The Next Generation Virgo Cluster Survey. XXXIV. Ultracompact Dwarf Galaxies in the Virgo Cluster

The primary source of data used in this study is the NGVS. The survey footprint covers the two main subclusters of Virgo (A and B, centered on M87 and M49, respectively) out to their virial radii (i.e., ${R}_{200}=5\buildrel{\circ}\over{.} 38$ for Virgo A and 333 for Virgo B). As described in Muñoz et al. (2014) and Liu et al. (2015a), the NGVS is an ideal resource for the study of compact stellar systems, e.g., GCs, UCDs, and dwarf nuclei. The NGVS imaging consists of short and long exposures, where the former can be used to find UCDs brighter than g ∼ 18.5 mag. Such objects are interesting given that they define the extremes of UCD formation (and, in some cases, even host SMBHs; Seth et al. 2014; Ahn et al. 2018).

Figure 1 shows the final observing status of the NGVS, organized by exposure length. We have excluded the r band as those observations had to be partially sacrificed due to CFHT's dome shutter failure in 2012A. For the long exposures, the survey is fully complete in the remaining bands, while only partial areal coverage was achieved for the short exposures in the u* (∼50% completeness) and i (∼57% completeness) bands.

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Near-infrared imaging has proven to be a powerful tool for UCD selection (Muñoz et al. 2014; Liu et al. 2015a). As shown in the upper-right corner of Figure 1, we have deep K_s-band images in the central 4 deg² of subcluster A (NGVS-IR; Muñoz et al. 2014), which we have previously used to select a high-purity UCD sample around M87 (Liu et al. 2015a). Alternatively, as shown in the bottom-right panel of Figure 1, K-band imaging from UKIRT Infrared Deep Sky Survey (UKIDSS; Lawrence et al. 2007) covers a large fraction of the NGVS footprint. About ∼70% of the bright objects $({g}_{0}\,\lt 21.5$ mag, where g₀ is the aperture-corrected magnitude measured within a 16 pixel diameter (∼3'') and corrected for Galactic extinction) in the NGVS have counterparts in the UKIDSS K band. Thus, although UKIDSS is much shallower than the NGVS-IR (5σ limiting magnitude ∼18.4 and ∼24.4 mag, respectively), it is nonetheless useful for separating UCDs from background galaxies (BGs) among the bright objects.

We summarize the combinations of imaging data at hand, separated by exposure length, in Figure 2. For the case of the long exposures (left panel), the footprint is simply divided into two areas depending on the availability of UKIDSS K-band imaging. The short-exposure map (right panel) is much more complicated owing to the incompleteness in the associated u*- and i-band imaging.

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Full details on the reduction of NGVS images can be found in Ferrarese et al. (2012). To generate a homogeneous catalog of compact objects, we run SExtractor (Bertin & Arnouts 1996) in double-image mode. We detect objects in the g band and then measure a set of parameters, including aperture magnitudes, in the u*giz bands. In this study, we measure the luminosity and color of all detected objects with aperture magnitudes. To minimize systematics, we apply aperture corrections that account for point-spread function (PSF) variations within, and between, fields. Specifically, we use corrected 30 diameter aperture magnitudes to represent total magnitudes and corrected 15 diameter aperture magnitudes to estimate colors.

For the catalog generation and magnitude correction, we follow the method of Liu et al. (2015a), with one exception. Liu et al. (2015a) subtracted models of the diffuse light from nearby massive galaxies (M87, M49, and M60), whereas this is avoided in the current analysis to have a homogeneous catalog. We generate independent catalogs based on the short- and long-exposure images and then merge them into one afterwards. We adopt measurements from the short-exposure catalog for those objects that are saturated in the long exposures; otherwise, measurements are taken from the long-exposure catalog.

In addition to the imaging that forms the basis of this study, there are many past spectroscopic programs targeting the Virgo cluster that we can draw upon. Ferrarese et al. (2012) summarized the relevant programs for Virgo compact stellar systems (i.e., GCs, UCDs, and dE, Ns) as of 2012; these include radial velocity measurements from various Multiple Mirror Telescope (MMT)/Hectospec, Magellan/IMACS, Very Large Telescope/VIMOS, and Anglo-Australian Telescope (AAT)/AAOmega programs (see the paper for details). Since then, a number of NGVS-motivated spectroscopic programs have been undertaken (see, e.g., Zhang et al. 2015, 2018; Toloba et al. 2016; Spengler et al. 2017; Longobardi et al. 2018). We have collected radial velocities from these and other previous works (Binggeli et al. 1985; Hanes et al. 2001; Côté et al. 2003; Brinchmann et al. 2008; Strader et al. 2011, 2012; Pota et al. 2013, 2015; Blom et al. 2014; Norris et al. 2014; Li et al. 2015; Forbes et al. 2017; Ko et al. 2017; Toloba et al. 2018), as well as from the NASA/IPAC Extragalactic Database (NED),²¹ the SIMBAD Astronomical Database²² (Wenger et al. 2000), and the Sloan Digital Sky Survey (SDSS; Abolfathi et al. 2018). In all, we have a total of 31,346 velocity measurements for objects in the NGVS footprint brighter than g₀ = 21.5 mag. This database includes foreground stars, GCs, UCDs, galaxies in Virgo, and BGs. In what follows, we make use of this large velocity catalog to eliminate contaminants from our photometric UCD selection as well as to recover UCDs that miss our cuts.

Size is the defining parameter of UCDs.²³ As shown by Liu et al. (2015a), the excellent image quality of the NGVS allows us to measure reliable sizes for compact objects in Virgo (mainly GCs, UCDs, and galactic nuclei) larger than ∼10 pc (see their Section 2.3). We measure half-light radii using the KINGPHOT package (Jordán et al. 2005), focusing on the g and i bands because of the former's depth and the latter's exquisite seeing. Comparisons of the two sets of r_h measurements show that they are consistent with each other (see Figure 3 in Liu et al. 2015a). Jordán et al. (2005) show that KINGPHOT r_h measurements are biased to larger values when ${r}_{h}\gtrsim {r}_{\mathrm{fit}}/2$ (where ${r}_{\mathrm{fit}}$ is the fitting radius within which we adopt KINGPHOT), which is ∼50 pc for an ${r}_{\mathrm{fit}}$ = 7 pixels (used in Liu et al. 2015a) at the distance of Virgo. This choice of ${r}_{\mathrm{fit}}$ is reasonable because previous works show that most UCDs are smaller than 40 pc (Brodie et al. 2011; Chiboucas et al. 2011; Strader et al. 2011; Penny et al. 2012). However, in the interests of determining whether there are larger UCDs in Virgo, we run KINGPHOT with ${r}_{\mathrm{fit}}=15$ pixels in this study. Thus, our KINGPHOT measurements would be biased for objects with ${r}_{h}\gtrsim 110$ pc.

The left panel of Figure 3 compares our UCD r_h measurements from Liu et al. (2015a) for the two values of ${r}_{\mathrm{fit}}$ above. We note that the larger ${r}_{\mathrm{fit}}$ yields slightly larger sizes when ${r}_{h}\lesssim 16$ pc. Otherwise, the two sets of r_h measurements are statistically equivalent, so we therefore adopt the KINGPHOT measurements made with ${r}_{\mathrm{fit}}$  = 15 pixels. The right panel of this figure shows a comparison between the r_h measurements from this work and those from previous studies. The blue circles are taken from Haşegan et al. (2005), who measured r_h using KINGPHOT and HST data (ACSVCS; Côté et al. 2004). The orange squares denote the r_h measurements from Ko et al. (2017), who used ISHAPE software and NGVS data. From this figure, we can see that our r_h measurements are consistent with the measurements from previous studies, even though they used different methodologies and/or data sets.

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In the left panel of Figure 4, we show the cuts employed as part of our ${u}^{* }{{giK}}_{s}$-based selection. There, we plot in the $({u}^{* }-i)$ versus $(i-{K}_{s})$ plane the ∼2000 objects from our spectroscopic catalog that satisfy our magnitude and ellipticity cuts. The points have been colored by their measured radial velocities and can be divided into three main groups: BGs (red dots; v ≳ 3500 km s⁻¹), Virgo members (green and cyan dots; 0 ≲ v ≲ 3500 km s⁻¹), and foreground stars (blue and purple dots; v ≲ 0 km s⁻¹).²⁵ It is clear that Virgo members can be readily distinguished from BGs and foreground stars in the ${u}^{* }{{iK}}_{s}$ color–color diagram. To isolate Virgo members, we therefore adopt the following color cuts:

$$\begin{eqnarray}&&\left\{\begin{array}{l}1.400\leqslant {({u}^{* }-i)}_{0}\leqslant 2.800;\\ -0.427\leqslant {(i-{K}_{s})}_{0}\leqslant 0.700;\\ {(i-{K}_{s})}_{0}\leqslant -1.127+0.700\times {({u}^{* }-i)}_{0};\\ {(i-{K}_{s})}_{0}\geqslant -1.917+0.900\times {({u}^{* }-i)}_{0}\end{array}\right.,\end{eqnarray} \tag{ 1 }$$

which are indicated by the irregular polygon in the figure.

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The right-hand panel of Figure 4 shows the ${(g-z)}_{0}$ color as a function of mean effective surface brightness, $\langle {\mu }_{g}{\rangle }_{e}$, which is the average surface brightness measured within the half-light radius. The points show those objects that passed our color cuts in the ${u}^{* }{{iK}}_{s}$ diagram and, again, are colored according to their radial velocities. It is clear from the distribution that we can use surface brightness to further improve the purity of our Virgo sample by removing BGs and some foreground stars. The dotted polygon shows the exact cuts in surface brightness that we adopt, which are described by the following functions:

$$\begin{eqnarray}&&\left\{\begin{array}{l}0.620\leqslant {(g-z)}_{0}\leqslant 1.500;\\ \langle {\mu }_{g}{\rangle }_{e}\geqslant 15.000\,\mathrm{mag}\,{\mathrm{arcsec}}^{-2};\\ \langle {\mu }_{g}{\rangle }_{e}\leqslant 18.750\,\mathrm{mag}\,{\mathrm{arcsec}}^{-2},\\ \,\,\,\,\,\,\,\,\,\,\,\,\mathrm{when}\,1.163\leqslant {(g-z)}_{0}\leqslant 1.500;\\ \langle {\mu }_{g}{\rangle }_{e}\leqslant 27.692-7.692\times {(g-z)}_{0},\\ \,\,\,\,\,\,\,\,\,\,\,\,\mathrm{when}\,0.909\leqslant {(g-z)}_{0}\leqslant 1.163;\\ \langle {\mu }_{g}{\rangle }_{e}\leqslant 20.700\,\mathrm{mag}\,{\mathrm{arcsec}}^{-2},\\ \,\,\,\,\,\,\,\,\,\,\,\,\mathrm{when}\,0.620\leqslant {(g-z)}_{0}\leqslant 0.909.\end{array}\right.\end{eqnarray} \tag{ 2 }$$

The combination of the cuts applied to this point leaves us with a broad sample of Virgo members that includes compact elliptical galaxies, galactic nuclei (in low-mass galaxies), UCDs, and GCs. To isolate the UCDs within this sample, we apply one final set of cuts based on our measured half-light radii, which are

$$\begin{eqnarray}&&\begin{array}{c}\left\{\begin{array}{l}11\lt \langle {r}_{h} \rangle \lt 100\,{\rm{pc}};\\ \displaystyle \frac{| {r}_{h,g}-{r}_{h,i}| }{ \langle {r}_{h} \rangle }\leqslant 0.5;\\ \displaystyle \frac{{r}_{h,g,{\rm{error}}}}{{r}_{h,g}}\leqslant 15{\rm{ \% }};\\ \displaystyle \frac{{r}_{h,i,{\rm{error}}}}{{r}_{h,i}}\leqslant 15{\rm{ \% }},\end{array}\right.\end{array}\end{eqnarray} \tag{ 3 }$$

where $\langle {r}_{h}\rangle$ represents the weighted mean of the half-light radii measured in the g and i bands. These cuts mimic ones often used in previous studies to separate UCDs and GCs (e.g., Brodie et al. 2011; Strader et al. 2011; Penny et al. 2012). Though arbitrary, this is not an unreasonable choice because the typical size of either the MW or extragalactic GCs is ∼3 pc, and most GCs are smaller than ∼10 pc (e.g., van den Bergh et al. 1991; Jordán et al. 2005). Furthermore, Liu et al. (2015a) have shown that r_h measurements based on NGVS imaging are reliable for bright objects (${g}_{0}\lt 21.5$ mag) larger than ${r}_{h}\sim 10$ pc (see Section 2.3 of their paper). The lower limit on $\langle {r}_{h}\rangle$ used in this study roughly matches the limiting resolution of NGVS imaging.

Given the lack of deep K_s-band imaging over most of the NGVS footprint, we have developed an alternative strategy for selecting UCDs based on the u*, g, i, z and (where available) K bands. As seen in Figure 1, NGVS imaging is not fully complete in the u* and i bands for the short exposures. As argued in Muñoz et al. (2014), the u* band is essential when selecting UCDs due to its sensitivity to young/hot stellar populations, which allows for the removal of background star-forming galaxies. The left panel of Figure 5 shows the ${u}^{* }{gz}$ color–color diagram for the same spectroscopic sample (following the same color-coding) as in Figure 4. In this case, we can see that the spaces occupied by BGs, Virgo members, and foreground stars more heavily overlap with each other. Nevertheless, the Virgo members still form a relatively tight sequence in this plane, such that we can select a sample of these objects with high completeness, albeit with more contamination. We adopt a color selection (represented by the polygon) within this diagram of the form:

$$\begin{eqnarray}&&\left\{\begin{array}{l}0.850\leqslant {({u}^{* }-g)}_{0}\leqslant 1.790;\\ 0.620\leqslant {(g-z)}_{0}\leqslant 1.500;\\ {(g-z)}_{0}\leqslant 0.190+0.770\times {({u}^{* }-g)}_{0};\\ {(g-z)}_{0}\geqslant -0.300+0.930\times {({u}^{* }-g)}_{0}.\end{array}\right.\end{eqnarray} \tag{ 4 }$$

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The objects that satisfy these cuts are plotted in the color versus surface brightness plane in the right-hand panel of Figure 5. Although many contaminants pass our color–color cuts, it is possible to eliminate most of these following the same cuts on surface brightness that we applied to our ${u}^{* }{{giK}}_{s}$ sample (Equation (2); dotted polygon in this panel). These cuts are not as effective as before, however, and leave behind a number of BGs (red dots). Fortunately, we can remove most of these residual contaminants wherever we have K-band data. Figure 6 shows the gzK color–color diagram for those objects from our spectroscopic catalog that satisfy our ${u}^{* }{gz}$ and surface brightness cuts. For a given ${(g-z)}_{0}$ color, BGs tend to be redder in ${(z-K)}_{0}$ than Virgo members, and we use the following relationship to isolate the latter:

$$\begin{eqnarray}&&{(z-K)}_{0}\leqslant 1.480+0.780\times {(g-z)}_{0}.\end{eqnarray} \tag{ 5 }$$

After this, we apply the same size cuts as before (Equation (3)) to arrive at our sample of UCD candidates.

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In this section, we compare the UCD catalogs derived from the two selection methods described above. For this comparison, the best region within the NGVS footprint is the center of subcluster A, where we have u*, g, i, z, K_s (NGVS-IR), and K (UKIDSS) band fluxes and radial velocities for ∼2000 objects. Among this sample, 71 are spectroscopically confirmed UCDs that were already known from previous work (mainly Strader et al. 2011 and Zhang et al. 2015).

As described in Section 3.1, we divide these objects into three groups according to their radial velocities: BGs ($v\gt 3500$ km s⁻¹), Virgo members ($0\lt v\lt 3500$ km s⁻¹), and foreground stars ($v\lt 0$ km s⁻¹). Within the "Virgo" group, we only consider two subclasses of objects: UCDs and galaxies classified in previous or contemporaneous studies as nucleated dwarf elliptical galaxies, which have identifiable point sources at their centers (Binggeli et al. 1985; Sánchez-Janssen et al. 2019; Ferrarese et al. 2020). Diffuse, non-nucleated dwarfs are explicitly excluded in our selection pipeline.

As listed in Table 1, we have 183 stars, 71 UCDs, 17 dE, Ns, and 841 BGs which satisfy our magnitude and ellipticity criteria (i.e., $14.0\lt {g}_{0}\lt 21.5$ mag and $e\lt 0.3$). Following this, we successively apply our color, surface brightness, and size cuts, with the choice of colors being the only variable. Table 1 presents the number of objects from each group that survive each step of our selection functions.

Table 1.  Application of Our Photometric UCD Selection Methods (${u}^{* }{{giK}}_{s}$, u*giz, and u*gizK) to a Spectroscopic Training Set

	${u}^{* }{{giK}}_{s}$				u*giz				u*gizK
Velocity	v < 0	0 < v < 3500		v > 3500	v < 0	0 < v < 3500		v > 3500	v < 0	0 < v < 3500		v > 3500
Obj. type	Stars	UCDs	dE, Ns	BGs	Stars	UCDs	dE, Ns	BGs	Stars	UCDs	dE, Ns	BGs
g0 < 21.5 & e < 0.3	183	71	17	841	183	71	17	841	183	71	17	841
Color–color Diagram	21	71	9	14	55	69	10	91	55	69	10	91
$\langle {\mu }_{g}{\rangle }_{e}$	8	69	6	1	10	68	7	17	10	68	7	17
$\langle {r}_{h}\rangle$	2	67	4	0	2	66	5	14	2	66	5	14
gzK	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	2a	66b	5c	1

Notes.

^aThese two "stars" lie in the NGVS-1+1 field, where many Virgo members have negative radial velocities. We consider these two objects as UCDs, in which case all three of our selection methods successfully cull the stars from our training set. ^bTwo of these objects are included in our final UCD catalog, while the remaining three have half-light radii of 0.0, 10.1, and 10.8 pc. ^cThese five objects are included in the Virgo Cluster Catalogue (VCC; Binggeli et al. 1985).

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For the ${u}^{* }{{giK}}_{s}$-based selection, the color and surface brightness cuts are quite effective at eliminating most of the contaminants. In the end, we find 2 stars (∼1%), 67 UCDs (∼94%), 4 dE, Ns (∼24%), and 0 BGs satisfying all of the criteria.²⁶ For comparison, we find that 2 stars (∼1%), 66 UCDs (∼93%), 5 dE, Ns (∼29%), and 14 BGs (∼2%) pass the cuts in our u*giz-based selection. Thus, both methods achieve a completeness of >90% with respect to UCD selection. Conversely, the former method is much better than the latter in culling BGs from the sample. With the addition of K-band data, though, we can reduce the number of BGs that pass our ${u}^{* }{giK}$-based selection from 14 to 1, which compares very favorably with the results of our ${u}^{* }{{giK}}_{s}$-based selection.

As for the other contaminants, we note that all three of our selection methods pass two objects from our training set that are labeled as foreground stars. In fact, these two objects are really UCDs that have negative radial velocities through their association with the M86 subgroup. This shows that the combination of optical and near-infrared photometry removes most foreground and background objects. Where this photometric combination falls short is in rejecting dE, Ns, but we can easily accomplish this through visual inspection because nuclei are surrounded by obvious envelopes.

To summarize, our tests in the central 4 deg² of subcluster A show that a u*gizK-based selection of UCDs can be a reliable alternative to that based on ${u}^{* }{{giK}}_{s}$. Hereafter, we mainly rely on our u*gizK selection method to detect UCD candidates wherever K-band data are available and u*giz otherwise.

Based on the material presented to this point, the selection of UCDs would ideally rely on data in the ${u}^{* }{gzK}$ bands for color and surface brightness cuts, and in the g and i bands for size cuts. However, as shown in Figure 2, we do not possess imaging in the u*, i, and K  bands over the full NGVS footprint. In Table 2, we list the available combinations of photometric data and the corresponding selection method applied in each case. Approximately 90% of bright objects (${g}_{0}\lt 21.5$ mag) detected in the NGVS have data in either the u*gizK or u*giz bands; all other objects are covered by some subsample of the five available bands.

Table 2.  Summary of Multiband Data Sets over the NGVS Footprint and the Corresponding UCD Selection Methods

Bands	${f}_{\mathrm{Objs}}$	Selection Method	${N}_{\mathrm{UCDs}}$	${f}_{\mathrm{UCDs}}$	${N}_{\mathrm{UCDs},\mathrm{class}=1}$	${f}_{\mathrm{UCDs},\mathrm{class}=1}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)
u*gizK	$59.0 \%$	${u}^{* }{gzK}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	286	34.5%	235	38.4%
u*giz	29.3%	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	465	56.2%	363	59.3%
u*gzK	2.4%	${u}^{* }{gzK}+\langle {\mu }_{g}{\rangle }_{e}+{r}_{h,g}$	4	0.5%	0	0.0%
u*gz	0.2%	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+{r}_{h,g}$	1	0.1%	0	0.0%
gizK	3.8%	${gzK}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	1	0.1%	0	0.0%
giz	0.1%	${gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	0	0.0%	0	0.0%
gzK	4.3%	${gzK}+\langle {\mu }_{g}{\rangle }_{e}+{r}_{h,g}$	9	1.1%	0	0.0%
gz	0.9%	${gz}+\langle {\mu }_{g}{\rangle }_{e}+{r}_{h,g}$	13	1.6%	0	0.0%
gi+spec	⋯	$({v}_{r}\lt 3500\,\mathrm{km}\,{{\rm{s}}}^{-1})+\langle {r}_{h}\rangle$	49	5.9%	14	2.3%
Total	100%	⋯	828	100%	612	100%

Note. (1) The available filter combinations, (2) the fraction of the parent sample covered by each filter combination, (3) the UCD selection method employed, (4) the number of UCD candidates selected, (5) the fraction of all UCD candidates selected, (6) the number of UCDs that survive visual inspection, and (7) the fraction of all classified UCDs.

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Table 2 also shows the number (${N}_{\mathrm{UCDs}}$) and the fraction (${f}_{\mathrm{UCDs}}$) of UCDs selected by each method. Most of our UCD candidates (∼91%) are selected through either the u*gizK- or u*giz-based methods, which were discussed in previous sections. It is noteworthy that only ∼37% (286) of these candidates are selected from ∼60% of our catalog that has u*gizK data. Proportionally, we expect to find ∼145 UCD candidates from ∼30% of the catalog. However, 465 candidates (∼60%) are selected from the ∼30% of the catalog that do not have K-band data. As described above, K-band data are efficient for eliminating BGs. This suggests that the portion of our UCD sample selected via the u*giz-based method is inflated through contamination by BGs. Note that the other selection methods we have employed contribute just 28 objects to our UCD sample (or ∼3%). In all, we have identified 779 UCD candidates based on photometry alone.

Finally, we note that if only g- and z-band data are available, we select UCD candidates using the following color cut:

$$\begin{eqnarray}&&0.620\leqslant {(g-z)}_{0}\leqslant 1.500.\end{eqnarray} \tag{ 6 }$$

Also, if i-band half-light radii are not available, we apply the following cuts to the corresponding g-band value:

$$\begin{eqnarray}&&\left\{\begin{array}{l}11\lt {r}_{h,g}\lt 100\,\mathrm{pc};\\ \displaystyle \frac{{r}_{h,g,\mathrm{error}}}{{r}_{h,g}}\leqslant 15 \% .\end{array}\right.\end{eqnarray} \tag{ 7 }$$

In Figures 5 and 6, we see that a few confirmed Virgo members fall outside our color selection windows. Some of these objects lie close to the window boundaries, however, and therefore could be UCD candidates. The purpose of our color selection criteria is, first and foremost, to reduce or eliminate contamination from BGs. For these few cases, if we know from their radial velocities that they are not background objects, then we do not require color criteria. We assume that the Virgo members are UCDs if they satisfy our size cuts (Equation (3) or (7) if i-band data are not available). This assumption is reasonable as most objects in the literature in this size range are UCDs. There are ∼8000 Virgo objects with v < 3500 km s⁻¹ and do not satisfy our color or/and surface brightness cuts. Among these objects, we find an additional 49 UCD candidates through this "perturbation" method and henceforth refer to them as "spectroscopically selected UCD."

In Table 1, we recover 66 of the 71 known UCDs using either our u*giz- or u*gizK-based methods (the remaining 5 do not meet all of our selection criteria). In reality, two of these five "missing" UCDs are included in the spectroscopically selected UCD sample. The three remaining UCDs have $\langle {r}_{h}\rangle =0.0$ (due to the bad image quality in this region), 10.1, and 10.8 pc individually: i.e., two of the three are slightly smaller than our size criterion.

As explained above, we have objectively selected 828 UCD candidates: 779 and 49 based on photometric and spectroscopic information, respectively. As a final hedge against contamination, we execute one last step—visual inspection of the NGVS images, whereby we classify each candidate as either a (1) = probable UCD; (2) = dwarf nucleus; (3) = background galaxy; (4) = blended object; (5) = star; or (6) = star-forming region.

Some contaminants can be difficult to identify from visual inspection alone, and in such cases, we classify objects using additional information. For example, a nucleated dwarf galaxy (class = 2) usually contains a nucleus at its photocenter (although some are slightly off centered) and a stellar halo component surrounding it. Some UCDs are also embedded in low-surface-brightness envelopes (e.g., Haşegan et al. 2005), making it difficult to distinguish dE, Ns from UCDs with envelopes. We therefore classify objects as dE, Ns only when they appear in either the VCC (Binggeli et al. 1985) or NGVS galaxy catalogs (Ferrarese et al. 2020). BGs are identified with the help of redshift measurements, and all objects with ${v}_{r}\gt 3500$ km s⁻¹ are immediately classified as such (class = 3). Blended objects (class = 4) are relatively easy to identify, although they may not be separable in NGVS images if they are too close. We make use of Gaia DR2 data (Riello et al. 2018) to help further separate UCDs and stars (class = 5), in that stars can have significant proper motions (i.e., 3σ significance) and UCDs can be resolved in Gaia imaging (see Voggel et al. 2020). Figure 7 shows the BP/RP flux-excess factor, which is defined as the flux ratio $({I}_{\mathrm{BP}}+{I}_{\mathrm{RP}})/{I}_{G}$, as a function of Gaia G-band magnitude. Briefly, the fluxes in the BP and RP bands (I_BP and I_RP) are measured in a window of 3.5 × 2.1 arcsec² while the flux in G band (I_G) is derived from PSF fitting. For point sources, the flux-excess factor should be ≳1 (the BP and RP filters overlap at around 6500 Å and are broader than the G band, especially at the red side; see Evans et al. 2018). As shown in Figure 7, most of Gaia targets have small flux-excess factors while the excess factor of extended objects can be much larger: e.g., most of our UCD candidates (blue circles) in Figure 7 have excess factors of 2–4. We draw a line at an excess factor of 1.7 and classify sources below this level as stars. Finally, the star-forming regions (class = 6) are also easy to identify due to their blue colors.

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In summary, among our 828 UCD candidates, we find 612 probable UCDs (598 identified on the basis of photometry alone), 41 nucleated dwarf galaxies, 132 BGs, 12 blended objects, 14 stars, and 17 star-forming regions. Representative images for these six types of objects are shown in Figure 8. As can be seen in the final two columns of Table 2, 235 of the photometrically identified UCDs are u*gizK selected while the remaining 363 are u*giz selected. The UCD candidates initially selected based on other methods (i.e., ${u}^{* }{gzK}$, ${u}^{* }{gz}$, gizK, giz, gzK, and gz) are classified as contaminants after visual inspection—one of the reasons that we only test the u*giz- and u*gizK-selection methods in Section 3.3.

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Tables 3 and 4 present observed and derived parameters for all of our UCD candidates. Since visual inspection is inevitably subjective, we list all 828 objectively selected candidates in these tables.²⁷ We plan to measure radial velocities in future spectroscopic campaigns and assess their Virgo membership directly. Indeed, some of these "contaminants" (such as apparent star-forming regions with UCD-like sizes) are interesting in their own right and will be investigated in future papers.

Table 3.  Photometric Properties of UCD Candidates

ID	Name	NGVSID	tobs	αJ2000	δJ2000	$E(B-V)$	g0	K	${({u}^{* }-g)}_{0}$	${(g-i)}_{0}$	${(g-z)}_{0}$	${{\rm{\Delta }}}_{\mathrm{env}}$	UCD
				(deg)	(deg)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
1	NGVS-UCD1	NGVS-J120652.65+113246.5	l	181.7193703	11.5462618	0.028	19.212 ± 0.002	⋯	0.554 ± 0.004	−0.034 ± 0.004	−0.034 ± 0.006	0.018	0
2	NGVS-UCD2	NGVS-J120717.93+113846.7	l	181.8247260	11.6463089	0.032	21.074 ± 0.003	⋯	0.984 ± 0.011	0.650 ± 0.007	0.822 ± 0.010	0.105	1
3	NGVS-UCD3	NGVS-J120734.18+113626.0	l	181.8924309	11.6072260	0.028	21.492 ± 0.004	⋯	1.062 ± 0.011	0.600 ± 0.007	0.709 ± 0.012	0.032	1
4	NGVS-UCD4	NGVS-J120755.71+113921.2	l	181.9821228	11.6558897	0.030	21.057 ± 0.003	⋯	0.892 ± 0.008	0.633 ± 0.006	0.725 ± 0.010	0.079	1
5	NGVS-UCD5	NGVS-J120757.12+121954.2	l	181.9879964	12.3317198	0.027	21.444 ± 0.004	⋯	1.089 ± 0.011	0.648 ± 0.007	0.723 ± 0.012	0.005	0
6	NGVS-UCD6	NGVS-J120811.52+131327.6	l	182.0480094	13.2243239	0.030	21.408 ± 0.004	⋯	0.910 ± 0.012	0.525 ± 0.009	0.673 ± 0.019	0.015	1
7	NGVS-UCD7	NGVS-J120827.25+132407.4	l	182.1135389	13.4020547	0.032	21.373 ± 0.004	⋯	0.920 ± 0.010	0.656 ± 0.007	0.724 ± 0.013	0.009	1
8	NGVS-UCD8	NGVS-J120846.23+121935.8	l	182.1926310	12.3266129	0.026	21.338 ± 0.003	⋯	0.970 ± 0.010	0.770 ± 0.007	0.852 ± 0.012	0.032	1
9	NGVS-UCD9	NGVS-J120855.90+121833.2	l	182.2329343	12.3092174	0.027	21.415 ± 0.004	⋯	1.032 ± 0.011	0.796 ± 0.007	0.892 ± 0.011	0.060	1
10	NGVS-UCD10	NGVS-J120925.56+132007.7	l	182.3565013	13.3354611	0.034	19.007 ± 0.001	⋯	0.877 ± 0.003	0.588 ± 0.002	0.711 ± 0.003	0.197	0

Note. (1) Identification number; (2) UCD name; (3) object name in NGVS catalog; (4) exposure time: l = selected using long-exposure data, s = selected using short-exposure data; (5) R.A. in decimal degrees; (6) decl. in decimal degrees; (7) Galactic extinction according to Schlegel et al. (1998); and (8) Galactic-extinction-corrected, aperture-corrected g-band magnitude found within a 16 pixel (∼3'') diameter aperture. For details, see Liu et al. (2015a); (9) UKIDSS (Lawrence et al. 2007) K-band magnitude within a 3'' diameter aperture; (10–12) color index measured in an 8 pixel (∼15) diameter aperture, Galactic extinction corrected; (13) envelope parameter: ${{\rm{\Delta }}}_{\mathrm{env}}\equiv {g}_{16}-{g}_{32}$, where g₁₆ and g₃₂ are magnitudes in 16 and 32 pixel diameter apertures; and (14) object flag: 0 = contaminant, 1 = confirmed or possible UCD.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 4.  Structural Properties and Other Information for UCD Candidates

Name	MB	MV	$\langle {r}_{h}\rangle$	$\mathrm{log}({M}_{* }/{M}_{\mathrm{odot}})$	vr	${v}_{\mathrm{source}}$	Class	Envelope	Method	Other Name
	(mag)	(mag)	(pc)		(km s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
NGVS-UCD1	−11.62	−11.38	14.03 ± 0.39	6.5	−38	SDSS	5	0	$({v}_{r}\lt 3500\mathrm{km}\,{{\rm{s}}}^{-1})+\langle {r}_{h}\rangle$	⋯
NGVS-UCD2	−9.68	−9.21	29.86 ± 0.76	6.3	⋯	⋯	1	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD3	−9.27	−8.76	15.34 ± 0.38	6.1	⋯	⋯	1	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD4	−9.70	−9.27	29.48 ± 0.54	6.2	⋯	⋯	1	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD5	−9.33	−8.80	22.44 ± 0.28	6.1	⋯	⋯	3	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD6	−9.36	−8.93	24.29 ± 1.07	6.0	⋯	⋯	1	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD7	−9.40	−8.97	24.51 ± 0.37	6.1	⋯	⋯	1	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD8	−9.41	−8.95	23.33 ± 0.37	6.2	⋯	⋯	1	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD9	−9.30	−8.80	25.00 ± 0.68	6.2	⋯	⋯	1	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯
NGVS-UCD10	−11.80	−11.39	65.92 ± 0.72	7.0	⋯	⋯	3	0	${u}^{* }{gz}+\langle {\mu }_{g}{\rangle }_{e}+\langle {r}_{h}\rangle$	⋯

Note. (1) UCD name; (2–3) absolute B- and V-band magnitude, calculated using the transformation equation $B={u}^{* }-0.8116({u}^{* }-g)+0.1313$, $V=g-0.2906({u}^{* }-g)+0.0885$ (http://www.sdss3.org/dr10/algorithms/sdssUBVRITransform.php#Lupton2005) and a distance modulus of 31.1 mag (Mei et al. 2007; Blakeslee et al. 2009); (4) weighted mean half-light radius in the g and i bands, $\langle {r}_{h}\rangle ={r}_{h,g}$ if an i-band measurement is not available; (5) stellar mass; (6) heliocentric radial velocity (or weighted mean value if multiple measurements are available); (7) the source of our adopted v_r measurement, SDSS: Abolfathi et al. (2018); NED: NASA/IPAC Extragalactic Database; SIMBAD: SIMBAD Astronomical Database (Wenger et al. 2000); VCC: Binggeli et al. (1985); NTT17: NTT 2017 program; AAT 12: AAT 2012 program; MMT 09: MMT 2009 program; Toloba2018: Toloba et al. (2018); Ko2017: Ko et al. (2017); MMT 14: MMT 2014 program; Keck: Keck program; C03: Côté et al. (2003); IMACS 16: Magellan/IMACS 2016 program; S11: Strader et al. (2011); (8) class parameter: 1 = probable UCD, 2 = dwarf nucleus, 3 = background galaxy, 4 = blended object, 5 = star, 6 = star-forming region; (9) envelope: 0 = lacks obvious envelope, 1 = has obvious envelope; (10) selection method; and (11) alternative names, if available.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Given the complexity of our methodology, Figure 9 summarizes our UCD selection function in the form of a flowchart. An inspection of this figure shows that our selection process involves two main channels: one based on photometry (right) and the other on spectroscopy (left), which we now describe.

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We begin with the photometric algorithm. There are 346,948 objects in the NGVS that satisfy our magnitude ($14.0\lt {g}_{0}\lt 21.5$ mag) and ellipticity (e < 0.3) cuts. All of these objects have g- and z-band data, while u*-, i- and K-data are more limited. Note that only objects detected in our short exposures lack u*- and i-band data (see Figure 2) and so are drawn from the bright end of the UCD luminosity function (UCDLF). We then apply successive cuts based on each object's color (or colors), surface brightness (Equation (2)), position in the gzK diagram (Equation (5); if K-band data are available), and half-light radius (Equation (3) if i-band data are available, otherwise Equation (7)). Our color cuts are based on the ${u}^{* }{gz}$ diagram (Equation (4)) for those objects having u*-band data; otherwise, we consider the $(g-z)$ color alone (Equation (6)).

These selection criteria dramatically reduce our original photometric sample from 346,948 objects to 779 candidate UCDs. With the assistance of Gaia (see Figures 7), 11 of these candidates are reclassified as stars. To further reduce the number of contaminants, we place a cut on radial velocities (when available) and visually inspect the candidates (see Figure 8). Another 51 candidates are removed for having a radial velocity in excess of v = 3500 km s⁻¹ and 119 more are removed following visual inspection. The latter group is comprised of 27 dE, Ns, 81 BGs, and 11 blended objects. Our final photometric UCD sample contains 598 UCD candidates.

We now describe the spectroscopic selection function depicted in Figure 9. As stated earlier, this path is intended to select UCD candidates that fall outside our color and/or surface brightness selection windows. Using this approach, we find 49 more candidates that meet our radius cuts, while visual inspection shows that they comprise 14 probable UCDs, 17 star-forming regions, 14 dE, Ns, 3 stars, and 1 blended object.

Overall, we have identified 612 UCD candidates, the majority of which (598) come from our photometric selection function. This constitutes the largest sample of UCD candidates identified to date. While we would prefer a simple and homogeneous selection, the lack of data in the u*, i, and K bands over the full NGVS footprint necessitates certain compromises. That said, the great majority (598/612 ≃ 97.7%) of these UCD candidates have been selected based on their u*giz or u*gizK colors.

We refer to the full group of candidates as the "all UCD sample." Within this group, 235 candidates have been selected on the basis of their u*gizK data, so we refer to this as the "u*gizK UCD sample." We also have a "spec-UCD sample," which contains the 203 candidates that have been spectroscopically confirmed as members of the Virgo cluster. The "all UCD sample" has the highest completeness but the largest number of contaminants. Conversely, the "spec-UCD sample" has the fewest contaminants but is inevitably biased by the choice of spectroscopic targets. Finally, the "u*gizK UCD sample" strikes the greatest balance between completeness, contamination, and homogeneity (see Table 1).

As nearest rich cluster of galaxies, many previous investigations have studied UCDs in Virgo (e.g., Haşegan et al. 2005; Jones et al. 2006; Evstigneeva et al. 2007b; Strader et al. 2011; Liu et al. 2015a; Zhang et al. 2015; Ko et al. 2017). Our sample contains 186 UCDs that have already been reported, while 29 systems from previous work are excluded. We list the properties of each member of the latter group in Table 5, including name, R.A., decl., ellipticity, magnitude, half-light radius, radial velocity, the sources of velocity measurements, and the primary reason why it is not included in our sample. Among these 29 UCDs, 6 are fainter than g₀ = 21.5 mag, 3 have high ellipticity (e > 0.3), 12 do not satisfy the radius criteria, 4 are located just outside the selection window in ${(g-z)}_{0}\,\mathrm{versus}\,{\mu }_{g}$ diagram, 2 are classified as BGs by gzK diagram, and 2 escaped detection in the NGVS images because they are projected close to saturated stars. We also note that 9 of these 29 UCDs lack radial velocity measurements.

Table 5.  The Properties of UCDs That Are in Previous Studies but Not Included in This Study

Name	${\alpha }_{{\rm{J}}2000}$	${\delta }_{{\rm{J}}2000}$	e	g0	$\langle {r}_{h}\rangle$	vr	${v}_{\mathrm{source}}$	Note
	(deg)	(deg)		(mag))	(pc))	(km s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
S1508	187.6308727	12.4235661	0.07	22.018	⋯	2419	S11	${g}_{0}\gt 21.5\,$ mag
S825	187.7126346	12.3554004	0.16	21.613	⋯	1142	S11	g0 > 21.5 mag
S723	187.7239811	12.3393933	0.07	21.737	⋯	1398	NED, S11	g0 > 21.5 mag
H44905	187.7378222	12.3944049	0.20	21.921	⋯	1564	NED, S11	${g}_{0}\gt 21.5\,$ mag
H30401	187.8279366	12.2624564	0.18	21.593	⋯	1323	NED, S11	g0 > 21.5 mag
T15886	188.1520299	12.3491986	0.23	22.974	⋯	1349	NED, S11	g0 > 21.5 mag
S991	187.6937514	12.3382605	0.34	20.701	16.67	1004	S11	e > 0.3
S672	187.7280306	12.3606434	0.31	20.739	15.50	735	S11	e > 0.3
NGVS-J124002.08+105517.2	190.0086686	10.9214418	0.50	21.338	3.48	⋯	⋯	e > 0.3
NGVS-J122926.23+081658.8	187.3593098	8.2829991	0.05	21.373	9.06	465	MMT 14	$\langle {r}_{h}\rangle \lt 11\,$ pc
NGVS-J123009.17+074127.5	187.5381980	7.6909633	0.08	19.449	10.76	⋯	⋯	$\langle {r}_{h}\rangle \lt 11\,$ pc
NGVS-J123015.56+083445.0	187.5648407	8.5791729	0.07	20.822	10.33	−129	MMT 14	$\langle {r}_{h}\rangle \lt 11\,$ pc
H20718	187.5818069	12.1568298	0.03	20.989	10.76	876	MMT 09,S11	$\langle {r}_{h}\rangle \lt 11\,$ pc
M87UCD-31	187.7305441	12.4110907	0.02	20.860	10.09	1301	MMT 09	$\langle {r}_{h}\rangle \lt 11\,$ pc
M87UCD-14	187.7681413	13.1784860	0.12	20.200	10.83	1345	MMT 09,AAT 12	$\langle {r}_{h}\rangle \lt 11\,$ pc
NGVS-J122849.25+075919.4	187.2051905	7.9887156	0.03	21.179	13.37	⋯	⋯	$| {r}_{h,g}-{r}_{h,i}| \gt ({r}_{h,g}+{r}_{h,i})/2$
NGVS-J123004.35+073932.2	187.5181421	7.6589449	0.09	21.437	11.19	1043	MMT 14	$| {r}_{h,g}-{r}_{h,i}| \gt ({r}_{h,g}+{r}_{h,i})/2$
S8005	187.6925322	12.4064233	0.02	20.444	27.91	1883	S11	$| {r}_{h,g}-{r}_{h,i}| \gt ({r}_{h,g}+{r}_{h,i})/2$
S9053	187.7013369	12.4946708	0.16	21.313	30.25	829	S11,IMACS 16	$| {r}_{h,g}-{r}_{h,i}| \gt ({r}_{h,g}+{r}_{h,i})/2$
S686	187.7242079	12.4718872	0.05	20.499	16.31	817	S11	$| {r}_{h,g}-{r}_{h,i}| \gt ({r}_{h,g}+{r}_{h,i})/2$
S6003	187.7922587	12.2744282	0.08	21.277	14.19	1818	S11	$| {r}_{h,g}-{r}_{h,i}| \gt ({r}_{h,g}+{r}_{h,i})/2$
NGVS-J122806.14+065909.0	187.0255686	6.9858243	0.19	20.200	27.66	⋯	⋯	${(g-z)}_{0}\,\mathrm{versus}\,{\mu }_{g}\,$ diagram
NGVS-J123949.21+110135.3	189.9550398	11.0264758	0.03	21.080	12.73	⋯	⋯	${(g-z)}_{0}\,\mathrm{versus}\,{\mu }_{g}\,$ diagram
NGVS-J124216.65+114428.6	190.5693756	11.7412681	0.06	21.273	12.44	⋯	⋯	${(g-z)}_{0}\,\mathrm{versus}\,{\mu }_{g}\,$ diagram
NGVS-J124244.72+111240.5	190.6863239	11.2112384	0.12	20.491	32.90	⋯	⋯	${(g-z)}_{0}\,\mathrm{versus}\,{\mu }_{g}\,$ diagram
NGVS-J122708.94+074228.3	186.7872607	7.7078639	0.08	19.340	47.81	⋯	⋯	${(g-z)}_{0}\,\mathrm{versus}\,{(z-{K}_{\mathrm{UKIDSS}})}_{0}\,$ diagram
NGVS-J122828.60+070228.2	187.1191854	7.0411563	0.11	20.646	28.26	⋯	⋯	${(g-z)}_{0}\,\mathrm{versus}\,{(z-{K}_{\mathrm{UKIDSS}})}_{0}\,$ diagram
S887	187.7038900	12.3654400	⋯	21.190	⋯	1811	S11	Fail to detect
H30772	187.7419100	12.2672800	⋯	20.750	⋯	1225	NED, S11	Fail to detect

Note. (1) UCD name, (2) R.A., (3) decl., (4) ellipticity, (5) g-band magnitude, (6) half-light radius, (7) radial velocity, (8) the source of velocity measurement, and (9) the reason why this UCD is not included in this study.

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The upper two panels of Figure 10 show number density maps for our all UCDs sample in Virgo. Durrell et al. (2014) found that the spatial distribution of Virgo GCs is similar to that of its X-ray-emitting gas, so we compare the distribution of UCDs (color-coded number density map) and X-ray gas (contours) in panel (a) of Figure 10. Consistent with Durrell et al. (2014), we find that the densest concentrations of UCDs (i.e., the brightest regions in the map) are located in the regions that have the greatest amount of X-ray gas. This finding is also consistent with the observed correlation between number of UCDs and the X-ray gas mass of their host (${N}_{\mathrm{UCD}}$ versus ${M}_{\mathrm{gas}};$ see Figure 17 in Liu et al. 2015a).

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The number density map shown in panel (b) is the same as in panel (a), but overlaid with known substructures in the cluster (i.e., the colored circles). The locations and radii of the substructures are taken from Boselli et al. (2014). Most of the UCDs are concentrated in subcluster A (green), subcluster B (blue), and subcluster C (yellow; see also Liu et al. 2015a). There are far fewer UCDs in the other three substructures: the W' (cyan), W (purple), and M clouds (red). This may be due, in part, to the fact that these three substructures are located farther away from us (Mei et al. 2007; Cantiello et al. 2018), making it more difficult to identify UCDs (by size). At the same time, the reduced gas mass (see the contours in panel (a)) in these substructures are also likely to be a factor. This is especially true for the M cloud, which shows no significant amount of X-ray gas. Based on the ${N}_{\mathrm{UCD}}$–${M}_{\mathrm{gas}}$ scaling relation (Liu et al. 2015a) then, the absence of UCDs in this region would not be surprising. In addition, the edges of the NGVS footprint cut through the M and W clouds. This may be another reason why we do not detect many UCDs in these regions.

The lower two panels of Figure 10 show number density maps for our u*gizK UCDs sample. As noted above, and as can be seen in the plots, this sample is noticeably cleaner. We also point out that the number densities from the all UCDs sample are higher in the regions without UKIDSS K-band data (above the white dashed lines in panels (a) and (b)), indicating elevated contamination in this region. The u*gizK UCDs are mainly concentrated around a handful of luminous galaxies: e.g., M87, M49, M60, M59, M86, and M89 (black crosses). The galaxies with low densities of UCDs cannot be seen in this map as we smooth the distribution using a large kernel (∼12' ∼ 60 kpc).

Table 8 of Liu et al. (2015a) presents estimates of the number density of contaminants in the NGVS based on four control fields. The mean density for our u*giz-selection method is 2.25 deg⁻². As demonstrated in Section 3.3, our u*gizK-selection method should be much cleaner by comparison. Indeed, Liu et al. (2015a) estimated the contaminant number density using their ${u}^{* }{{giK}}_{\mathrm{VISTA}}$ selection method to be just 0.9 deg⁻² (the last row of their Table 8). The contours in panel (d) represent number densities of ${{\rm{\Sigma }}}_{\mathrm{UCD}}=5,8,15,30$ and $60\,{\deg }^{-2}$. We note that there are a few regions with ${{\rm{\Sigma }}}_{\mathrm{UCD}}\gt 5\,{\deg }^{-2}$ that fall outside of any known substructures. They may be intracluster UCDs or UCDs associated with low- or intermediate-mass galaxies (e.g., Fahrion et al. 2019). We intend to focus on these regions in future papers.

Our homogeneous sample provides us with an opportunity to carry out a study of the UCDLF. The left panel of Figure 11 shows histograms of z-band magnitudes for a variety of UCD samples, which are identified in the upper-left corner. The distribution for the all UCDs sample (blue, short-dashed histogram) has a higher peak value than all other UCD samples, which we suspect is due to contamination (especially at the faint end). Note that the truncation at ${z}_{0}\sim 21.0$ mag is the result of our magnitude cut at ${g}_{0}=21.5$ mag and is therefore artificial.

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For the other, smaller samples of UCDS, we find a peak at roughly ${z}_{0}\sim 19.75$ mag. Note that the spec UCDs sample (orange dotted line) may be biased because brighter UCDs are more amenable to spectroscopic follow-up. The u*gizK UCDs sample (green solid line) has higher completeness than the spec UCDs sample but is limited by the shallow UKIDSS K-band imaging, which may cause us to miss some objects at the faint end. The UCD sample from Liu et al. (2015a; black long-dashed line) is the best available based strictly on the ${u}^{* }{{giK}}_{s}$ selection method, where the K_s-band data reach to ∼24 mag. For comparison, we also show in Figure 11 the GCLF from the ACSVCS (cyan line), which exhibits the well-known turnover for this population (e.g., Jordán et al. 2007; Villegas et al. 2010). Despite the fact that three of our UCDLFs also exhibit turnovers, we cannot ensure that these features are authentic. It is quite probable that, depending on where we place our (subjective) size cut (set at r_h = 11 pc), the prominence and location of this peak would change.

The right panel of Figure 11 shows the distributions of stellar mass for UCDs and nuclei. Stellar masses have been determined using the relationships between stellar mass-to-light ratios and colors from Bell et al. (2003). We calculate four sets of stellar masses, based on the relations for $(u-g)$, $(u-i)$, $(u-z)$ and $(g-z)$ colors (see their Table 7), and use the mean value for each object in the figure. Other than the all UCDs sample, there appears to be a peak in the UCD stellar mass function at ${M}_{* }\sim {10}^{6.6}\,{M}_{\odot }$, roughly equivalent to that seen in the UCDLF. Again though, because of our selection criteria, we cannot be sure whether this is a genuine characteristic of the UCD population.

The magenta lines in both panels of Figure 11 show the luminosity and mass functions for the all nuclei sample that consists of 551 dE, N nuclei. The nuclei LF shows a clear turnover around ${z}_{0}\sim 20.5$ mag and ${M}_{* }\sim {10}^{6.2}\,{M}_{\odot }$, and covers a larger stellar mass range (${10}^{5.0}\lesssim {M}_{* }\lesssim {10}^{8.5}\,{M}_{\odot }$) than UCDs. Sánchez-Janssen et al. (2019) studied the mass function of nuclei in the Virgo core region and found a peak at ${M}_{* }\sim {10}^{6.08}\,{M}_{\odot }$, which is consistent with the result in this study.

It is well established that bimodal color distributions are a common feature of GC systems in massive elliptical galaxies (e.g., Gebhardt & Kissler-Patig 1999; Kundu & Whitmore 2001; Peng et al. 2006b). Interestingly, a bimodal color distribution has also been observed for the UCDs surrounding M87 (Liu et al. 2015a), making it the only galaxy in the Virgo cluster that shows significant UCD color bimodality.²⁸ With our new UCD sample, we can examine for the first time the color distribution for UCDs distributed over the entire Virgo cluster.

Figure 12 shows the color distribution for the ACSVCS GCs (the first row, magenta histogram), bright GCs (the second row, cyan histograms), u*gizK UCDs (the third row, green histograms), and bright nuclei (the fourth row, purple histogram). All objects are brighter than g₀ = 21.5 mag. Because we have only g and z data for the ACSVCS GCs, the first row shows only a ${(g-z)}_{0}$ distribution. By contrast, a total of six color indices—${({u}^{* }-g)}_{0}$, ${({u}^{* }-i)}_{0}$, ${({u}^{* }-z)}_{0}$, ${(g-i)}_{0}$, ${(g-z)}_{0}$ and ${(i-z)}_{0}$—are shown (from left to right) in the second, third, and fourth rows. The distributions of GCs, UCDs, and nuclei have red tails for all indices except ${(i-z)}_{0}$ for the nuclei. To quantify the bimodality of color distributions, we use Gaussian Mixture Modeling (GMM; Muratov & Gnedin 2010) and assume a homoscedastic distribution: i.e., two subpopulations having the same dispersions. As described by Muratov & Gnedin (2010), a dimensionless peak separation ratio D (see Equation A3 in their paper) should be larger than 2 for a bimodal distribution. We measure D for the color distribution in each panel of Figure 12. The D parameters for GCs and UCDs are larger than 2 while those for nuclei are smaller than 2. In addition, the unimodal distribution is rejected at a level better than 1% for bright GCs and better than 0.1% for ACSVCS GCs and u*gizK UCDs.

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The best-fit GMM models are shown in Figure 12 as well. For those distributions found to be bimodal, blue and red curves are used to represent the individual components (with vertical dashed lines marking their respective means), while the black curves represent their sums. Conversely, where unimodal distributions are favored, we show the best-fit Gaussians (black curves) and the corresponding means (vertical dashed lines).

In the case of a bimodal color distribution, GMM also yields the probability that a given object belongs to the blue or red component. We therefore calculate the fraction of objects belonging to the blue subpopulation, ${f}_{\mathrm{blue}}$. ${f}_{\mathrm{blue}}$, based on the ${(g-z)}_{0}$ color index, is 77% (±4%), 84% (±1%), and 89% (±3%) for ACSVCS GCs, bright GCs, and UCDs. Based on ACSVCS data, Peng et al. (2006b) concluded that the blue GC fraction for individual galaxies ranges from 85% to 40% and decreases with increasing host galaxy luminosity.

There are two main reasons why the blue fractions are different between ACSVCS and bright GCs. First, the blue fraction of bright GCs is calculated over the entire cluster that contains many more dwarf galaxies (which have higher ${f}_{\mathrm{blue}}$) than the ACSVCS galaxy sample. Second, as described in Jordán et al. (2005), almost all GCs in the Virgo cluster can be resolved in ACSVCS imaging, which enables a very clean GC selection (see Peng et al. 2006b; Jordán et al. 2009), while our bright GC sample is contaminated by many BGs when the K-band data are not available (see Table 1). Therefore, our bright GC sample contains more dwarf galaxies and is less pure than the ACSVCS GC sample, causing it to have a higher blue fraction. For nuclei, we can see from the last row of Figure 12 that the vast majority are blue with just a few having red colors. Because a unimodal distribution is preferred for this group, we are unable to calculate a blue fraction on the basis of GMM alone. However, considering that the blue and red components for GCs and UCDs cross at ${(g-z)}_{0}\sim 1.1$, we can split the nuclei distribution at this color to calculate their blue fraction. In so doing, we find ${f}_{\mathrm{blue}}\sim 95 \%$.

To summarize, for objects brighter than g₀ = 21.5, GMM fitting shows that GCs and UCDs exhibit bimodal color distributions while the nuclei follow a unimodal distribution with a small tail to red colors. Ordering these groups of compact stellar systems by ${f}_{\mathrm{blue}}$, from low to high, yields ACSVCS GCs < bright GCs ≲ UCDs < bright nuclei.

In order to select UCDs, we have measured half-light radii for all bright objects (${g}_{0}\lt 21.5$) in the NGVS footprint using KINGPHOT. The left panel of Figure 13 plots $\langle {r}_{h}\rangle$ versus ${(g-z)}_{0}$ for our all (blue open circles), u*gizK (green filled semicircles), and spec UCDs samples (orange filled semicircles), and spec GCs sample (cyan dots). It is worth noting that the majority of UCDs with very blue colors, ${(g-z)}_{0}\lesssim 0.7$, lack radial velocity measurements, a situation we aim to improve upon through dedicated spectroscopic follow-up. The right panel shows the distribution of half-light radii for both UCDs and GCs. The dotted horizontal line marks $\langle {r}_{h}\rangle =11$ pc, the size used to separate GCs from UCDs, while the dotted vertical line indicates the color, ${(g-z)}_{0}=1.1$, used to divide the UCDs into blue and red subpopulations (see Section 4.3).

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The mean r_h of UCDs is $\overline{{r}_{h}}=19.8$ pc with a standard deviation of ${\sigma }_{{r}_{h}}=6.8$ pc. For subpopulations, the mean r_h and standard deviations are $\overline{{r}_{h}}=20.0$ pc and ${\sigma }_{{r}_{h}}=6.8$ pc for the blue UCDs, and $\overline{{r}_{h}}=14.6$ pc and ${\sigma }_{{r}_{h}}=3.8$ pc for the red UCDs. The blue UCDs are larger and cover a wider range in half-light radius than red ones.

As discussed in Liu et al. (2015a), when comparing to HST-based values, we find that we overestimate the half-light radii of smaller objects (${r}_{h}\lesssim 11$ pc). Thus, we suspect that many diffuse GCs are included in our UCD sample. This may explain why we see such a high degree of similarity between the color distributions of our NGVS-based samples of GCs and UCDs.

At the time of writing, SMBHs have been detected in four Virgo UCDs. These objects (all of which were objectively identified by our selection function) are indicated by the large circles in the left panel of Figure 13). These are M60-UCD1 (Seth et al. 2014), M59cO (Ahn et al. 2017), VUCD3 (Ahn et al. 2017) and M59-UCD3 (Ahn et al. 2018). Interestingly, all four objects are quite red, with colors of ${(g-z)}_{0}\sim 1.35$. Based on the color–magnitude relation for UCDs, we know that the redder systems tend to be brighter. To date, no blue UCD is known to contain a SMBH, although we have many promising bright, blue UCD candidates in our sample. These are obvious targets for future spectroscopic searches for SMBHs.

As noted above, we find no significant color differences between our UCD and GC samples. However, some UCDs, by virtue of their extreme or unusual properties, have a special significance for understanding the origin of these systems and their relationship to "normal" GCs. In this section, we pause to consider these unique UCDs.

4.5.1. The Brightest UCDs

We begin with the subset of UCDs that are known to contain an SMBH. The first such detection was made in M60-UCD1, where Seth et al. (2014) found a SMBH of mass $\sim 2.1\times {10}^{7}\,{M}_{\odot }$. The inferred mass fraction (15%) suggests that the progenitor of M60-UCD1 was a dwarf galaxy. Soon afterwards, an even more massive system in Virgo, M59-UCD3, was coreported by Liu et al. (2015b) and Sandoval et al. (2015). Later, Ahn et al. (2018) showed that this UCD also contains an SMBH of mass $4.2\times {10}^{6}\,{M}_{\odot }$. SMBHs have also been found in two more Virgo UCDs, M59cO and VUCD3 (Ahn et al. 2017). The discovery that UCDs can harbor SMBHs is crucial evidence of a dE, N origin for at least some UCDs.

One property that unifies the four UCDs with known SMBHs is their luminosity: they are all very bright. Based on this, we have carried out a search for bright UCDs using the NGVS short exposures. Figure 14 presents g-band cutouts for the nine brightest UCD candidates in our sample, which shows that M59-UCD3, M60-UCD1, and M59cO are the brightest three UCDs in all of Virgo, and the only three brighter than ${g}_{0}=18$ mag. The next brightest UCD, NGVS-UCD 761, with g₀ = 18.74 and ${(g-z)}_{0}=1.11$, represents a new detection and is a tantalizing target for future SMBH searches.

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Figure 15 shows the locations of the 23 UCDs in Virgo that are brighter than g₀ = 19.5 mag. The red stars represent the three brightest systems. We note that the third- (M59cO) and fourth-brightest UCDs (NGVS-UCD 761) are separated by a significant magnitude gap (${\rm{\Delta }}{g}_{0}=0.84$ mag). The fourth- (g₀ = 18.74 mag) to ninth-ranked (g₀ = 18.98 mag) UCDs are shown as black squares in Figure 15, while blue triangles represent UCDs in the range of $19.0\lt {g}_{0}\lt 19.5$ mag.

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Interestingly, all 23 UCDs with ${g}_{0}\lt 19.5$ mag are located in Virgo's three main subclusters (black dotted circles). About half of these objects are in Cluster A (centered on M87)—4 with $18.5\lt {g}_{0}\lt 19.0$ and 11 $19.0\lt {g}_{0}\lt 19.5$. Curiously, the brightest three UCDs are all located in Cluster C, a much smaller subcluster centered on M60. On the contrary, only one bright UCD (ranked 20th; g₀ = 19.39) is found in Cluster B (centered on M49). It is puzzling why Cluster C is so special in this regard. Perhaps the fact that this substructure contains two massive galaxies in close proximity to one another makes it a conducive environment for forming bright UCDs (e.g., through tidal stripping).

4.5.2. The Largest UCDs

Figure 16 shows g-band cutouts for the nine largest UCDs in our sample. The largest, NGVS-UCD 769 ($\langle {r}_{h}\rangle =58$ pc.²⁹ ), also happens to be the brightest (g₀ = 19.11 mag) and reddest one (${(g-z)}_{0}=1.27$) of this subsample; the remaining eight all have ${(g-z)}_{0}\lesssim 1.1$. There is, interestingly, no overlap between the nine brightest and nine largest UCDs in our sample. Only two of the largest UCDs currently have measured radial velocities.

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We note that three UCDs in Figure 16 (NGVS-UCD 549, 506 and 757) have bright neighbors. Recall that when we measure the half-light radius of an object, KINGPHOT fits the image using PSF-convolved King models within a fitting radius ${r}_{\mathrm{fit}}$ (15 pixels here). In Figure 3, we compare r_h measurements based on different fitting radii, ${r}_{\mathrm{fit}}=7$ or 15 pixels. The measurements are fully consistent even for the UCDs surrounding the three most luminous galaxies in the Virgo cluster (M87, M49, and M60). We conclude then that light from neighboring galaxies does not seriously affect our r_h measurements. In addition, we test our measurement procedure by injecting artificial UCDs across a range of environments covered by the NGVS footprint. We find that the KINGPHOT measurements are quite robust unless the UCD falls very close to a bright point source, like the blended objects shown in Figure 8.

Using the ACSVCS data, Jordán et al. (2005) found that the vast majority of GCs in the Virgo cluster are smaller than r_h = 10 pc, with their average size being $\langle {r}_{h}\rangle =2.70\,\pm 0.35$ pc. In addition, they found no correlation between half-light radius and luminosity for bright GCs (z ≤ 22.9 mag). Meanwhile, using ACSVCS data as well, Côté et al. (2006) found that nuclei follow a size–magnitude relation, with more luminous nuclei having larger half-light radii. A similar result has been found for UCDs, although not as tight (i.e., more luminous UCDs are usually larger; Côté et al. 2006; Penny et al. 2014). Dabringhausen et al. (2012) have also reported that UCDs follow a size–magnitude relation, while GCs do not.

It is worth pointing out that several GCs in our MW are also larger than r_h = 10 pc (van den Bergh & Mackey 2004). Such extended star clusters (ESCs) have also been found around other nearby galaxies, e.g., M31 (Huxor et al. 2005, 2014), Scl-dE1 (Da Costa et al. 2009), M51 (Hwang & Lee 2008), and NGC 6822 (Hwang et al. 2011). These ESCs mainly populate the faint end of the GCLF (Peng et al. 2006a; Liu et al. 2016), with those around the MW and M31 being fainter than ${M}_{V}=-7$ (van den Bergh & Mackey 2004; Hwang et al. 2011). Conversely, the typical UCD is brighter than ESCs by two magnitudes or more ($-13\lt {M}_{V}\lt -9$ mag; Willman & Strader 2012), and by more still for the largest UCDs. Therefore, it is quite likely that the largest UCDs in Virgo originate under different circumstances than "normal" GCs.

4.5.3. UCDs with Asymmetric/Tidal Features

If tidal stripping of dE, Ns produce UCDs, then we should be able to find some objects undergoing such a transformation (i.e., UCDs that exhibit asymmetries and/or tidal features). Of course, this exercise may be complicated by short transformation timescales and/or potentially low surface brightnesses of any stripped material (Pfeffer & Baumgardt 2013). Nonetheless, a few UCDs with asymmetric or tidal features have indeed been found in recent years through deep surveys (e.g., Jennings et al. 2015; Mihos et al. 2015; Voggel et al. 2016; Schweizer et al. 2018). Another potential complication surrounds the interpretation of such features—for instance, several GCs around the MW are known to possess prominent tidal structures, such as NGC 6715 (Ibata et al. 1994; Bellazzini et al. 2008), Palomar 5 (Odenkirchen et al. 2001), and ω Cen (Ibata et al. 2019). However, most of these objects have been flagged by other studies as unusual members of the MW GC system (Johnson et al. 2015; Milone et al. 2017; Gratton et al. 2019), such that they are commonly held as remnants of nucleated satellites that were disrupted by the MW's tidal field (e.g., Bekki & Freeman 2003; Majewski et al. 2003; Küpper et al. 2015).

The high sensitivity of the NGVS images (μ_g ≲ 29 mag arcsec⁻²; Ferrarese et al. 2012) allows us to search for such features within our UCD sample. Our search indeed results in a handful of UCDs with apparent asymmetries. If confirmed as being tidal in origin, these features would offer direct evidence that at least some UCDs are the descendants of nucleated galaxies.

Figure 17 shows one candidate tidal structure associated with NGVS-UCD 330. This UCD (v_r = 1628 km s⁻¹) is a satellite of VCC 1250 (v_r = 1963 km s⁻¹). It was previously identified as VCC 1250_1 by Haşegan et al. (2005), who also noted that it appeared to be embedded in a diffuse envelope. Both the NGVS and HST images in Figure 17 reveal an asymmetric structure emanating from this object and pointing toward VCC 1250. Thus, NGVS-UCD 330 may be an example of a UCD caught in the act of losing what remains of its diffuse envelope. The putative tidal stream associated with this UCD is unusual in that we only detect one arm. However, we cannot rule out the second arm as being hidden by projection or surface brightness effects. Follow-up spectroscopy of this object would help us determine its origins.

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4.5.4. UCDs with Envelopes

Using HST imaging, Haşegan et al. (2005) found three UCDs in Virgo that are embedded within shallow envelopes—evidence that they may be related to the nuclei of dE, Ns with extremely low surface brightness and/or compact stellar halos. There are 22 UCD candidates in our sample that also have HST imaging from the ACSVCS (Côté et al. 2004). We have checked these HST images to look for envelopes. Some systems, like NGVS-UCD 298 (top panel of Figure 18), show no evidence of envelopes in either the ACSVCS or NGVS images. Others, like NGVS-UCD414 (middle panel of Figure 18), have small envelopes that are visible only in the ACSVCS images thanks to its exceptional image quality. The remainder, like NGVS-UCD 190 (bottom panel of Figure 18), have large (yet still diffuse) envelopes that can be seen in both ACSVCS and NGVS images. In all, we find about half of the 22 UCD candidates with HST imaging are embedded in diffuse envelopes that are visible in space-based images.

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The above comparison demonstrates that we can detect envelopes around UCDs in the NGVS imaging, provided they are large enough. Our search reveals 41 instances of such features, and these cases have been flagged accordingly in Table 4. Most of these UCDs are found around M87 and M60/M59, with just a couple located in subcluster B. Note that, in this section, we have focused on UCDs with envelopes that are obvious based on visual inspection, which is admittedly subjective. Because this sample is not suitable for statistical analysis, we will postpone the detailed investigation of the properties of UCD envelopes to future work (K. Wang et al. 2020, in preparation). In the next section though we will introduce a parameter, Δ_env, to examine basic properties of the envelope.

Figure 19 presents NGVS g-band images for four UCDs (upper four panels) and HST F475W (∼SDSS g-band) images for two UCDs (lower two panels) that are confirmed radial velocity members of the Virgo cluster and possess clear stellar envelopes. We see in both sets of imaging that these envelopes have near-zero ellipticity. From a morphological perspective, UCDs with diffuse envelopes look quite similar to dE, Ns, adding weight to the argument of an evolutionary connection between the two classes. Moreover, NGVS-UCD 719 (lower-left panel of Figure 19, also known as M59cO; Chilingarian & Mamon 2008) and NGVS-UCD 753 (lower-right panel of Figure 19, also known as M60-UCD1; Strader et al. 2013) are two of the four UCDs known to possess central SMBHs (Seth et al. 2014; Ahn et al. 2017). We do not, however, observe any tidal features around them (e.g., Küpper et al. 2010; Jennings et al. 2015; Schweizer et al. 2018).

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As with tidal features, the interpretation of envelopes around Virgo UCDs is also potentially complicated by the fact that similar structures have recently been detected around the MW GCs NGC 7089 (Kuzma et al. 2016) and NGC 1851 (Kuzma et al. 2018). Once again though, these GCs are unusual in their chemistries (e.g., possessing broad dispersions in their abundances of iron and neutron-capture elements; Johnson et al. 2015; Milone et al. 2017), suggesting that they are actually the remnant nuclei of disrupted nucleated galaxies.