COMPARATIVE STUDY OF ASYMMETRY ORIGIN OF GALAXIES IN DIFFERENT ENVIRONMENTS. I. OPTICAL OBSERVATIONS

In 1973, Karachentseva used a simple method for identifying isolated galaxies. By inspecting the blue prints of the Palomar Observatory Sky Survey (POSS), she selected all the galaxies in the Zwicky catalog (Zwicky et al. 1961–1968) whose nearest neighbor has a size within a factor of 4 of the major-axis diameter of the target galaxy and lies more than 20 diameters away from it. This definition implies that a galaxy with a diameter of 20 kpc and a peculiar velocity on the order of 150 km s⁻¹ has not been influenced by a similar mass galaxy during the last ∼3 Gyr (Turner et al. 1979). The KIGs are observed in the nearby universe (z < 0.14 with median z = 0.02) and have apparent magnitudes brighter than 15.7, which is the limit of the Zwicky catalog (Zwicky et al. 1961–1968). Members in this catalog have north declination δ ⩾ −3°, the majority being at high galactic latitudes (|b| ⩾ 20°).

In the early 1970s, Karachentsev (1972) compiled what was at that time the first list of pairs of galaxies, the Catalog of Isolated Pairs of Galaxies (KPGs). Using the Zwicky catalog, the KPGs were selected from visual inspection of the POSS prints based solely on their observed properties, like apparent separation, apparent magnitudes, and angular diameters, and without reference to apparent signs of interaction. The pairs of galaxies in the KPG are also located in the nearby universe (z < 0.06 with median z = 0.02), all have north declination ⩾−3°, high galactic latitude (|b| ⩾ 20°), and photographic magnitudes brighter than 15.7. This catalog is considered suitable for studying galaxies in pairs because of its size, completeness, and relatively unbiased selection (Hernández-Toledo et al. 1999).

Subsequent spectroscopic observations revealed that only half of the KPGs in the initial catalog have small relative velocities, Δv < 100 km s⁻¹, while the remaining pairs have relative velocities extending upward and as far as 10,000 s⁻¹ (Karachentsev 1987). Later on various attempts to establish solid criteria to determine true pairs based on the relative velocity of the member galaxies were made. For example, Turner (1976) proposed that physical pairs must have Δv < 425 km s⁻¹. According to Makino & Hut (1997), pairs of galaxies have a higher probability to show effects due to interaction when the difference in radial velocity between the two galaxies is comparable or lower than their internal velocity dispersion. In the same vein, Patton et al. (2000) suggested Δv ⩽ 500 km s⁻¹. For our sample we have followed the latter authors and selected pairs with Δv ⩽ 500 km s⁻¹.

In Figure 1, we show the linear separation and difference in radial velocity between the members of the KPG pairs. The majority are close pairs of galaxies, with spatial separation lower than 50 kpc and difference in radial velocity lower than or equal to 150 km s⁻¹. For comparison, our Local Group of galaxies as viewed at a comparable redshift (z ∼ 0.02) would look like a pair with a spatial separation of 772 kpc (Ribas et al. 2005) and a difference in radial velocity equal to 112 km s⁻¹. Therefore, the galaxies in the KPG are much closer than the two major galaxies in our Local Group.

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In the early 1980s, Paul Hickson conducted a visual search for CGs using red POSS prints in order to obtain a homogeneous sample that could be subjected to statistical analysis. Hickson's Compact Groups Catalog forms one of the most studied samples to date (Hickson 1982). The HCGs are small systems of three to eight galaxies in apparent close proximity in the sky. The space density of galaxies is very high, often exceeding that of the cores of large clusters of galaxies (Hickson et al. 1992). The relatively low velocity dispersions, which are generally comparable to galaxy rotation velocities, make interactions and mergers common in these systems (Hickson et al. 1992). Many galaxies in the HCG show morphological peculiarities indicative of gravitational interactions (Mendes de Oliveira & Hickson 1994; Coziol & Plauchu-Frayn 2007).

In 1992, Hickson et al. (1992) obtained spectroscopic observations for almost all the galaxies in the HCG (462 galaxies) and found that only 92 groups are real bounded systems with at least three members and with a median radial velocity dispersion of 200 km s⁻¹. The HCGs are nearby universe structures (with z< 0.14 and median redshift z = 0.03), which are located well beyond the Virgo Cluster (Hickson et al. 1992). For our study, we have selected groups from Hickson et al. (1992) with velocity dispersions σ_v⩽ 800 km s⁻¹.

In Figure 2, we show the distribution of absolute B magnitude versus the virgocentric velocity for 308 HCG galaxies (top), 938 KPG galaxies (middle), and 777 KIG galaxies (bottom). Only galaxies inside the range 900 km s⁻¹⩽ v_vir⩽ 13,000 km s⁻¹, with M_B ⩽ −15, and satisfying the previous selection criteria, are plotted in this figure. One can see that the KPG and KIG surveys scan comparable volumes. The HCG survey, on the other hand, being slightly deeper, contains galaxies with lower luminosity (M_B ⩽ −18) above v_vir = 8000 km s⁻¹. This difference will be taken into account during our analysis.

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Based on the samples, we set up our targets on galaxies with declinations in the range −32° ⩽ δ ⩽ +55° and the semi-major axis in the range 05 ⩽ a ⩽ 35, which allows for optimal spatial resolution. Also, to minimize inclination corrections for photometric data and to evaluate basic structural parameters, we have applied an ultimate criterion based on the semi-minor to semi-major axis ratio, keeping galaxies with b/a ⩾ 0.4 (or i ⩽ 70°). Only in a few cases, in the HCG, applying this last criterion was impossible.

Our final selection for the observed galaxies also depended on the time allocated for observation and the weather conditions. We were able to observe in total 214 galaxies: 37 KIGs, 71 KPGs, and 106 HCGs. All the galaxies have redshifts z < 0.04. The properties of these galaxies are reported in Tables 1–3. For each of the galaxies, we have double checked the morphological type. Most of the KIG galaxies already had their morphology determined by Sulentic et al. (2006). In the cases where our CCD images and isophotal study suggested a bar, we have added this information to their morphological description.

In Figure 3, we compare the characteristics of the observed samples with the characteristics of the galaxies in their respective catalogs. One can see that the observed samples reproduce the absolute and morphological distribution of their parent samples relatively well. The results of nonparametric statistical tests (Mann–Whitney), presented in Table 4, are consistent with no differences in absolute magnitude and size, although there seems a slight tendency for the observed KIGs to be nearer than the galaxies in their parent sample.

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Table 4. Properties of Observed Versus Catalog Galaxies

Sample	MB	PMW	DB	PMW	Vvir	PMW
	(mag)		(kpc)		(km s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
KIG	−20.46/−20.30	0.070	25/22	0.153	4934/6296	$\underline{0.0003}$
KPG	−20.35/−20.32	0.619	23/23	0.752	5123/6326	0.0177
HCG	−20.19/−20.01	0.119	26/24	0.050	7150/7970	0.6847

Notes. Columns: (1) sample identification; (2) median M_B value of the observed/catalog galaxies; (3) probability P for M_B; (4) median value D_B of the observed/catalog galaxies; (5) probability P for D_B; (6) median v_vir value of the observed/catalog galaxies; and (7) probability P for v_vir. P values were obtained from Mann–Whitney tests. Underlined values indicate statistically significant differences between two samples.

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Surface photometry was carried out on each galaxy. This was done within STSDAS² with the ELLIPSE task (Jedrzejewski 1987). The algorithm used by this task derives various geometric parameters, such as surface brightness μ, ellipticity , P.A., and the harmonic amplitude B₄. This last parameter is related to the standard fourth-order Fourier cosine coefficient, a₄ (Bender et al. 1988), normalized to the semi-major axis a at which the ellipse was fitted ($a_{4}/a = B_{4}\sqrt{1-\epsilon }$). Another important parameter is the V−I color index profile. This profile is obtained by measuring the V and I magnitude profiles, subtracting one from the other.

The only requirement for ELLIPSE to work is an initial guess of the geometric center, , and of the P.A., of the galaxy. The geometrical center of a galaxy is determined by locating the peak in light distribution (see Coziol & Plauchu-Frayn 2007). The default and P.A. were 0.05 and 0, respectively. The task ELLIPSE is applied keeping the geometric center fixed and allowing and P.A. to vary. This method yields surface brightness and color profiles that match the local variations of the structural components. We also restrict the fit of ellipses in the central part of the galaxy to a radius larger than the seeing (see Figure 4) and minimize the light contribution from companion galaxies (important only for the HCGs and KPGs) by stopping the task manually at the maximum radius possible.

The isophotal parameters measured by ELLIPSE provide important information on the physical morphology and are intimately related to the dynamical properties of the galaxies (see Barth et al. 1995; Coziol & Plauchu-Frayn 2007). For example, large variations in P.A. ∼ 20°, or twists (Nieto et al. 1992), usually reflect inhomogeneous mass distributions (Zaritsky & Lo 1986), while variations reflect bars, dust, mass perturbations, or small disks in the central regions of early-type galaxies. Early isophotal studies have shown that large isophotal twists are only measured in interacting galaxies, suggesting that they are the consequence of close encounters or mergers (Kormendy 1982; Bender & Möllenhoff 1987). In our analysis, we define a twist, θ, as a variation in P.A. accompanied by a monotonically varying ellipticity with amplitude Δ ⩾ 0.1. This definition allows differentiating between variations of P.A. produced by triaxiality and from those produced by interactions (Kormendy 1982; Bender & Möllenhoff 1987).

The isophotal deviations from the pure ellipse, quantified by the a₄ coefficient, determine the characteristic shape of the isophote: boxy (a₄ < 0), consistent with a pure elliptical or round isophote (a₄ ∼ 0), or disky (a₄>0), consistent with a slightly pointed isophote. Elliptical galaxies with disky isophotes tend to be faint. They generally contain a rapidly rotating stellar population with a nearly isotropic velocity dispersion. Elliptical galaxies with boxy isophotes tend to be luminous and massive. They have anisotropic velocity dispersion and are thought to be supported by pressure rather than stellar rotation. These differences suggest two distinct formation scenarios for boxy and disky elliptical galaxies. Numerical simulations have shown that the formation processes depend highly on the initial conditions: initial mass ratios, individual angular momentum, and dust and gas contents of the merging galaxies (Hernquist 1993; Barnes 1996). The general idea is that mergers between unequal-mass, gas-rich galaxies tend to produce disky early-type remnants, while mergers with equal-mass, high-density, and gas-poor galaxies tend to produce boxy remnants (Naab & Burkert 2003).

The concentration index, C, is a measure of the light concentration of a galaxy profile, having high values for centrally concentrated light profiles. It is well known that the concentration index has a tight correlation with morphological type (Abraham et al. 1994; Shimasaku et al. 2001); early-type galaxies tend to have the most concentrated light profiles, while late-type galaxies have the least concentrated ones. Interactions between galaxies can also perturb the stellar material, changing the light profiles of the galaxies in the process and affecting their concentration index.

Because we are studying nearby galaxies, the spatial resolution of our CCD images allows us to measure the C parameter at different radii. Based on the isophotal profiles of the galaxies, we have estimated C values inside and outside a physical radius r₀, independent of the distribution of light. To estimate this radius, we have used the major axis at 25 mag arcsec⁻² (Paturel et al. 2003) as given in Hyperleda and determined the linear diameters in B magnitude, D_B, for the galaxies in the HCG, KPG, and KIG catalogs estimating the median of the three distributions. The median value obtained is 23 kpc. In our sample, a few galaxies (20% of the sample: 26 HCGs, 12 KPGs, and 4 KIGs) turned out to have a D_B that is smaller than this value. Consequently, we have used two different r₀; one is equal to 5 kpc (approximately D_B/4) for the standard size galaxies (approximately M_V < −20) and the other is half of this value, 2.5 kpc, for galaxies with smaller diameters. For our analysis we give three concentration indices: one inside r₀, C(r < r₀) = μ(r = r₀)–μ(r < r₀), one outside r₀, C(r>r₀) = μ(r>r₀) − μ(r = r₀), and a global (or total) concentration index C_Total = μ(r>r₀) − μ(r < r₀).

For the sake of comparison, in our analysis we have also chosen a radius which depends on the light distribution in the galaxies. We have used the Petrosian, R_P, and effective radii, R_e, as determined based on a modified form of the Petrosian (1976) system (Graham et al. 2005). In this system, R_P is defined as the projected radius where 1/η(R_P) = 0.2. The Petrosian index, η(R) = 〈I〉_R/I(R), is the ratio of the intensity of an isophote at radius R and the average intensity within that radius, as measured using circular apertures. In the case of small galaxies, where the faint central surface brightness does not allow us to reach 1/η(R_P) = 0.2, we have used 1/η(R_P) = 0.4 instead. In Tables 6 and 7, for all the galaxies in our analysis we give R_P; R_e, the magnitude inside the effective radius; M_e, a concentration index, which is defined as the ratio of radii that contain 90% and 50% of the Petrosian flux, R_90%/R_50%; the surface brightness at the effective radius, μ_e; and the color at this radius.

Finally, as a complementary analysis, we have constructed a V−I color map for each observed galaxy. We present these maps in the bottom right part of Figure 4. In these maps, bright regions are consistent with red stellar population or dust extinction and dark regions are consistent with blue stellar populations. These color distribution maps were found to be extremely useful in detecting tidal tails, galaxy satellites, dusty patches, and common envelopes in galaxies.

Another useful method for the study of morphology consists of estimating the level of asymmetry of a galaxy (e.g., Abraham et al. 1994, 1996; Schade et al. 1995; Conselice 1997; Conselice et al. 2000; Coziol & Plauchu-Frayn 2007; Hutchings & Proulx 2008). The leitmotif behind this method is that the level of asymmetry of a galaxy reflects something about its history of formation and evolution. For example, galaxies that are old and already well evolved, or galaxies that formed in isolation, are expected to possess fairly symmetric distributions of light. On the other hand, galaxies affected by interactions or mergers sometime during their evolution are expected to show more complex distributions.

The interpretation of asymmetry may seem straightforward enough for early-type galaxies, but it is not that simple for later-type spiral galaxies. Various studies have shown that in late-type spirals, asymmetric structures may result from intrinsic processes related to star formation (Schade et al. 1995; Conselice et al. 2000). Extra care must be taken, therefore, before drawing conclusions about the origin of asymmetries in any sample of galaxies. In Coziol & Plauchu-Frayn (2007), it was shown that the asymmetric structure analysis is complementary to the isophotal one: there is a one-to-one relation between the variations of isophotal characteristic parameters and the existence of asymmetries related to inhomogeneous distribution of mass produced by interaction effects. Applying the two analyses in parallel yields a high confidence level when interpreting the results.

For the present analysis we have used a slightly different measure of asymmetry than that found in the literature (also different from the one used in Coziol & Plauchu-Frayn 2007). This was done in order to make the interpretation more straightforward. The principle of the asymmetry method is relatively simple (see Coziol & Plauchu-Frayn 2007 for details). The image of a galaxy is rotated by 180° and divided from the original image. Any differences in the distribution of light (asymmetries) appear under the form of excesses of light (bright regions), together with their corresponding shadows (dark regions) on the opposite side (see Figure 4).

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To measure the asymmetry level, the residual images are smoothed using boxes of size equal to the seeing in pixels, reducing the noise. Ellipses are then fitted to the residual image of each galaxy, keeping the center, ellipticity, and P.A. fixed. The level of asymmetry as a function of semi-major axis a is estimated by the following formula:

$$\begin{equation} A(a)_{180^\circ }\equiv \frac{I_0}{I_{180^\circ }}, \end{equation} \tag{ 1 }$$

where I(a)₀ is the intensity in the original image and I(a)₁₈₀ is the intensity in the rotated image. This formula yields values between 1 (completely symmetric) and >1 (completely asymmetric).

Compared with the residual images (I₀/I₁₈₀) it is easy to verify that asymmetries in our analysis appear as structures in the asymmetry curve. The amplitudes of these structures are proportional to their relative intensities. For example, an asymmetry of A = 1.2 indicates a concentration of light 20% brighter than the intensity at that radius on the opposite side. This corresponds to a high level of asymmetry. On the other hand, a level of asymmetry of A = 1.0 indicates that the intensity of light is the same on both sides (complete symmetry). In our analysis, a symmetric distribution of light yields a flat asymmetry curve (see the bottom left graphic in Figure 4).

For our asymmetry analysis, determining the center of the galaxies around which the rotation is done is a crucial step. If this is not done carefully, spurious asymmetries can be produced. The method we used (finding the peak in luminosity; see Coziol & Plauchu-Frayn 2007) is simple and yields excellent results. It has also the advantage to correspond to the same center as used during the isophotal analysis. As a check, one can verify that, as expected, at the center of the galaxies the asymmetry curves have a level of 1 (minimum asymmetry). Moreover, real asymmetries produce isophotal structures that are detected by our first analysis based on ellipses fitting. Therefore, we are secure that no spurious asymmetries are produced by our method.

Our analysis is not sensitive to sky gradients because it applies to the inner part of the galaxies, minimizing the possible contamination by foreground stars. When needed, foreground stars were eliminated using masks (using IMEDIT in IRAF). When a star was found lying very near the body of a galaxy, a special mask was used within ELLIPSE itself. In cases where it was impossible to eliminate the contaminating star, the galaxy was rejected.

For our analysis, we have divided our samples into three morphology groups: early type (E–S0), intermediate type (Sa–Sb), and late type (Sbc–Im). The median characteristics of the galaxies in these three different groups are reported in Tables 8–10 for properties measured at radius r₀ and in Tables 11–13 for properties measured at radius R_e. We now discuss the variations of the various characteristics encountered in each group depending on their environments. To check for the statistical significance of the variations observed, nonparametrical tests (Kruskal–Wallis or Mann–Whitney and Dunn's post-tests) were also performed. All the tests were done at a level of significance of 95%, which is the standard for these kinds of tests. Description of the tests used can be found in Coziol (2003). The results of the statistical tests are reported in the last columns of Tables 8–10 and Tables 11–13.

Table 8. Properties of Early-type Galaxies in Different Environments

Property	HCG	KPG	PMW
(1)	(2)	(3)	(4)
MV	−20.3	−20.4	0.4006
MI	−21.7	−21.5	0.0992
$\mu _{<r_{0}}$	20.4	20.4	0.2233
$\mu _{>r_{0}}$	22.4	23.0	0.0026
$(V-I)_{<r_{0}}$	1.34	1.25	0.0017
$(V-I)_{>r_{0}}$	1.33	1.21	0.0100
$C_{<r_{0}}$	1.1	1.4	0.0040
$C_{>r_{0}}$	0.7	0.7	0.1193
$A_{<r_{0}}$	1.00	1.00	0.0716
$A_{>r_{0}}$	1.01	1.01	0.0830

Notes. Columns: (1) properties measured in each sample (all values are medians): absolute magnitude in V inside r₀, absolute magnitude in I inside r₀, surface brightness in V inside and outside r₀, V−I color inside and outside r₀, concentration index inside and outside r₀, asymmetry level inside and outside r₀; (2) and (3) galaxies in HCGs and KPGs, respectively; (4) P values from Mann–Whitney tests, where underlined values indicate statistically significant differences.

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Table 9. Properties of Early-type Galaxies as Measured Using R_e

Property	HCG	KPG	$P_{\rm {MW}}$
(1)	(2)	(3)	(4)
MV	−20.4	−20.2	0.0669
MI	−21.7	−21.3	$\underline{0.0368}$
μV	20.2	19.5	$\underline{0.0124}$
(V − I)	1.32	1.20	$\underline{0.0036}$
R90/R50	2.2	2.3	0.2320
Re	2	1	$\underline{0.0002}$

Notes. Columns: (1) properties measured in each sample (all values are medians): absolute magnitude in V inside R_e, absolute magnitude in I inside R_e, surface brightness in V at R_e, V−I color at R_e, concentration index, defined by the ratio of the radii containing 90% and 50% of the Petrosian flux, and effective radius in kiloparsec; (2) and (3) galaxies in HCG and KPG, respectively; (4) P values from Mann–Whitney tests, where underlined values indicate statistically significant differences.

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Table 10. Properties of Intermediate-type Galaxies in Different Environments

Property	HCG	KPG	KIG	HCG–KPG	HCG–KIG	KPG–KIG
(1)	(2)	(3)	(4)	(5)	(6)	(7)
MV	−20.0	−20.1	−20.3	0.3646	0.0631	$\underline{0.0291}$
MI	−21.4	−21.3	−21.4	0.4051	0.1983	0.1200
$\mu _{<r_{0}}$	20.5	20.6	20.4	0.4315	0.2913	0.2470
$\mu _{>r_{0}}$	22.5	22.5	23.3	0.1697	$\underline{0.0004}$	$\underline{0.0034}$
$(V-I)_{<r_{0}}$	1.37	1.30	1.21	0.1368	$\underline{0.0167}$	0.1232
$(V-I)_{>r_{0}}$	1.31	1.26	1.17	0.3642	0.1937	0.2245
$C_{<r_{0}}$	0.8	0.7	1.2	0.3713	$\underline{0.0017}$	$\underline{0.0032}$
$C_{>r_{0}}$	0.8	1.1	1.5	$\underline{0.0296}$	$\underline{0.0132}$	0.1344
$A_{<r_{0}}$	1.01	1.01	1.01	0.2415	0.4933	0.2815
$A_{>r_{0}}$	1.04	1.08	1.06	0.0960	0.3628	0.1300

Notes. Columns: (1) properties measured in each sample (all values are medians): absolute magnitude in V inside r₀, absolute magnitude in I inside r₀, surface brightness in V inside and outside r₀, V−I color inside and outside r₀, concentration index inside and outside r₀, asymmetry level inside and outside r₀; (2)–(4) galaxies in HCG, KPG, and KIG, respectively; (5)–(7) P values from Dunn's post-tests, where underlined values indicate statistically significant differences.

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Table 11. Median Values of Intermediate-type Galaxies as Measured Using R_e R_e

Property	HCG	KPG	KIG	HCG–KPG	HCG–KIG	KPG–KIG
(1)	(2)	(3)	(4)	(5)	(6)	(7)
MV	−20.7	−20.5	−20.3	0.2536	0.2375	0.5000
MI	−21.7	−21.7	−21.4	0.3837	0.1465	0.2848
μV	21.1	20.9	20.5	0.1445	$\underline{0.0054}$	0.0511
(V − I)	1.23	1.17	1.09	0.3083	0.0517	0.1417
R90/R50	2.1	2.1	2.2	0.0714	0.1363	$\underline{0.0156}$
Re	4	4	3	0.2367	$\underline{0.0059}$	0.0863

Notes. Columns: (1) properties measured in each sample (all values are medians): absolute magnitude in V inside R_e, absolute magnitude in I inside R_e, surface brightness in V at R_e, V−I color at R_e, concentration index, defined by the ratio of the radii containing 90% and 50% of the Petrosian flux, and effective radius in kiloparsec; (2)–(4): galaxies in HCG, KPG, and KIG, respectively; (5)–(7): P values from Dunn's post-tests. Underlined values indicate statistically significant differences.

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Table 12. Properties of Late-type Galaxies in Different Environments

Property	HCG	KPG	KIG	HCG–KPG	HCG–KIG	KPG–KIG
(1)	(2)	(3)	(4)	(5)	(6)	(7)
MV	−19.1	−19.2	−19.4	0.2265	$\underline{0.0290}$	0.1657
MI	−20.3	−20.7	−20.8	0.3303	0.0560	0.1797
$\mu _{<r_{0}}$	21.2	20.9	21.0	$\underline{0.0250}$	0.1530	0.1758
$\mu _{>r_{0}}$	22.4	22.6	22.7	0.2172	0.2961	0.4617
$(V-I)_{<r_{0}}$	1.27	1.26	1.30	0.3723	0.3455	0.1833
$(V-I)_{>r_{0}}$	1.27	1.15	1.30	0.4493	0.1280	0.0794
$C_{<r_{0}}$	0.6	0.7	0.6	0.2092	0.4323	0.1943
$C_{>r_{0}}$	0.7	0.9	0.8	0.0963	$\underline{0.0123}$	0.2601
$A_{<r_{0}}$	1.03	1.02	1.01	0.3392	$\underline{0.0007}$	$\underline{0.0019}$
$A_{>r_{0}}$	1.09	1.15	1.08	0.0801	0.1400	$\underline{0.0004}$

Note. Lines and columns are the same as defined in Table 7.

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Table 13. Properties of Late-type Galaxies as Measured Using R_e

Property	HCG	KPG	KIG	HCG–KPG	HCG–KIG	KPG–KIG
(1)	(2)	(3)	(4)	(5)	(6)	(7)
MV	−20.4	−19.9	−20.8	0.0707	0.0793	$\underline{0.0030}$
MI	−21.7	−21.0	−21.9	0.0960	0.1988	$\underline{0.0035}$
μV	21.4	21.5	21.6	0.4866	0.2081	0.0890
(V − I)	1.25	1.03	1.12	$\underline{0.0156}$	0.1021	0.0715
R90/R50	1.9	1.8	1.8	0.3304	0.0996	0.1170
Re	5	3	5	0.0802	0.1448	$\underline{0.0064}$

Note. Lines and columns are the same as defined in Table 12.

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5.1.1. Early-type (E–S0) Galaxies

In Figures 6 and 7, we show the variations of the isophotal parameters in early-type galaxies internal to r₀ (Figure 6) and external to r₀ (Figure 7). In each graph, the x-axis represents the absolute magnitude in V, as estimated inside r₀.

In this morphology group, there are only three galaxies that belong to the KIGs. We have discarded these from our statistical tests. The KPG galaxies in this morphology group tend to be slightly bluer than the HCG, and this is independent of the radius and absolute magnitude of the galaxies. This is confirmed by our statistical tests (see Tables 8 and 9 for r₀ and R_e, respectively). Inside the half-radius, the HCG galaxies tend to be less concentrated than the KPG galaxies. This is also confirmed by our statistical tests (see Table 8).

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The higher concentration and bluer color observed for the E–S0 KPG galaxies are consistent with the idea of recent gas accretion and an increase of star formation in the center of these galaxies. Outside the half-radius, there are no differences in concentration between the KPGs and the HCGs. This also agrees with the absence of difference based on R_90%/R_50%, since this parameter is estimated at comparable radii (Table 9).

There are no significant differences between the KPG and HCG galaxies in surface brightness inside the half-radius. Farther out the HCG galaxies tend to have slightly higher surface brightness than the KPGs (see Table 8). Since we are observing in the optical, this suggests older stellar populations or more relaxed structures as a whole in the HCGs, which is also consistent with the slightly redder colors for the HCG galaxies.

Due to the low value of R_e compared to r₀, the statistical tests find higher surface brightness on average for the early-type KPG galaxies as compared to the HCGs (see Table 9). This is consistent with our interpretation of more relaxed populations of stars in the HCGs than in the KPGs.

In terms of asymmetry, we do not find any significant differences among the samples. This morphological type appears to be very symmetric independent of the environment. This suggests similar formation mechanisms for these galaxies.

For early-type galaxies, we can verify what types of isophotes are prevailing: boxy with a₄ < 0 or disky with a₄>0. In Figure 8, we show the values of a₄ as measured at the half-radius for the E–S0 galaxies in different environments. One can see that both the HCG and KPG E–S0 galaxies tend to occupy the region of disky galaxies: 38 out of 57 (67%) of the HCGs and 15 out of 25 (60%) of the KPGs. The ellipticity of these galaxies is also quite high. This is consistent with the hypothesis of similar mechanisms for the formation of these galaxies in both environments. For example, the transformation of later-type spirals through gas accretion and star formation in the central part would be one way to produce E–S0-like galaxies that have disky rather than boxy isophotes.

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Evidence in favor of similar mechanisms for the formation of E–S0 galaxies in the KPGs and HCGs can also be found in the high frequency of detection of isophotal twists in both samples: 40% (10/25) in the KPGs and 51% (29/57) in the HCGs. The levels of the twists in these galaxies are shown in Figure 9 as a function of absolute magnitude in V. We consider large twists to be those with values θ>20°. The median values of θ are 25° and 20° for the KPGs and HCGs, respectively.

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In Figure 10, we show how the isophote parameter a₄ and twist θ vary with the ellipticity difference Δ = _max − _min. Values of Δ>0 indicate that the galaxies are generally rounder in their centers than in their periphery. Large values in Δ together with large |a₄|> 0.7 and θ>20° suggest the galaxies were possibly affected by interactions. No significant differences are observed between the HCGs and the KPGs, suggesting, once again, similar formation mechanisms.

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In Figure 3, we show the distribution of the morphology of the galaxies in the different catalogs. We observe a clear increase in the number of earlier-type galaxies among the HCGs compared with the KPGs and KIGs. The fact that we found a higher number of S0 galaxies among the HCGs than among the KPGs suggests interactions and mergers are possible mechanisms responsible for forming these galaxies. At the same time, the fact that we also find S0 galaxies among the KPGs suggests the environments of these galaxies must have some level of similarity. For example, one may assume they are different structures forming in a common or comparable low-density environment: both form at the periphery of large-scale structures.

5.1.2. Intermediate-type (Sa–Sb) Galaxies

In Figures 11 and 12, we show the variations in the Sa–Sb group of the isophotal parameters internal (Figure 11) and external (Figure 12) to r₀. In Figure 11, the KIGs tend to be slightly brighter than the KPGs and slightly bluer than the HCGs. This is confirmed by statistical tests (Table 10). However, the difference in luminosity may be due to the fact that there are no small-sized Sa–Sb galaxies in the KIGs as compared to the KPGs and HCGs (clearly visible in Figure 11). Indeed, when we compare the magnitudes inside R_e the differences vanish (Table 11).

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We see a trend for the HCGs to be redder than the KPGs or KIGs (Table 10). This suggests slightly older nuclear stellar populations in the HCG galaxies. However, statistical tests are inconclusive on this matter, except between the HCGs and KIGs inside r₀. The trend toward redder color for the HCGs is also visible using R_e, but again, statistical tests are inconclusive (Table 11).

Also from Figure 11 and Table 10 one can see that the KIG galaxies are more concentrated than the HCGs and KPGs inside r₀. In terms of R_90%/R_50%, the statistical tests only support a difference in concentration between the KIG and KPG galaxies (Table 11). However, the HCG galaxies are observed to have a greater R_e than the KIG galaxies (Table 11) and to have lower surface brightness at R_e (Table 11).

In Figure 12, the trend in concentration seems to continue outside r₀: the HCG galaxies seem less concentrated than the galaxies in the other two samples (Table 10). Also in Table 10 we find differences in surface brightness outside the half-radius, the HCGs and KPGs having higher surface brightness than the KIG galaxies.

The differences observed suggest different distributions in mass. In particular, the intermediate KIG galaxies seem smaller in size and more compact than the KPG and HCG galaxies. This may be explained by the isolation status of the KIG: stars in galaxies that have experienced interactions are expected to occupy higher energy orbits than those in galaxies that formed in isolation, and consequently isolated galaxies may be expected to be more compact or less spatially extended.

In Figure 11, no difference is observed in the asymmetry level. However, outside the half-radius, Figure 12, the KPG galaxies tend to be slightly more asymmetric than the HCG galaxies, even though this is not confirmed by the statistical test (Table 10).

5.1.3. Late-type (Sbc–Im) Galaxies

In Figures 13 and 14, we show the variations for the late-type galaxies of the isophotal parameters internal (Figure 13) and external (Figure 14) to r₀. In this group, we observe no obvious differences between the different parameters. The statistical tests (see Table 12) suggest small differences between the HCG and KIG galaxies in terms of magnitudes, with the KIG galaxies being slightly brighter than the HCG galaxies both inside r₀ and R_e.

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The HCG galaxies also seem to have lower surface brightness inside r₀ than the KPG galaxies and to be less concentrated than the KIG galaxies outside r₀. The KPG galaxies seem to be bluer than the HCGs inside R_e and to be smaller than the KIG galaxies. We do not find any other differences based on R_e among the samples (see Table 13). In terms of size and concentration, the trends seem contrary to what are observed for the intermediate types.

The most significant differences observed are in the level of asymmetry: the KIG galaxies turned out to be more symmetric than the KPG or the HCG galaxies. The asymmetry level does not seem significantly different between the HCG and KPG galaxies.

So far, our analysis has shown differences in the characteristics of the galaxiesthat are consistent with evidence for interaction effects due to their different environments. However, the fact that we observe different behaviors between morphology groups suggests we must be careful in our interpretation of asymmetries in terms of interactions. For example, in intermediate- and late-type spiral galaxy asymmetric features may be related to internal processes, like density waves or stochastic star formation propagation, which are not necessarily produced by interactions. Moreover, in multiple systems such as compact groups (or clusters of galaxies), a sequence of interaction events may exist that are correlated with the morphology of the galaxies: early-type galaxies, for example, may have entered the systems before late-type ones and would be expected to show less evidence of interactions than spirals for this reason.

In order to better determine the origin of the asymmetries observed in the various galaxies of our sample, we have meticulously reinspected the residual images produced by our asymmetry analysis and redistributed the galaxies in our sample in six different types of asymmetry, independent of the morphology. In type 1, we have put all the "symmetric" galaxies or galaxies with "intrinsic" asymmetries related to star formation clumps and/or spiral arms. Examples of galaxies with a type 1 asymmetry are shown in Figure 15. In type 2, we have regrouped all the galaxies where the asymmetry is possibly due to dust or to the inclination of the galaxy on the plane of the sky. Examples of galaxies with a type 2 asymmetry are presented in Figure 16. In type 3, we find the most obvious evidence of galaxy interactions under the forms of tidal tails, plumes, connecting bridges, or a common envelop between galaxies. Examples of galaxies with a type 3 asymmetry are presented in Figure 17. We put galaxies that are highly asymmetric, but for which the cause is not obvious in type 4. Examples of galaxies of this type can be found in Figure 18. In type 5, we have regrouped the cases where the asymmetry may be due to a smaller mass satellite galaxy. Examples of galaxies showing a type 5 asymmetry are shown in Figure 19. Finally, in type 6 we have regrouped the cases where the asymmetry is accompanied by a possible double nucleus. Examples of galaxies with this last type of asymmetry are shown in Figure 20.

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The distribution of asymmetry types in the different samples is presented in Figure 21. In the KIG sample, 60% of the galaxies have an asymmetry of type 1 and 8% show an asymmetry of type 2. Therefore, slightly less than 70% of the KIG galaxies are unperturbed. In this group, we do find some "asymmetric" galaxies; however. they are either of type 4 (19%) or of type 5 (13%). In general, and as expected, evidence of interactions is largely missing in the KIGs.

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The contrast with the KPGs is significant; as much as 52% are classified as type 3, which are obvious cases of recent interactions. Of the remaining asymmetric galaxies, 8% are classified as type 4, 6% as type 5, and another 3% as type 6. The rest of the galaxies are either type 1 (27%) or type 2 (4%). Therefore, almost 70% of the KPG galaxies show asymmetries consistent with "genuine" interactions.

In the case of the HCGs, 31% are classified as type 3, 6% as type 4, 6% as type 5, and 1% as type 6, summing up the evidence for genuine interactions to 44%. The number of "symmetric" galaxies, 44% of type 1 and 12% of type 2, is consequently higher than that in the KPGs.