CATALOGS OF COMPACT GROUPS OF GALAXIES FROM THE ENHANCED SDSS DR12

We use the FoF algorithm of Barton et al. (1996) to identify compact groups in the spectroscopic sample. For each galaxy, the FoF finds neighboring galaxies within a fixed projected physical spatial distance (${\rm{\Delta }}D$) and rest-frame line-of-sight velocity linking length (${\rm{\Delta }}V$). The linking lengths are redshift and local density independent in contrast with some other approaches that use variable linking lengths (i.e., Huchra & Geller 1982; Tago et al. 2010; Robotham et al. 2011; Tempel et al. 2014). We use a fixed linking length here to identify systems where galaxies are separated by approximately their physical size regardless of redshift.

We bundle linked galaxies into a single galaxy system (e.g., Turner & Gott 1976; Huchra & Geller 1982; Barton et al. 1996; Tago et al. 2010; Robotham et al. 2011; Tempel et al. 2014). By construction, the resultant compact group candidates we identify have a projected physical size that is essentially redshift independent (see Section 4.1).

We test various linking lengths for the FoF. We start from a projected linking length of ${\rm{\Delta }}D\leqslant 50\,{h}^{-1}\,\mathrm{kpc}$ and a radial linking length of $| {\rm{\Delta }}V| =1000\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ following Barton et al. (1996) who identified compact groups from the CfA2 and SSRS redshift surveys. Barton et al. (1996) used these linking lengths because they approximately matched the median separation between Hickson compact group galaxies. Their compact groups thus have physical properties similar to the Hickson compact groups (Barton et al. 1996; Walker et al. 2016).

The linking lengths of ${\rm{\Delta }}D\leqslant 50\,{h}^{-1}\,\mathrm{kpc}$ and $| {\rm{\Delta }}V| =1000\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ we choose identify 42 of the 57 Hickson compact groups. The groups we miss would require a larger linking length of ${\rm{\Delta }}D\leqslant 125\,{h}^{-1}\,\mathrm{kpc}$. In general, the projected linking length of ${\rm{\Delta }}D=50\,{h}^{-1}\,\mathrm{kpc}$ and the rest-frame line-of-sight velocity of $| {\rm{\Delta }}V| \leqslant 1000\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (Barton et al. 1996) actually identify compact groups with physical sizes and galaxy number densities similar to the Hickson compact groups (see Section 4.1). Woods et al. (2010) demonstrate that these linking lengths minimize interlopers with discordant redshifts while recovering systems similar to the original Hickson compact groups. These linking lengths also have the advantage that they are often used to identify close pairs (Barton et al. 2000; Lin et al. 2004). Thus, our catalog can be combined with catalogs of close pairs in the literature and future analyses of these compact groups can be compared to previous work on pairs.

We also apply the FoF algorithm with an even tighter rest-frame line-of-sight linking length $| {\rm{\Delta }}V| \leqslant 500\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and indicate these groups in Table 1. Previous studies of tight galaxy pairs showed that pairs with this tighter separation are more likely to be bound (Barton et al. 2000; Patton et al. 2000; Hawkins et al. 2003; De Propris et al. 2007). The subset of compact groups with this tighter radial linking length can be used for comparison with these previous galaxy pair samples.

Table 1.  Catalog of MLCGs

ID	R.A.	Decl.	nmem	za	Rgra	$\mathrm{log}\rho$ a	σa	NCb	Subsetc	V1CG	V2CG
	(J2000)	(J2000)			(${h}^{-1}$ kpc)	(h3 Mpc−3)	$(\mathrm{km}\,{{\rm{s}}}^{-1})$			subsample	subsample
MLCG0001	251.559814	31.722052	3	0.0534 ± 0.0005	30.1 ± 4.3	4.42 ± 0.29	287 ± 70	1	N	...	...
MLCG0002	140.182175	33.686241	4	0.0229 ± 0.0003	36.8 ± 2.9	4.28 ± 0.13	170 ± 31	7	S	...	...
MLCG0003	146.524597	34.623241	3	0.1318 ± 0.0010	20.7 ± 1.4	4.91 ± 0.10	628 ± 164	0	N	...	...
MLCG0004	154.741531	37.298065	3	0.0480 ± 0.0003	32.9 ± 5.5	4.30 ± 0.42	210 ± 37	1	S	V1CG003	...
MLCG0005	158.222275	12.086633	3	0.0330 ± 0.0004	12.3 ± 3.2	5.58 ± 0.72	242 ± 71	4	S	V1CG004	...

Notes.

^aThe error is the $1\sigma$ deviation derived from 1000 time bootstrap resamplings. ^bNumber of neighboring galaxies in a comoving cylinder of ${\rm{\Delta }}R\lt 700\,{h}^{-1}\,\mathrm{kpc}$ and rest frame $| {\rm{\Delta }}V| \lt 1000\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$. ^cDesignations for groups that contain sub-groups identified with a tighter radial linking length of $| {\rm{\Delta }}V| \lt 500\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$. "S" indicates a group containing sub-groups; "N" designates a group with no tighter subgroup.

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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Hickson and others (e.g., Iovino et al. 2003; Lee et al. 2004; de Carvalho et al. 2005; McConnachie et al. 2009; Díaz-Giménez et al. 2012) apply additional criteria to define compact groups. We apply the similar population and compactness criteria applied by McConnachie et al. (2009). These criteria are a modified version of the original Hickson (1982) approach.

• 1.  
  The population limit requires $\geqslant 2$ additional members within ${\rm{\Delta }}r\lt 3\,{\rm{mag}}$ of the brightest group member. Here r is the SDSS extinction- and k-corrected r-band model magnitude. This criterion eliminates groups that contain one dominant galaxy surrounded by much fainter satellite galaxies.
• 2.  
  The compactness criterion, μ_r < 26 mag arcsec⁻², (μ_r is the r-band surface brightness averaged over the group radius) excludes groups containing only low-luminosity, low surface brightness galaxies.

In the Appendix, we briefly discuss the typical groups that we eliminate with these additional criteria and comment on possible avenues that could be explored further by including these systems. We do not apply an isolation criterion because, as we discuss below, this criterion artificially selects against nearby groups. The isolation criterion originally applied by Hickson (1982) and others requires that there be no other galaxies within an annulus of ${R}_{\mathrm{gr}}\lt {R}_{\mathrm{nogal}}\lt 3{R}_{\mathrm{gr}}$. Here R_gr is the radius of the smallest circle encompassing all group members and R_nogal is the distance between the nearest non-member galaxy with ${\rm{\Delta }}r\lt 3\,{\rm{mag}}$ and the group center. The catalogs of Barton et al. (1996) and McConnachie et al. (2009) apply a modified isolation criterion where the limiting apparent magnitude for objects in the exclusion annulus is the survey limit rather than within ${\rm{\Delta }}r\lt 3\,{\rm{mag}}$ of the brightest group member.

We identify groups consisting of at least three galaxies. Hickson (1982) originally defined compact groups with at least four member galaxies, and some previous compact group surveys use his definition (McConnachie et al. 2009; Mendel et al. 2011; Díaz-Giménez et al. 2012). However, subsequent spectroscopic observations show that many of the compact group candidates selected photometrically contain only three member galaxies with accordant redshifts (Hickson et al. 1992; Pompei & Iovino 2012; Sohn et al. 2015).

Most previous compact group catalogs have been extracted from magnitude-limited surveys (e.g., Barton et al. 1996; Iovino et al. 2003; McConnachie et al. 2009). We also construct a sample from the SDSS DR12 magnitude-limited redshift survey to obtain the largest possible sample of candidate compact groups (MLCG hereafter). In addition, we define two volume-limited samples of compact groups to explore the selection biases inherent in the magnitude-limited catalog. The two volume-limited samples include (Figure 1) galaxies with ${M}_{r}\lt -19.0$ and 0.01 < z < 0.0741 (V1) and galaxies with M_r < −20.0 and 0.01 < z < 0.1154 (V2). To construct volume-limited compact group catalogs, we apply the FoF algorithm to the two volume-limited samples independently. Table 2 lists the number of groups in each catalog and specifies the limiting survey parameters.

Table 2.  The Compact Group Samples

Sample	Magnitude Limit	z Range	${N}_{{\rm{sample}}}$ a	$N\geqslant 3$ CGs	$N\geqslant 4$ CGs	N = 3 CGs
MLCGs	$17.77\,({m}_{r})$	[0.01, 0.20]	654066	1588	312	1276
V1CGs	$-19.0\,({M}_{r})$	[0.01, 0.0741]	149573	670	122	548
V2CGs	$-20.0\,({M}_{r})$	[0.01, 0.1154]	210834	297	36	261

Note.

^aNumber of galaxies in each sample.

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We compare the physical properties of compact group candidates in the MLCG with previous catalogs that are also selected from magnitude-limited samples (e.g., McConnachie et al. 2009; Sohn et al. 2015). We examine some of the selection biases in the MLCG by comparing it with the two volume-limited subsets of the catalog, V1CG and V2CG (Section 6).

Fiber-positioning constraints in the SDSS introduce a systematic undersampling of regions that are dense on the sky (Strauss et al. 2002; Park & Hwang 2009; Shen et al. 2016). This undersampling leads to an incomplete catalog of compact group candidates just as it leads to an incomplete sample of close pairs. Shen et al. (2016) considered the impact of the SDSS DR6 incompleteness on samples of close pairs with separations $\leqslant 100\,{h}_{70}^{-1}\,\mathrm{kpc}$. They conclude that the fraction of missing pairs increases steeply with redshift for z > 0.09. Our volume-limited compact group candidate samples (Section 3.2.2) provide a measure of the bias introduced by the SDSS incompleteness. In spite of the SDSS incompleteness, the MLCG serves as a finding list, albeit incomplete, of candidate compact systems.

3.2.1. The MLCG

The MLCG contains 1588 compact groups: 312 compact groups contain $N\geqslant 4$ members, and 1276 group candidates contain N = 3 members. There are more N = 3 compact groups than $N\geqslant 4$ compact groups at all redshifts. Figure 2 shows the distribution of the number of members in the MLCG systems. Table 1 lists the MLCG compact group candidates including ID, R.A., decl., the number of members, group redshift, group size, galaxy number density, and rest-frame line-of-sight velocity dispersion. We also note whether or not the group contains a tighter compact group satisfying the rest-frame line-of-sight linking length $| {\rm{\Delta }}V| \leqslant 500\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$, V1CGs, and V2CGs. Table 3 lists the 5178 member galaxies contained in the compact groups of Table 1. We include the Group ID, Galaxy ID, R.A., decl., morphology, r-band extinction- and k-corrected model magnitude, u−r color, stellar mass, redshift, and its source.

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Table 3.  Catalog of MLCG Members

Group ID	Galaxy IDa	R.A.	Decl.	Morph.b	rc	u − rc	z	$\mathrm{log}({M}_{\mathrm{stellar}}/{M}_{\odot })$	z Sourced
MLCG0001	1237661387083284633	251.569153	31.726006	1	15.02	2.82	0.0541 ± 0.00002	${10.761}_{0.068}^{0.116}$	SDSS
MLCG0001	1237661387083284634	251.560486	31.725866	2	15.82	2.78	0.0522 ± 0.00002	${10.403}_{0.181}^{0.239}$	SDSS
MLCG0001	1237661387083284893	251.549835	31.714281	1	17.47	2.58	0.0538 ± 0.00003	${9.568}_{0.136}^{0.249}$	SDSS
MLCG0002	1237661383844036794	140.154343	33.706100	1	16.62	2.10	0.0224 ± 0.00002	${9.145}_{0.086}^{0.152}$	SDSS
MLCG0002	1237661383844102154	140.191086	33.704514	1	14.73	3.79	0.0231 ± 0.00001	${10.233}_{0.063}^{0.129}$	SDSS
MLCG0002	1237661383844102157	140.200195	33.679672	1	16.65	2.45	0.0224 ± 0.00001	${9.016}_{0.109}^{0.256}$	SDSS
MLCG0002	1237661383844037025	140.183090	33.654678	2	17.73	1.73	0.0236 ± 0.00001	${8.416}_{0.115}^{0.236}$	SDSS

Notes.

^aSDSS DR12 object ID. ^bGalaxy morphology. 1 indicates early types and 2 indicates late types. ^cThe SDSS extinction- and k-corrected model magnitudes. ^dSource of the galaxy redshift.

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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We also examine the morphological composition of the compact groups (Table 4). The fraction of early-type galaxies in the MLCG is 64.0 ± 0.01%, exceeding the fraction in the Hickson compact groups (i.e., 51 ± 2%, Hickson et al. 1988). The early-type fraction for $N\geqslant 4$ compact groups (69.8 ± 0.01%) exceeds the fraction for N = 3 compact groups (62.0 ± 0.01%). The error in the fraction of early-type galaxies is the $1\sigma$ deviation from 1000 bootstrap resamplings.

Table 4.  Morphological Composition

Catalog	CG Type	Ngalaxy	Early Types	Late Types
MLCGs	Total	5178	3316 (64.0 ± 0.01%)	1862 (36.0 ± 0.01%)
	$N\geqslant 4$	1350	943 (69.8 ± 0.01%)	407 (30.2 ± 0.03%)
	N = 3	3828	2373 (62.0 ± 0.01%)	1455 (38.0 ± 0.01%)
V1CGs	Total	2175	1493 (68.6 ± 0.01%)	682 (31.4 ± 0.01%)
	$N\geqslant 4$	531	405 (76.3 ± 0.02%)	126 (23.7 ± 0.02%)
	N = 3	1644	1088 (66.2 ± 0.01%)	556 (33.8 ± 0.01%)
V2CGs	Total	930	704 (75.7 ± 0.01%)	226 (24.3 ± 0.01%)
	$N\geqslant 4$	147	127 (86.4 ± 0.03%)	20 (13.6 ± 0.03%)
	N = 3	783	577 (73.7 ± 0.02%)	206 (26.3 ± 0.02%)

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Figure 3 shows the velocity dispersion of the MLCG compact groups as a function of redshift in the range 0.01 < z < 0.19. We calculate the rest-frame line-of-sight velocity dispersion of each compact groups, σ_CG, from Equation (1) of Danese et al. (1980). As expected, the average velocity dispersion of $N\geqslant 4$ compact group is generally larger than for N = 3 compact groups.

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There are 256 compact groups with very large velocity dispersion ${\sigma }_{\mathrm{CG}}\geqslant 400\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$, overlapping the distribution for galaxy clusters (∼400–1300 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$, Rines et al. 2013). Compact group candidates with large σ_CG also appear in other catalogs (e.g., Barton et al. 1996; Pompei & Iovino 2012; Sohn et al. 2015). To examine the possibility that these higher velocity dispersion groups are merely superpositions along the line-of-sight, we compare the velocity dispersion distribution of the MLCG systems with the distribution for a set of ∼3000 randomly selected triplets and quadruplets in the same redshift and apparent magnitude range. To construct these random superpositions, we first pick a galaxy at a randomly chosen MLCG redshift and then randomly select two or three other galaxies within $| {\rm{\Delta }}V| \leqslant 1000\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ without attention to the projected spatial separation. The velocity dispersion distribution of these random samples is broad with $40\,\,\mathrm{km}\,{{\rm{s}}}^{-1}\lt {\sigma }_{\mathrm{los}}\lt 2300\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ with a median value of ${\sigma }_{\mathrm{los}}\sim 604\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$, a factor of three larger than for the MLCG objects. Figure 4 shows the probability distribution of the MLCG velocity dispersions (red) along with the distributions for the fictitious groups randomly selected from the survey redshift distribution. The distribution for the fictitious distribution (black) is appropriately weighted for the N = 3 and $N\geqslant 4$ samples. Both the Kolmogorov–Shmirnov and the Anderson–Darling k-sample tests reject the hypothesis that these distributions are derived from the same parent distribution (p = 0). The overlap of the two distributions suggest that MLCG systems with ${\sigma }_{\mathrm{CG}}\geqslant 500\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ may often contain superpositions. Furthermore, we can estimate an upper limit on the fraction of MLCG systems with ${\sigma }_{\mathrm{CG}}\lesssim 400\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ that may be contaminated by interlopers by computing the integral of the product of the distributions in the region of overlap. The limit is about 18%. Obviously the probability that a candidate compact group includes a superposition increases as the velocity dispersion increases.

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Figure 5 shows the total observed stellar masses of the compact groups in the MLCG as a function of redshift. The stellar masses range from $9.2\times {10}^{8}\,{M}_{\odot }\lt {M}_{\mathrm{stellar}}\lt 6.9\times {10}^{11}\,{M}_{\odot }$, similar to compact groups in the SDSS DR6 (Coenda et al. 2015). The median observed total stellar mass of the MLCG systems increases as the group redshift increases. This dependence results from the nature of the parent magnitude-limited sample.

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3.2.2. Volume-limited Subsamples of the MLCG

Volume-limited subsamples have the advantage that the physical properties of the candidate systems should be the same throughout the volume. Each volume-limited sample also contains systems with a narrow range of total stellar mass. The two volume-limited samples we select highlight compact systems with stellar masses in the ranges: $6.1\times {10}^{9}\,{M}_{\odot }\,\lt {M}_{\mathrm{MLCG}}\lt 6.9\times {10}^{11}\,{M}_{\odot }$ (V1CG) and $6.5\times {10}^{9}\,{M}_{\odot }\lt {M}_{\mathrm{MLCG}}\lt 5.2\times {10}^{11}\,{M}_{\odot }$ (V2CG).

The sample V1CG contains 670 groups in the redshift range 0.01 < z < 0.075 (Table 5). These groups are similar to the median groups in the MLCG for the redshift range 0.06 < z < 0.08. In contrast with the MLCG systems (red points in Figure 5), the median stellar mass for the V1CG groups is essentially constant throughout the sample redshift range. In Table 1 we indicate the MLCG groups that are also contained in the V1CG.

Table 5.  Catalog of V1CGs

IDa	R.A.	Decl.	nmem	zb	Rgrb	$\mathrm{log}\rho$ b	σb	NCc
	(J2000)	(J2000)			(${h}^{-1}$ kpc)	(h3 Mpc−3)	($\,\mathrm{km}\,{{\rm{s}}}^{-1}$)
V1CG001	198.227173	1.012775	3	0.0723 ± 0.0008	37.8 ± 5.4	4.12 ± 0.32	482 ± 116	8
V1CG002	139.935760	33.744308	3	0.0202 ± 0.0012	13.0 ± 1.5	5.52 ± 0.19	866 ± 207	2
V1CG003	154.741531	37.298065	3	0.0480 ± 0.0003	32.9 ± 5.5	4.30 ± 0.41	210 ± 37	1
V1CG004	158.222275	12.086633	3	0.0330 ± 0.0004	12.3 ± 3.0	5.58 ± 0.68	242 ± 68	5
V1CG005	127.709404	28.573534	3	0.0657 ± 0.0000	31.2 ± 3.7	4.37 ± 0.25	26 ± 4	1

Notes.

^aMember galaxies are contained in the MLCG galaxy catalog (Table 3). ^bThe error is the $1\sigma$ deviation derived from 1000-times bootstrap resamplings. ^cThe number of neighboring galaxies in the comoving cylinder.

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V2CG contains 297 groups in the redshift range 0.01 < z < 0.116 with larger total stellar masses (Table 6). For z ≲ 0.02 the median total stellar mass drops because the survey volume is too small to contain many of the most massive objects. For $z\geqslant 0.02$, the median total stellar mass of the systems is approximately constant throughout the redshift range. The median matches the median for the MLCG for redshifts greater than z > 0.09. The V2CG systems are a subset of both the V1CG systems and the MLCG systems. Table 1 indicates group membership in these subsamples.

Table 6.  Catalog of V2CGs

IDa	R.A.	Decl.	nmem	zb	Rgrb	$\mathrm{log}\rho$ b	σb	NCc
	(J2000)	(J2000)			(${h}^{-1}$ kpc)	(h3 Mpc−3)	($\mathrm{km}\,{\rm{s}}-1$)
V2CG001	154.930054	37.472149	3	0.0933 ± 0.0002	35.7 ± 1.8	4.20 ± 0.09	144 ± 35	1
V2CG002	142.154663	36.477848	3	0.0862 ± 0.0003	35.8 ± 4.9	4.19 ± 0.36	183 ± 42	0
V2CG003	206.682205	45.697647	4	0.0648 ± 0.0002	34.6 ± 2.9	4.36 ± 0.13	128 ± 30	8
V2CG004	210.859863	41.869808	3	0.1130 ± 0.0001	40.8 ± 4.5	4.02 ± 0.22	73 ± 17	0
V2CG005	179.164658	11.389394	3	0.0682 ± 0.0005	33.2 ± 5.2	4.29 ± 0.33	357 ± 113	5

Notes.

^aMember galaxies are contained in the MLCG galaxy catalog (Table 3). ^bThe error is the $1\sigma$ deviation derived from 1000 time bootstrap resamplings. ^cThe number of neighboring galaxies in the comoving cylinder.

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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In Section 6 we use the V1CG and V2CG subsets of the MLCG to examine the properties of compact group candidates of the same stellar mass as a function of redshift. We also discuss the use of these samples as a basis for discussing the impact of the SDSS fiber-positioning constraints on the identification of compact group candidates.

The SDSS DR6 compact group candidate sample of McConnachie et al. (2009) is the largest catalog previously available; it includes 2297 compact group candidates drawn from a magnitude-limited sample with $14.5\leqslant r\leqslant 18.0$ (catalog A) and 74,791 compact group candidates from a magnitude-limited sample with $14.5\leqslant r\leqslant 21.0$ (catalog B). McConnachie et al. (2009) identified these compact group candidates by applying all of Hickson's criteria to the SDSS DR6 photometric galaxy sample.

Because the primary identification of the McConnachie et al. (2009) groups is photometric, the interloper fraction is substantial. By measuring additional redshifts, Sohn et al. (2015) estimate that the fraction is greater than 40%. Mendel et al. (2011) pruned the McConnachie et al. (2009) catalog by using photometric redshifts. However, the uncertainty in photometric redshifts (median $\sim 2800\,\mathrm{km}\,{{\rm{s}}}^{-1}$) is large compared with the typical velocity separation among candidate group member galaxies. In spite of these limitations, the McConnachie et al. (2009) SDSS DR6 compact group candidate sample provides a basis for comparison with the MLCG. The comparison tests the impact of different group selection methods.

We match the MLCG compact groups with group candidates in catalogs A and B of McConnachie et al. (2009) based on angular separation. We count the number of MLCG systems matched (D_sep < R_gr) with group candidates in either catalog, where D_sep is the angular separation between the MLCG system and a McConnachie et al. (2009) group candidate, and R_gr is the angular radius of the MLCG. Only 242 (15%) of the MLCG systems overlap with compact group candidates identified by McConnachie et al. (2009). This low matching rate results primarily from (1) the MLCG inclusion of galaxies with r < 14.5 and from (2) differences in the group identification algorithm.

We next examine the reasons that individual MLCG systems are missing from the McConnachie et al. (2009) catalog in more detail. First, there are 384 (24%) groups in the MLCG that contain bright (r < 14.5) member galaxies excluded from the input galaxy catalog. Most of these groups are located at z < 0.05 where McConnachie et al. (2009) identified only a few compact group candidates (Sohn et al. 2015). Second, 1228 (77%) MLCG systems do not satisfy the isolation criterion originally applied by Hickson (1982) and followed by McConnachie et al. (2009). These groups have one or more non-member galaxies (${\rm{\Delta }}r\lt 3$ mag) within the isolation annulus (${R}_{\mathrm{gr}}\lt {R}_{\mathrm{GCD}}\lt 3{R}_{\mathrm{gr}}$), where R_GCD is the groupcentric distance and R_gr is the projected group radius (see Section 5.1 for further discussion). Third, 311 (20%) triplets in the MLCG satisfy all of the McConnachie et al. (2009) group candidate selection criteria except that there are only three members with accordant redshifts. The total number of compact groups that violate each of the selection criteria of McConnachie et al. (2009) exceeds the total number of MLCG systems because some MLCG groups violate more than one criterion.

Figure 6 shows examples of MLCG systems absent from previous catalogs. These groups either contain bright members with r < 14.5 or they violate the isolation criterion. The member galaxies show active interacting features, indicating that they are physically bound systems rather than superpositions of galaxies along the line of sight. These examples underscore the impact of deriving a compact group catalog from a complete redshift survey.

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We compare the physical properties of the MLCG systems with the Hickson compact groups (Hickson et al. 1992) and with the SDSS DR6 compact groups (McConnachie et al. 2009; Sohn et al. 2015). The SDSS DR6 compact groups we consider (SDSS DR6 compact groups hereafter) have spectroscopic redshifts from our FLWO/FAST observations and the literature, including SDSS DR12 (Sohn et al. 2015). The identification of these systems was adapted from Hickson's criteria (catalog A of McConnachie et al. 2009). Thus, this comparison provides a measure of the way apparent compact group properties might depend on the selection method.

Figure 7 compares the distributions of physical properties of the compact groups including redshift, velocity dispersion, projected group radius, and number density. The redshift range of the MLCG systems, 0.01 < z < 0.19, covers the range for the Hickson compact groups, but differs from the range for the SDSS DR6 compact groups (0.03 < z < 0.20 with a median z ∼ 0.08). Because we include bright galaxies and because we do not apply an isolation criterion, we find more compact groups at z < 0.03 (See Section 5.1). We miss compact group candidates at z > 0.09 because of the SDSS incompleteness (see Section 3.2) and magnitude limit.

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The MLCG systems have rest-frame velocity dispersions σ_CG $\leqslant \,880\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ with a median of $194\pm 4\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$, similar to that for other samples. For example, the median velocity dispersions are $204\pm 13\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ for the Hickson compact groups, and $207\pm 31\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ for the SDSS DR6 compact groups. The similar selection limit for the radial separation between member galaxies (i.e., $| {\rm{\Delta }}V| \lt 1000\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$) essentially dictates that the velocity dispersion of the samples be similar.

The projected sizes of the MLCG systems differ from those of groups in other catalogs. The MLCG systems have R_gr ranging from 4 to $94\,{h}^{-1}\,\mathrm{kpc}$. The median R_gr = $32.0\pm 0.3\,{h}^{-1}$ kpc is similar to that for the Hickson compact groups, $38.6\,\pm 7.1\,{h}^{-1}\,\mathrm{kpc}$. However, the median size of the SDSS DR6 compact groups, $57.8\pm 1.5\,{h}^{-1}\,\mathrm{kpc}$, is much larger than that for the MLCG systems or for the Hickson compact groups (McConnachie et al. 2009; Sohn et al. 2015).

Because the SDSS DR6 compact groups are apparently larger than the compact groups identified in other catalogs, the resulting galaxy number density appears to be smaller. The galaxy number density is

$$\begin{eqnarray}&&\rho =\displaystyle \frac{3N}{4\pi {R}_{\mathrm{gr}}^{3}},\end{eqnarray} \tag{ 1 }$$

where N is the number of members and R_gr is the projected group radius in ${h}^{-1}$ Mpc. The median galaxy number density of the MLCG systems is $\mathrm{log}(\rho /[{h}^{-3}\,{{\rm{Mpc}}}^{3}])=4.36\pm 0.01$. The median is $\mathrm{log}(\rho /[{h}^{-3}\,{{\rm{Mpc}}}^{3}])=4.27\pm 0.09$ for the Hickson compact groups and $\mathrm{log}(\rho /[{h}^{-3}\,{{\rm{Mpc}}}^{3}])=3.65\pm 0.04$ for the SDSS DR6 compact groups. In other words, the number density of the MLCG systems is similar to that of the Hickson compact groups, but higher than that of the SDSS DR6 compact groups (bottom right panel of Figure 7).

In principle, over the redshift range we explore here, the physical properties of the compact group candidates identified by an algorithm should not depend strongly on redshift. In Figure 8, we compare properties of the catalogs as a function of redshift beginning with the R_gr. The median R_gr of the MLCG systems varies little with redshift; in contrast, the sizes of compact groups in the catalog from McConnachie et al. (2009) and its subsamples (Mendel et al. 2011; Sohn et al. 2015) increase significantly with redshift. One possibility is that Sohn et al. (2015) selected larger groups for their follow-up redshift measurements. However, the median R_gr of compact group candidates based on photometric redshifts (Mendel et al. 2011) shows a similar trend. Thus we suspect that the trend in group size in the sample of McConnachie et al. (2009) is related to the isolation criterion. Because there is a fixed magnitude limit for defining the isolation radius, the surface number density of possible interlopers is approximately fixed to the number density at the catalog limit. The brightest member of an SDSS DR6 group must fainter than r = 14.5, and thus most searches for interlopers in the isolation radius reach the magnitude limit, r = 18. A relatively nearby group with a large physical size has a correspondingly large isolation region, thus increasing the probability that the group candidate will be removed from the sample, because an interloper appears in the isolation region.

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Because the median group size in previous samples varies with redshift, the galaxy number density obviously also varies; the galaxy number density tends to be lower at higher redshift compared to the MLCG systems. The lower density at greater redshift increases the probability that the group candidate contains interlopers and decreases the probability of selecting a very dense system where galaxy–galaxy interactions are likely. In other words, intrinsic systematics in the selection potentially may lead to artificially biased physical conclusions about the properties of the candidate systems as a function of redshift.

Figure 9 shows an example cone diagram indicating the locations of some of the MLCG systems. The points are the SDSS galaxies in the magnitude-limited sample. The MLCG systems reside in diverse environments, consistent with results from previous studies (Ramella et al. 1994; Barton et al. 1996; Ribeiro et al. 1998; Mendel et al. 2011; Pompei & Iovino 2012; Díaz-Giménez & Zandivarez 2015).

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To study the local environments of compact groups quantitatively, we define the number of neighboring galaxies (N_C) around each compact group within a comoving cylinder of ${\rm{\Delta }}R\lt 700\,{h}^{-1}\,\mathrm{kpc}$ and rest frame $| {\rm{\Delta }}V| \lt 1000\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (Barton et al. 2007; Woods et al. 2010) centered on the group mean position and redshift. We count N_C for 1538 compact groups within a volume-limited sample with M_r < −20.0 and 0.01 < z < 0.115 extracted from the SDSS DR12 spectroscopic sample (blue box in Figure 1). We exclude compact group member galaxies from the N_C count. We also estimate N_C for 254 SDSS DR6 compact groups (out of 332 groups) for comparison.

Figure 10 displays the N_C distribution for the MLCG systems and for the SDSS DR6 compact groups. Both group samples show a similar range of N_C, but the distributions differ. There are more MLCG systems with larger numbers of neighbors. This difference results from the absence of an isolation criterion in the MLCG selection algorithm.

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N_C has been used as an environment measure in both theoretical and observational studies of tight galaxy pairs. For example, in a theoretical investigation, Barton et al. (2007) segregated local environments of galaxy pairs at N_C = 8 and Woods et al. (2010) followed the procedure in the interpretation of observations. Woods et al. (2010) estimated that 32% of galaxy pairs are located in dense environments with N_C > 8. When they computed N_C, they included a pair member galaxy for counting N_C; in contrast we exclude the compact group member galaxies. Thus, N_C = 8 in their studies corresponds to N_C = 7. Among MLCG systems, 23% are in denser regions (N_C > 7), apparently somewhat lower than the fraction for galaxy pairs. However, our lower number may result from the SDSS undersampling of dense regions; this issue is much less important for pair samples from Woods et al. (2010). Woods et al. (2010) constructed pair catalogs based on the SHELS survey (Geller et al. 2005, 2014). The catalog for this survey is 97% complete to the survey limit and thus the biases are negligible.

The bottom panel of Figure 10 shows the fraction of compact groups in the denser environments as a function of redshift. The fraction changes little in the redshift range $0.02\leqslant z\leqslant 0.12$. The fraction of MLCG systems in denser environments always exceeds that for the SDSS DR6 groups as a result of the differences in the group identification algorithm.

In his identification of compact groups, Hickson applied an isolation criterion to compensate for observational limitations and to avoid systems embedded in massive clusters (Hickson 1982). Barton et al. (1996) pointed out that the availability of large complete redshifts surveys obviates the need for applying an isolation criterion in the initial selection of compact group candidates. They emphasize that the large angular size of the isolation region for low-redshift systems artificially removes them from a catalog. Figure 8 of Barton et al. (1996) shows that groups with larger isolation regions have smaller sizes for groups selected from the CfA redshift survey. Here, again the limiting apparent magnitude for the definition of the isolation radius is the limiting apparent magnitude of the catalog rather than a limit three magnitudes fainter than the brightest group member. Eliminating the isolation criterion includes these nearby groups at the expense of including compact group candidates that are substructures in massive systems. However, the compact group candidates within massive systems or in dense regions can be removed after the initial selection. In contrast, the low-redshift systems cannot be recovered.

The probability of rejection as a result of the isolation criterion can increase with decreasing redshift depending on the details of the application. The lowest redshift compact group candidates have larger angular size and a correspondingly more extensive isolation region than more distant compact group candidates. Figure 7(a) shows the difference between the redshift distribution of the MLCG systems and the SDSS DR6 compact groups. Because McConnachie et al. (2009) remove r < 14.5 galaxies, they might miss some nearby groups, thus accounting for the difference. To test this conjecture, Figure 11 plots the redshift distribution of the MLCG systems containing only $r\geqslant 14.5$ galaxies in analogy with the SDSS DR6 sample. Although we remove 407 MLCG systems containing bright members, we still identify plenty of compact groups in the local universe (z < 0.05) where SDSS DR6 compact systems are absent or rare.

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Because we do not apply an isolation criterion in the selection algorithm, we also include compact group candidates in dense surroundings (see Figure 10). Indeed, the fraction of the MLCG systems in dense environments (N_C > 7) is larger than for the SDSS DR6 compact groups at all redshifts. Interlopers may occur more often in high-density regions, thus producing some of the MLCG systems with inflated line-of-sight velocity dispersions. Barton et al. (2007) emphasize that a study of some aspects of galaxy evolution in tight pairs and compact groups requires specialization to relatively low-density environments. As in pair studies, candidate systems in dense surroundings can be removed after the general group selection.

The diverse local environments of compact groups have been discussed previously (e.g., Ramella et al. 1994; Ribeiro et al. 1998; Andernach & Coziol 2005; Mendel et al. 2011; Díaz-Giménez et al. 2012; Pompei & Iovino 2012; Díaz-Giménez & Zandivarez 2015). The fraction of embedded compact groups changes significantly depending on the group identification method and on the definition of the local environment. For example, Ramella et al. (1994) suggested that 76% of 29 Hickson compact groups are embedded, and Mendel et al. (2011) showed that 50% of the SDSS DR6 compact groups are within $1\,{h}_{70}^{-1}$ Mpc of rich groups. In contrast, Pompei & Iovino (2012) found that 33% of the compact groups in the second Digitized Palomar Observatory Sky Survey (DPOSS II) are embedded in rich groups. Díaz-Giménez & Zandivarez (2015) also found that only 27% of compact groups reside in loose groups in the 2MASS compact group catalog. A direct comparison with the MLCG systems is difficult because we use a different environment measure.

Compact group properties may depend on the local environments. We compare the physical properties of groups segregated by N_C in Figure 12. Panels (a)–(f) show redshift, r-band surface brightness, size, galaxy number density, velocity dispersion, and stellar mass of the MLCG systems. The plots show that properties related to the group identification, including redshift, surface brightness, size, and number density, are consistent irrespective of the local environment. In contrast with the 2MASS compact group sample (Díaz-Giménez & Zandivarez 2015), we find no dependence of the MLCG projected size on environment. The dependence found by Díaz-Giménez & Zandivarez (2015) may result from the group identification algorithm (see Section 5.1). On the other hand, the velocity dispersion and stellar mass of N_C > 7 MLCG systems tend to be larger than for ${N}_{C}\leqslant 7$ groups. This result is consistent with the comparison between "isolated" and "embedded" compact groups in the DPOSS II (Pompei & Iovino 2012) and the SDSS DR6 samples (Sohn et al. 2015). These results are understandable because the interloper fraction may be enhanced in dense environments and because galaxies with greater stellar mass tend to inhabit denser regions (e.g., Bolzonella et al. 2010; Damjanov et al. 2015). Table 7 lists the range and the median of the properties of the MLCG systems in different environments.

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Table 7.  Comparison between Compact Groups in Different Environments

Properties		All CGs	${N}_{C}\leqslant 7$ CGs	${N}_{C}\gt 7$ CGs
z	Range	[0.011, 0.188]	[0.014, 0.112]	[0.019, 0.112]
	median	0.050 ± 0.001	0.049 ± 0.001	0.053 ± 0.003
Rgr	Range	[4.9, 94.1]	[4.9, 83.7]	[8.9, 94.1]
(${h}^{-1}$ kpc)	median	32.0 ± 0.3	31.8 ± 0.3	33.6 ± 0.8
$\mathrm{log}\rho$	Range	[3.29, 6.77]	[3.39, 6.77]	[3.29, 6.00]
(${h}^{3}{{\rm{Mpc}}}^{-3}$)	median	4.36 ± 0.01	4.37 ± 0.01	4.31 ± 0.03
σ	Range	[1, 879]	[1, 866]	[1, 879]
(km s−1)	median	194 ± 4	171 ± 4	353 ± 14
fETG		64.0 ± 0.7	60.4 ± 0.8	78.6 ± 1.3

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We also compare the properties of member galaxies in the ${N}_{C}\leqslant 7$ and N_C > 7 MLCG systems in Figures 12(g) and (h). The properties of member galaxies including the fraction of early-type galaxies and the u−r color distribution differ. The fraction of early-type galaxies is higher in N_C > 7 compact groups (78.5 ± 1.3%) than in ${N}_{C}\leqslant 7$ compact groups (60.2 ± 0.8%). The member galaxies in N_C > 7 compact groups are, on average, redder than those in ${N}_{C}\leqslant 7$ compact groups as one might expect based on the known relations between galaxy properties and local density (e.g., Park et al. 2007; Blanton & Moustakas 2009).

The differences in physical properties are qualitatively insensitive to the definition of "dense" environments for N_C = 3, 5, 7, 10, 15, and 20. The MLCG systems in denser environments show larger velocity dispersion, larger stellar mass, and higher early-type fraction; other properties are essentially environment independent.