make up roughly 4% of all our UDGs, consistent with our finding 1 out of 43.
7. 7.  
   We confirm the earlier findings of a color−local density relation for UDGs (Greco et al. 2018; Tanoglidis et al. 2021) with the statistically strong result that UDGs in low-density environments are highly unlikely to lie on the galaxy red sequence (only 1 out of 15 in our sample). Furthermore, we find that UDGs in high-density environments are mostly red (20 out of 29 in our sample), which in reality is likely to be an even stronger effect because some systems may be projected onto the high-density environment of the Coma cluster.
8. 8.  
   We find two potentially passive, large UDGs in the field, suggesting that the cluster environment is not required to quench star formation. The sample is small; one of the two UDGs may be sufficiently close to Coma to have experienced the cluster environment and the optical color of the second is only marginally consistent with it being on the galaxy red sequence. More such objects must be identified to confirm this finding and establish whether passive, field UDGs exist.
9. 9.  
   We detect NUV flux from a large fraction of the UDGs in sparse environments (10 out of the 20 in our sample for which we have GALEX data). This result is consistent with the results of Greco et al. (2018) and we interpret it to mean that recent or ongoing star formation is common among field UDGs and likely to be episodic.
10. 10.  
    While previous findings (Mancera Piña et al. 2019) showed a weak relation between axis ratio (b/a) and size (r_e ) for UDGs in the cluster environment and a lack of any trend between the two quantities for UDGs outside of the cluster environment, we confirm similar results using standardized in lieu of r_e . For various reasons that we discuss, however, we recommend against physical interpretations of this result at the current time.
11. 11.  
    We find no statistically significant difference in the axis ratios of UDGs in the Coma cluster and field, although there is a suggestion that the field UDGs have a narrower distribution of b/a. This result merits subsequent study with larger samples.

Spectroscopic observations of UDG candidates provides necessary confirmation of the UDG’s physical characteristics, and they are particularly important for establishing candidates in low-density environments where association cannot be used to assign a distance. We will continue observationally expensive programs in the optical, such as reported here, and in the radio (Karunakaran et al. 2020) to supplement indirect distance constraints on UDGs.

J.K., D.Z., and R.D. acknowledge financial support from NSF AST-1713841 and AST-2006785. K.S. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC). We made use of the online cosmology calculator as described in Wright (2006) and thank Barry Rothberg and Olga Kuhn, our LBT support astronomers, for their help during our observation runs. In particular, Olga Kuhn helped us to navigate through the MODS data reduction pipeline. In addition, we like to thank Wen-fai Fong who took our calibration data for our 2017 February observation run. And lastly, we thank the anonymous referee for the thorough comments and suggestions, which has improved our manuscript.

The LBT is an international collaboration among institutions in the United States, Italy, and Germany. LBT Corporation partners are: The University of Arizona on behalf of the Arizona university system; Instituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, the Astrophysical Institute Potsdam, and Heidelberg University; The Ohio State University, and The Research Corporation, on behalf of The University of Notre Dame, University of Minnesota, and University of Virginia. This paper uses data taken with the MODS spectrographs built with funding from NSF grant AST-9987045 and the NSF Telescope System Instrumentation Program (TSIP), with additional funds from the Ohio Board of Regents and the Ohio State University Office of Research.

The authors made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Facility: LBT (MODS); GALEX - .

Software: Astropy 3.2.1 (Astropy Collaboration et al. 2013, 2018), COLOSSUS 1.2.11 (Diemer 2018), IPython 4.0.0 (Pérez & Granger 2007), Matplotlib 3.1.0 (Hunter 2007), NumPy 1.16.4 (Oliphant 2006; van der Walt et al. 2011), pandas 0.25.1 (McKinney 2010), scikit-learn 0.21.2 (Pedregosa et al. 2011), SciPy 1.3.0 (Oliphant 2007; Millman & Aivazis 2011) seaborn 0.9.0 (Waskom et al. 2016), Cosmology Calculator (Wright 2006), GALFIT 3.0.5 (Peng et al. 2002, 2010), IRAF 2.16 (Tody 1986, 1993), L.A. Cosmic (van Dokkum 2001), MODS Data Reduction Pipeline 1.3p1 (Pogge et al. 2010).

We have focused our spectroscopic observations on UDGs from the SMUDGes catalog that have large angular extents. We do this in an attempt to select those that are the physically largest as well. As our redshifts show, we have a mixed selection of objects in the end, including some nearby, small galaxies. Here, we motivate, in somewhat more detail, why we aim to study the physically largest UDGs.

Zaritsky (2017) suggested, on the basis of the two UDGs with velocity dispersion measurements at the time, that UDGs satisfy a scaling relation satisfied by other galaxies (Zaritsky et al. 2006, 2008, referred to, in reference to its antecedent, as Fundamental Manifold or FM). By using the FM relation to estimate the velocity dispersions of other UDGs, that study suggested that UDGs span a range of masses and that effective radius correlates with halo mass. The latter is a result of the FM relation and the fact that UDGs have roughly the same surface brightness due to how they are selected.

Here, we revisit the earlier finding by examining the much larger set of UDGs that currently have a measured velocity dispersion. As before, the sample is still a mix between systems with integrated stellar dispersions and dispersions measured using individual globular cluster velocities. We adopt velocity dispersions from a range of sources (Beasley & Trujillo 2016b; van Dokkum et al. 2017; Toloba et al. 2018; Chilingarian et al. 2019; Martín-Navarro et al. 2019; van Dokkum et al. 2019b) and structural parameters from references therein. With a few exceptions that we now describe, we have used the data as presented and include all known UDGs with velocity dispersion measurements. For DF44, there are conflicting results (van Dokkum et al. 2017, 2019b) that are not understood. The original van Dokkum et al. (2017) dispersion measurement was modified by van Dokkum et al. (2019b) after a modest error was identified in the original treatment, but the revised value is still discrepant within the internal uncertainties with their new value. We opt to average these two values and adopt the larger of the presented uncertainties. From the set of Virgo UDGs presented by Toloba et al. (2018), we exclude VLSB-D which has r_e = 13.4 ± 0.2 kpc. This scale length is much larger than any other UDG. We conclude that it is a tidal feature rather than a galaxy, as we did with our largest candidate as well. Lastly, we have excluded two UDGs near NGC 1052 with measured velocity dispersions (NGC1052-DF2, NGC1052-DF4; Danieli et al. 2019; van Dokkum et al. 2019a) because of their controversial nature and suggestions that they may be dark matter free and therefore quite different from the other systems (van Dokkum et al. 2018; Trujillo et al. 2019; Danieli et al. 2020). We discuss farther below why their exclusion does not qualitatively affect our conclusion.

We estimate the enclosed masses with the half-light radii using the estimator developed by Walker et al. (2009). As shown in Zaritsky (2012), this particular mass estimator has near equivalency to the FM scaling relation used by Zaritsky (2017), facilitating our comparison. In Figure A1 we place the UDGs on the enclosed mass–radius plane for comparison to the models (Navarro−Frenk−White halos), the Zaritsky (2017) result using the scaling relation (dotted line), and a standard linear least-squares fit to the data.

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Although the data have significant scatter, the best-fit line is a close match to the previous results and confirms the suggestion that as one considers UDGs with larger half-light radii, one tends to systems with enclosed masses that correspond to increasingly more massive halos. A similar, related approach has also been used by Lee et al. (2020) to estimate masses for their sample of UDGs, which included confirmation of the original relation with additional data.

Finally, we return to the issue of the two UDGs projected near NGC 1052 that we exclude. These two have small enclosed masses within their effective radii (∼10⁸ M_⊙ or less), ∼1–3 kpc depending on the adopted distance. As such, including them in the fitting results in a steeper relation, strengthening our case for a relationship between size and mass, but leading to a worse fit overall for the simple functional form we adopt.