2.1 CFHTLS data

The data used in this work were obtained from the seventh and the final data release of the CFHTLS (T0007, 2012) which is covering a total of 155 deg $^2$ . The CFHTLS was carried out using MegaCam, a mosaic imager, mounted at the 3.6 m CFH Telescope and completed in 2009, is an optical five bands $u^{*}, g', r', i'/y', z'$ ) survey consisting of four wide and deep fields. MegaCam has 36 $2\,048\times 4\,612$ pixels CCDs with a pixel scale of 0.186" pixel^-1. Thus, each MegaCam pointing yields a field of view of $\sim$ 1 deg $^2$ . In this work, we used CFHTLS W1 (72 deg $^2$ , 8 $^\circ$ $\times$ 9 $^\circ$ ), the widest field of the survey, to identify IfEs. Coordinates and limiting magnitudes of the CFHTLS-W1 can be seen from Table 1.

Table 1. Equatorial and galactic coordinates of the CFHTLS-W1, limiting magnitudes for extended objects in each photometric band and the total effective survey area are given. Other major extragalactic surveys in the same field are listed in the last row.

The CFHTLS raw data were reduced and were made public by the former laboratory TERAPIX of the IAP.Footnote a Image stacking and astrometry were performed using SWARP (Bertin Reference Bertin2006) and photometry was performed with SExtractor (Bertin & Arnouts Reference Bertin and Arnouts1996). Data released by TERAPIX includes images, object catalogues, mask files, and photometric redshifts. For the present work, we revisited mask files provided by TERAPIX. Although we updated masks with a more conservative approach, due to the overmasked regions in the original data release, we have more galaxies in our catalogue. The original object catalogue provided by TERAPIX includes 2 623 690 ( $r \leq24$ ) galaxies whereas our catalogue includes 2 812 065 ( $ r \leq24$ ) galaxies. These galaxy counts obtained with all five-band magnitudes $u^{*}, g', r', i'/y', z'$ ) are measured by omitting galaxies with missing magnitude in any band. Contents of the object catalogues can be found on relevant pages at CFHT webpage.Footnote b

Photometric redshifts of the objects were computed using LePhare at TERAPIX and Laboratoire d’Astrophysique Marseille (Ilbert et al. Reference Ilbert2006; Coupon et al. Reference Coupon2009). Several spectroscopic surveys, such as VVDS and COSMOS, have been used for the calibration of those photometric redshifts. Typical photometric redshift error for elliptical galaxies in the CFHTLS is $ \unicode{x03C3}_{z}=0.03\times(1+ z)$ (Coupon et al. Reference Coupon2009). The bias shown by Coupon et al. (Reference Coupon2009) is mostly at the lowest ( $z<0.1$ ) and highest ( $z>0.9$ ) redshift regimes. But for our sample (i.e. elliptical galaxies) we did not apply any correction to the redshift bias as it is negligible for elliptical galaxies in the range of our study.

Coupon et al. (Reference Coupon2009) provide a detailed comparison of the photometric redshifts with spectroscopic redshifts obtained from various sources. Here, we only provide the $zspec-zphot$ comparison for our galaxy sample used for the analysis in Section 3. Figure 1 shows the comparison for 668 galaxies from our sample where we could compile spectroscopic redshifts from the surveys Sloan Digital Sky Survey (SDSS), Galaxy and Mass Assembly (GAMA), and VIPERS. It is seen from the figure that the photometric redshifts of our sample galaxies are in good agreement with spectroscopic ones. The outlier fraction of $\unicode{x03B7} = 4\%$ shown in Figure 1 is comparable for the same magnitude range of Coupon et al. (Reference Coupon2009).

Figure 1. Comparison of photometric redshifts used in this study with corresponding spectroscopic redshifts. Spectroscopic redshifts were compiled from SDSS, GAMA, and VIPERS galaxy redshift surveys. Blue, red, and grey points represent IfEs, BCGs, and cluster ellipticals, respectively.

LePhare is a template fitting photometric redshift algorithm based on galaxy spectral energy distributions (SED) (Arnouts et al. Reference Arnouts, Cristiani, Moscardini, Matarrese, Lucchin, Fontana and Giallongo1999; Ilbert et al. Reference Ilbert2006). There are five spectral types (E, Sbc, Scd, Irr, SB) associated with galaxies once the best match is obtained with LePhare during the SED fitting procedure. These spectral types have been adopted from the observed galaxy spectra given by Coleman et al. (Reference Coleman, Wu and Weedman1980) and Kinney et al. (Reference Kinney, Calzetti, Bohlin, McQuade, Storchi-Bergmann and Schmitt1996) and used similarly with Ilbert et al. (Reference Ilbert2006). Four spectra from Coleman et al. (Reference Coleman, Wu and Weedman1980) and two spectra from Kinney et al. (Reference Kinney, Calzetti, Bohlin, McQuade, Storchi-Bergmann and Schmitt1996) were extrapolated into 66 spectral templates and optimised specifically for CFHTLS to represent a wide range of galaxies (Coupon et al. Reference Coupon2009). We make use of these associated spectral types given in the photometric redshift catalogue for the galaxy selection.

Due to the different contents of the object catalogue and the photometric redshift catalogue we created a working catalogue for our study by merging the necessary parameters from those two catalogues.

2.2 Selection criteria for IfEs

We selected elliptical galaxies from our working catalogue based on their spectral type given by LePhare and their magnitude. We applied a magnitude cut at $ r\leq 21.8$ to obtain a flux-limited sample. 90 872 elliptical galaxies remain in our catalogue after the selection. Each elliptical galaxy is checked for the isolation criteria given by Zaritsky et al. (Reference Zaritsky, Smith, Frenk and White1993, Reference Zaritsky, Smith, Frenk and White1997) which was also used by Smith et al. (Reference Smith, Martínez and Graham2004) and Niemi et al. (Reference Niemi, Heinämäki, Nurmi and Saar2010). The isolation criteria require that the magnitude difference between a neighbour galaxy and the IfE candidate must be greater than 0.7 mag for galaxies within a projected distance of 1 Mpc and greater than 2.2 mag within 500 kpc (for a schematic description of the criteria see Figure 1 in Smith et al. Reference Smith, Martínez and Graham2004). To do that, we created a galaxy catalogue, that is, 2.2 mag fainter than our elliptical galaxy sample. This reference, fainter, galaxy catalogue contains 2 812 065 ( $r \leq 24$ ) galaxies as it was mentioned in the previous section. Selection of the elliptical galaxies was made so that the reference galaxy catalogue does not contain galaxies fainter than the r-band limiting magnitude for the extended objects given in Table 1. The morphology of the neighbouring galaxies is not taken into account in our isolation criteria.

To apply the isolation criteria, mini galaxy catalogues for each elliptical galaxy have been created. These mini catalogues were built from galaxies around the IfE candidate with a projected radius of 1.25 Mpc at the photometric redshift of the galaxy. To account for the large photometric redshift errors, we considered that two galaxies may be at the same redshift if the difference of their photometric redshifts satisfies $\Delta{z}\leq2\unicode{x03C3}_{z}$ . If this criterion is fulfilled, the IfE candidate is excluded from the list.

Afterwards, for the remaining candidates, with a conservative approach, projected physical distances between the IfE candidates and their neighbouring galaxies are computed at the lowest photometric redshift of each considered pair. Magnitude differences and projected distances are taken into account to check isolation criteria. Three hundred and sixty-nine galaxies satisfying the criteria are identified as isolated. However, some of the IfE candidates are located near the edge of the field (W1) or too close to masked areas around the bright stars, ghosts, or other image defects. To ensure that our IfE identification is not biased by the presence of these regions where the number of galaxies may artificially be depleted, we checked whether each candidate is closer to the edge by a projected distance of less than 1 Mpc. 24 candidates satisfying this criterion are omitted. Similarly, the fraction of masked areas within a disc of 1 Mpc radius surrounding each IfE candidate was computed. If the masked fraction of the 1 Mpc region around the IfE is higher than 10% then that IfE is also omitted. 28 candidates in such conditions are excluded from the list. Thus, a total of 317 IfE candidates remained. Positions of those candidates as well as IfEs near masked areas are shown in Figure 2.

Figure 2. Positions of IfEs shown on the RA-Dec plot. In the figure; red dots are the whole CFHTLS-W1 galaxy catalogue, cyan crosses are 28 IfEs near the masked regions, green squares are 24 IfEs near the field edges, yellow crosses are 89 non-eliptic isolated galaxies, black diamond is a X-ray point source possibly counterpart of an IfE (see Section 5 for details), black triangles are fossil groups identified by Adami et al. (Reference Adami2018), and blue crosses are the final 228 IfEs candidates.

Since the selection of IfE candidates is based on measured spectral types, we also removed galaxies classified mistakenly as ellipticals due to the template fitting procedure adopted by LePhare. To do that, we created true colour image of each isolated galaxy using STIFFFootnote c (Bertin Reference Bertin2012) from g, r, and i band CFHTLS images. 89 IfE candidates are excluded from the list after a visual inspection of those images. Excluded candidates are in general lenticular galaxies or face-on spirals with a high bulge-to-disc ratio where SED fitting fails. Thus, 228 IfEs galaxies remained in our final list. In this way, the purest possible sample is obtained. The density of those 228 IfEs is 3 IfE/sq.deg. One elliptical galaxy in almost every 400 in our magnitude range is an IfE. This makes the IfE fraction in elliptical galaxies 0.25%. This fraction decreases to $8.1 \times 10^{-3}\%$ when all galaxies (regardless of type) in our working catalogue (i.e. 2 812 065) are considered. Properties of these IfEs are given in Table A.1. Colour images of some illustrative IfEs are given in Figure A.1 in the Appendix.

2.3 Reliability of the IfE selection

To test our IfE identification method and to validate the effect of photometric redshift errors, we used a spectroscopic control sample. This control sample is derived from the GAMA survey. GAMA is a spectroscopic survey to study the evolution of galaxy groups and clusters (Driver et al. Reference Driver2009). The GAMA survey was carried out at the Anglo-Australian Telescope using the AAOMega instrument, a high multiplex fiber unit, to cover as many galaxy members as possible of groups and clusters. As a strategy, galaxy groups and clusters are pointed more than once during the GAMA survey to overcome the difficulties of placing fibres. This strategy leads to high-density coverage over the surface area of groups and clusters. GAMA survey reaches $r<19.8$ which corresponds to the redshift regime of $z\leq0.5$ . A total of 300 000 galaxy spectra have been obtained (Baldry et al. Reference Baldry2010, Reference Baldry2014; Robotham et al. Reference Robotham2010).

Figure 3. Fraction of CFHTLS-W1 galaxies brighter than $r<19.5$ covered by the GAMA-G02 survey.

Among the survey areas, G02 is the only one overlapping with CFHTLS-W1. We cross-matched galaxies in the G02 field with W1 and plotted them as a function of the match ratio. In Figure 3 it can be seen that the GAMA survey is not homogeneous over the entire CFHTLS-W1. The densest area is between $-6^{\circ} < \unicode{x03B4} < -4^{\circ}$ . There are 33 277 galaxies from G02 spread over the W1 but 17 793 of them lie above roughly $ \unicode{x03B4} > -6^{\circ}$ . Thus, our control sample was drawn from galaxies belonging to that area in order to test our identification method. CFHTLS-W1 and GAMA-G02 catalogues were cut within the same field $-6^{\circ} < \unicode{x03B4} < -4^{\circ}$ and with $r\leq19.5$ . This leaves 11 657 and 11 282 galaxies in the CFHTLS and GAMA catalogues, respectively. This yields 97% completeness ( $r\leq19.5$ ) for GAMA when compared with CFHTLS. Matching G02 and W1 catalogues led to a galaxy sample that includes galaxy spectral types, magnitudes, and photometric and spectroscopic redshifts. Elliptical galaxies were selected according to their spectral types. Since IfE candidates should be 2.2 mag brighter than the neighbour galaxies, we applied a cut at $r\leq17.3$ for ellipticals. Thus, the final control sample consists of 11 282 galaxies ( $r\leq19.5$ ) and 130 ellipticals ( $r\leq17.3$ ).

When IfE candidates are determined from the control sample using their spectroscopic redshifts, a typical redshift error of $\unicode{x03C3}_{z}=0.003$ is applied. This corresponds to a radial velocity of 1 000 km s^–1 and is considered as a limit for the separation of two galaxies (Colbert et al. Reference Colbert, Mulchaey and Zabludoff2001). As a result, 38 amongst 130 elliptical galaxies in our control sample were identified as IfE.

Then, we run our selection procedure for the very same galaxies but this time using their photometric redshifts. In this approach, we took into account two aspects: redshift error and implication of this error on the radii we used. Thanks to the spectroscopic sample we can show the impact of photometric redshifts on our IfE identification. For the photometric redshift error we used 1 $\unicode{x03C3}_{ \textrm z \textrm p}$ , 2 $\unicode{x03C3}_{ \textrm z \textrm p}$ , and 3 $\unicode{x03C3}_{ \textrm z \textrm p}$ where $\unicode{x03C3}_{ \textrm z \textrm p}=0.03\times(1+ z_{c} )$ with $z_{c}$ being the central galaxy’s redshift. To demonstrate the effect on the radius, we use somewhat lower redshifts conservatively. We computed the projected radius with a factor of $\unicode{x03C3}_{\rm zp}$ smaller than the candidate elliptical galaxy’s actual redshift. As a result, to check the isolation criteria, we use the larger, more conservative, radius. We computed these modified radii using redshifts with 1 $\unicode{x03C3}_{ \textrm z \textrm p}$ , 2 $\unicode{x03C3}_{ \textrm z \textrm p}$ , and 3 $\unicode{x03C3}_{ \textrm z \textrm p}$ smaller than the central galaxy’s redshift (i.e. candidate elliptical) as $z= z_{c}- \textrm d \textrm z$ where $ \textrm d \textrm z$ is the relevant $\unicode{x03C3}_{ \textrm z \textrm p}$ . Results of these tests are given in Table 2. $ r_{ \textrm c \textrm o \textrm r}$ in Table 2 denotes these modified (i.e. larger) radii.

Table 2. Results obtained from the spectroscopic control sample constructed from the GAMA survey. Six cases listed in the table include different photometric redshift error with and without the usage of modified radii ( $r_{ \textrm c \textrm o \textrm r}$ ). In each case, IfEs determined with photometric redshift are matched with the spectroscopically determined 38 IfEs. Number of these matches and their corresponding completeness and purity values are also given.

Results of the run with photometric redshifts are 21, 12 and 7 IfEs candidates for 1 $\unicode{x03C3}_{ \textrm z \textrm p}$ , 2 $\unicode{x03C3}_{ \textrm z \textrm p}$ , 3 $\unicode{x03C3}_{ \textrm z \textrm p}$ , respectively. When compared with 38 IfEs identified spectroscopically in the same area, 18 (86%), 10 (78%), and 7 (100%) IfEs are found in common. This gives a high purity though the completeness is below 60%. When this same comparison is done together with the radius correction ( $r_{ \textrm c \textrm o \textrm r}$ ) 11, 5, and 2 IfEs are identified, respectively (see Table 2). Balancing sample purity versus completeness, we decided to use 1 $\unicode{x03C3}_{ \textrm z \textrm p}$ error both on photometric redshift and the radius correction (i.e. Case 4 in Table 2). This choice results in a completeness of approximately 30%, as given in the Table 2.

2.4 BCGs and cluster ellipticals

To understand environmental effects on elliptical galaxy evolution, we built a BCG sample from the same survey. Thus, we can compare elliptical galaxies in two different and opposite environments; isolated fields and dense regions. Since BCGs may be considered special galaxies in clusters, we also create a sample of elliptical galaxies from the same clusters with our BCG sample.

The galaxy clusters, where BCGs and cluster ellipticals were drawn, were detected in the whole CFHTLS-W1 by the WaZP optical cluster finder. Details of the WaZP cluster finder can be found in Aguena et al. (Reference Aguena2021), Euclid Collaboration et al. (2019), Dietrich et al. (Reference Dietrich2014). Basically, the algorithm uses a galaxy catalogue that includes positions (RA and Dec) and photometric redshifts. Overdensities are determined with the help of wavelet filtering and no assumption on the underlying galaxy population is made. The cluster centre is defined by the position of the overdensity peak, which does not always coincide with the BCG. Once an overdensity is detected, it is ranked by the signal-to-noise ratio with respect to the local background of galaxy density. This local galaxy density is computed for the radius and the richness ( $\unicode{x03BB}$ ) computation of the cluster. Therefore, cluster radius and richness are computed jointly where the radius is determined as 200 times the local galaxy density, and richness is the sum of the membership probabilities within this radius (i.e. $R_{200}$ ).

There are 3 337 cluster detections with a $\textrm S \textrm N \textrm R > 3$ in the whole W1 region. However, to underline the impact of higher density we keep the richest systems in our cluster catalogue by applying a richness cut of $\unicode{x03BB} \geq 25$ . This selection yields 309 galaxy clusters with a median richness of $\unicode{x03BB}_{ \textrm {med}}\sim35$ whereas the parent cluster catalogue in the CFHTLS-W1 has a median richness of $\unicode{x03BB}_{\textrm{med,all}}$ $\sim10$ (Benoist et al., in preparation). Afterwards, we identify the BCGs of these clusters as briefly explained below.

An elliptical galaxy is identified as a BCG based on the following criteria:

• • Being 0.5 Mpc around the cluster centre

• • Having a redshift consistent with the cluster with a $\varDelta z = 0.03\times(1+z_{ \textrm c \textrm l})$

• • Having a $(r-i)$ colour consistent (within $\pm 0.3$ ) with model elliptical galaxy colours for the corresponding redshift

Then, the BCG is the brightest galaxy in a cylinder defined by the criteria given above.

We select elliptical galaxies from the same clusters as the BCGs. Cluster ellipticals were selected from the core region of clusters with a $r < 0.5$ Mpc projected radius using their LePhare defined spectral types (i.e. MOD<23) and photometric redshifts. When selecting cluster ellipticals, the BCGs are excluded in order not to create any bias. These galaxies were also selected based on their membership probability which is computed by WaZP as given in Castignani & Benoist (Reference Castignani and Benoist2016). A relatively conservative membership probability of $P_{ \textrm m \textrm e \textrm m} > 0.7$ is applied for the selection which yields a total of 3 958 elliptical galaxies in those 309 rich clusters.

Following the selection of BCGs and cluster ellipticals, we apply the same magnitude cut (i.e. $r \leq 21.8$ ) in order to obtain comparable flux-limited samples with IfEs. Thus, the number of BCGs dropped to 261, and the number of cluster ellipticals dropped to 2 087 as the final sample used for the analysis.

In Section 3 we provide a comparison of these BCGs and cluster ellipticals with our IfEs.

2.4.1 The early-type fraction

We have not performed a visual inspection for the BCGs and cluster ellipticals as we did for IfEs due to their excess numbers (see Table 3). In fact, the collective existence of many galaxies in rich clusters makes cluster detection more reliable. Moreover, our cluster elliptical sample is drawn from the cluster core with high membership probabilities. Selecting galaxies from the inner parts of clusters ensures their types as indicated by the morphology–density relation.

Table 3. Description of the galaxy samples used in this study. The table lists number of galaxies ( $r \leq 21.8$ ), redshift range and the median redshift for each sample.

Nevertheless, we examined their $M_{u} - M_{r}$ colours to test our selection. Galaxy colours show a bimodal distribution where elliptical galaxies are seen in the red sequence and are mostly called as red and dead. Blue, star-forming galaxies (e.g. spirals or late-types) are found in the blue cloud. There are some galaxies in between these groups called green valley galaxies (see Figure 2 in Schawinski et al. Reference Schawinski2014).

To determine the separation between red and blue galaxies we used member galaxies from clusters with richness $\unicode{x03BB} > 15$ (i.e. $\sim1\,200$ clusters) in the CFHTLS-W1 (Cakir et al., in preparation). Thus, we make use of 60 606 cluster members where we implemented a Gaussian mixture model (i.e. GMM) which is an unsupervised clustering algorithm. The best separation in the colour space of the two populations was obtained as $(M_{u}-M_{r}) \sim 1.7$ and shown in Figure 4. The red-dashed line in the figure denotes this separation. In SDSS, similar exercise was done by Strateva et al. (Reference Strateva2001), and they obtained $(M_{u}-M_{r}) \sim 2.2$ for the separation of blue and red galaxies.

Figure 4. $M_{u}-M_{r}$ colour-magnitude diagram for the galaxy samples. Red-dashed line is the separation of red and blue galaxy populations obtained with GMM at 1.7.

We then apply the obtained separation to $(M_{u}-M_{r})$ colours of our BCGs and cluster ellipticals. Ninety-three per cent of our BCGs (245 red, 16 blue) and cluster ellipticals (1 949 red, 138 blue) are located on the red sequence. This does not guarantee a correct morphology but still provides a strong indication of their early-type nature.

2.5 Stellar masses

We compute stellar masses for our galaxy sample in order to compare galaxy sizes for a given mass range.

To obtain stellar masses we make use of the Code Investigating GALaxy Emission (CIGALE) (Burgarella, Buat, & Iglesias-Páramo Reference Burgarella, Buat and Iglesias-Páramo2005; Noll et al. Reference Noll, Burgarella, Giovannoli, Buat, Marcillac and Muñoz-Mateos2009; Boquien et al. Reference Boquien, Burgarella, Roehlly, Buat, Ciesla, Corre, Inoue and Salas2019) using apparent magnitudes of galaxies in five bands (i.e. ugriz). Galaxy magnitudes were converted to fluxes as CIGALE requires. For the redshift prior we use photometric redshifts provided by TERAPIX.

Stellar masses were computed assuming a single stellar population model of Bruzual & Charlot (Reference Bruzual and Charlot2003), a Chabrier (Reference Chabrier2003) IMF, and the solar metallicity. We adopt Calzetti et al. (Reference Calzetti, Armus, Bohlin, Kinney, Koornneef and Storchi-Bergmann2000) for dust attenuation law. Then, we run CIGALE for a range of input parameters as $\tau$ = [100–2 000] Myr, age=[500–13 000] Myr, and E(B-V)=[0.0–0.2]. Since our sample consists of elliptical galaxies, we use a star formation history with a single burst and a single exponential declining law for star formation rate (SFR) as described in Boquien et al. (Reference Boquien, Burgarella, Roehlly, Buat, Ciesla, Corre, Inoue and Salas2019):

(1) \begin{equation} SFR(t) \propto \frac{t}{\tau^{2}} \times exp(\!-t/\tau) \ for \ 0\leq t \leq t_{0},\end{equation}

where $t_0$ is the age of the Universe, $\tau$ is the star formation timescale (or decay time) and t is the look-back time.

The median value of stellar masses for the whole sample (i.e. 2 576 galaxies) given in Table 3 is $\textrm{log} (M_{\rm med})=10.83\,{\rm M}_\odot$ , and the median error is 0.10 dex. In order to check our mass estimation, we compared our masses with masses given by Guglielmo et al. (Reference Guglielmo2018). They built a spectrophotometric galaxy catalogue for the X-ray detected and spectroscopically confirmed groups and clusters within the northern field of the XXL survey which significantly overlaps with CFHTLS-W1. Their catalogue contains 24 336 galaxies with $z<0.6$ and $r<20$ . In total; 2 225 member galaxies for 132 groups/clusters, and 22 111 field galaxies. Stellar masses given in their catalogue were computed by using LePhare for the galaxies having at least two observed magnitudes and a spectroscopic redshift. A cross-match of our sample with their catalogue revealed 297 galaxies (52 IFEs, 27 BCGs, and 218 cluster ellipticals) in common. The comparison of the stellar masses is shown in Figure 5. Based on the common galaxies, stellar masses from both studies are in good agreement. The dispersion between both estimates is comparable with the typical error of stellar masses computed with CIGALE in this study. The rms value of the one-to-one comparison is 0.155 dex, but it becomes 0.082 dex when we exclude the outliers.

Figure 5. Comparison of stellar masses computed in this study and those in Guglielmo et al. (Reference Guglielmo2018).The rms value of 0.155 of the residuals is comparable with the typical error on the stellar mass we computed in this study. IfEs, BCGs, and cluster ellipticals are denoted by blue, red, and grey points, respectively.

For a detailed comparison of three elliptical galaxy samples in our study, we divided them into four redshift bins. To obtain a reliable comparison and the scaling relations given in Section 4, we also compute our mass completeness limits for each redshift bin by following the approach of Pozzetti et al. (Reference Pozzetti2010), similarly with Ilbert et al. (Reference Ilbert2013), Shi et al. (Reference Shi, Toshikawa, Lee, Wang, Cai and Fang2021).

The recipe we employ for the determination of the mass completeness limits is as follows:

• • For each redshift bin we identify the 20% faintest galaxies in the i-band

• • For those galaxies we apply the empirical relation given by Pozzetti et al. (Reference Pozzetti2010) and compute $ \textrm l \textrm o \textrm g(M_{ \textrm l \textrm i \textrm m})$

  (2) \begin{equation} \log(M_{\rm lim}) = \log(M_{*}) + 0.4 (i - i_{\rm lim}) \end{equation}

• • We then take the 2 $\unicode{x03C3}$ upper envelope of the $ \textrm{log} (M_{ \textrm{lim}})$ distribution as the representative limit value

Obtained mass completeness limits for the four redshift bins are as follows: $ \textrm{log} (M_{ \textrm{lim}})=8.98\,{\rm M}_\odot$ for $0.1< z\leq0.3$ , $ \textrm{log} (M_{\textrm{lim}})=9.54\,{\rm M}_\odot$ for $0.3<z\leq0.5$ , $ \textrm{log} (M_{\textrm{lim}})=9.89\,{\rm M}_\odot$ for $0.5< z\leq0.7$ , and $ \textrm{log} (M_{ \textrm{lim}})=10.39\,{\rm M}_\odot$ for $0.7<z\leq0.9$ .

3.1 Brightness and colour

Apparent and absolute magnitude distributions of IfEs, BCGs, and cluster ellipticals are given in Figure 7. Absolute magnitude distribution indicates that IfEs are intrinsically brighter than cluster ellipticals but slightly fainter than BCGs.

Figure 7. r-band apparent (left) and absolute magnitude (right) distributions of IfEs, BCGs, and cluster ellipticals. Histograms are given as normalised.

The similarity in absolute magnitudes of IfEs with BCGs may be explained by the scenario of fossil group collapse (Ponman et al. Reference Ponman, Allan, Jones, Merrifield, McHardy, Lehto and Luppino1994; Jones, Ponman, & Forbes Reference Jones, Ponman and Forbes2000; Reda et al. Reference Reda, Forbes, Beasley, O’Sullivan and Goudfrooij2004) for their formation as the merging of several galaxies could contribute to the final luminosity of the isolated galaxy.

As our galaxy samples span a large redshift range of $0.1 \leq z \leq$ 0.9, to for account evolutionary effects, rest-frame colours obtained by LePhare are used for the comparison.

$M_g-M_i$ distributions that are given in Figure 8 look similar for the three groups of galaxies. This can be attributed to their early-type nature where they are expected to concentrate on the so-called red sequence of the bimodal galaxy colour distribution. However, a two-sample Kolmogorov–Smirnov (K–S) test reveals differences that are statistically significant. We applied the K–S test to our samples with a pairwise approach as (IfEs—BCGs), (IfEs—cluster ellipticals), and (BCGs—cluster ellipticals). p-values of $1.91 \times 10^{-2}$ and $1.27 \times 10^{-7}$ obtained for the IfEs–cluster ellipticals and BCGs–cluster ellipticals, respectively, indicate the colour distribution of both IfEs and BCGs significantly different than cluster ellipticals. However, for the IfE–BCG comparison, a p-value of 0.12 is obtained which suggests we can not differentiate these two groups statistically.

Figure 8. Colour distribution of IfEs, BCGs, and cluster ellipticals. Blue, red, and gray histograms represent IfEs, BCGs, and cluster ellipticals, respectively.

Mean $M_g-M_i$ colours and corresponding standard deviations of the samples are as follows: IfEs (1.039, 0.051), BCGs (1.053, 0.064), and cluster ellipticals (1.031, 0.057). Based on these values we also applied a one-way analysis of variance (ANOVA) test to see whether these three groups have differences in their rest-frame colour distributions. A one-way ANOVA test reveals a p-value of $3.8 \times 10^{-9}$ which also suggests there is a significant difference amongst these samples.

3.2 Environmental density

Due to the isolation criteria used in this study, the environment of IfEs is not totally empty which is also the case in Niemi et al. (Reference Niemi, Heinämäki, Nurmi and Saar2010). Neighbouring galaxies are the ones that do not affect the IfE selection as described in Section 2.2. Those galaxies are mostly the faint ones as implied by the selection criteria.

Figure 9. Normalised histogram of neighbouring galaxies (down to $0.4 L^{*}$ ) as a function of distance from parent galaxies. A total of 904 galaxies for IfEs (blue), 10 384 galaxies for BCGs (red), and 59 779 galaxies for cluster ellipticals (grey) are shown.

We computed the environmental density within the 1 Mpc radius for each IfE and BCG in our sample. Since BCGs and respective cluster ellipticals are in the same environment we did not compute the densities for the cluster ellipticals.

For the density computation, we count galaxies up to $0.4 L^{*}$ where $L^{*}$ is the characteristic luminosity of the galaxy luminosity function. The reason for this upper luminosity limit is to prevent any magnitude bias when we compute the densities. When CFHTLS-W1 limiting magnitude is taken into account, $0.4 L^{*}$ remains brighter for the redshift range of our study. When counting neighbouring galaxies we impose that they are in the same redshift cylinder as we did in the IfE selection and we used $L^{*}$ values for the corresponding redshift.

Among our IfEs we have 37 candidates without any neighbour galaxy down to $0.4 L^{*}$ within the 1 Mpc projected radius. IfE with the densest environment has 21 neighbouring galaxies which correspond to a projected density of 6.7 gal Mpc-2 (ID#174).

The fact that BCGs are located in denser environments can be seen in Figure 9. In the figure, we show the number density of neighbouring galaxies as a function of the distance between our galaxy of interest (e.g. IfE or BCG). Especially for closer distances, such as $r<0.5$ Mpc, densities around BCGs are almost eight times higher than IfEs.

In Figure 10 we show the stellar mass of IfEs, BCGs, and cluster ellipticals as a function of the local (i.e. 1 Mpc) environmental density. Due to the same number of neighbouring galaxies, some IfEs have discrete density values. However, there seems a trend in the IfE stellar mass with increasing environmental density. This trend does not seem valid for BCGs and cluster ellipticals where the stellar masses of them look almost constant or vary very slowly with density. This may be explained by the cease of the major merging events for BCGs as shown by De Lucia & Blaizot (Reference De Lucia and Blaizot2007) using the Millennium Simulation. In their study, they showed that 80% of the stellar masses of BCGs are already formed by $z\sim 3$ . This result can also be considered valid for the other ellipticals in clusters since they are residing in similar environments. The trend for IfEs mainly arises due to the wide range of environments in which they are located. There is approximately a magnitude difference in stellar masses of the IfEs residing in lower and higher densities. This could be the result of merger-driven mass growth for IfEs where such events were identified observationally by Reda et al. (Reference Reda, Forbes, Beasley, O’Sullivan and Goudfrooij2004) and from simulations by Niemi et al. (Reference Niemi, Heinämäki, Nurmi and Saar2010). There are no close companion galaxies being merged with IfEs as imposed by the isolation criteria. Thus, morphological disturbances can be investigated for tracing recent or past merging events as we also point out in Figure 17.

Figure 10. Comparison of stellar masses with corresponding environmental densities for the three samples of galaxies. Densities given here were computed as the projected densities within the 1 Mpc of the galaxy of interest.

3.3 Star formation activity

Star formation activity in elliptical galaxies is not very common (Holmberg Reference Holmberg1958; Conselice Reference Conselice2014; Madau & Dickinson Reference Madau and Dickinson2014). However, some elliptical galaxies show excess star formation activities (Pipino et al. Reference Pipino, Kaviraj, Bildfell, Babul, Hoekstra and Silk2009; Hicks, Mushotzky, & Donahue Reference Hicks, Mushotzky and Donahue2010; Edman, Barton, & Bullock Reference Edman, Barton and Bullock2012; Lacerna et al. Reference Lacerna, Hernández-Toledo, Avila-Reese, Abonza-Sane and del Olmo2016). This is mainly related to the environment. For instance in clusters, BCGs may have high SFRs (Liu, Mao, & Meng Reference Liu, Mao and Meng2012) due to interaction with galaxies inside the cluster (e.g. cannibalism of dwarf galaxies) (Whiley et al. 2008; Lidman et al. Reference Lidman2012; Lavoie et al. Reference Lavoie2016) or the cooling flows towards BCG (Edwards et al. Reference Edwards, Robert, Mollá and McGee2009; McDonald et al. Reference McDonald2016).

As $ \textrm H\unicode{x03B1}$ line is generally the most prominent feature of star-forming galaxies, we compiled $ \textrm H\unicode{x03B1}$ emission line fluxes to determine whether galaxies in our study show any star formation activity. CFHTLS is an imaging survey, hence we do not have spectra for our galaxies. Thus, we used SDSS Data Release 12 to access the spectral information for our targets. From SDSS DR12, we used the table emissionLinesPort (Sarzi et al. Reference Sarzi2006; Cappellari & Emsellem Reference Cappellari and Emsellem2004; Maraston & Strömbäck Reference Maraston and Strömbäck2011; Thomas, Maraston, & Johansson Reference Thomas, Maraston and Johansson2011) to obtain fluxes. Some of our target galaxies are at the limit of a 2.5 m telescope for spectroscopy, therefore we imposed a S/N $\geq$ 3 for reliable results when selecting spectra. In this way, we could obtain $ \textrm H\unicode{x03B1}$ fluxes for 63 IfEs, 46 BCGs, and 39 cluster ellipticals.

We then used the equation below given by Kennicutt (Reference Kennicutt1998) to determine SFRs using $ \textrm H\unicode{x03B1}$ line fluxes.

(3) \begin{equation} SFR \ (H\alpha) = 7.9 \times 10^{-42} L_{H\alpha}\,{\rm M}_{\odot} {\rm yr}^{-1}\end{equation}

$ \textrm H\unicode{x03B1}$ line fluxes obtained from SDSS were converted to luminosities using redshifts, and their corresponding luminosity distances within the standard $\Lambda$ CDM cosmology.

Mean (SFR) for IfEs, BCGs, and cluster ellipticals are as follows: 0.15, 0.18, and 0.14 $ \textrm M_{\odot} \textrm{yr}^{-1}$ , respectively.

Table 4. Statistical properties (size, mean, standart deviation, and median) of effective radii (in kpc) and r-band absolute magnitudes for IfEs, BCGs, and cluster ellipticals with a cut in absolute magnitude as $-24 \leq M_{r} \leq -22$ for different redshift bins.

Table 5. Size–luminosity relation best-fitting parameters for different populations in different redshift bins.

In order to prevent bias due to large mass differences amongst these samples we also computed the specific star formation rate (sSFR) where sSFR is defined as $ \textrm sSFR \equiv \textrm SFR /M_{*} $ . Figure 11 shows the distribution of sSFR for IfEs, BCGs, and cluster ellipticals. The distributions were represented with similar Gaussian functions. We also applied K–S and ANOVA tests to see whether there are significant differences between the distributions. However, based on both K–S and ANOVA test results it is difficult to distinguish these samples statistically. The p-value of the ANOVA test was obtained as 0.70 whereas the p-values for K–S tests for the sample pairs are as follows: 0.99 (IfEs–BCGs), 0.97 (IfEs–cluster ellipticals), and 0.93 (BCGs–cluster ellipticals).

Figure 11. Distribution of specific SFR values for IfEs, BCGs, and cluster ellipticals. Blue, red, and gray histograms represent IfEs, BCGs, and cluster ellipticals, respectively.

4.1 Size–luminosity relation

In order to check this relation, we make use of effective radii in r-band of our sample galaxies as measured by SExtractor and given in the CFHTLS T0007 official catalogue. Using MegaCam pixel scale (i.e. 0.186" pixel^-1), they were first converted to angular units (i.e. arcseconds) and then to the physical units (i.e. kpc) by taking into account the photometric redshifts together with the standard cosmological model.

We apply a cut, $-24 \leq M_{r} \leq -22$ , to the absolute magnitudes of the three samples to prevent any bias introduced by their distributions. This magnitude cut ensures the largest overlap between the samples. We then divided our samples into four redshift bins as [0.1,0.3], [0.3,0.5], [0.5,0.7], and [0.7,0.9]. However, it is worth noting that there is only one IfE in the last redshift bin. For each redshift bin, we computed the statistics as given in Table 4. As it can be expected due to the merger-driven size growth in dense environments (Lidman et al. Reference Lidman2013; Lavoie et al. Reference Lavoie2016), BCGs are larger than the two other early-type populations in all redshift bins. BCGs are larger than IfEs with a minimum difference of median $ \textrm{log} R_{ e}$ is 8% at $0.7< z\leq0.9$ and increases to 23% at $0.1< z\leq0.3$ . When compared with elliptical galaxies in rich clusters, both BCGs and IfEs are larger. IfEs are larger than cluster ellipticals for the first three redshift bins as 10%, 4%, and 8% for redshift bins with an increasing order (see Table 4). Only for the last redshift bin (i.e. $0.7< z\leq0.9$ ) cluster ellipticals 4% larger than IfEs. We recall the low statistics due to a single IfE in the last bin. Similarly, BCGs are larger than cluster ellipticals as 35%, 24%, 20%, and 5%.

Afterwards, we applied linear regressions to the size–luminosity relations. Results are obtained for the whole sample without a cut in magnitude but applied separately for each redshift bin. Table 5 lists coefficients for the individual size–luminosity relations of each galaxy population in each redshift bin as well as the whole redshift range.

Figure 12 shows the best fits for the three samples. To obtain intrinsic scatter of the three populations, 1 000 bootstrap realisations were performed. The resulting confidence intervals are shown with blue, grey, and red shaded areas for IfEs, BCGs, and cluster ellipticals, respectively. The distribution of data and their confidence intervals are also shown in Figure 12.

Figure 12. Absolute magnitude versus effective radius relation. Blue, red, and grey points denote IFEs, BCGs, and cluster ellipticals, respectively. Similary, blue, red, and grey solid lines are the best fits. Typical errors on both parameters are given as representative at the bottom left of the plot. Statistics of the distributions are given in Table 4 and coefficients of the linear regressions are given in Table 5. For clarity, histograms at the sides are given as normalised.

In Figure 12, IfEs and BCGs have similar size–luminosity relations (i.e. slopes) except for the offsets in their average size and luminosity. However, the slope for the cluster ellipticals is significantly different from those two samples.

Obtained $\log R_{e} - M_{r}$ relations for IfEs, BCGs, and cluster ellipticals in our sample are given in Equations (4), (5), and (6), respectively. Equations given below are obtained from the whole redshift range (i.e. $0.1 \leq z \leq 0.9$ ).

(4) \begin{equation}\log(R_{e})(IfE) = (\!-0.167\pm0.009)\times M_{r} + (\!-3.044\pm0.202) \end{equation}

(5) \begin{equation}\log(R_{e})(BCG) = (\!-0.173\pm0.012)\times M_{r} + (\!-3.106\pm0.274) \end{equation}

(6) \begin{equation}\log(R_{e})(Cl.Ell) = (\!-0.128\pm0.002)\times M_{r} + (\!-2.138\pm0.048) \end{equation}

4.2 Mass–size relation

Similarly to the size–luminosity relation, we investigate the mass–size relation of each galaxy population separately. Samples are divided into four redshift bins as in the previous section. Masses of our sample galaxies were computed as described in Section 2.5.

To ensure covering the same mass range, we select a sub-sample of our galaxies with masses $10.2< \textrm{log}(M_{*}/ \textrm M_\odot)\leq12.0$ similarly in Kelkar et al. (Reference Kelkar, Aragón-Salamanca, Gray, Maltby, Vulcani, De Lucia, Poggianti and Zaritsky2015). The lower limit of this adopted mass range is higher than our mass completeness limits for each redshift bin.

Sample sizes and statistics on the mass ( $\textrm{log}(M_{*}/ \textrm M_\odot)$ ) and effective radius ( $\log R_{e}$ ) are given in Table 6 for each redshift bin.

BCGs are more massive than both IfEs and cluster ellipticals in almost all redshift bins. In the last bin (i.e. $0.7 \leq z \leq 0.9$ ) IfEs seem larger by 0.02 dex but since there are only two IfEs in this bin results are not totally reliable. Thus, it can be stated that BCGs are the largest in our galaxy samples if we omit this very last redshift bin. The smallest mass difference between BCGs and IfEs occurs at $0.5 \leq z \leq 0.7$ as 0.07 dex whereas the largest difference at $0.1 \leq z \leq 0.3$ as 0.44 dex. Both BCGs and IfEs are more massive than cluster ellipticals in all redshift bins. The mass difference between BCGs and cluster ellipticals is 0.08 (1.03) dex at the highest (lowest) redshift bin. The same behaviour is also seen for IfEs when compared with cluster ellipticals, with 0.10 dex being the smallest and 0.59 dex being the largest difference.

Table 6. Statistical properties (size, mean, standard deviation, and median) of effective radii (in kpc) and mass for IfEs, BCGs, and cluster ellipticals with a cut in stellar masses as $10.2< \textrm{log}(M_{*}/ \textrm M_\odot)\leq12.0$ from Kelkar et al. (Reference Kelkar, Aragón-Salamanca, Gray, Maltby, Vulcani, De Lucia, Poggianti and Zaritsky2015) for different redshift bins.

Table 7. Mass–size relation best-fitting parameters for different populations in different redshift bins.

Mass–size relations for IfEs, BCGs, and cluster ellipticals are shown in Figure 13 and corresponding best fits are given in the Equations (7), (8), and (9). Blue, red, and grey shaded areas in the figure represent the 95% confidence intervals obtained by bootstrapping 1 000 realisations. For the clarity of the figure, errors are not overplotted but a representative error (median) is given in the upper left. BCGs and IfEs have comparable slopes in mass–size relations and are steeper than cluster ellipticals, similarly to the size–luminosity relation given in Figure 12.

Figure 13. Stellar mass versus effective radius relation. Blue, red, and grey points represent IFEs, BCGs, and cluster ellipticals, respectively. Similary, blue, red, and grey solid lines are the best fit for IfEs, BCGs, and cluster ellipticals, respectively. Statistics of the distributions are given in Table 6 and coefficients of the linear regressions are given in Table 7. For clarity, histograms at the sides are given as normalised.

Equations (7), (8), and (9) obtained for the whole redshift range but coefficients for each redshift bin are given in Table 7.

(7) \begin{equation}\log(R_{e})(IfE) = (0.405\pm0.022)\times {\log(M_{*}/{\rm M}_\odot)} + (\!-3.802\pm0.247) \end{equation}

(8) \begin{equation}\log(R_{e})(BCG) = (0.379\pm0.029)\times {\log(M_{*}/{\rm M}_\odot)} + (\!-3.437\pm0.331) \end{equation}

(9) \begin{equation}\log(R_{e})(Cl.Ell) = (0.324\pm0.007)\times {\log(M_{*}/{\rm M}_\odot)} + (\!-2.874\pm0.072) \end{equation}