Color Dispersion as an Indicator of Stellar Population Complexity: Insights from the Pixel Color–Magnitude Diagrams of 32 Bright Galaxies in Abell 1139 and Abell 2589

Our data set was obtained using the MegaCam mounted on the 3.6 m Canada–France–Hawaii Telescope in 2012–2013, as a part of the KYDISC project. Among the 14 nearby clusters at 0.016 ≤ z ≤ 0.145 observed in the KYDISC project, the target clusters in this paper are A1139 and A2589, which are at very similar low redshifts (z ∼ 0.04). This similarity in redshift makes the pCMD comparison much easier, because the galaxies in the two target clusters have almost the same conversion factors from angular size to physical scale (∼0.8 kpc arcsec^–1) and central wavelengths at the rest frame. See Table 1 of Lee et al. (2017) for the basic information on the two target clusters.

In the g and r bands, each cluster was deeply imaged with total exposure time of 2940 s. After pre-processing and image stacking, the final resampled pixel scale was 0185 and the stellar full width at half maximum was about 08. Based on the redshift information retrieved from the Sloan Digital Sky Survey (York et al. 2000), NASA Extragalactic Database,⁶ and SIMBAD Astronomical Database,⁷ cluster members were selected using the difference in recession velocity from the host cluster ($| {\rm{\Delta }}{v}_{\mathrm{rec}}| \leqslant 3{\sigma }_{\mathrm{cl}}$) and the clustercentric distance (R ≤ 2R₂₀₀), where σ_cl and R₂₀₀ are the velocity dispersion and virial radius of a given cluster, respectively. More details about the KYDISC project and its data products are described in Oh et al. (2018).

In this paper, we investigate the bright (${M}_{r}\leqslant -21.3$ mag) galaxies in A1139 and A2589 using pCMD analysis. Among the selected cluster members, there are 16 and 15 galaxies brighter than the magnitude cut in A1139 and A2589, respectively. In addition to these 31 member galaxies, there is a bright galaxy (A1139-00004) that satisfies $| {\rm{\Delta }}{v}_{\mathrm{rec}}| \leqslant 3{\sigma }_{\mathrm{cl}}$ but is located at 2.2 × R₂₀₀ distance from the A1139 center. This galaxy is not a member of A1139 in our selection criteria, but we include it in our sample. Since this paper is not focused on environmental effects, the important fact is that this galaxy is at a distance from us similar to those of the cluster members, not its actual membership.

In this paper, we do not apply k-correction to either pixel surface brightness or total magnitude, because the k-correction based on two-band color may not be sufficiently reliable, particularly when the photometric uncertainty is large (e.g., faint pixels). Lee et al. (2017) did not apply k-correction to pixel surface brightness either, but they applied it to total magnitude when selecting cluster members for comparison with BCGs. Thus, the sample in this paper does not exactly coincide with the comparison sample in Lee et al. (2017). Despite this difference, we decided that the photometric consistency between the pixel and total magnitudes is more important in this paper.

The basic information on our sample galaxies is summarized in Table 1. The right ascensions (R.A.) and declinations (decl.) are for the J2000 epoch. All magnitudes and surface brightness in this paper were corrected for Galactic extinction using the method of Schlafly & Finkbeiner (2011), in the AB magnitude system. Figure 1 presents the spatial distribution of the selected sample galaxies, while their total CMDs are shown in Figure 2. The r-band portrait images of our sample galaxies are displayed in Figure 3.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 1.  Basic Information on the Sample Galaxies

Name	R.A.	Decl.	Redshift	Mr	g − r	$| {\rm{\Delta }}{v}_{\mathrm{rec}}| /{\sigma }_{\mathrm{cl}}$	$R/{R}_{200}$	B/T	Morphology
	(hh:mm:ss)	(dd:mm:ss)		(mag)	(mag)
A1139-00001	10:58:11.0	+01:36:17	0.038	−22.801	0.842	0.88	0.27	0.94	elliptical (BCG)
A1139-00002	10:59:17.9	+01:09:12	0.039	−22.202	0.756	0.21	1.15	0.61	S0
A1139-00003	10:58:51.5	+01:39:02	0.040	−22.187	0.803	0.04	0.62	0.82	elliptical
A1139-00004	11:00:32.4	+02:06:57	0.039	−22.165	0.675	0.26	2.17	0.21	barred spiral
A1139-00005	10:58:26.7	+01:22:59	0.041	−22.151	0.823	0.69	0.37	0.70	disky elliptical
A1139-00006	10:58:57.2	+01:26:13	0.041	−22.083	0.695	1.12	0.57	0.26	barred? spiral
A1139-00007	10:59:20.5	+01:35:56	0.039	−22.059	0.826	0.48	0.83	0.69	elliptical
A1139-00008	11:00:01.9	+01:46:34	0.040	−22.039	0.841	0.30	1.40	0.42	spiral (bulge-dominated)
A1139-00009	10:59:06.8	+01:52:52	0.041	−21.934	0.759	0.56	1.15	0.65	spiral (bulge-dominated)
A1139-00010	10:58:15.2	+01:36:58	0.039	−21.841	0.828	0.32	0.31	0.58	elliptical
A1139-00011	10:57:51.9	+01:40:40	0.041	−21.808	0.809	1.04	0.46	0.44	edge-on disk
A1139-00012	10:58:13.0	+01:36:25	0.039	−21.807	0.818	0.85	0.28	0.64	elliptical
A1139-00013	10:57:46.6	+01:15:13	0.039	−21.778	0.817	0.41	0.64	0.87	edge-on disk
A1139-00014	10:57:43.4	+01:34:02	0.039	−21.705	0.808	0.41	0.28	0.77	disky elliptical
A1139-00015	10:59:05.8	+01:10:55	0.039	−21.693	0.540	0.57	1.02	0.03	spiral
A1139-00016	10:59:11.4	+01:48:33	0.040	−21.442	0.655	0.10	1.04	0.44	barred spiral
A1139-00017	11:00:01.1	+01:06:44	0.039	−21.334	0.709	0.59	1.55	0.09	barred? spiral
A2589-00001	23:23:57.5	+16:46:38	0.041	−23.807	0.838	0.09	0.04	0.98	elliptical (BCG)
A2589-00002	23:25:42.0	+17:31:55	0.041	−22.000	0.849	0.06	1.04	0.44	edge-on disk
A2589-00003	23:23:08.5	+17:30:28	0.038	−21.970	0.572	1.12	0.89	0.17	barred? spiral
A2589-00004	23:24:31.4	+16:52:05	0.036	−21.907	0.482	1.89	0.20	0.39	barred? spiral
A2589-00005	23:23:51.4	+16:38:41	0.035	−21.747	0.448	2.20	0.20	0.09	spiral
A2589-00006	23:22:37.1	+16:29:19	0.037	−21.706	0.818	1.36	0.55	0.72	elliptical
A2589-00007	23:23:59.1	+16:48:40	0.043	−21.654	0.863	0.39	0.03	0.91	spiral (bulge-dominated)
A2589-00008	23:23:53.5	+16:52:48	0.045	−21.653	0.875	1.17	0.09	0.30	disky elliptical
A2589-00010	23:23:56.8	+16:44:60	0.038	−21.500	0.837	1.01	0.07	0.68	elliptical
A2589-00011	23:25:55.6	+17:29:21	0.046	−21.466	0.591	1.55	1.03	0.03	spiral
A2589-00012	23:25:13.4	+16:24:26	0.039	−21.427	0.856	0.78	0.63	0.40	disky elliptical
A2589-00013	23:24:05.8	+16:47:31	0.042	−21.426	0.879	0.09	0.06	0.73	edge-on disk
A2589-00014	23:23:55.8	+16:55:00	0.041	−21.390	0.853	0.06	0.13	0.62	disky elliptical
A2589-00015	23:23:02.1	+17:32:20	0.038	−21.381	0.775	1.24	0.93	0.69	barred? spiral
A2589-00018	23:23:54.4	+16:40:50	0.045	−21.321	0.828	1.24	0.16	0.68	elliptical

Download table as:  ASCIITypeset image

Figure 4 shows the r-band surface brightness (μ_r) maps, which reveal the internal structures of our sample galaxies more clearly. Based on Figures 3 and 4, authors J.H.L., M.P., and H.R.L. visually classified the morphological types of our sample galaxies into the following classes:

• 1.  
  typical elliptical (E): well-defined elliptical structures without any disturbed features,
• 2.  
  disky elliptical (disky E): overall elliptical morphology with slightly disky internal structures (but not significantly different from typical elliptical galaxies),
• 3.  
  lenticular (S0): hosting a faint disk component and not significantly inclined (face-on),
• 4.  
  edge-on disk: largely inclined S0 or late-type (but mostly bulge-dominated in our sample),
• 5.  
  barred spiral: spiral arms connected to a bar structure (a question mark is denoted when the bar is ambiguous), and
• 6.  
  spiral: spiral arms without a bar structure.

Since the bulge fraction affects the overall properties of a late-type galaxy, a mark of "BD" is additionally noted for a bulge-dominated, late-type galaxy. The morphological classification is sometimes ambiguous: E versus disky E, disky E versus S0, and S0 versus bulge-dominated spiral. However, the small ambiguity between some types does not significantly matter here, because we are mainly focused on the difference between broadly divided early- and late-type galaxies rather than between individual fine classes. Note that the classification in this paper was conducted independently of that in the KYDISC catalog, and thus they may not necessarily coincide with each other. For example, A1139-00008 is listed as an S0 galaxy in the KYDISC catalog, but we classify it as a bulge-dominated spiral, because of very faint ambient features around it. As a quantitative indicator of morphology, we also estimated the bulge-to-total ratio (B/T) of each galaxy, based on the decomposition into Sérsic component (bulge) + exponential component (disk) using the GALFIT code (Peng et al. 2002, 2010).

Zoom In Zoom Out Reset image size

Figure 5 presents the g − r color maps of our sample galaxies. The internal distributions of stellar populations are revealed in these maps, which are particularly useful in visually inspecting the interactions with neighbor galaxies (e.g., A1139-00009 and A1139-00017). Note that our morphological classification is not based on these color maps, but only on the light distributions in the r band.

Zoom In Zoom Out Reset image size

Infrared color is a useful tool to diagnose star formation and nucleus activities of galaxies (Asssef et al. 2010; Jarrett et al. 2011, 2017; Ko et al. 2016). In this paper, we use Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) data. WISE mapped the whole sky in four infrared bands: 3.4, 4.6, 12, and 22 μm (W1, W2, W3, and W4) with angular resolutions of 61, 64, 65, and 120, respectively.

From the WISE website,⁸ we retrieved infrared magnitudes for our target galaxies. For most point-like sources in the WISE data, the recommended magnitude type is the profile-fit magnitude, but we use the elliptical aperture magnitude instead, because our targets are mostly extended sources even in the WISE images. The elliptical apertures in the WISE photometry are based on cross-matching with the Two Micron All Sky Survey Extended Source Catalog (2MASS XSC; Skrutskie et al. 2006). However, the aperture magnitude is not available for one of our targets (A2589-00014), which means that this object looks like a point source in the infrared images although it is an extended source at higher resolution. Thus, we use the profile-fit magnitude only for A2589-00014.

We adopt the [4.6]–[12] (W2 − W3) color as a star formation indicator, because the [12] band flux is sensitive to star formation activity whereas the [4.6] band flux reflects age-independent stellar mass. On the other hand, the [3.4]–[4.6] (W1 − W2) color is known to be an indicator of active galactic nuclei (AGNs), owing to its sensitivity to hot dust (Jarrett et al. 2017). These color indices are used to describe the star formation properties of the sample galaxies.

Before plotting final pCMDs, target images need to be appropriately processed to minimize the influence of contaminants and to improve the signal-to-noise ratio (S/N) of each pixel. Lee et al. (2017) established a procedure for the pCMD analysis, which includes contaminant-masking and pixel-smoothing. The procedure is summarized as follows.

• 1.  
  Trim a sufficient area around a target galaxy.
• 2.  
  Detect objects using the Source Extractor (SE; Bertin & Arnouts 1996) with sufficiently large background mesh sizes (to detect relatively large contaminants).
• 3.  
  Use the SE again with small background mesh sizes (to detect small and faint contaminants).
• 4.  
  Mask the pixels within the apertures of any detected non-target objects.
• 5.  
  Smooth pixels by adopting a smoothing kernel with a seeing-sized (008) aperture.

In Lee et al. (2017), this procedure worked well, because the target galaxies were BCGs with relatively simple shapes and few complex substructures.

In this paper, on the other hand, the targets are galaxies of various morphologies, from elliptical to spiral. Because elliptical galaxies (and most edge-on disk galaxies) do not show complex structures in their r-band images, there is no problem in applying SE-detection-based masking to them. In the case of late-type galaxies, however, this does not work well, because the SE hardly distinguishes between contaminants (companions or foreground/background objects) and galaxy substructures (spiral arms, star-forming clumps, and bars). For a few late-type galaxies, SE-detection-based masking removes more than 80% of the entire image for a target galaxy, which is obviously over-masking.

Thus, we apply SE-detection-based masking adaptively according to the target morphology and the masking performance. That is, the full procedure is applied if SE-detection-based masking does not cause over-masking (e.g., A1139-00003). On the other hand, if this method (step 2 and/or step 3 in the procedure) appears to over-mask the target galaxy, the masking step is omitted (e.g., A1139-00004). During this adaptation, we intended to minimize the omission of masking. That is, the masking step is omitted only when it obviously over-masks the target galaxy, whereas it is conducted when it is unclear whether the target is over-masked or not. Among our sample galaxies, there was rarely an ambiguous situation and thus we decided the final masking sets relatively easily.

However, adaptive masking has a fundamental weakness: late-type galaxies with complicated structures tend to be masked too little, compared to early-type galaxies with simple structures. Because late-type galaxies are expected to have remaining contaminants that were not sufficiently masked in the SE-detection-based masking process, a supplementary process is necessary. For this, we additionally masked the pixels that correspond to the pCMD outliers. The processes are listed as follows.

• 1.  
  Estimate the 5, 50, and 95 percentiles in the pixel g − r color distribution at given μ_r, using the pCMD after the SE-detection-based masking.
• 2.  
  Define ${\sigma }_{1}\equiv {(g-r)}_{50 \% }-{(g-r)}_{5 \% }$ and ${\sigma }_{2}\,\equiv \,{(g-r)}_{95 \% }-{(g-r)}_{50 \% }$ as a function of μ_r.
• 3.  
  Define pCMD outliers as the pixels with $g-r\,\lt {(g-r)}_{50 \% }-2{\sigma }_{1}$ or $g-r\gt {(g-r)}_{50 \% }+2{\sigma }_{2}$, at given μ_r.
• 4.  
  Mask the pCMD outliers and their neighboring pixels within 08 (seeing size).

Figure 6 schematically summarizes the entire masking procedure to yield the final pCMDs (the standard procedure on the left). The plots in the second row of the left side in Figure 6 show the surface brightness contour maps of the sample galaxies after the adaptive (SE-detection-based) masking. The plots in the third row of the left side show the pCMDs after SE-detection-based masking and smoothing with the 08-aperture spline kernel (Lee et al. 2017), with the pCMD outliers marked (see Appendix A for the full plots of the whole sample). The pCMD outliers of late-type galaxies mostly outnumber those of early-type galaxies, which means that many remaining contaminants in late-type galaxies are additionally masked in this process.

Zoom In Zoom Out Reset image size

Note that the pCMD outlier masking is not perfect either. There may still be remaining contaminants or there may be some over-masking, particularly for fine substructures in the target galaxies. For example, the BCG of A2589 (A2589-00001) is thought to have vestiges of infalling low-mass, star-forming satellites, which was revealed from the analysis of its pCMD outliers in Lee et al. (2017). Such fine features are mostly washed out in the pCMD outlier masking process. Thus, this process cannot be used if we want to inspect the fine substructures in target galaxies. However, it does not significantly affect the main features of the pCMD backbones, because the number of outliers is typically much smaller than that of the pixels in the main features. The plots in the fourth row in Figure 6 present the μ_r contour maps after masking the pCMD outliers and their neighboring pixels within 08. After this two-step masking process, the final pCMDs are yielded as shown in Figure 7.

Zoom In Zoom Out Reset image size

In the standard procedure, the SE-detection-based masking process for contaminants has two weaknesses. One is that late-type galaxies cannot be sufficiently masked using this method, which is ameliorated to some extent by using the pCMD outlier masking as described in Section 3.1. However, another weakness remains: "adaptive masking" can cause a bias when we compare the pCMD properties between different morphological types. As already mentioned, late-type galaxies tend to be less suitable for SE-detection-based masking than early-type galaxies. Among the 13 spiral galaxies, SE-detection-based masking was completely omitted for four spirals (A1139-00004, A2589-00003, A2589-00004, and A2589-00011), while full masking was applied to only two spirals (A1139-00008 and A2589-00007). On the other hand, full masking was applied to every elliptical galaxy. That is, the masking processes for early- and late-type galaxies are not identical in the standard procedure, and thus a comparison of the final pCMDs between galaxies with different morphological types may not be appropriate.

To address this issue, we try an alternative masking procedure that does not depend on subjective "adaptation" according to galaxy morphology. This procedure is based on the idea that the light from contaminants tends to be brighter than the brightness expected at the distance from the target galaxy center. The detailed procedure is as follows.

• 1.  
  Trim a sufficient area around a target galaxy.
• 2.  
  Trim the image again with a radius of ${f}_{c}\times R{80}_{(22.2-23.2)}$, where f_c is a fixed value and $R{80}_{(22.2-23.2)}$ is the 80 percentile in the distribution of distance to center, among pixels with 22.2 ≤ μ_r ≤ 23.2 mag arcsec⁻²; we empirically choose f_c = 1.5 (see Appendix A for the trimming area for each sample galaxy).
• 3.  
  Estimate the 10 and 50 percentiles in the distribution of distance to center, among pixels with given ${\mu }_{r}$ ($R{10}_{{\mu }_{r}}$ and $R{50}_{{\mu }_{r}}$, respectively).
• 4.  
  Mask pixels with μ_r and radial distance (R) satisfying $R-R{10}_{{\mu }_{r}}\gt {f}_{R}\times (R{50}_{{\mu }_{r}}-R{10}_{{\mu }_{r}})$, where we empirically choose f_R = 5.
• 5.  
  Conduct the additional pCMD outlier masking as described in Section 3.1.

These processes depend on a few control parameters being empirically determined, which is a weakness. Nevertheless, this method has the considerable merit that it can be consistently applied to target galaxies regardless of their morphological type.

The plots in the second row of the right side in Figure 6 show the surface brightness contour maps after this μ_r-radius-relation-based (R(μ_r)-based) masking. The overall area masked by the R(μ_r)-based method tends to be smaller (under-masking) than that by the SE-detection-based method. Thus, the role of the pCMD outlier masking is more important in the alternative procedure, because it augments the weak performance of the R(μ_r)-based masking. In this procedure, the number of pCMD outliers is, on average, not so different between early- and late-type galaxies, unlike in the standard procedure. This is because the alternative masking procedure is free from the morphology bias caused by subjective "adaptation."

The final pCMDs after alternative masking are presented as pixel number density contours in Figure 8. The overall features of the pCMDs in Figure 8 are not significantly different from those after standard masking in Figure 7, but some small details appear to differ. Such differences are revealed in Figure 9, which shows the pixel number density contours for the pCMD residuals (Figure 7 subtracted by Figure 8). In most cases, the pixels in the pCMDs after the alternative procedure outnumber those after the standard procedure (blue contours). This means that the alternative procedure is less efficient in masking contaminants than the standard procedure, at least for early-type galaxies. The opposite case is much rarer (red contours) even for late-type galaxies. It is hard to increase the masking efficiency of the alternative procedure by adjusting f_R, because a too small f_R value frequently results in unreasonable masking.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In summary, the alternative procedure is not sufficient in the aspect of masking efficiency, but the results from it are necessary when a technically fair comparison without any morphology bias is required. In Section 4, we mainly analyze the results from the standard procedure, to take advantage of its masking efficiency (mainly for early-type galaxies). However, the results from the alternative procedure are also used to check the effect of morphology bias, and these are fully presented in Appendix B.

In the final pCMDs (Figures 7 and 8), early-type galaxies show simple pCMD features, whereas late-type galaxies show significantly curved pCMDs. As introduced in Section 1, those features are called prime sequences and inverse-L features in Lanyon-Foster et al. (2007), respectively. However, such a dichotomic division is not always obvious. Some early-type galaxies have considerably disturbed features at their bright parts (A1139-00007, A2589-00008, and A2589-00014) and, besides, the pCMDs of some bulge-dominated late-type galaxies or edge-on disk galaxies are similar to those of early-type galaxies (A2589-00007 and A2589-00013). That is, galaxies even of similar morphological types have some variety in their pCMD features, and this variety is broader in late-type galaxies.

In early-type galaxies, the unusual features (deviations from the prime sequences) seem to be closely related to tidal interactions with nearby neighbors or companions. The prime sequences of the elliptical galaxies show curvatures different from one another, which implies that their formation histories are not entirely homologous, as discussed in Lee et al. (2017). Different internal dust extinction may also be responsible for such variety (Lee et al. 2011, 2012). The only face-on S0 galaxy in our sample (A1139-00002) shows a blue pCMD-tip feature, which indicates that this galaxy may have experienced central star formation activity very recently.

The (barred and unbarred) spiral galaxies show complex and diverse features in their pCMDs. The pCMD structure of a spiral galaxy is roughly described as consisting of a (red and bright) bulge part and a (blue and faint) disk part, which form an overall inverse-L feature. However, whereas this division is quite clear in some spiral galaxies (A1139-00016, A2589-0004, and A2589-00011), some others show more complicated and amorphous features (A1139-00017 and A2589-00015). The bulge-dominated spiral galaxies (A1139-00008, A1139-00009, and A2589-00007) show relatively simple pCMD features compared to the other spiral galaxies, but these are more distorted than the pCMDs of typical elliptical galaxies.

Finally, some edge-on disk galaxies (A1139-00013 and A2589-00013) have pCMDs similar to those of elliptical galaxies, but some others do not (A1139-00011 and A2589-00002). The former appear quite elliptical in their r-band images (Figure 3), but they were classified into edge-on disks because an edge-on dust lane was found (A1139-0013) or the morphology was too elongated to be an elliptical galaxy (A2589-00013). The latter are clearly different from elliptical galaxies in their appearance.

One of the main purposes of this paper is to establish a quantitative method using pCMDs to distinguish between galaxies with different morphological types. For a quantitative comparison of the pCMD features, we devised several parameters describing the features of pCMDs as listed in Table 2.

Table 2.  Parameters Describing pCMD Features

pCMD Parameter	Description
μr(tip)	Minimum (brightest) r-band surface brightness among all pixels
$\min {(g-r)}_{{\mu }_{r}\leqslant 23.2}$	Minimum (bluest) value of mean g − r color at ${\mu }_{r}\leqslant 23.2$ mag arcsec−2
max ${(g-r)}_{{\mu }_{r}\leqslant 23.2}$	Maximum (reddest) value of mean g − r color at μr ≤ 23.2 mag arcsec−2
$\min {(\sigma (g-r))}_{{\mu }_{r}\leqslant 21.2}$	Minimum (tightest) value of g − r color dispersion at μr ≤ 21.2 mag arcsec−2
max ${(\sigma (g-r))}_{{\mu }_{r}\leqslant 21.2}$	Maximum (most dispersed) value of g − r color dispersion at μr ≤ 21.2 mag arcsec−2
max ${(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$	Maximum value of g − r color dispersion at 20.0 ≤ μr ≤ 21.0 mag arcsec−2
max ${(\sigma (g-r))}_{18.5\leqslant {\mu }_{r}\leqslant 19.5}$	Maximum value of g − r color dispersion at 18.5 ≤ μr ≤ 19.5 mag arcsec−2

Note. The "mean g − r color" and "g − r color dispersion" indicate the quantities estimated using the pixels with fixed μ_r. That is, $\min {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ is the bluest value among the "mean g − r colors as a function of μ_r," not the g − r color of the bluest pixel among the whole pixels. In the text, "the minimum (maximum) g − r color" indicates "the minimum (maximum) value of mean g − r color as a function of μ_r."

Download table as:  ASCIITypeset image

4.2.1. Reliability Limits

4.2.2. Galaxy Morphology and pCMD Parameters

We now investigate the relationship between the pCMD parameters and galaxy morphology, and its physical implication. Figure 10 presents the basic correlations between the pCMD parameters, with the morphological types denoted. The trends between the parameters in the whole sample are mostly not obvious, but Figure 10(b) shows a notable anti-correlation between $\min {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ and $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$. This anti-correlation appears to be closely related with galaxy morphology, in the context that elliptical galaxies tend to have larger $\min {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ and smaller $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ than galaxies of other types. This is a quantitative expression of the fact that the elliptical galaxies hardly have blue pixels and their pCMDs tend to be tightly bound.

Zoom In Zoom Out Reset image size

A similar plot was shown in Figure 13 of Lanyon-Foster et al. (2007), in which the mean pixel color and the mean pixel color dispersion were compared. Although Lanyon-Foster et al. found a correlation between those mean values, its scatter was larger than that in our Figure 10(b). This indicates that the minimum pixel color and the maximum pixel color dispersion are better indicators of galaxy morphology than the mean values. On the other hand, the minimum pixel color dispersion (Figure 10(a)) or the maximum pixel color (Figures 10(c)–(d)) seems to be less efficient even than the mean values. The reason is not difficult to understand: even late-type galaxies may have small $\min (\sigma (g-r))$ values due to their bulges, and large $\max (g-r)$ values due to significant dust extinction in their disks as well as in their bulges.

In Figure 11, we examine how well galaxy morphology is distinguished by pCMD colors and μ_r(tip). In Figure 11(a), the elliptical galaxies are distributed in a small domain, whereas the spiral galaxies show a much wider distribution. Most spiral galaxies tend to have pixel colors bluer than those of early-type galaxies, but the $\max {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ values of some late-type galaxies are similar (A1139-00017 and A1139-00006) or even larger (A2589-00015). On the other hand, $\min {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ seems to divide elliptical galaxies from spiral galaxies better than $\max {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ does, except for bulge-dominated spiral galaxies (A1139-00008 and A2589-00007) and edge-on disk galaxies. This is because $\max {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ represents the color of a late-type galaxy's bulge, which is known to be similar to an elliptical galaxy in its properties (Dressler 1987; Fisher & Drory 2008),¹⁰ whereas $\min {(g-r)}_{{\mu }_{r}\leqslant 23.2}$ is strongly affected by the disk parts. In Figure 11(b), the μ_r(tip) is brighter than 18.0 mag arcsec⁻² for all elliptical galaxies in our sample. On the other hand, many spiral galaxies have fainter μ_r(tip), but some have μ_r(tip) as bright as those of elliptical galaxies (A2589-00003 and A2589-00004). These results show that the combination of pCMD colors and μ_r(tip) moderately divides early- and late-type galaxies, albeit not perfectly.

Zoom In Zoom Out Reset image size

Next, we test the capability of pCMD color dispersion parameters to classify galaxy morphology in Figure 12. The combination of color dispersion divides early- and late-type galaxies as nicely as or even better than the color index combination does. This indicates that the complexity of stellar populations at given ${\mu }_{r}$ as well as their mean age and metallicity is an important feature discriminating between early- and late-type galaxies. After examining various combinations, we found that the best combination to discriminate galaxy morphology is $\min {(\sigma (g-r))}_{{\mu }_{r}\leqslant 21.2}$ and $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$. In Figure 12(b) (zoomed-in in Figure 13(a)), the elliptical galaxies are well separated from the spiral galaxies, and even from the bulge-dominated spiral galaxies, unlike in Figure 11. This seems to be mainly because $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ represents how complex the stellar populations are at the region where the disk component starts to surpass the bulge component in a typical late-type galaxy. It consequently reflects the disk dominance in a galaxy, because stellar populations in a disk tend to be much more complex than those in a bulge. See the plots in the second row of Figure 6 (and Appendix A) for the spatial areas covered by the pixels with 20.0 ≤ μ_r ≤ 21.0 in each galaxy.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

However, although the $\min {(\sigma (g-r))}_{{\mu }_{r}\leqslant 21.2}$ versus $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ plot seems to distinguish early-type (E, disky E, and S0) galaxies from spiral galaxies almost perfectly, the edge-on disk galaxies are still mixed with the elliptical galaxies in this plot. To distinguish them, a parameter that is not from a pCMD is necessary: the axis ratio (b/a). Figure 12(d) (zoomed-in in Figure 13(b)) shows that the edge-on disk galaxies are separated from the early-type galaxies in the b/a versus $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ plot, due to their small b/a values. In summary, at least in our sample, the early-type galaxies are well distinguished from the other galaxies in the parameter space of $\min {(\sigma (g-r))}_{{\mu }_{r}\leqslant 21.2}$, $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$, and axis ratio. The pCMDs from the alternative masking procedure also give consistent results (Appendix B).

In Figure 14, we compare the pCMD color dispersion parameters with B/T, one of the most frequently used indicators of galaxy morphology. The performance of B/T for morphological classification is not bad: the elliptical and spiral galaxies are mostly separated by B/T. However, it fails to distinguish between elliptical galaxies and bulge-dominated spiral galaxies. Since $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ even distinguishes between these galaxies, B/T appears to perform more poorly than color dispersion. Note that the structural decomposition may be improved if one makes more effort, such as a more careful setup of masks and better initial guess, and more various component-functions for more realistic fitting (Peng et al. 2010; Kim et al. 2016). However, the possibility of improvement in structural decomposition in this way inversely highlights the strength of the pCMD approach, which is simple and is negligibly dependent on such technical conditions.

Zoom In Zoom Out Reset image size

Another main purpose of this paper is to understand the relationship between stellar population complexity and recent star formation activity in a galaxy. While the former is measured by the pCMD color dispersion, we use photometric information in the infrared bands to estimate the star formation activities of the target galaxies.

Jarrett et al. (2017) showed how the infrared color–color ([3.4]–[4.6] versus [4.6]–[12]) diagram classifies galaxies according to their star formation and AGN activities. Based on the scheme, Figure 15 shows that the morphological types of our sample galaxies are strongly correlated with their star formation activities. While all of our sample galaxies are in the non-AGN domain ([3.4]–[4.6] < 0.8), the spiral galaxies are clearly redder (more active star formation) than the elliptical galaxies in the [4.6]–[12] color, except for two bulge-dominated spiral galaxies. Edge-on disk galaxies are in the intermediate domain between elliptical and spiral galaxies, although several elliptical galaxies and two bulge-dominated spiral galaxies also share that domain. Note that the edge-on disk galaxies in our sample tend to be bulge-dominated rather than disk-dominated, and thus they may be intrinsically similar to bulge-dominated spiral galaxies.

Zoom In Zoom Out Reset image size

In Figure 16, we compare the pCMD parameters and the total infrared colors of the sample galaxies. There is a strong correlation between [4.6]–[12] and min(g − r)${}_{{\mu }_{r}\leqslant 23.2}$, whereas max(g − r)${}_{{\mu }_{r}\leqslant 23.2}$ shows no clear correlation with [4.6]–[12]. The former trend is as expected, because blue optical color and red infrared color are commonly the signals of star formation activity. Since star-forming spiral galaxies often have red bulges, the latter trend is also understood. However, when we consider the elliptical galaxies only, no significant correlation is found between [4.6]–[12] and min(g − r)${}_{{\mu }_{r}\leqslant 23.2}$. That is, the elliptical galaxies with small excess in infrared color show no difference in min(g − r)${}_{{\mu }_{r}\leqslant 23.2}$ from those without infrared-color excess. On the other hand, for the elliptical galaxies, min($\sigma (g-r)$)${}_{{\mu }_{r}\leqslant 21.2}$ and max($\sigma (g-r)$)${}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ appear to be correlated with [4.6]–[12]: the elliptical galaxies with larger [4.6]–[12] tend to have larger min($\sigma (g-r)$)${}_{{\mu }_{r}\leqslant 21.2}$ and max($\sigma (g-r)$)${}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$, as shown in panels (c) and (d) of Figure 16.

Zoom In Zoom Out Reset image size

The Pearson correlation coefficients and their p-values between several pCMD parameters and the WISE color are listed in Table 3. This table quantitatively shows that min(g − r)${}_{{\mu }_{r}\leqslant 23.2}$, min($\sigma (g-r)$)${}_{{\mu }_{r}\leqslant 21.2}$, and max($\sigma (g-r)$)${}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ are significantly correlated or anti-correlated with [4.6]–[12], whereas max(g − r)${}_{{\mu }_{r}\leqslant 23.2}$ shows no significant correlation for the whole sample. On the other hand, such trends are somewhat different when only elliptical galaxies are considered: min($\sigma (g-r)$)${}_{{\mu }_{r}\leqslant 21.2}$ shows a marginal correlation and max($\sigma (g-r)$)${}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ shows a stronger correlation. It is also noted that max(g −r)${}_{{\mu }_{r}\leqslant 23.2}$ has a marginal correlation with [4.6]–[12] when elliptical and disky elliptical galaxies are considered together, while it has an anti-correlation when spiral galaxies are considered only. None of these trends significantly changes even when we use the results from the alternative procedure (Appendix B).

Table 3.  Correlations with the WISE [4.6]–[12] Color

pCMD Parameters	All		E		E + disky E		Spirals
min(g − r)${}_{{\mu }_{r}\leqslant 23.2}$	−0.87	(0.000)	0.03	(0.935)	0.19	(0.506)	−0.62	(0.052)
max(g − r)${}_{{\mu }_{r}\leqslant 23.2}$	−0.25	(0.173)	0.37	(0.330)	0.54	(0.044)	−0.72	(0.019)
min($\sigma (g-r)$)${}_{{\mu }_{r}\leqslant 21.2}$	0.64	(0.000)	0.66	(0.052)	0.37	(0.190)	−0.44	(0.199)
max($\sigma (g-r)$)${}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$	0.86	(0.000)	0.80	(0.010)	0.77	(0.001)	0.19	(0.602)

Note. Pearson correlation coefficients (and p-values) with the WISE [4.6]–[12] color, for all galaxies (All; 32), elliptical galaxies (E; 9), elliptical + disky elliptical galaxies (E + disky E; 14), and barred + unbarred spiral galaxies (Spirals; 13), based on the pCMDs after the standard masking procedure.

Download table as:  ASCIITypeset image

Table 4 lists the pCMD parameter values of the sample galaxies from the standard procedure and their WISE colors, which are used in Figures 10–16. The WISE colors used in Appendix B are the same as those in Table 4.

Table 4.  pCMD Parameters from the Standard Procedure, and WISE Colors

Name	$\min (g-r)$	$\max (g-r)$	${\mu }_{r}$(tip)	$\min (\sigma (g-r))$	$\max (\sigma (g-r))$	$\max (\sigma (g-r))$	$\max (\sigma (g-r))$	[3.4]–[4.6]	[4.6]–[12]
	${}_{{\mu }_{r}\leqslant 23.2}$	${}_{{\mu }_{r}\leqslant 23.2}$		${}_{{\mu }_{r}\leqslant 21.2}$	${}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$	${}_{18.5\leqslant {\mu }_{r}\leqslant 19.5}$	${}_{{\mu }_{r}\leqslant 21.2}$
A1139-00001	0.798	0.879	17.44	0.007	0.012	0.013	0.013	−0.025 ± 0.012	0.500 ± 0.096
A1139-00002	0.727	0.799	16.80	0.011	0.013	0.013	0.017	−0.017 ± 0.009	0.285 ± 0.167
A1139-00003	0.710	0.909	17.98	0.006	0.011	0.012	0.016	−0.052 ± 0.012	0.522 ± 0.167
A1139-00004	0.552	0.928	18.29	0.041	0.088	0.071	0.103	0.080 ± 0.012	2.794 ± 0.026
A1139-00005	0.805	0.870	17.35	0.005	0.012	0.012	0.012	−0.031 ± 0.010	0.558 ± 0.118
A1139-00006	0.613	0.879	17.77	0.012	0.055	0.037	0.055	0.057 ± 0.010	2.881 ± 0.022
A1139-00007	0.761	0.930	17.24	0.011	0.017	0.048	0.049	0.002 ± 0.009	1.289 ± 0.057
A1139-00008	0.799	0.896	17.78	0.007	0.028	0.017	0.028	0.008 ± 0.010	1.224 ± 0.097
A1139-00009	0.658	0.925	17.81	0.019	0.033	0.049	0.049	0.114 ± 0.011	2.114 ± 0.032
A1139-00010	0.777	0.872	17.03	0.009	0.013	0.014	0.014	−0.033 ± 0.011	0.368 ± 0.174
A1139-00011	0.721	1.139	18.41	0.034	0.059	0.136	0.136	0.024 ± 0.010	1.924 ± 0.041
A1139-00012	0.779	0.874	17.18	0.008	0.013	0.015	0.015	−0.018 ± 0.013	0.547 ± 0.122
A1139-00013	0.760	0.911	17.71	0.015	0.037	0.052	0.052	−0.011 ± 0.010	1.190 ± 0.067
A1139-00014	0.769	0.887	17.32	0.009	0.011	0.017	0.017	−0.009 ± 0.011	0.019 ± 0.303
A1139-00015	0.388	0.786	19.14	0.014	0.073	0.016	0.074	0.053 ± 0.016	3.220 ± 0.021
A1139-00016	0.575	0.815	17.51	0.018	0.091	0.033	0.091	0.111 ± 0.014	3.000 ± 0.024
A1139-00017	0.512	0.968	18.54	0.039	0.133	0.116	0.136	0.159 ± 0.009	3.571 ± 0.011
A2589-00001	0.837	0.919	17.52	0.003	0.009	0.005	0.016	−0.068 ± 0.011	0.510 ± 0.085
A2589-00002	0.696	1.081	16.93	0.010	0.087	0.070	0.087	−0.014 ± 0.012	0.926 ± 0.100
A2589-00003	0.514	0.727	17.16	0.028	0.106	0.055	0.123	0.237 ± 0.010	3.647 ± 0.011
A2589-00004	0.276	0.814	17.35	0.013	0.101	0.032	0.101	0.117 ± 0.012	3.454 ± 0.016
A2589-00005	0.404	0.733	18.20	0.019	0.124	0.044	0.124	0.117 ± 0.017	3.352 ± 0.023
A2589-00006	0.792	0.870	17.39	0.004	0.009	0.009	0.009	−0.049 ± 0.014	−0.289 ± 0.454
A2589-00007	0.825	0.912	17.54	0.004	0.020	0.010	0.020	0.001 ± 0.012	1.026 ± 0.085
A2589-00008	0.828	0.963	17.51	0.007	0.019	0.048	0.048	−0.007 ± 0.013	1.355 ± 0.063
A2589-00010	0.821	0.904	17.71	0.008	0.014	0.032	0.032	−0.036 ± 0.021	1.283 ± 0.117
A2589-00011	0.528	0.820	18.82	0.019	0.161	0.029	0.161	0.087 ± 0.014	3.276 ± 0.024
A2589-00012	0.817	0.909	17.58	0.007	0.012	0.010	0.015	−0.014 ± 0.012	0.698 ± 0.137
A2589-00013	0.837	0.937	17.02	0.004	0.010	0.006	0.011	−0.049 ± 0.012	0.684 ± 0.117
A2589-00014a	0.779	0.950	17.66	0.007	0.012	0.023	0.023	−0.048 ± 0.045	1.267 ± 0.169
A2589-00015	0.646	1.136	18.46	0.050	0.127	0.157	0.157	0.168 ± 0.011	2.271 ± 0.033
A2589-00018	0.796	1.008	17.75	0.008	0.011	0.022	0.023	−0.019 ± 0.015	0.634 ± 0.294

Note.

^aThe WISE colors of A2589-00014 are based on the profile-fit magnitudes, whereas those of all the other targets are based on the elliptical aperture magnitudes. See Section 2.3 for details.

Download table as:  ASCIITypeset image

There are some fundamental difficulties in masking contaminants. In the case of early-type galaxies or edge-on disk galaxies, the masking is relatively easy: SE-detection-based masking works well, because those galaxies have hardly any confusing internal substructures. After SE-detection-based masking, possible remaining contaminants will be covered by the pCMD outlier masking, although it may sometimes over-mask internal substructures such as tidal debris.

What does matter is masking in late-type galaxies. Basically, it is very difficult to perfectly mask contaminants in and around a face-on, late-type galaxy with complex spiral arms, because its substructures and contaminants are often too similar to be distinguished. Thus, in the standard procedure, we omitted SE-detection-based masking for such targets, and only conducted pCMD outlier masking, which works alone to some extent. However, this means that different masking processes are applied to early- and late-type galaxies, which may cause inappropriate comparison of the pCMD features between galaxies with different morphological types.

The alternative masking procedure was devised to complement this weakness of the standard procedure. Through the alternative procedure, fair comparison is possible between galaxies of any morphological types. However, $R({\mu }_{r})$-based masking is less efficient than SE-detection-based masking for early-type galaxies. It may fail to mask faint contaminants or those very close to the target galaxy center. Moreover, $R({\mu }_{r})$-based masking may not cover the faint outskirts of a contaminating object due to the limit of the masking algorithm. Thus, it is recommended to rely on the standard masking procedure if the sample consists of only early-type and edge-on galaxies. The main purpose of the alternative masking procedure is to check how reliable the results from the standard procedure are, by comparing them with the results from a self-consistent masking procedure.

Section 4.2.2 and Appendix B show that the results from the standard procedure and from the alternative procedure are not significantly different from each other. This is because our analysis in this paper focuses on the major trend in the pCMD of each galaxy rather than its fine features. The consistency between the results from the different procedures, despite the weakness of each masking procedure, indicates that the major trend of a pCMD is hardly influenced by the details of the masking methods.

We tested various combinations of parameters measured from the pCMDs of our sample galaxies to examine how galaxies of different morphological types are quantitatively distinguished in their pCMD features. As a result, we found that the best parameter set to classify galaxy morphology based on pCMDs is a combination of the minimum color dispersion at μ_r ≤21.2 mag arcsec⁻² and the maximum color dispersion at 20.0 ≤ μ_r ≤ 21.0 mag arcsec⁻², assisted by axis ratio (Figure 13).

Although these parameters were empirically selected, the underlying mechanism in which they work is relatively easy to understand. As revealed in the pCMDs and the μ_r contour maps, $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ represents how complex the stellar populations are at the regions where the disk component begins to be dominant in a typical late-type galaxy. In other words, $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ is dominated by the bulge stellar populations for an early-type galaxy, whereas it is largely affected by the disk stellar populations for a late-type galaxy. That makes $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ a good indicator of disk dominance, because disks tend to have complex stellar populations that are spatially not uniform whereas bulges and elliptical galaxies have relatively uniform stellar populations.

Figure 17 shows 12 examples of radial profiles with structural decomposition using GALFIT, which partially supports this interpretation (but not perfectly). For galaxies with B/T > 0.6, the stellar populations at 20.0 ≤ μ_r ≤ 21.0 mag arcsec⁻² are dominated by bulge components; for galaxies with B/T < 0.5, the stellar populations at 20.0 ≤μ_r ≤ 21.0 mag arcsec⁻² are affected more significantly by disk components.

Zoom In Zoom Out Reset image size

Nevertheless, the bulge–disk decomposition does not completely explain the performance of $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$, because there are some exceptional cases. For example, some bulge-dominated spiral galaxies (A1139-00009 and A2589-00007) have large B/T ratios and their stellar populations at 20.0 ≤ μ_r ≤ 21.0 mag arcsec⁻² seem to be dominated by their bulge components. Despite the fact that their B/T ratios are even larger than that of the S0 galaxy A1139-00002 (0.65 and 0.91 versus 0.61), their $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ values are also larger (0.036 and 0.020 versus 0.015). On the other hand, a disky elliptical galaxy A2589-00012 has a relatively small B/T (0.40), but its $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ is as small as 0.015. This indicates that the bulge-disk decomposition is not the only reason that $\max {(\sigma (g-r))}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ works. A spiral galaxy, even though it is extremely bulge-dominated (e.g., A2589-00007), seems to have more complex stellar populations compared to an early-type galaxy with a similar B/T ratio. That is, the pCMD color dispersion is a good indicator for detecting such a fine difference in stellar populations that is hardly caught in classical methods of structural decomposition.

Note that μ_r = 21.2 mag arcsec⁻² is the analysis limit for color dispersion in our data and thus its performance at μ_r > 21.2 mag arcsec⁻² cannot be probed in this paper. If deeper images with sufficient S/N even at μ_r > 21.2 mag arcsec⁻² are used, the usefulness of color dispersion as an indicator of galaxy morphology may be even greater, because the photometric properties of the fainter part of a disk will be reflected. For example, in Figure 17, the disk component of A1139-00002 (S0) is small, but it becomes relatively dominant at R > 10'' (total μ_r ≳ 22.2 mag arcsec⁻²). Thus, it may be useful even in distinguishing between elliptical and S0 galaxies if the color dispersion at lower surface brightness is available.

On the other hand, $\min {(\sigma (g-r))}_{{\mu }_{r}\leqslant 21.2}$ represents the minimum complexity of stellar populations, typically (but not necessarily) at the brightest center. Although elliptical galaxies and bulges of late-type galaxies typically have simple structures, they may show unusual substructures sometimes, which result in large color dispersions at their pCMD tips (e.g., A1139-00007 and A2589-00008). Since such substructures are thought to originate from mergers or interactions, $\min {(\sigma (g-r))}_{{\mu }_{r}\leqslant 21.2}$ can be used as a simple indicator of recent mass assembly events of a target galaxy: a larger value giving a more complex history of recent mass assembly on average. This may not be a very precise indicator, but will be useful particularly in a statistical study, because it can be conveniently applied to galaxies in bulk, if appropriate corrections are conducted for the difference in redshift and spatial resolution.

It is interesting that the best parameter to characterize galaxy morphology is color dispersion rather than color index itself. In other words, for morphological classification of galaxies, it is more effective to compare how well mixed the stellar populations are rather than to see how old or metal-rich on average they are. The latter also works to some extent, but it fails to discriminate bulge-dominated spiral galaxies from elliptical galaxies in our results. This is not strange because the correlation between galaxy morphology and galaxy color is known to be not very tight (e.g., blue early-type galaxies and red late-type galaxies; Lee et al. 2006, 2008; Tojeiro et al. 2013).

However, for the generalized application of morphological classification using the pCMD features, additional work is required. First of all, a much larger number of galaxies with well-classified morphological types need to be tested to get more reliable criteria of morphological classification. Our sample size of 32 is absolutely insufficient to establish criteria that can be generally applied. Furthermore, it is necessary to examine how the criteria of morphological classification change as a function of image resolution. Since the pCMD features strongly depend on image resolution (Lee et al. 2011, 2012; Conroy & van Dokkum 2016), its effect on the pCMD classification should be seriously considered, in order to apply this method to galaxies at various redshifts. Nevertheless, if these issues are addressed, the pCMD classification method will be a valuable technique to automatically classify a huge number of galaxies in future imaging surveys using next-generation facilities such as the Large Synoptic Survey Telescope (Ivezic et al. 2008).

In Section 4.3, the elliptical galaxies show a marginal correlation between their min($\sigma (g-r)$)${}_{{\mu }_{r}\leqslant 21.2}$ and [4.6]–[12] (Figure 16(c)) and a stronger correlation between max($\sigma (g-r)$)${}_{20.0\leqslant {\mu }_{r}\leqslant 21.0}$ and [4.6]–[12] (Figure 16(d)). Since the color dispersion reflects how complex stellar populations are in a galaxy, this result indicates that the elliptical galaxies with more complex stellar populations tend to have recently experienced more active star formation (or vice versa). According to some previous studies, the recent growth of massive elliptical galaxies mainly depends on dry mergers rather than gas-rich mergers (Naab et al. 2006; Kormendy et al. 2009; Bernardi et al. 2011). On the other hand, some other studies found evidence of recent star formation activity probably triggered by mergers in some massive elliptical galaxies (Kaviraj et al. 2009; Fernández-Ontiveros et al. 2011; Sheen et al. 2016). Our result supports the latter findings: the recent star formation activity and mass growth of massive elliptical galaxies appear to be correlated with each other in our sample. Thus, the recent growth of those elliptical galaxies may not entirely depend on dry mergers, and gas-rich minor mergers may have occurred.

One may suspect that the complexity of stellar populations in those galaxies may not necessarily originate from merger events, but may be naturally caused by recent star formation not from merger origins. Even in that case, however, the recent star formation must have been spatially non-uniform at scales larger than 600 pc (∼08 in our images) to enlarge the color dispersion in a pCMD. It may require anisotropic infall of gas. Gas interactions without disturbance of stellar orbits can be such an origin, which may occur even for cluster galaxies with high encounter velocities (Park & Hwang 2009). Although the exact origin of the recent star formation cannot be determined in this paper, it is plausible that some environmental effects acted on the large color dispersion in a pCMD.

The interpretation of the max(g − r)${}_{{\mu }_{r}\leqslant 23.2}$ versus [4.6]–[12] plot (Figure 16(b)) is somewhat complicated. At first glance, the data points seem to be randomly scattered in this plot. However, as shown in Table 3, we find two opposite trends when we inspect the subsamples of the elliptical + disky elliptical galaxies and the spiral galaxies: the elliptical galaxies with infrared-color excess tend to have redder maximum pCMD color, but the spiral galaxies are getting bluer in the optical band as infrared color increases.

These two opposite trends imply that multiple physical origins may be involved in the max(g − r)${}_{{\mu }_{r}\leqslant 23.2}$ versus [4.6]–[12] relation. For example, the marginal correlation of elliptical + disky elliptical galaxies may result from dust remnants in some elliptical galaxies. That is, elliptical galaxies that have recently experienced star formation may have remaining dust, which cause red infrared color (due to remaining warm dust) and red optical color (by dust extinction) at the same time. On the other hand, spiral galaxies with redder infrared color may have more active current star formation, unlike elliptical galaxies, and thus they tend to have blue optical color due to a large amount of young stars that cannot be sufficiently obscured by dust. It will be worth checking if these trends are maintained in a sufficiently large sample of galaxies in future studies.