The Luminosity Profiles of Brightest Cluster Galaxies

The Luminosity Profiles of Brightest Cluster Galaxies

arXiv:1109.0996v1 [astro-ph.CO] 5 Sep 2011

C.J. Donzelli, H. Muriel IATE, Observatorio Astron´ omico OAC, Laprida 854, X5000BGR, C´ ordoba, Argentina Consejo Nacional de Investigaciones Cient´ıficas y Técnicas (CONICET), Avenida Rivadavia 1917, C1033AAJ, Buenos Aires, Argentina

J. P. Madrid Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn, VIC 3122, Australia

ABSTRACT We have derived detailed R band luminosity profiles and structural parameters for a total of 430 brightest cluster galaxies (BCGs), down to a limiting surface brightness of 24.5 magarcsec−2 . Light profiles were initially fitted with a Sérsic’s R1/n model, but we found that 205 (∼ 48%) BCGs require a double component model to accurately match their light profiles. The best fit for these 205 galaxies is an inner Sérsic model, with indices n ∼ 1 − 7, plus an outer exponential component. Thus, we establish the existence of two categories of the BCGs luminosity profiles: single and double component profiles. We found that double profile BCGs are brighter (∼ 0.2 mag) than single profile BCG. In fact, the Kolmogorov-Smirnov test applied to these subsamples indicates that they have different total magnitude distributions, with mean values MR = −23.8 ± 0.6 mag for single profile BCGs and MR = −24.0 ± 0.5 mag for double profile BCGs. We find that partial luminosities for both subsamples are indistinguishable up to r = 15 kpc, while for r > 20 kpc the luminosities we obtain are on average 0.2 mag brighter for double profile BCGs. This result indicates that extra-light for double profile BCGs does not come from the inner region but from the outer regions of these galaxies. The best fit slope of the Kormendy relation for the whole sample is a = 3.13 ± 0.04. However, when fitted separately, single and double profile BCGs show different slopes: asingle = 3.29 ± 0.06 and adouble = 2.79 ± 0.08. Also, the logarithmic slope of the metric luminosity α is higher in double profile BCGs (αdouble = 0.65 ± 0.12) than in single profile BCGs (αsingle = 0.59 ± 0.14). The mean isophote outer ellipticity (calculated at µ ∼ 24 mag arcsec−2 ) is higher in double profile BCGs (edouble = 0.30 ± 0.10) than in single profile BCGs (esingle = 0.26 ± 0.11). Similarly, the mean absolute value of inner minus outer ellipticity is also higher in double profile BCGs On the other hand, we did not find differences between these two BCGs categories when we compared global cluster properties such as the BCG-projected position relative to the cluster X-ray center emission, X-ray luminosity, or BCG orientation with respect to the cluster position angle. Subject headings: galaxies: clusters: general — galaxies: elliptical and lenticular

1.

verse today. BCGs are so massive (Mstar > 1011 M⊙ ) that their formation and evolution is closely tied to the large scale structure of the universe (Conroy et al. 2007). Semi-analytical mod-

Introduction

Brightest cluster galaxies (BCGs) are the most massive and most luminous galaxies in the uni-

1

els show how BCGs are formed through complex hierarchical merging of many small galaxies and originate within the densest dark matter halos of primordial density fluctuations. BCGs reside only in overdense regions of the Universe such as galaxy clusters and groups where merging occurs at a high rate over cosmic time (de Lucia & Blaizot 2007). It is precisely the accretion of numerous stellar systems that give the BCGs their apparently homogenous properties. For instance, their total luminosities are relatively constant and can be used as standard candles (Lauer & Postman 1992). For several decades the luminosity profiles of elliptical galaxies were modeled with the empirical R1/4 de Vaucouleurs law (de Vaucouleurs 1948). However Lugger (1984) and Schombert (1986) showed that most elliptical galaxies have a flux excess at large radii with respect to the R1/4 model. Schombert (1987) modelled the BCG light profiles with a power law rather than the de Vaucouleurs law underscoring the different nature of BCGs and standard elliptical galaxies. A model used virtually by every author in recent years to fit the light profiles of a wide range of stellar systems is the generalization of the de Vaucouleurs law introduced by Sérsic (1963, 1968). The Sérsic model in the form R1/n is a mixture of bulge and disk components using only three free parameters (µe , re , and ns ) instead of four (µe , re , µ0 , and r0 ) (see Section 3 and the comprehensive review of Graham and Driver 2005). More recently, several papers have suggested that a simple Sérsic R1/n law does not properly model the luminosity profile of some elliptical (usually cD) galaxies. Gonzalez et al. (2003, 2005) found that the best fit to the light profiles of 30 BCGs was a double R1/4 de Vaucouleurs profile. Seigar et al. (2007) studied the light profiles of five cD galaxies and showed that a Sérsic plus an exponential function are necessary to accurately reproduce an inner and an outer component present in their surface brightness profiles. Donzelli et al. (2007) estimated that roughly half of 82 elliptical galaxies belonging to the 3CR radio catalog also require a Sérsic + exponential model to properly fit their light profiles. Using numerical simulations Hopkins et al. (2009) propose that dissipational mergers are at the origin of the double components light profiles in the core of elliptical galaxies. According to their models a violent re-

laxation of stars whose parent galaxies participate in the merger is responsible for the creation of an outer component while a central starburst gives rise to the inner component. We use a homogeneous and uniquely large sample of ground-based imaging of Abell clusters to carefully examine the luminosity profiles of 430 BCGs and determine the best fitting function and structural parameters. This is key to properly constrain dynamical models and the merging history of these galaxies. The paper is organized as follows. In Section 2, we present the observations and reductions, while in Section 3 we describe data processing. Light profile fitting procedure and structural parameters are discussed in Section 4, while in Section 5 we discuss the results and in Section 6 we summarize the conclusions. 2.

Observations

BCG images used in this work were provided by M. Postman (STScI) who kindly gave us access to the raw data. They were obtained under photometric conditions using the KPNO 2.1 m and 4 m telescopes, and the CTIO 1.5 m telescope between 1989 November and 1995 April over a total of 13 observing runs (see Table 1). Five of these runs are described in more detail in Postman & Lauer (1995). Briefly, all the images were acquired in the Kron-Cousins Rc band and have typically exposure times of 200-600 s. During these runs seeing conditions were very good to fair, namely, FWHM = 1”-2”, and nights were photometric. In order to flat field the images a series of dome flats were obtained each night. This allowed for flatfielding with a typical accuracy better than 0.5% of the sky level. Photometric calibration was obtained by observing 10-15 Landolt (1983) standard stars per night. This also enabled us to calculate extinction coefficients and to check the zero point on each night of the observing runs. The overall photometric accuracy was better than 0.02 mag, much smaller than the typical errors of the BCG photometric parameters, which are more sensitive to background subtraction, and fitting models. One of the key points of this homogeneous sample is that approximately 50 BCGs were observed in common between the different runs. Many of

2

these BCGs were actually observed in five or more runs. This not only allowed us to verify and compare reductions for all observing runs, but also to improve the accuracy of the luminosity profiles as discussed in the next section. The rms scatter for the integrated magnitudes of the galaxies is 0.03 mag, while for the luminosity profiles at µR = 22.5 mag arcsec−2 is 0.11 mag arcsec−2 . 3.

ordinates, ellipticity, and position angle of the isophotes), and construct a model BCG galaxy that is subtracted from the original image. The residual image is then used to extract the luminosity profile of the overlapping galaxies. The process is repeated several times until the profile of the target galaxy converges. Isophote fitting was performed down to a count level of 2σsky ; i.e., the fitting procedure was stopped when the isophote level was around twice the background dispersion (pixel-to-pixel variance), which in our case corresponds to surface magnitudes between µR ∼ 23.5 - 24.5 mag arcsec−2 , depending on the observational run when the cluster was observed. For each cluster, we usually obtain the luminosity profiles for the three brightest galaxies in the field. This preliminary selection is made by eye. In those cases where the selection is not obvious, we also obtain additional luminosity profiles, i.e., for the five brightest galaxies. The final BCG selection is made through the galaxy metric luminosity, that is the luminosity enclosed in a radius of 14.5 kpc, we also included galaxy redshift to ensure cluster membership. Redshift data were obtained from the NASA/IPAC Extragalactic Database (NED). As discussed in the introduction, there are a wide variety of functions to perform luminosity profile fitting. We adopted the Sérsic profile Rβ , where the concentration parameter β = 1/n is the inverse of the Sérsic index (Sérsic 1968):

Data Processing and Sky Level

All images were processed following the standard recipes: bias and flat field corrections using IRAF routines. After this process we carefully inspect the images in order to determine the best method to subtract the sky background. Gauging the sky is a crucial step since sky subtraction has a significant influence on the faint end of the luminosity profiles and therefore on the structural parameters we derive. In most cases a twodimensional first-degree polynomial was sufficient to give an accurate fit to the sky, and we used the residuals distribution to estimate the uncertainty of the sky level σsky . The importance of sky cleaning is summarized in detail in Coenda et al. (2005). Similar tests were made to measure the effect of seeing on the luminosity profiles. The effects of seeing dictate that the minimum radius for a suitable fit to the luminosity profile is r = 1.5×FWHM, this is particularly true for large galaxies, i.e., apparent radius greater than ∼ 12×FWHM (Coenda et al. 2005). We show in detail in the next section that BCG galaxies were relatively bright and extended and in most cases the apparent radius of the galaxy was greater than 20′′ . 4.

io h r β n −1 . I(r) = Ie exp − bn re

(1)

In this equation Ie is the intensity at r = re the radius that encloses half of the total luminosity (also known as the effective radius or half-light radius). In this context bn can be calculated using bn ∼ 2n − 0.33 (Caon et al. 1993). We use the nfit1d routine within STSDAS to find the coefficients that best fit the light profiles of each galaxy. This task uses a χ2 minimization scheme to fit the best non linear functions to the light profiles tables we obtained with ellipse (Schombert & Bothun 1987). The fitting procedure is carried out only in the portion of the galaxy surface brightness profile where the signalto-noise ratio was greater than 3 (S/N > 3). We

Luminosity Profiles and Profile Fitting

We use the ellipse routine (Jedrzejeswki, 1987) within Space Telescope Science Analysis System (STSDAS) to extract the luminosity profiles of the BCGs. We apply this routine to the processed, sky subtracted images. In many cases galaxy overlapping is an issue due to the crowded fields around BCGs. To solve this, we apply the technique described in Coenda et al. (2005) which consists in masking the overlapping regions before profile extraction. Then we obtain the luminosity profile and structural parameters (center co3

did this in order to avoid the regions at the faint end of the luminosity profiles, in which errors are large. Moreover, we have also excluded the inner 3”-4” of the luminosity profiles to avoid the blurring effects of seeing (see the test described in Coenda et al. 2005). Errors on the structural parameters were calculated following the method described by Coenda et al. (2005). Briefly, this technique consists of creating test images with model galaxies that have known luminosity profile parameters. Then we artificially add and subtract to those images a constant value corresponding to σsky . Finally we extract and refit the new luminosity profile as explained above. These newly obtained parameters give us the respective upper and lower limits. To a first approximation a single Sérsic model provides a good fit to the light profile of our sample of BCGs, as shown by Graham et al. (1996). However, for almost half of the sample we noticed that a single Sérsic function fails to properly reproduce the BCGs surface brightness in the range ∼ 22.0 mag arcsec−2 . Note that this case is very similar to that presented in La Barbera et al. (2008, their Figure 18). It is evident that the Sérsic function do not properly fit the luminosity profiles of these elliptical galaxies in the inner 4′′ , where the residuals are almost ∼ 0.3 mag arcsec−2 . It is not necessary to have very deep luminosity profiles, as in the case of Seigar et al. (2007), to realize that for certain galaxies, even in regions of bright surface luminosity, a single Sérsic model cannot account for the concave shape of the luminosity profile. For these galaxies their light profiles were best fitted adding to the Sérsic model of Equation (1) an outer exponential function (Freeman, 1970): r . I(r) = I0 exp − r0

with a second Sérsic function since it has three degrees of freedom instead two. However, in terms of the χ2 coefficient it is not better than the Sérsic plus exponential fit. Figure 1 shows a good example: the case of BCG A0690 where clearly a single Sérsic function cannot account for the concavity of the luminosity profile. Even when the fitting becomes adequate at the faint end of the profile, the model cannot reproduce the surface magnitude in the interval between 7 and 15 kpc, which corresponds to a surface magnitude in the range of 21-22 mag arcsec−2 . Error bars in this region have approximately the size of the squares. On the other hand, Figure 2 shows a much better fit due to the inclusion of the exponential component (dashed line) in the fitting model. We show that the 21-22 mag arcsec−2 region is now in perfect agreement with the model and the fitting functions can also properly describe the faint end of the luminosity profile. In fact, the reduced χ2 coefficient we obtain with a Sérsic + Exponential model is about one order of magnitude smaller than those obtained with the single Sérsic fit. As a general rule, for most of those cases that are initially fitted with the single Sérsic function and in which n > 8 and re > 300 kpc, it is necessary to include the exponential component to obtain a proper fit. Intensity parameters are then converted into surface brightness, expressed in mag arcsec−2 by the equation m = −2.5log(I), while units of re , and r0 are converted to kpc. Errors for re and r0 are smaller than 15% while for µe , and µ0 errors are below 0.20 mag arcsec−2 . Total luminosities of both Sérsic and the exponential components are finally computed using the derived photometric parameters and integrating separately both components of Equations (1) and (2) as follows: L=

(2)

Z

∞

I(r)2πrdr,

(3)

0

which yields

In this equation I0 is the central intensity and r0 is the length scale. The inclusion of this equation in the fitting function does not necessarily means that the galaxy has a disk component in the usual sense of rotation-supported stellar system. We have chosen the exponential function since it is the simplest function to account for the ”extra-light” observed in the above mentioned galaxies. It is worth to mention that we also tried

LSersic = Ie re2 π

2exp(b) Γ(2/β) βk 2/β

(4)

for the Sérsic component and Lexp = 2πI0 r02

(5)

for the exponential component. Γ(2/β) is the gamma function. Total apparent magnitudes 4

are then converted into absolute magnitudes. Throughout this paper we assume a Hubble constant H0 = 70 km s−1 M pc−1 together with ΩM = 0.27 and ΩΛ = 0.73.

5.

ellipticities. We calculated an average outer ellipticity e = 0.32 ± 0.09, which is slightly higher than the average found for double profile BCGs (see the next section). In general terms we have also noticed that the inner components of the double profile BCGs have effective radii re ∼ 1 − 10 kpc and Sérsic indices n ∼ 1 − 6, being the averages re = 5 ± 4 kpc and n = 3.7 ± 1.5 respectively. This values are quite similar to those reported by Gonzalez et al. (2003) in their preliminary paper for a sample of 31 BCGs. However, these authors use a different approach to fit the luminosity profiles. They use two Sérsic functions instead our Sérsic + exponential approach.

Results and Discussion

Table 2 lists the photometric parameters obtained through the fitting procedure described in Section 3 for all BCGs of the sample. Columns 16 list the Abell BCG name, Sérsic parameters µe , re , n, exponential parameters µ0 and r0 . Columns 7-10 give absolute magnitude of the Sérsic component, absolute magnitude of the exponential component, total absolute magnitude of the BCG and Sérsic to exponential component light ratio. Column 11 contains the logarithmic slope of the metric luminosity or α parameter which is defined as α = d(Log(Lm ))/d(log(rm )), where Lm is the total BCG luminosity within a circular aperture of radius rm centered on the BCG nucleus. Following Postman & Lauer (1995) we have calculated this parameter at r = 14.5 kpc. Columns 12-15 list the inner ellipticity (measured at 10′′ ), outer ellipticity (measured at ∼ 23 − 24 mag arcsec−2 ), and inner and outer position angles of the isophotes where the ellipticities are measured. Position angles are from north to east and the typical observed errors are ∼ 5o , while typical errors for ellipticities are 0.06. Finally, column 16 lists the metric absolute magnitude also calculated at r = 14.5 kpc. The data above show that 225 out of 430 BCGs, or 52% of the sample, have a single Sérsic luminosity profile, while the remaining 205 BCGs (48%) need a double component of Sérsic + exponential to properly fit their luminosity profiles. We note that we find 27 galaxies (∼ 6% of the whole sample) that have n < 1.5 for the inner Sérsic component, which is nearer to an exponential rather than a de Vaucoleurs profile (n ∼ 4). Moreover, all but three, have double component luminosity profiles. This is particularly interesting since it has been suggested that BCGs usually have high Sérsic indices (Graham et al. 1996). However, Seigar et al. (2007) observe an inner exponential behavior in 3 out of 5 galaxies of their sample, suggesting that this may be more common in cD galaxies than previously thought. A visual inspection of these galaxies reveals that they have high

5.1.

Single Profile BCGs versus Double Profile BCGs

A question that arises after our analysis is to establish if single profile BCGs actually differ in morphology from double profile BCGs. The models of the light profiles we apply do not imply conjectures on galaxy morphologies. Are BCGs with single and double profile of a different nature? If so, is this difference environmental or intrinsic? In order to answer these questions we carried out a series of tests in which we explored BCGs properties together with the global cluster properties. One of them is the Kormendy relation (KR; Kormendy 1977) which is presented in Figure 3. This is an empirical scaling relation between surface brightness µe and effective radius re and it represents the projection of the Fundamental Plane (Djorgovski & Davies 1987). For the case of single profile BCGs both µe and re are directly obtained from the fitting profile. However, in the case of double profile BCGs, we calculate these parameters from the double profile, i.e., using the sum of the Sérsic and exponential profiles. A linear regression applied to the whole sample gives µe = 18.72(±0.06) + 3.13(±0.05) log(re /kpc) The slope of the KR obtained for all BCGs is aBCG = 3.13 ± 0.05 which is similar to the value obtained by Oegerle & Hoesel (1991) for a sample of 43 BCGs (i.e., aBCG = 3.12 ± 0.14). However, Bildfell et al. (2008) obtain for a sample of BCGs selected from 48 X-ray luminous clus5

ters (aBCG = 3.44 ± 0.13), which is considerably steeper than our value and than the value of ”normal” ellipticals aellip = 3.02 ± 0.14 (Oegerle & Hoesel, 1991). Nevertheless, when we apply the same analysis to single profile and double profile BCGs separately we obtain for single profile BCGs

be seen in Figure 5 where we plot the absolute integrated magnitude versus the radius of the circular diaphragm expressed in kpc. The vertical line indicates r = 14.5 kpc where metric luminosity and alpha parameter are calculated. Average integrated luminosities beyond 20 kpc are ∼ 0.2 mag brighter for double profile BCGs. We have applied the K-S test to both subsamples and results indicate that they do not statistically differ for r = 5, 10, and 14.5 kpc, while for larger radii the integrated luminosity distribution are truly different at the 99 % confidence level. We highlight that r = 20 kpc is close to value for which the Sérsic component equals the exponential component (see the case for A0690 in Figure 2). From the data tabulated in Table 2, it is straightforward to compute the radius where ISersic = Iexp for each of the double profile BCGs. Averaging these values we find < r >= 13 ± 5 kpc at < µ >= 22.5 ± 0.7 mag arcsec−2 . In other words, this result corroborates that the extra-light observed in double profile BCGs originates in the intermediate regions of the galaxies and not in the inner regions. The same conclusion can also be derived from Figure 6 where we plotted the total sum of the luminosity profiles corresponding to the single and double profile BCGs. Prior to the sum, individual profiles are normalized to their effective radii. Note that the extra-light of the double profile BCGs becomes apparent in the region 1 < r/re = 0.30±0.10 for double profile BCGs and < esingle >= 0.26±0.11 for single profile BCGs. A 6

K-S test applied to these data indicates that the ellipticity distributions for single and double profile BCGs are statistically different at a 98.3% confidence level. Similar results are obtained for the inner minus outer ellipticity of these subsamples. We obtain an average < ∆edouble >= 0.15 ± 0.10 for the double profile BCGs, while for single profile BCGs we have < ∆esingle >= 0.10 ± 0.09. Again, the K-S test indicates different distributions at 99.9% confidence level. The logarithmic slope of the metric luminosity (calculated at r = 14.5 kpc) α is also higher in double profile BCGs (< αdouble >= 0.65 ± 0.12) than in single profile BCGs (< αsingle >= 0.59 ± 0.14). Figure 9 presents the distributions of α for single and double profile BCGs respectively. A K-S test applied to these data establishes that the distributions are statistically different at a 99.9% confidence level. The presence of isophote twisting was also explored. We calculated the outer minus inner position angle of the isophotes for those galaxies with ellipticities greater than 0.15 since position angle errors associated with rounder isophotes are large. We found similar values for both single and double profile BCGs (< ∆pa >= 8o ± 9o ). 5.3.

BCG A0690 in Figure 10. The agreement between model and measurements is excellent and the Hopkins model properly accounts for the luminosity profile. We also compared the rms and χ2 values with those obtained with our original Sérsic + exponential model and we find that both models are equally good. In other words, our approach and the Hopkins model are, from a mathematical point of view, equivalent. The results of fitting exponential + Sérsic models to our double profile galaxies are summarized in Table 3, which lists the same 10 parameters as in Table 2. In this case Sérsic parameters µe , re and n correspond to the outer component, while the exponential µ0 and r0 parameters correspond to the inner component. Obtained χ2 values indicate that this fit proved to be equally good as the inner Sérsic + outer exponential form. However, for some galaxies we inexorably obtained unrealistic (≥ 300 kpc) effective radius using the Hopkins model, this is not the case for the Sérsic + exponential approach. Given that our results suggest that the extra-light comes from the intermediate regions (see also the next section), we believe that the Sérsic + exponential profile fitting is the appropriate selection for the BCGs analized in the present work.

S´ ersic + Exponential or Exponential + S´ ersic?

5.4.

By combining a large set of hydrodynamical simulations spanning a broad range of luminosity profiles of various masses, Hopkins et al. (2009) show an alternative way to separate luminosity profiles into an inner starburst component and outer pre-starburst component for ”cusp” ellipticals which are formed via gas-rich mergers. These authors show that dissipational mergers give rise to two-component luminosity profiles which can be accounted by an exponential function (inner component) plus a Sérsic model (outer component). The exponential function accounts for the extra-light that was formed in a compact central starburst and makes the inner light profile of the galaxy deviate from a single Sérsic in the galaxy core. The outer component was formed by violent relaxation of the stars already present in the precursor galaxies. We fitted to our double component BCGs an exponential (inner) + Sérsic (outer) model in the order proposed by Hopkins et al. (2009). As an example, we show the results of this fitting for the

Extra-light and D-cD Envelopes

Around ∼ 20% of giant elliptical galaxies have extensive, low-luminosity envelopes. These galaxies are known as D type, and those with the largest envelopes are denominated cD galaxies (Mackie, 1992). The envelopes, which are seen as deviations from the de Vaucouleurs profile, are quite faint, occur below 24 mag arcsec−2 in the V band, and they extend well beyond 100 kpc in projected size. Thus, only few giant ellipticals have confirmed envelopes. We explore if the extra-light found at intermediate radii is related to an eventual cD envelope. From the works of Kemp et al. (2007), Seigar et al. (2007), Mackie (1992), and Schombert (1986, 1987, 1988), we have found 24 BCGs, cataloged as cD galaxies with confirmed envelopes, in common with our sample. These are: A85, A150, A151, A193, A262, A358, A539, A779, A1177, A1238, A1767, A1795, A1809, A1904, A1913, A2028, A2147, A2162, A2199, A2366, A2572, A2589, A2634,and A2670. Table 2 shows that 19 (79%) of 7

these 24 galaxies are double profile BCGs, while 5 (21%) are single profile BCGs. Note that three galaxies (A151, A1767, and A2589) from those five single profile BCGs, have re > 100 kpc, and n > 6. These parameters are very close (see Section 4) to the limit (re > 300 kpc, n > 8) where it is necessary to include an additional exponential profile to obtain a reasonable fit. On the other hand, one must also note that a visual classification as cD, does not necessarily imply the presence of an envelope. Schombert (1986), and Seigar et al. (2007) cataloged A496, A505, A1691, A2029, A2052, A2107, A2197, and A2666, as cDs without envelopes. For all those galaxies, except A2197, our surface profile modeling is consistent with just one component. These results strongly suggest that the extralight found in double component BCGs at intermediate radii is related to the faint envelope. Moreover, they indicate that this component is not only confined to the outskirt of the parent galaxy. Galaxy halos generally considered an outer component in galaxy structure appear to originate in the inner regions of BCGs. 5.5.

mostly interacting galaxies with two or three near companions, while the five single profile BCGs with unkown classification appear to us as normal ellipticals. We have scrutinized the infrared emission of a subsample of our BCGs using data from Quillen et al. (2008). They report on an imaging survey with the SpitzerSpaceT elescope of 62 BCGs with optical line emission. We have 12 BCGs in common with Quillen et al. (2008), 6 having single component luminosity profiles and 6 having double component luminosity profiles. Analysis of the 24-8 µm flux ratios shows that only one (17%) of single profile BCG (A2052) have infrared excess, while for double profile BCGs this number increases to 4 (67%). Infrared excess is a star formation signature. In fact, O’Dea et al. (2010) in their study of seven BCGs using HubbleSpaceT elescope(HST ) ultra-violet and Spitzer infrared data found that all these galaxies have extended UV continuum and L − α emission as well as an infrared excess. Based on their findings O’Dea et al. (2010) confirm that the BCGs they study are actively forming stars. Moreover, they suggest that the IR excess is indeed associated with star formation and they also confirm that the FUV continuum emission extends over a region ∼ 7-28 kpc. Although these results are only for a few BCGs in our sample, they suggest that the ”extra-light” observed in the double profile BCGs indicates active star formation in the intermediate regions of these galaxies.

BCGs Morphologies and IR Emission

Although a visual inspection of our BCGs suggests that they all are early-type galaxies, we probe the possibility that the differences we observe in the profiles are due to actual differences in the morphology. The Galaxy Zoo project (http://zoo1.galaxyzoo.org/) provides the morphological types for a large sample of galaxies observed by the Sloan Digital Sky Survey (SDSS; Lintott et al. 2010). In this catalog 66 of the BCGs studied here have a morphological classification: 31 (47%) are single profile BCGs, while 35 (53%) are double profile BCGs. The Lintott et al. (2010) catalog gives the probability that a particular galaxy is an early-type galaxy or latetype (spiral) galaxy. We find that both single and double profile BCGs have the same probability to be classified as elliptical galaxies in the Galaxy Zoo catalog. However, from the 31 single profile BCGs with morphological classification only 5 (16%) belong to the ’unknown’ category, while for the 35 double profile BCGs in the catalog this number rises up to 9 (26%). It is also interesting to note that a visual inspection of these nine double profile BCGs with unknown morphology are

5.6.

Global Cluster Properties

In this section we compare BCGs properties to those of the host cluster such as cluster X-ray luminosity, the projected distance of the BCG with respect to the center of the X-ray emission and the BCG position angle with respect to that of the cluster. We have used data taken from Ledlow et al. (2003) to determine the offset in kpc between the X-ray peak and the optical position of the BCG. X-ray cluster luminosities were taken from Sadat et al. (2004) data, while the position angle of the clusters are obtained from Plionis (1994), Rhee & Katgert (1987), and Binggeli (1982). In this case we have only selected those clusters with ellipticities > 0.15, since for smaller ellipticities position angles have large errors.

8

of the deviation from the Sérsic law of the light profile in the inner regions of galaxies i.e. cusps and evacuated cores (Ferrarese et al. 2006). However, HST detectors do not provide the field of view necessary to truthfully derive the structural parameters of galaxies with a light profile that deviates from a single Sérsic law at large radii.

Single and double profile BCGs have similar orientations relative to the whole cluster and X-ray luminosity distributions. We did not observe any difference between the single profile and double profile BCG samples with respect to the cluster position angle and X-ray cluster luminosity. However, Bildfell et al. (2008) report that brighter BCGs are located closer to the X-ray peak emission. In our case, considering that on average double profile BCGs are brighter than single profile BCGs we should observe larger offsets in single profile BCGs. Nevertheless, we find no significant differences between single profile and double profile BCGs offsets with respect to the X-ray center emission of the cluster. Moreover, we do not find any correlation between the total absolute magnitude and X-ray offset. Figure 11 shows that there is no obvious trend between the total absolute magnitude of both single profile and double profile BCGs. 6.

7.

Acknowledgments

We are thankful to M. Postman (STScI) for giving us access to the data used in this study. We also wish to thank the anonymous referee for his useful comments which helped to clarify and strengthen this paper. This research has made use of the NASA Astrophysics Data System Bibliographic services (ADS) and the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This work has been partially supported with grants from Consejo Nacional de Investigaciones Cient´ıficas y Técnicas de la Rep´ ublica Argentina (CONICET), Secretar´ıa de Ciencia y Tecnolog´ıa de la Universidad de Córdoba and Ministerio de Ciencia y Tecnolog´ıa de Córdoba, Argentina.

Conclusions

We have established the existence of two subpopulations of BCGs based on their luminosity profiles. We analyze a uniquely large sample of 430 BCGs and find that 48% of these galaxies have a light profile that deviates from the standard single Sérsic model. The luminosity profiles of these galaxies are in fact better described by a double component model consisting of an inner Sérsic profile and an outer exponential component. The necessity of an outer exponential component conveys the presence of extra-light at intermediate radii corresponding to surface magnitudes ∼ 22magarcsec−2. We have found strong evidence from a subsample of 24 BCGs that extralight is closely related to the presence of a faint envelope. Similarly, from other subsample of 12 BGCs we also found evidence that links extra-light and star formation. This work highlights the need to cover a large spatial scale when deriving the structural parameters of large galaxies. Accurate parameters can only be obtained when the entire galaxy is considered and this often requires the creation of composite light profiles using data from different telescopes as clearly illustrated by Kormendy et al. (2009). HST detectors provide a superb spatial resolution that has been fundamental for the study

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Fig. 1.— BCG A0690 luminosity profile with the single Sérsic fitting. Upper scale is in arcsec.

Fig. 2.— Inner Sérsic (short dashed line) + outer exponential (long dashed line) fitting model for A0690 luminosity profile.

11

Fig. 3.— Kormedy relation for sample galaxies. Black dots represent single profile BCGs, while red dots represent double profile BCGs. Best fits for both subsamples are also shown.

Fig. 5.— Integrated absolute magnitudes vs. diaphragm radius in kpc. The vertical line indicates where alpha parameter and metric magnitudes are calculated.

Fig. 4.— Total magnitude distributions for single (black line) and double profile (red line) BCGs.

Fig. 6.— Luminosity profiles obtained using the stacking technique for all single and double profile BCGs. Prior to the stacking the individual profiles were normalized at the effective radius.

12

Fig. 7.— Outer ellipticity distributions for single (black line) and double profile (red line) BCGs.

Fig. 9.— α parameter distributions for single (black line) and double profile (red line) BCGs.

Fig. 8.— Outer minus inner ellipticity distributions for single (black line) and double profile (red line) BCGs.

Fig. 10.— Exp + Sérsic model fit for A0690 luminosity profile. Outer Sérsic (short dashed line) and inner exponential (long dashed lined) can be observed.

13

Fig. 11.— BCGs total absolute magnitude vs. X-ray offset for the whole BCG sample.

14

Table 1 BCGs Imaging Runs Run 1 2 3 4 5 6 7 8 9 10 11 12 13

Date

Observatory

Pixel Scale (”)

FOV (’)

1989 Oct 1989 Nov 1990 Nov 1991 Mar 1991 Apr 1993 Sep 1993 Nov 1994 May 1994 May 1994 Oct 1994 Dec 1995 Apr 1995 Apr

CTIO KPNO 4m CTIO KPNO 2.1m CTIO KPNO 2.1m CTIO KPNO 2.1m CTIO KPNO 2.1m CTIO CTIO KPNO 2.1m

0.273 0.299 0.273 0.304 0.434 0.304 0.434 0.304 0.434 0.304 0.434 0.434 0.304

3.6 4.0 3.6 5.2 7.4 5.2 7.4 5.2 7.4 5.2 7.4 7.4 5.2

15

Table 2 BCGs Photometrical Parameters Name (1)

µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)

A0014 A0027 A0071 A0074 A0075 A0076 A0077 A0080 A0085 A0086 A0102 A0114 A0116 A0117 A0119 A0126 A0133 A0134 A0147 A0150 A0151 A0152 A0154 A0158 A0160 A0161 A0168 A0171 A0174 A0179 A0189 A0193 A0194 A0195 A0208 A0225 A0240 A0245 A0246 A0257 A0260 A0261 A0262 A0267 A0268 A0279 A0292 A0295 A0311 A0326 A0347 A0357 A0358 A0376 A0396 A0397 A0399 A0401

26.65 24.41 20.73 23.24 21.86 24.08 26.39 21.59 21.43 22.55 23.73 22.73 21.44 24.06 26.71 20.74 21.10 21.19 21.75 20.93 25.86 18.92 21.82 19.06 20.38 20.53 24.51 22.75 20.44 21.14 21.13 18.60 18.59 21.62 21.66 25.24 24.61 21.95 23.73 19.86 20.95 20.19 20.33 25.90 20.23 22.81 23.37 21.47 22.79 21.06 20.95 21.61 23.57 25.76 20.47 20.31 21.82 28.27

387.58 32.51 5.18 23.04 10.58 34.80 190.00 5.92 12.43 14.89 32.22 20.87 9.44 47.47 247.61 3.10 7.64 5.86 10.17 6.34 146.25 1.38 11.13 1.66 3.04 3.65 48.01 17.23 3.71 5.27 7.32 1.78 1.30 8.16 7.95 84.64 55.91 8.70 24.12 2.99 6.17 4.08 3.18 105.21 2.85 18.86 45.49 4.64 15.71 5.91 3.99 7.00 32.81 94.82 2.35 3.82 10.41 968.92

5.08 7.58 5.49 6.45 4.74 7.58 6.94 2.24 0.86 6.17 7.41 5.85 4.52 6.06 7.87 3.61 1.11 4.72 6.06 1.91 8.06 5.65 5.21 4.15 1.04 4.74 7.41 6.49 0.98 3.73 3.06 4.13 1.53 6.58 5.32 7.09 5.38 3.28 6.33 4.26 4.50 2.60 1.75 6.29 3.70 5.29 3.11 2.99 5.43 3.14 3.66 2.51 5.13 8.00 1.66 3.44 1.22 7.46

— — — — — — — — 21.63 — — — — — — — 21.46 — — 22.01 — 20.93 22.33 20.97 21.05 22.33 — — 21.56 21.92 — 21.52 19.95 — 22.36 — — — — 21.13 21.85 21.69 21.16 — 22.80 22.56 — 21.44 22.36 — — — — — — 21.78 21.83 —

— — — — — — — — 26.00 — — — — — — — 23.80 — — 26.20 — 11.80 28.00 10.20 12.50 23.50 — — 13.02 16.30 — 22.00 7.70 — 26.80 — — — — 11.90 20.90 15.30 16.60 — 14.30 30.60 — 17.30 38.00 — — — — — — 19.20 33.30 —

-26.65 -23.67 -23.28 -24.05 -23.55 -24.09 -25.65 -22.29 -23.47 -23.76 -24.36 -24.26 -23.74 -24.73 -25.77 -21.78 -22.87 -22.98 -23.64 -22.91 -25.51 -22.24 -23.76 -22.28 -21.49 -22.64 -24.38 -24.04 -21.97 -22.62 -23.15 -22.84 -21.51 -23.42 -23.37 -24.95 -24.50 -23.02 -23.70 -22.91 -23.17 -22.79 -21.54 -24.66 -22.31 -24.01 -25.01 -21.84 -23.59 -22.87 -21.82 -22.68 -24.34 -24.66 -20.87 -22.66 -22.92 -27.25

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -24.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -24.23 0.00 0.00 -23.89 0.00 -23.32 -23.72 -22.90 -23.18 -23.40 0.00 0.00 -22.89 -22.93 0.00 -23.97 -23.12 0.00 -23.76 0.00 0.00 0.00 0.00 -23.21 -23.46 -23.00 -23.33 0.00 -21.89 -23.76 0.00 -23.48 -24.38 0.00 0.00 0.00 0.00 0.00 0.00 -23.38 -24.65 0.00

-26.65 -23.67 -23.28 -24.05 -23.55 -24.09 -25.65 -22.29 -24.68 -23.76 -24.36 -24.26 -23.74 -24.73 -25.77 -21.78 -24.50 -22.98 -23.64 -24.26 -25.51 -23.66 -24.50 -23.39 -23.38 -23.84 -24.38 -24.04 -23.27 -23.54 -23.15 -24.30 -23.34 -23.42 -24.34 -24.95 -24.50 -23.02 -23.70 -23.83 -24.08 -23.65 -23.52 -24.66 -22.88 -24.65 -25.01 -23.70 -24.81 -22.87 -21.82 -22.68 -24.34 -24.66 -20.87 -23.83 -24.85 -27.25

— — — — — — — — 0.49 — — — — — — — 0.29 — — 0.40 — 0.37 1.04 0.56 0.21 0.50 — — 0.43 0.75 — 0.36 0.23 — 0.70 — — — — 0.75 0.76 0.83 0.19 — 1.47 1.25 — 0.22 0.48 — — — — — — 0.51 0.20 —

1.10 0.59 0.49 0.54 0.55 0.57 0.91 0.46 1.30 0.56 0.61 0.59 0.58 0.76 0.83 0.26 0.93 0.47 0.49 0.75 0.78 0.84 0.66 0.71 0.78 0.67 0.65 0.63 0.66 0.63 0.40 0.59 0.68 0.50 0.67 0.78 0.86 0.57 0.62 0.64 0.62 0.57 0.76 0.90 0.47 0.81 0.88 0.66 0.80 0.38 0.32 0.35 0.76 0.73 0.22 0.61 1.13 1.02

0.35 0.24 0.06 0.28 0.09 0.05 0.13 0.11 0.11 0.26 0.13 0.16 0.17 0.12 0.12 0.04 0.07 0.14 0.16 0.11 0.17 0.04 0.22 0.13 0.03 0.05 0.06 0.14 0.02 0.22 0.42 0.04 0.25 0.09 0.06 0.15 0.09 0.21 0.16 0.26 0.12 0.10 0.07 0.19 0.14 0.11 0.31 0.11 0.17 0.42 0.30 0.41 0.17 0.05 0.47 0.14 0.23 0.26

0.56 0.28 0.05 0.30 0.23 0.17 0.51 0.06 0.35 0.17 0.11 0.28 0.17 0.28 0.33 0.09 0.43 0.05 0.09 0.43 0.26 0.28 0.39 0.12 0.24 0.31 0.25 0.12 0.16 0.38 0.50 0.23 0.36 0.05 0.33 0.27 0.21 0.27 0.39 0.42 0.33 0.18 0.41 0.33 0.27 0.24 0.58 0.44 0.53 0.11 0.21 0.47 0.28 0.27 0.35 0.40 0.43 0.58

56.5 -54.0 51.1 42.2 85.0 -66.4 -62.5 -64.2 -27.3 70.6 -64.2 72.9 5.5 -7.7 34.8 -38.6 33.7 10.5 33.6 -2.9 73.5 39.0 -38.9 -59.4 -73.1 4.9 -25.6 86.5 5.9 -27.3 -2.8 -69.9 56.6 -84.7 10.7 81.2 4.6 -65.2 17.8 9.9 46.3 -2.7 -73.6 78.4 2.7 40.2 -84.9 76.4 15.7 21.5 -76.7 -42.1 3.9 -82.9 7.7 39.2 46.5 35.8

52.0 -61.2 31.1 39.6 60.4 -118.7 -64.0 -71.0 -32.1 74.8 -41.3 73.6 15.5 -19.9 35.9 38.9 22.4 1.6 31.6 -4.8 76.9 17.2 -44.1 -48.6 -92.1 -42.9 -26.5 30.7 -64.9 -25.6 -6.7 -73.3 60.5 11.2 25.5 81.6 9.3 -81.4 11.0 24.1 73.2 -9.8 42.0 72.0 -11.5 47.6 -85.6 67.0 29.0 87.7 -66.5 -39.9 11.0 81.7 7.7 60.5 39.8 24.7

-22.87 -22.18 -22.45 -22.93 -22.74 -22.80 -23.04 -21.98 -23.18 -22.90 -22.97 -23.01 -22.93 -23.20 -23.01 -21.55 -22.95 -22.40 -22.83 -22.81 -23.11 -22.64 -23.05 -22.58 -22.44 -22.07 -22.83 -23.00 -22.53 -22.35 -22.24 -22.88 -22.58 -22.69 -22.95 -22.92 -22.74 -22.30 -22.42 -22.76 -22.89 -22.81 -22.21 -22.58 -22.06 -23.10 -22.94 -22.76 -22.83 -22.22 -21.28 -21.85 -22.87 -22.71 -20.42 -22.87 -22.80 -23.01

16

Table 2—Continued Name (1)

µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)


20.33 22.20 21.68 25.05 18.82 22.01 25.74 20.95 20.90 24.64 23.13 22.59 25.23 21.03 19.33 21.41 22.20 21.69 20.09 21.59 22.11 20.35 20.38 20.55 21.76 23.54 21.18 21.59 23.12 21.72 24.11 20.14 21.65 22.59 24.10 20.80 20.70 21.94 24.42 17.97 24.18 21.15 21.03 22.18 19.48 22.10 21.81 20.74 21.87 22.54 22.61 20.89 19.43 19.77 20.27 20.33 21.19 23.46

4.04 9.26 7.33 61.90 1.65 8.26 101.00 2.41 5.92 78.09 21.69 16.32 84.14 5.56 2.39 7.07 10.71 9.57 3.86 11.11 13.01 4.19 3.79 4.44 7.99 24.95 5.32 8.46 30.92 10.91 29.04 4.99 9.54 17.78 40.05 4.44 7.99 10.39 57.38 0.68 30.16 7.34 3.79 9.14 1.93 14.38 6.50 5.67 9.13 12.29 18.69 6.10 1.90 2.90 3.93 4.44 7.93 28.91

1.09 3.88 4.55 6.80 3.51 4.35 5.62 3.58 2.90 6.80 5.56 4.98 6.54 4.76 2.48 4.08 4.26 3.44 1.28 2.87 4.72 4.74 4.88 4.29 5.62 4.52 3.30 2.68 5.13 3.07 5.59 2.21 5.24 3.75 6.33 2.17 3.72 3.70 6.85 2.87 7.04 4.35 1.17 5.75 4.03 3.89 5.24 5.21 4.59 6.41 4.90 5.08 2.58 3.89 5.41 1.58 3.86 5.38

21.26 21.95 — — 21.71 — — 21.51 22.44 — — — — 22.31 — 20.39 23.00 23.30 23.03 — — — 22.95 22.00 — — — — — — 22.34 21.33 22.54 — — 23.23 21.60 22.30 — 19.55 — 22.88 — — 22.16 22.90 23.01 21.91 22.63 — — 23.28 20.89 22.23 22.73 21.67 — —

12.40 26.00 — — 6.80 — — 9.70 30.00 — — — — 22.30 — 6.60 51.50 57.80 29.20 — — — 26.60 13.30 — — — — — — 31.40 23.30 28.30 — — 23.50 27.20 26.25 — 4.20 — 33.50 — — 14.80 25.20 23.90 23.70 20.10 — — 33.50 11.80 13.50 18.60 15.70 — —

-22.27 -22.91 -22.85 -24.48 -22.43 -22.92 -24.57 -21.31 -23.03 -25.29 -23.98 -23.75 -25.15 -22.91 -22.63 -22.98 -23.33 -23.48 -22.64 -23.84 -23.22 -22.94 -22.92 -22.17 -23.27 -23.89 -22.56 -23.26 -24.96 -23.22 -23.64 -23.23 -23.72 -23.90 -24.43 -22.31 -23.57 -23.30 -24.94 -21.21 -23.70 -23.48 -21.53 -23.03 -22.14 -23.89 -22.61 -23.36 -23.19 -23.35 -23.98 -23.15 -21.96 -22.52 -23.10 -22.82 -23.52 -24.33

-23.03 -24.02 0.00 0.00 -21.29 0.00 0.00 -22.44 -23.79 0.00 0.00 0.00 0.00 -23.15 0.00 -22.45 -24.52 -24.46 -23.28 0.00 0.00 0.00 -23.09 -21.67 0.00 0.00 0.00 0.00 0.00 0.00 -24.01 -24.29 -23.65 0.00 0.00 -22.42 -23.97 -23.60 0.00 -22.38 0.00 -23.61 0.00 0.00 -22.50 -23.92 -22.70 -23.76 -22.68 0.00 0.00 -22.94 -23.30 -22.02 -22.46 -23.31 0.00 0.00

-23.47 -24.36 -22.85 -24.48 -22.75 -22.92 -24.57 -22.77 -24.23 -25.29 -23.98 -23.75 -25.15 -23.79 -22.63 -23.50 -24.83 -24.83 -23.76 -23.84 -23.22 -22.94 -23.76 -22.70 -23.27 -23.89 -22.56 -23.26 -24.96 -23.22 -24.59 -24.64 -24.44 -23.90 -24.43 -23.12 -24.54 -24.21 -24.94 -22.70 -23.70 -24.30 -21.53 -23.03 -23.09 -24.66 -23.41 -24.33 -23.71 -23.35 -23.98 -23.80 -23.58 -23.05 -23.58 -23.84 -23.52 -24.33

0.50 0.36 — — 2.86 — — 0.35 0.50 — — — — 0.80 — 1.63 0.34 0.40 0.55 — — — 0.86 1.58 — — — — — — 0.71 0.38 1.06 — — 0.90 0.69 0.76 — 0.34 — 0.89 — — 0.72 0.97 0.92 0.69 1.60 — — 1.22 0.29 1.59 1.79 0.64 — —

0.62 0.86 0.40 0.70 0.41 0.49 0.78 0.81 0.63 0.84 0.61 0.55 0.84 0.50 0.27 0.64 0.76 0.67 0.39 0.69 0.50 0.32 0.51 0.52 0.49 0.73 0.47 0.69 0.96 0.50 0.85 0.73 0.66 0.70 0.76 0.49 0.58 0.86 0.71 0.47 0.62 0.63 0.23 0.43 0.58 0.86 0.61 0.64 0.65 0.58 0.54 0.44 0.70 0.43 0.53 0.64 0.50 0.73

0.27 0.12 0.28 0.19 0.03 0.21 0.16 0.20 0.21 0.14 0.19 0.24 0.29 0.04 0.07 0.34 0.15 0.16 0.23 0.18 0.13 0.17 0.01 0.07 0.06 0.10 0.17 0.02 0.06 0.17 0.23 0.21 0.10 0.23 0.03 0.10 0.16 0.12 0.25 0.36 0.11 0.09 0.45 0.11 0.08 0.20 0.10 0.08 0.07 0.06 0.35 0.19 0.06 0.10 0.05 0.17 0.36 0.06

0.37 0.32 0.32 0.47 0.09 0.16 0.37 0.28 0.37 0.17 0.31 0.17 0.41 0.36 0.02 0.14 0.38 0.57 0.35 0.11 0.15 0.08 0.04 0.21 0.16 0.35 0.23 0.07 0.01 0.14 0.49 0.27 0.20 0.29 0.06 0.12 0.41 0.32 0.45 0.27 0.27 0.30 0.51 0.13 0.18 0.22 0.16 0.24 0.11 0.06 0.41 0.24 0.29 0.14 0.16 0.25 0.32 0.15

22.4 -20.1 -61.2 -75.5 8.0 12.5 -8.6 26.5 9.0 -51.9 -53.3 -61.2 -34.1 -11.3 -64.1 64.4 -43.4 -68.4 29.5 31.9 -4.4 -60.2 -52.3 84.6 76.2 26.8 58.0 -60.2 -81.9 -77.2 7.4 23.7 41.7 -53.4 71.6 26.2 -23.7 -36.5 -22.9 -10.2 6.5 -29.8 -31.6 68.6 -27.0 -81.9 -54.6 7.7 -50.0 52.8 -21.3 -9.1 -31.5 9.6 -46.6 -88.3 31.5 -9.4

24.7 -12.5 -25.0 -70.3 48.6 -2.2 -3.9 31.0 33.0 11.0 -49.9 -44.8 -29.2 -2.0 -47.6 82.7 -56.8 -67.1 42.1 -22.7 34.3 46.9 16.2 -86.6 78.8 -1.1 41.3 31.1 4.2 67.5 10.4 30.7 53.0 -54.3 -49.6 69.8 -21.0 -34.6 -27.4 -5.7 86.0 -28.1 -29.9 -9.1 -8.2 57.3 -61.3 -18.1 -39.3 1.8 -18.6 -29.4 -53.8 0.1 -41.8 -89.8 25.1 -14.6

-22.57 -22.72 -22.06 -22.56 -22.18 -22.25 -22.75 -21.95 -22.83 -23.39 -22.90 -22.69 -23.05 -22.59 -22.06 -22.73 -22.79 -22.87 -22.54 -23.07 -22.54 -22.37 -22.63 -22.58 -22.51 -22.60 -22.39 -22.81 -23.54 -22.46 -22.55 -23.20 -23.06 -22.79 -22.86 -22.23 -23.10 -22.85 -22.98 -22.17 -22.39 -22.95 -21.08 -22.29 -22.07 -23.00 -22.19 -22.99 -22.71 -23.05 -22.70 -22.55 -22.65 -22.35 -22.76 -22.92 -22.59 -22.99

17


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)


20.73 21.28 20.49 21.39 22.65 21.49 19.97 22.08 20.03 23.13 21.45 20.80 23.57 21.58 20.93 19.77 19.39 21.00 17.37 21.28 20.34 24.32 21.99 19.76 21.93 23.96 21.66 24.04 22.79 23.00 21.74 21.90 23.35 19.58 20.96 23.87 19.71 20.54 22.35 22.00 20.75 19.78 24.90 20.83 20.07 15.76 23.78 20.47 22.55 23.08 23.34 21.56 20.41 25.23 21.22 20.71 22.04 20.94

6.52 6.61 4.99 6.74 15.08 6.31 3.11 9.21 3.54 20.88 10.10 5.69 21.29 9.28 7.84 2.69 2.34 4.64 0.82 7.21 6.21 38.01 9.41 3.67 10.26 35.95 8.47 52.80 15.86 25.76 7.06 10.47 22.75 3.02 5.57 34.05 1.74 4.45 16.82 9.05 6.44 3.06 76.44 6.07 4.01 0.36 67.02 4.95 22.89 17.18 39.24 7.88 5.81 101.01 7.12 5.77 13.08 6.02

2.26 5.03 2.33 4.83 6.67 3.56 3.95 6.41 2.62 6.41 1.87 2.93 4.74 2.54 2.42 1.85 4.18 4.67 2.54 4.42 1.59 6.80 4.13 2.54 4.98 5.38 5.05 5.08 6.62 5.56 5.88 4.98 3.34 4.27 5.49 6.85 1.10 3.45 5.85 5.92 3.46 3.17 8.20 5.15 1.44 2.89 3.08 0.96 2.99 6.80 6.21 6.58 3.27 6.02 5.62 1.06 3.40 1.88

23.01 21.20 21.97 22.45 23.46 — 21.58 — 22.42 22.29 23.94 21.80 21.85 23.43 — 21.22 21.81 22.15 20.26 — — — 23.29 21.67 22.52 — — — — — 22.66 — — 20.60 — — 19.63 21.48 22.29 — 22.32 20.37 — 22.38 21.70 22.56 — 21.81 — — — — 22.04 — 21.18 21.30 — 21.70

47.10 16.30 20.90 22.60 49.00 — 16.30 — 22.00 29.00 95.70 16.70 20.50 39.10 — 9.80 12.10 22.50 4.70 — — — 34.60 23.70 51.90 — — — — — 19.90 — — 9.90 — — 7.40 15.60 34.30 — 20.90 11.00 — 19.50 21.10 4.50 — 24.20 — — — — 22.40 — 27.70 17.80 — 27.50

-23.31 -23.18 -22.88 -22.92 -23.51 -22.70 -22.74 -23.21 -22.78 -23.70 -23.21 -23.14 -23.48 -23.33 -23.41 -22.18 -22.52 -22.67 -21.97 -23.05 -23.44 -24.07 -23.09 -22.84 -23.50 -24.18 -23.32 -24.98 -23.80 -23.97 -22.99 -23.50 -23.66 -23.17 -23.21 -24.34 -21.20 -22.88 -24.23 -23.29 -23.50 -22.85 -25.19 -23.46 -22.66 -22.00 -25.38 -22.58 -24.39 -23.57 -25.00 -23.49 -23.53 -25.30 -23.52 -22.70 -23.75 -22.83

-24.22 -23.71 -23.39 -22.99 -23.60 0.00 -23.35 0.00 -23.18 -23.62 -24.60 -23.25 -23.63 -23.44 0.00 -22.54 -22.25 -23.48 -21.72 0.00 0.00 0.00 -23.20 -23.82 -24.92 0.00 0.00 0.00 0.00 0.00 -22.72 0.00 0.00 -23.30 0.00 0.00 -23.67 -23.34 -24.25 0.00 -23.17 -23.77 0.00 -22.92 -23.76 -19.48 0.00 -24.01 0.00 0.00 0.00 0.00 -23.54 0.00 -24.93 -23.83 0.00 -24.37

-24.61 -24.23 -23.92 -23.71 -24.31 -22.70 -23.84 -23.21 -23.75 -24.41 -24.87 -23.95 -24.31 -24.14 -23.41 -23.12 -23.14 -23.90 -22.61 -23.05 -23.44 -24.07 -23.90 -24.19 -25.18 -24.18 -23.32 -24.98 -23.80 -23.97 -23.62 -23.50 -23.66 -23.99 -23.21 -24.34 -23.78 -23.89 -24.99 -23.29 -24.10 -24.16 -25.19 -23.98 -24.10 -22.10 -25.38 -24.27 -24.39 -23.57 -25.00 -23.49 -24.29 -25.30 -25.19 -24.16 -23.75 -24.60

0.43 0.62 0.62 0.93 0.92 — 0.57 — 0.69 1.08 0.28 0.91 0.87 0.90 — 0.72 1.28 0.47 1.26 — — — 0.90 0.41 0.27 — — — — — 1.28 — — 0.89 — — 0.10 0.65 0.98 — 1.35 0.43 — 1.65 0.36 10.17 — 0.27 — — — — 0.99 — 0.27 0.35 — 0.24

0.72 0.78 0.55 0.57 0.54 0.44 0.65 0.48 0.63 0.71 0.66 0.64 0.95 0.75 0.50 0.52 0.43 0.68 0.24 0.33 0.48 0.63 0.55 0.57 0.73 0.54 0.51 0.72 0.50 0.56 0.65 0.54 0.81 0.63 0.44 0.66 0.67 0.70 0.75 0.49 0.65 0.78 0.73 0.55 0.61 0.67 1.02 0.52 0.92 0.55 0.58 0.48 0.59 0.81 0.65 0.85 0.64 0.81

0.18 0.28 0.19 0.06 0.15 0.17 0.11 0.22 0.30 0.13 0.12 0.18 0.28 0.16 0.27 0.22 0.06 0.08 0.10 0.23 0.43 0.17 0.10 0.19 0.18 0.22 0.21 0.39 0.21 0.13 0.08 0.23 0.16 0.25 0.10 0.08 0.51 0.20 0.16 0.12 0.20 0.24 0.25 0.09 0.23 0.12 0.24 0.32 0.18 0.08 0.33 0.16 0.25 0.09 0.27 0.12 0.29 0.10

0.30 0.12 0.38 0.32 0.24 0.16 0.33 0.28 0.49 0.42 0.07 0.21 0.32 0.17 0.09 0.30 0.19 0.43 0.13 0.30 0.20 0.31 0.12 0.36 0.57 0.29 0.22 0.32 0.22 0.24 0.19 0.10 0.23 0.15 0.10 0.12 0.58 0.29 0.33 0.29 0.18 0.14 0.41 0.25 0.37 0.12 0.48 0.41 0.07 0.16 0.43 0.11 0.22 0.39 0.07 0.16 0.30 0.34

-40.4 -86.8 -10.0 -51.2 36.6 -44.3 68.8 -32.0 44.6 47.5 39.5 -81.6 -7.6 -47.1 66.5 -50.2 13.8 -79.9 -46.5 44.9 -46.1 59.4 -26.0 86.8 38.9 -8.8 88.8 80.3 -56.0 4.1 59.6 59.1 -61.3 72.4 -79.8 48.0 -12.1 48.0 -17.7 -88.4 -48.9 -74.2 73.4 -85.0 83.1 19.0 47.4 59.4 -34.3 -53.0 -44.4 -34.9 -85.8 -47.5 30.0 -19.2 83.4 9.5

-60.3 -85.6 -17.5 -82.0 51.1 -50.1 69.7 -75.3 43.7 39.8 -15.0 -65.2 -12.4 -25.8 88.5 -46.5 -42.3 -77.7 -43.0 53.4 -45.3 55.8 -38.3 -86.2 55.4 -7.6 77.4 78.8 -62.1 -10.8 44.0 69.5 -65.9 70.3 -65.4 52.9 -10.0 44.1 -32.1 -54.0 -52.9 -71.1 65.8 -68.0 86.4 18.6 42.8 55.1 -14.1 -20.1 -45.1 -39.2 -76.0 -3.6 12.5 -28.6 75.8 15.4

-22.84 -22.98 -22.74 -22.55 -22.55 -22.12 -22.76 -22.25 -22.26 -22.77 -22.87 -22.95 -22.72 -22.81 -22.75 -22.38 -22.42 -22.56 -22.10 -22.43 -22.76 -22.56 -22.61 -22.81 -22.89 -22.75 -22.53 -23.05 -22.67 -22.74 -22.50 -22.66 -22.45 -23.12 -22.56 -22.80 -22.57 -22.82 -23.26 -22.39 -23.01 -23.19 -23.21 -23.01 -22.85 -21.75 -23.00 -22.78 -23.16 -22.63 -23.26 -22.69 -23.10 -23.16 -22.82 -23.00 -22.70 -22.94

18


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)


22.88 21.78 22.29 22.01 21.04 22.75 23.22 20.62 23.78 23.37 21.50 21.91 21.99 19.74 20.94 21.89 26.26 19.37 19.94 19.89 21.57 26.30 20.57 24.76 21.19 24.15 23.87 23.19 21.06 22.28 21.86 20.85 21.65 19.25 21.42 21.18 21.13 22.53 21.28 20.84 23.96 23.19 19.63 24.51 20.02 25.16 22.07 22.83 22.52 19.64 20.16 17.19 20.41 21.35 25.06 21.75 23.47 20.33

45.78 12.38 10.97 10.76 7.22 18.26 26.32 5.55 49.81 18.80 9.54 12.00 10.73 2.78 5.80 11.28 201.64 1.43 3.62 4.84 10.27 439.41 3.67 73.57 5.15 44.25 27.62 35.86 5.41 14.87 9.98 7.19 7.05 3.71 5.64 7.95 6.67 13.34 7.12 8.91 52.68 19.05 1.42 44.68 3.49 71.27 6.98 15.13 15.75 3.60 4.35 0.43 3.97 5.54 57.29 12.37 26.80 4.55

2.38 4.93 4.90 6.06 2.53 4.98 5.24 2.30 5.18 6.13 2.83 4.76 6.02 5.29 3.09 6.29 6.41 4.08 3.55 2.07 3.32 5.78 5.21 3.89 3.80 4.27 7.30 3.68 6.21 3.23 6.45 3.92 3.19 1.54 5.00 1.40 2.19 6.41 4.02 1.87 3.86 5.99 4.35 6.37 4.18 5.00 5.18 7.14 6.13 1.64 1.55 4.10 1.55 3.64 6.71 3.91 6.99 1.79

— 22.81 23.24 — — 21.80 — 22.40 — — — 21.85 — 22.10 21.44 — — 19.76 21.98 21.90 22.78 — 21.94 — 21.86 — — — 21.87 23.15 — 22.46 — 20.32 — 21.82 — — — — — — 21.02 — 22.17 21.19 21.67 — — 21.32 21.97 20.31 21.31 — — — — 23.43

— 45.50 27.90 — — 28.20 — 22.50 — — — 22.30 — 23.00 16.10 — — 4.70 22.70 22.30 35.40 — 26.20 — 21.00 — — — 15.10 78.10 — 28.20 — 13.50 — 26.90 — — — — — — 8.60 — 17.80 17.60 17.50 — — 16.50 17.40 3.20 16.30 — — — — 90.80

-25.46 -24.07 -23.26 -23.64 -23.28 -23.99 -24.14 -23.07 -25.08 -23.54 -23.41 -23.88 -23.55 -22.89 -22.96 -23.76 -25.74 -21.59 -22.99 -23.61 -23.68 -27.40 -22.54 -24.58 -22.51 -24.21 -23.90 -24.64 -23.20 -23.58 -23.53 -23.40 -22.66 -23.05 -22.66 -22.76 -22.73 -23.56 -23.22 -23.73 -24.86 -23.68 -21.31 -24.28 -22.88 -24.40 -22.57 -23.58 -23.91 -22.87 -22.75 -20.86 -22.33 -22.62 -24.22 -23.91 -24.16 -22.81

0.00 -24.37 -22.84 0.00 0.00 -24.37 0.00 -23.23 0.00 0.00 0.00 -23.80 0.00 -23.58 -23.42 0.00 0.00 -22.38 -23.61 -23.86 -23.86 0.00 -23.90 0.00 -23.52 0.00 0.00 0.00 -22.99 -25.04 0.00 -23.38 0.00 -23.88 0.00 -23.91 0.00 0.00 0.00 0.00 0.00 0.00 -22.39 0.00 -22.86 -23.83 -23.44 0.00 0.00 -23.56 -23.05 -20.70 -23.59 0.00 0.00 0.00 0.00 -25.23

-25.46 -24.98 -23.82 -23.64 -23.28 -24.95 -24.14 -23.90 -25.08 -23.54 -23.41 -24.59 -23.55 -24.04 -23.96 -23.76 -25.74 -22.81 -24.10 -24.49 -24.52 -27.40 -24.17 -24.58 -23.88 -24.21 -23.90 -24.64 -23.85 -25.29 -23.53 -24.14 -22.66 -24.29 -22.66 -24.23 -22.73 -23.56 -23.22 -23.73 -24.86 -23.68 -22.73 -24.28 -23.62 -24.91 -23.84 -23.58 -23.91 -24.02 -23.66 -21.54 -23.89 -22.62 -24.22 -23.91 -24.16 -25.34

— 0.76 1.47 — — 0.70 — 0.87 — — — 1.08 — 0.53 0.65 — — 0.49 0.57 0.79 0.84 — 0.28 — 0.39 — — — 1.21 0.26 — 1.02 — 0.47 — 0.35 — — — — — — 0.37 — 1.02 1.69 0.45 — — 0.53 0.76 1.15 0.31 — — — — 0.11

1.09 0.69 0.63 0.57 0.44 0.86 0.60 0.60 0.76 0.60 0.58 0.76 0.56 0.57 0.67 0.34 0.90 0.46 0.65 0.56 0.71 1.05 0.72 0.88 0.42 0.80 0.67 0.79 0.72 0.81 0.48 0.57 0.49 0.60 0.42 0.81 0.41 0.56 0.44 0.52 0.90 0.73 0.60 0.74 0.57 1.12 0.86 0.52 0.55 0.59 0.58 0.22 0.82 0.36 0.68 0.62 0.67 0.57

0.39 0.18 0.12 0.15 0.36 0.10 0.09 0.13 0.21 0.11 0.36 0.17 0.04 0.16 0.30 0.26 0.18 0.48 0.12 0.21 0.20 0.26 0.12 0.16 0.25 0.04 0.18 0.13 0.06 0.23 0.07 0.24 0.15 0.29 0.12 0.15 0.10 0.07 0.16 0.35 0.21 0.26 0.19 0.07 0.21 0.15 0.06 0.07 0.15 0.14 0.13 0.22 0.17 0.33 0.13 0.32 0.07 0.15

0.57 0.33 0.23 0.07 0.37 0.41 0.29 0.26 0.34 0.17 0.33 0.35 0.00 0.10 0.40 0.29 0.36 0.44 0.12 0.06 0.32 0.52 0.44 0.35 0.35 0.38 0.09 0.26 0.08 0.64 0.08 0.36 0.26 0.37 0.20 0.36 0.23 0.19 0.10 0.30 0.37 0.33 0.40 0.26 0.22 0.18 0.27 0.16 0.09 0.15 0.29 0.35 0.10 0.36 0.44 0.21 0.17 0.11

-18.6 64.7 -15.0 36.0 -33.6 -20.0 48.6 -80.8 40.6 1.9 -43.1 20.9 24.3 14.6 48.3 28.4 15.6 -35.5 -34.2 -51.1 -81.1 20.5 -55.2 34.6 -26.1 39.0 2.9 -71.3 21.1 12.8 16.4 5.1 -15.0 -39.7 -8.2 27.1 27.2 14.9 -36.6 -80.6 -57.8 76.8 68.1 38.5 -61.2 4.4 -86.3 50.6 68.6 -30.6 7.2 6.1 8.6 -47.7 -80.5 -77.3 -12.2 31.0

-22.2 54.7 -8.4 54.2 -28.7 -29.8 37.8 -87.1 42.9 21.2 82.3 44.4 -72.1 -24.2 46.9 26.9 9.7 -35.4 -56.8 -45.9 -81.4 26.6 -55.8 35.5 27.1 29.1 11.1 -63.5 16.3 11.9 -70.5 1.0 -17.7 -35.3 -3.6 33.3 3.4 13.0 -74.4 -76.1 -53.3 72.4 72.4 17.9 -68.0 20.1 89.4 49.7 85.0 -21.7 -4.4 4.8 -67.8 -49.8 -75.2 -70.1 -34.9 22.6

-23.23 -23.26 -22.60 -22.77 -22.53 -23.23 -22.91 -22.88 -23.26 -22.44 -22.59 -23.18 -22.76 -22.52 -22.72 -22.59 -22.86 -21.96 -22.88 -23.44 -23.05 -23.58 -22.43 -22.56 -21.89 -22.71 -22.51 -23.09 -22.84 -22.68 -22.68 -22.81 -22.17 -23.24 -21.98 -22.81 -22.34 -22.66 -22.59 -22.97 -22.94 -22.61 -21.72 -22.73 -22.67 -22.99 -22.59 -22.67 -23.01 -23.08 -22.81 -21.03 -22.76 -21.98 -22.46 -22.92 -23.03 -22.65

19


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)


23.75 21.10 21.25 20.29 19.86 20.93 21.70 21.60 21.19 20.52 23.97 19.18 28.54 21.93 19.91 20.79 24.53 21.60 24.10 22.56 20.33 23.01 23.31 20.46 21.24 22.08 26.51 23.94 22.97 21.13 24.31 21.85 20.71 20.15 22.31 21.70 22.17 19.33 22.79 22.38 19.85 22.20 20.27 21.68 21.80 21.11 21.39 20.74 18.86 22.96 19.91 19.41 19.88 18.95 19.64 22.24 20.76 19.71

31.01 8.46 8.03 4.35 3.45 5.61 6.56 7.66 7.10 3.78 36.62 2.54 725.91 6.60 2.30 6.60 51.76 10.49 37.52 15.00 4.66 22.64 22.24 3.20 2.74 10.53 104.60 50.12 25.07 7.49 40.53 8.54 5.35 2.80 16.35 9.87 14.97 2.05 16.32 14.39 3.12 12.53 5.19 7.93 6.84 7.02 4.80 4.48 1.55 22.83 5.63 2.00 1.44 2.21 2.34 13.42 3.80 2.58

6.94 2.60 2.36 5.13 3.82 2.81 1.30 2.83 4.65 4.31 5.18 1.37 9.52 4.83 1.02 1.69 6.13 3.10 4.48 5.56 3.16 6.58 5.46 4.29 3.94 5.62 6.13 4.15 6.37 5.43 6.45 6.41 6.45 2.84 6.62 1.27 5.43 4.59 6.10 4.42 3.32 5.10 2.62 5.26 2.75 4.93 5.59 5.29 5.08 4.63 3.68 2.67 1.01 3.68 2.82 4.15 1.68 5.21

— 22.33 — 22.37 22.23 22.25 21.52 — 22.03 23.00 21.65 21.31 — 20.54 20.50 21.94 — — 21.48 — 21.27 — — 21.22 19.76 22.42 — — — 21.75 — — — 21.25 — 22.08 — 21.75 — — 21.11 — — — — 22.16 22.11 22.48 21.75 — 21.04 21.66 22.05 21.01 22.01 — — 21.53

— 31.60 — 26.20 22.80 18.50 26.60 — 17.90 22.60 22.80 17.30 — 12.00 6.10 25.50 — — 17.00 — 20.60 — — 13.20 3.50 20.60 — — — 22.30 — — — 18.60 — 32.30 — 9.30 — — 7.20 — — — — 20.23 24.50 15.90 10.20 — 19.90 8.70 5.70 8.50 11.90 — — 19.00

-24.20 -23.52 -23.25 -23.40 -23.16 -22.98 -22.20 -22.92 -23.44 -22.69 -24.28 -22.43 -26.43 -22.40 -21.62 -23.11 -24.49 -23.67 -24.14 -23.83 -22.98 -24.38 -23.94 -22.48 -21.04 -23.40 -24.53 -24.77 -24.34 -23.69 -24.24 -23.32 -23.43 -22.08 -24.12 -22.91 -24.13 -22.58 -23.73 -23.70 -22.59 -23.73 -23.36 -23.29 -22.46 -23.46 -22.41 -22.91 -22.48 -23.97 -23.63 -22.12 -20.29 -22.71 -21.72 -23.69 -22.04 -22.92

0.00 -23.98 0.00 -23.70 -23.51 -23.04 -24.59 0.00 -23.14 -22.66 -24.04 -23.62 0.00 -23.65 -22.44 -23.95 0.00 0.00 -23.58 0.00 -24.00 0.00 0.00 -23.37 -21.67 -22.94 0.00 0.00 0.00 -23.88 0.00 0.00 0.00 -23.88 0.00 -24.29 0.00 -21.98 0.00 0.00 -21.86 0.00 0.00 0.00 0.00 -23.21 -23.66 -22.37 -22.16 0.00 -23.89 -21.88 -20.41 -22.23 -21.67 0.00 0.00 -23.89

-24.20 -24.52 -23.25 -24.32 -24.10 -23.76 -24.71 -22.92 -24.05 -23.43 -24.91 -23.93 -26.43 -23.95 -22.86 -24.36 -24.49 -23.67 -24.65 -23.83 -24.35 -24.38 -23.94 -23.76 -22.15 -23.95 -24.53 -24.77 -24.34 -24.54 -24.24 -23.32 -23.43 -24.07 -24.12 -24.56 -24.13 -23.08 -23.73 -23.70 -23.04 -23.73 -23.36 -23.29 -22.46 -24.10 -23.96 -23.43 -23.08 -23.97 -24.52 -22.76 -21.10 -23.25 -22.45 -23.69 -22.04 -24.27

— 0.65 — 0.76 0.72 0.95 0.11 — 1.33 1.03 1.25 0.34 — 0.33 0.47 0.46 — — 1.67 — 0.39 — — 0.44 0.56 1.53 — — — 0.84 — — — 0.19 — 0.28 — 1.74 — — 1.97 — — — — 1.26 0.32 1.64 1.34 — 0.78 1.26 0.90 1.56 1.04 — — 0.41

0.60 0.73 0.49 0.61 0.51 0.63 1.01 0.49 0.63 0.56 0.86 0.50 0.78 0.90 0.55 0.80 0.78 0.54 1.05 0.59 0.67 0.58 0.57 0.81 0.36 0.63 0.92 0.93 0.61 0.70 0.71 0.48 0.43 0.87 0.55 1.03 0.60 0.54 0.63 0.62 0.46 0.59 0.63 0.45 0.49 0.63 0.65 0.53 0.55 0.70 0.68 0.46 0.34 0.40 0.47 0.66 0.32 0.74

0.21 0.26 0.28 0.03 0.03 0.13 0.18 0.22 0.19 0.07 0.29 0.23 0.12 0.18 0.05 0.06 0.20 0.37 0.24 0.05 0.18 0.21 0.19 0.09 0.11 0.25 0.28 0.13 0.26 0.09 0.09 0.18 0.21 0.05 0.36 0.19 0.16 0.24 0.22 0.25 0.16 0.21 0.24 0.14 0.07 0.26 0.18 0.15 0.17 0.27 0.14 0.16 0.42 0.27 0.17 0.03 0.18 0.11

0.35 0.41 0.26 0.26 0.48 0.29 0.43 0.22 0.28 0.16 0.53 0.18 0.51 0.38 0.16 0.26 0.42 0.36 0.37 0.31 0.45 0.37 0.30 0.22 0.07 0.45 0.30 0.32 0.32 0.08 0.44 0.23 0.17 0.18 0.23 0.50 0.18 0.29 0.25 0.42 0.20 0.26 0.18 0.03 0.10 0.36 0.50 0.23 0.26 0.24 0.28 0.15 0.38 0.33 0.23 0.29 0.26 0.49

27.1 86.2 13.2 -89.8 -18.0 -70.0 50.4 81.3 14.5 -61.4 29.7 -85.8 -11.1 75.2 -76.0 77.2 -43.3 84.9 32.3 -49.4 31.0 62.9 16.9 -27.1 1.8 -35.3 -76.0 -64.7 60.6 81.4 43.8 17.7 -78.3 -17.3 88.0 21.5 -37.4 51.7 42.8 63.4 -62.5 -34.6 42.4 65.4 -53.4 -14.2 -2.6 -89.4 28.6 10.5 -69.5 46.4 -44.4 -62.6 -18.4 66.1 27.3 78.6

25.5 83.0 3.0 -52.5 -40.0 89.6 50.7 75.1 1.9 -48.7 31.8 -19.2 5.0 73.8 -70.8 -86.4 -55.4 85.9 32.0 -50.5 34.3 86.1 28.3 -8.4 -9.3 -27.8 -36.4 -80.7 60.7 -39.7 45.0 19.0 -81.0 8.3 77.0 21.6 1.5 51.8 32.0 75.7 -58.7 -31.0 35.2 30.1 -37.0 -10.8 -15.7 -77.9 34.4 11.6 -92.9 65.0 -41.4 -65.8 14.5 75.8 33.6 67.6

-22.76 -23.06 -22.68 -23.05 -23.00 -22.80 -22.70 -22.31 -22.93 -22.35 -23.01 -22.81 -22.96 -22.44 -22.47 -23.15 -22.78 -22.78 -22.92 -22.87 -22.98 -23.17 -22.73 -22.81 -21.95 -22.65 -22.27 -23.00 -23.05 -23.28 -22.78 -22.55 -22.66 -22.64 -22.76 -22.76 -23.06 -22.09 -22.54 -22.71 -22.60 -22.78 -22.62 -22.51 -22.12 -22.87 -22.28 -22.92 -22.17 -22.72 -23.44 -22.22 -20.49 -22.44 -21.78 -22.89 -21.73 -22.84

20


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)


21.38 22.51 23.29 23.36 21.99 23.73 22.53 23.86 20.44 22.00 22.38 19.63 26.40 21.92 18.96 20.72 22.79 24.03 20.30 21.72 24.95 21.67 20.51 18.69 19.83 23.58 24.37 22.71 20.80 22.52 18.38 23.10 23.84 23.45 23.18 19.77 23.10 23.28 20.01 19.61 20.06 22.28 21.60 20.23 21.83 20.94 22.95 21.09 21.63 20.15 21.91 14.82 20.91 21.71 24.08 21.84 21.20 22.44

7.57 13.82 32.22 20.33 8.22 45.61 11.53 38.66 3.42 10.57 15.17 2.88 186.16 10.00 2.03 4.07 12.73 47.17 6.54 7.84 71.55 8.16 5.83 1.70 2.86 32.96 25.14 14.77 5.23 11.20 1.22 20.44 25.55 30.76 20.63 2.00 19.45 22.96 4.49 2.40 2.40 7.98 7.72 4.04 13.08 5.94 20.24 4.95 7.82 3.80 10.08 0.24 7.24 7.91 29.06 13.47 5.15 22.42

4.69 5.24 3.58 5.75 4.55 4.33 4.55 4.83 4.65 3.44 5.24 3.11 6.90 2.11 3.22 3.28 4.67 6.41 1.89 5.18 6.54 4.18 5.78 3.60 3.04 6.10 6.80 5.88 3.32 7.35 2.70 6.29 5.78 6.02 7.04 6.02 6.49 5.99 1.84 0.93 2.07 5.56 4.93 5.59 3.11 4.12 4.12 6.06 6.25 2.38 3.46 2.79 2.87 5.38 6.45 3.07 5.65 3.31

— — — 23.01 21.93 — — — 21.50 21.64 — 21.50 — — 21.38 22.92 — — 20.87 21.70 22.01 22.01 22.82 20.69 21.83 — — — 21.92 — 21.27 — — — — — — — 21.61 20.28 — — — 21.02 23.26 23.16 23.28 21.71 — 22.75 — 19.08 22.28 23.40 — — 21.91 —

— — — 32.60 23.03 — — — 10.40 18.40 — 11.20 — — 21.04 25.49 — — 12.80 16.70 33.50 24.50 27.10 8.10 9.70 — — — 17.64 — 11.10 — — — — — — — 16.00 7.50 — — — 26.10 80.22 36.36 42.50 16.80 — 22.40 — 4.00 30.50 56.80 — — 15.90 —

-23.31 -23.58 -24.43 -23.67 -23.01 -24.88 -23.17 -24.45 -22.55 -23.34 -23.92 -22.77 -25.55 -22.97 -22.73 -22.47 -23.04 -24.81 -23.67 -23.18 -24.87 -23.03 -23.76 -22.63 -22.52 -24.45 -23.18 -23.56 -22.94 -23.20 -22.09 -24.05 -23.85 -24.43 -23.91 -22.19 -23.72 -24.02 -23.06 -21.74 -21.54 -22.69 -23.41 -23.20 -23.81 -23.24 -23.90 -22.72 -23.43 -22.69 -23.19 -22.02 -23.37 -23.12 -23.60 -23.77 -22.66 -24.41

0.00 0.00 0.00 -23.46 -23.84 0.00 0.00 0.00 -22.43 -23.60 0.00 -22.59 0.00 0.00 -24.11 -22.96 0.00 0.00 -23.55 -23.31 -24.50 -23.67 -23.20 -22.68 -21.92 0.00 0.00 0.00 -23.16 0.00 -22.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -23.23 -22.88 0.00 0.00 0.00 -24.89 -25.06 -23.55 -23.77 -23.14 0.00 -22.82 0.00 -22.67 -23.91 -24.16 0.00 0.00 -22.83 0.00

-23.31 -23.58 -24.43 -24.32 -24.26 -24.88 -23.17 -24.45 -23.24 -24.23 -23.92 -23.43 -25.55 -22.97 -24.38 -23.50 -23.04 -24.81 -24.36 -24.00 -25.45 -24.15 -24.27 -23.41 -23.01 -24.45 -23.18 -23.56 -23.81 -23.20 -23.27 -24.05 -23.85 -24.43 -23.91 -22.19 -23.72 -24.02 -23.90 -23.21 -21.54 -22.69 -23.41 -25.09 -25.36 -24.16 -24.59 -23.70 -23.43 -23.51 -23.19 -23.14 -24.43 -24.51 -23.60 -23.77 -23.50 -24.41

— — — 1.22 0.46 — — — 1.12 0.79 — 1.18 — — 0.28 0.63 — — 1.11 0.89 1.40 0.56 1.68 0.95 1.73 — — — 0.81 — 0.52 — — — — — — — 0.85 0.35 — — — 0.21 0.32 0.75 1.12 0.68 — 0.89 — 0.55 0.61 0.38 — — 0.86 —

0.43 0.63 0.88 0.69 0.81 0.84 0.50 0.81 0.61 0.81 0.69 0.48 0.84 0.73 0.66 0.54 0.58 0.71 0.61 0.75 0.88 0.79 0.60 0.54 0.49 0.67 0.59 0.56 0.64 0.48 0.70 0.56 0.71 0.73 0.59 0.32 0.54 0.67 0.56 0.64 0.24 0.49 0.49 0.83 0.81 0.52 0.82 0.72 0.52 0.47 0.39 0.46 0.68 0.58 0.64 0.69 0.65 0.74

0.29 0.12 0.16 0.26 0.22 0.32 0.46 0.16 0.17 0.28 0.16 0.15 0.24 0.32 0.25 0.19 0.25 0.33 0.50 0.12 0.33 0.27 0.27 0.33 0.07 0.19 0.25 0.13 0.21 0.14 0.09 0.32 0.16 0.11 0.10 0.20 0.10 0.32 0.26 0.13 0.46 0.07 0.20 0.12 0.07 0.12 0.22 0.21 0.10 0.09 0.27 0.44 0.28 0.07 0.11 0.18 0.04 0.24

0.30 0.13 0.44 0.38 0.45 0.43 0.49 0.32 0.29 0.46 0.17 0.31 0.48 0.14 0.45 0.18 0.36 0.16 0.39 0.14 0.59 0.48 0.39 0.34 0.13 0.20 0.36 0.27 0.30 0.12 0.28 0.34 0.39 0.14 0.20 0.28 0.24 0.39 0.26 0.16 0.48 0.15 0.13 0.31 0.37 0.44 0.34 0.33 0.06 0.15 0.35 0.40 0.44 0.41 0.18 0.16 0.12 0.38

-59.6 -54.9 -71.3 84.0 -59.4 35.2 74.3 30.6 76.4 20.3 34.3 -5.3 -40.0 67.0 63.0 -30.2 70.5 16.0 -2.1 33.2 9.2 -26.5 38.0 -81.9 -2.9 11.3 -26.8 33.2 -12.1 -69.1 -67.3 0.9 87.1 63.3 -59.8 -50.7 -82.5 64.0 0.6 -11.3 -78.7 84.4 27.9 77.4 -45.8 48.5 19.5 11.8 -34.1 3.9 52.1 -70.5 64.4 81.2 36.0 60.3 -79.5 76.1

-53.9 37.2 -74.5 85.7 -48.3 33.8 67.3 16.0 79.6 18.8 52.3 -16.0 -39.4 70.4 68.7 -44.7 65.7 22.2 -2.1 62.9 6.7 -37.1 61.4 -64.7 -34.0 25.5 -29.0 51.3 -21.4 -26.7 -17.0 2.6 92.6 59.7 30.3 -66.8 87.3 60.6 -6.8 -8.0 -85.9 84.5 33.3 63.4 -42.7 47.7 17.8 21.7 71.5 1.2 54.9 -70.6 67.9 69.2 29.9 19.8 -75.0 45.6

-22.51 -22.59 -23.02 -22.62 -22.80 -23.04 -22.08 -22.90 -22.41 -22.89 -22.84 -22.75 -22.80 -22.33 -22.77 -22.21 -22.08 -22.89 -23.21 -22.87 -23.06 -22.57 -22.96 -22.65 -22.46 -22.99 -21.82 -22.57 -22.71 -22.38 -22.33 -22.59 -22.56 -23.06 -22.94 -21.40 -22.57 -22.72 -22.98 -22.68 -21.07 -21.90 -22.55 -23.19 -23.15 -22.83 -22.82 -22.44 -22.58 -22.63 -22.24 -22.17 -22.87 -22.56 -22.28 -22.88 -22.55 -23.15

21


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)


26.19 24.18 25.64 22.46 20.70 24.66 21.28 24.02 22.24 22.94 22.03 22.33 22.17 21.91 23.03 22.27 22.33 23.55 22.15 24.73 18.15 20.62 22.28 21.93 21.95 23.47 20.62 25.51 21.12 22.15 20.94 25.38 21.58 22.10 21.57 22.29 24.07 20.88 22.02 25.22 21.89 23.23 22.34 20.21 20.21 24.14 21.57 22.33 22.21 22.03 22.36 19.25 18.69 22.30 22.70 22.46 21.98 21.05

202.47 56.46 99.66 16.24 4.42 53.10 6.22 32.71 14.03 17.98 4.76 11.85 17.15 8.42 11.69 20.56 9.53 20.03 18.39 112.07 1.61 5.86 15.39 7.10 10.15 36.59 4.88 232.87 6.30 11.42 3.70 74.80 10.17 10.36 6.64 19.27 41.74 7.19 8.90 71.69 10.61 19.73 11.69 4.32 2.79 65.96 8.81 12.68 13.72 10.94 12.13 2.00 1.56 7.13 16.45 16.31 8.89 8.54

5.78 3.28 7.87 5.78 4.85 7.04 4.81 5.46 5.15 5.71 6.10 5.65 5.52 5.26 5.81 6.02 4.00 5.78 4.05 4.63 4.88 3.57 2.92 5.78 4.13 7.75 4.22 4.57 5.68 6.17 5.99 8.20 1.46 1.05 0.81 2.46 8.00 1.47 4.78 6.99 6.37 6.13 5.88 3.04 1.22 5.85 7.04 6.37 4.35 5.18 6.25 2.44 2.56 6.10 5.56 5.62 5.26 1.44

— — — 23.25 23.22 — 22.69 — 22.33 21.47 21.98 22.40 — — — — — 21.46 — — 20.60 — 22.96 — — — — — — 20.69 — — 23.35 — — — — 22.01 — — — 23.09 21.57 22.32 21.23 — — — — — — 21.84 20.44 — 23.07 — 22.47 22.26

— — — 46.90 19.60 — 26.70 — 36.20 25.30 17.50 42.40 — — — — — 20.20 — — 14.10 — 72.90 — — — — — — 17.80 — — 56.40 — — — — 32.00 — — — 41.10 20.00 23.17 11.40 — — — — — — 14.90 8.30 — 36.40 — 23.20 31.00

-25.71 -25.09 -24.90 -23.93 -22.86 -24.43 -23.17 -23.97 -23.91 -23.80 -21.76 -23.51 -23.84 -23.05 -22.78 -24.70 -22.81 -23.39 -24.42 -25.76 -23.22 -22.54 -23.74 -22.78 -23.35 -24.10 -22.99 -26.54 -23.22 -22.94 -22.24 -24.22 -23.20 -22.55 -22.01 -24.10 -24.45 -23.09 -22.96 -24.63 -23.16 -23.73 -23.39 -22.99 -21.47 -25.33 -23.01 -23.48 -23.61 -23.49 -23.60 -22.28 -22.44 -22.40 -23.75 -24.07 -23.19 -23.36

0.00 0.00 0.00 -23.85 -22.08 0.00 -23.43 0.00 -24.36 -24.43 -23.02 -24.64 0.00 0.00 0.00 0.00 0.00 -23.91 0.00 0.00 -23.98 0.00 -25.21 0.00 0.00 0.00 0.00 0.00 0.00 -23.74 0.00 0.00 -24.27 0.00 0.00 0.00 0.00 -24.32 0.00 0.00 0.00 -23.84 -23.74 -23.28 -22.71 0.00 0.00 0.00 0.00 0.00 0.00 -22.92 -23.16 0.00 -23.54 0.00 -23.24 -24.08

-25.71 -25.09 -24.90 -24.64 -23.29 -24.43 -24.06 -23.97 -24.91 -24.91 -23.31 -24.97 -23.84 -23.05 -22.78 -24.70 -22.81 -24.43 -24.42 -25.76 -24.42 -22.54 -25.46 -22.78 -23.35 -24.10 -22.99 -26.54 -23.22 -24.17 -22.24 -24.22 -24.62 -22.55 -22.01 -24.10 -24.45 -24.62 -22.96 -24.63 -23.16 -24.54 -24.33 -23.90 -23.01 -25.33 -23.01 -23.48 -23.61 -23.49 -23.60 -23.40 -23.61 -22.40 -24.41 -24.07 -23.97 -24.53

— — — 1.07 2.06 — 0.79 — 0.66 0.56 0.31 0.36 — — — — — 0.62 — — 0.50 — 0.26 — — — — — — 0.48 — — 0.37 — — — — 0.32 — — — 0.90 0.73 0.77 0.32 — — — — — — 0.56 0.51 — 1.22 — 0.95 0.52

0.88 1.14 0.74 0.64 0.44 0.70 0.67 0.75 0.68 0.80 0.85 0.76 0.57 0.45 0.58 0.60 0.56 0.82 0.68 0.99 0.61 0.46 0.80 0.43 0.54 0.64 0.39 1.16 0.40 0.76 0.32 0.65 0.90 0.78 0.49 0.91 0.61 0.90 0.47 0.72 0.42 0.70 0.78 0.56 0.64 0.79 0.45 0.55 0.54 0.50 0.56 0.58 0.61 0.56 0.70 0.61 0.65 0.90

0.38 0.29 0.08 0.08 0.20 0.21 0.13 0.18 0.17 0.23 0.37 0.15 0.31 0.29 0.10 0.08 0.04 0.24 0.32 0.13 0.19 0.21 0.20 0.13 0.14 0.09 0.15 0.24 0.07 0.14 0.07 0.13 0.10 0.31 0.31 0.13 0.17 0.17 0.23 0.22 0.31 0.22 0.05 0.11 0.13 0.31 0.28 0.02 0.35 0.22 0.12 0.16 0.20 0.05 0.08 0.15 0.22 0.14

0.57 0.39 0.02 0.33 0.22 0.47 0.26 0.29 0.47 0.45 0.51 0.39 0.27 0.26 0.09 0.06 0.09 0.34 0.14 0.35 0.42 0.07 0.57 0.05 0.11 0.05 0.12 0.64 0.12 0.45 0.13 0.34 0.22 0.41 0.25 0.19 0.18 0.36 0.31 0.38 0.44 0.47 0.32 0.30 0.20 0.48 0.14 0.11 0.41 0.31 0.23 0.26 0.04 0.24 0.37 0.14 0.32 0.21

-56.2 66.6 -88.9 -43.7 38.7 39.7 37.5 50.6 0.2 -54.7 15.9 64.5 -12.5 3.1 -68.2 22.3 -88.9 -35.6 -35.9 -22.8 28.4 72.8 89.7 -50.0 -0.8 60.3 5.2 1.7 30.0 68.6 -66.8 -65.4 59.0 19.5 -50.9 -34.1 -55.5 67.9 -45.7 -46.5 8.4 -87.8 63.5 -13.0 7.3 24.4 -46.5 39.8 38.7 -37.2 -68.2 21.6 -4.3 72.8 -20.2 5.2 -27.8 67.4

-63.4 70.6 34.5 -39.8 38.8 38.8 57.1 43.8 -5.8 -34.6 15.3 79.2 -26.0 3.0 69.6 87.4 47.3 -49.2 -40.1 -21.0 47.3 -45.3 84.0 -41.9 -12.5 8.7 73.2 3.8 -64.2 67.2 -63.9 -70.8 51.9 32.7 -52.7 -34.8 -67.1 -46.1 -42.1 -44.2 5.4 79.9 56.7 -0.3 -2.2 23.9 -39.1 12.8 25.9 -43.4 -31.7 10.3 84.7 39.8 -52.9 -13.3 -43.8 62.2

-22.56 -22.94 -22.84 -23.02 -22.42 -22.67 -22.73 -22.47 -23.16 -23.05 -21.71 -22.89 -22.70 -22.14 -21.95 -22.58 -22.22 -22.68 -23.18 -23.26 -23.18 -22.11 -22.88 -22.20 -22.62 -22.76 -22.50 -23.14 -22.61 -22.64 -21.78 -22.41 -22.80 -21.97 -21.66 -23.08 -22.84 -23.03 -22.11 -22.57 -22.13 -22.59 -22.91 -22.80 -22.16 -23.24 -22.15 -22.65 -22.52 -22.60 -22.70 -22.44 -22.63 -21.74 -22.89 -23.05 -22.60 -23.12

22


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

S/e (10)

α (11)

ein (12)

eout (13)

pain (14)

paout (15)

Mmetric (16)

A3809 A3822 A3825 A3826 A3836 A3837 A3844 A3851 A3864 A3869 A3879 A3880 A3886 A3895 A3912 A3915 A3959 A3969 A3985 A4008 A4038 A4049 A4053 A4059

26.22 24.77 17.26 22.59 22.31 23.70 20.25 20.01 26.28 21.94 19.19 23.46 22.04 23.38 21.36 22.41 17.17 21.92 23.46 22.76 23.76 21.75 21.81 24.17

144.88 66.64 0.61 26.06 15.43 21.38 2.77 3.52 226.18 10.51 2.12 31.92 11.71 25.51 7.55 12.82 0.62 11.74 38.82 21.08 31.17 9.04 9.74 77.05

7.30 6.41 4.05 3.19 4.98 6.67 4.37 1.16 6.67 6.41 3.89 3.83 5.05 3.91 0.99 6.45 3.18 4.78 3.07 4.29 7.41 5.32 7.35 4.41

— — 20.68 — 22.58 — 24.30 20.95 — — 21.61 — — — 21.97 23.36 20.67 — — — — 23.39 — —

— — 4.40 — 64.40 — 56.02 11.90 — — 11.50 — — — 16.90 29.33 6.00 — — — — 43.40 — —

-25.16 -24.87 -21.79 -24.65 -24.16 -23.56 -22.28 -22.29 -26.15 -23.50 -22.67 -24.24 -23.69 -23.85 -22.57 -23.74 -21.92 -24.00 -24.74 -24.10 -23.96 -23.26 -23.63 -25.49

0.00 0.00 -21.26 0.00 -25.49 0.00 -23.32 -23.23 0.00 0.00 -22.55 0.00 0.00 0.00 -23.02 -22.95 -22.07 0.00 0.00 0.00 0.00 -23.48 0.00 0.00

-25.16 -24.87 -22.31 -24.65 -25.77 -23.56 -23.67 -23.61 -26.15 -23.50 -23.36 -24.24 -23.69 -23.85 -23.57 -24.17 -22.75 -24.00 -24.74 -24.10 -23.96 -24.12 -23.63 -25.49

— — 1.62 — 0.29 — 0.38 0.42 — — 1.13 — — — 0.66 2.08 0.87 — — — — 0.81 — —

0.81 0.68 0.28 0.81 0.80 0.58 0.41 0.56 0.88 0.45 0.56 0.89 0.54 0.75 0.91 0.71 0.46 0.67 0.92 0.71 0.57 0.57 0.51 0.98

0.13 0.30 0.34 0.35 0.15 0.14 0.13 0.28 0.25 0.19 0.23 0.05 0.20 0.23 0.17 0.17 0.42 0.13 0.44 0.22 0.15 0.08 0.10 0.22

0.44 0.37 0.26 0.38 0.43 0.16 0.21 0.27 0.58 0.27 0.25 0.38 0.15 0.36 0.26 0.29 0.45 0.08 0.61 0.34 0.36 0.12 0.12 0.41

87.0 -22.8 -46.8 -22.6 -45.5 7.2 57.3 -88.6 -45.9 -51.1 -52.4 20.9 -2.7 2.5 34.8 86.9 22.6 -24.5 30.5 57.3 -39.3 66.6 -85.0 -22.1

88.9 -19.0 -67.6 -23.0 -23.7 0.7 107.8 78.1 -44.6 -52.5 -37.5 -37.4 5.1 -6.2 15.8 87.3 20.3 -106.5 30.4 51.8 -47.1 47.8 -71.0 -23.2

-22.70 -22.87 -21.53 -23.17 -23.30 -22.45 -21.75 -22.68 -23.18 -22.61 -22.42 -22.85 -22.74 -22.61 -22.62 -22.85 -21.72 -23.02 -22.55 -22.91 -22.60 -22.71 -22.71 -23.21

Note.—Col. (1), Abell Cluster; col (2), effective surface magnitude; col. (3), effective radius (kpc); col. (4), n parameter; col. (5), central surface magnitude; col. (6), scale length (kpc); col. (7),Sersic absolute magnitude; col. (8), exponential absolute magnitude; col. (9), total absolute magnitude; col. (10), S´ ersic/exponential ratio; col. (11), α parameter; col. (12), inner ellipticity; col. (13), outer ellipticity; col. (14), inner position angle ; col. (15), outer position angle; col. (16), Metric absolute magnitude.

23

Table 3 BCGs Photometrical Parameters (Hopkins model) Name (1)

µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

e/S (10)


23.72 23.23 24.34 22.77 25.18 22.05 25.42 22.64 24.83 23.41 23.80 24.02 23.15 25.52 22.21 23.88 23.88 23.08 23.51 25.12 25.48 24.12 21.35 24.88 28.01 27.66 24.16 23.68 24.86 23.71 23.86 23.55 21.45 24.10 23.22 26.34 24.11 24.11 23.77 22.78 23.26 23.68 25.96 22.80 25.24 24.75 24.61 24.61 24.10 25.40 23.56 22.87 22.88 22.89 23.88 25.50 21.74 25.48

47.0 39.0 49.2 20.5 106.4 14.2 92.5 18.5 69.3 34.9 17.9 52.5 25.6 146.2 8.8 37.9 62.9 21.0 40.2 73.3 97.6 39.2 10.1 65.0 334.8 267.4 29.6 51.2 69.3 19.1 59.1 37.2 7.6 44.4 60.2 97.5 51.3 36.7 28.4 20.3 17.5 24.5 159.9 26.3 74.8 52.6 52.3 49.6 31.3 70.1 29.8 22.1 20.5 15.7 25.1 92.3 6.9 70.4

0.6 1.2 3.5 1.4 3.5 1.7 4.6 1.9 5.7 1.8 4.0 3.1 3.5 3.6 2.3 2.9 1.8 1.5 1.4 3.8 4.8 3.8 1.6 4.5 4.3 4.0 3.6 2.9 4.6 3.4 4.9 3.1 0.8 3.3 2.6 6.1 3.1 5.0 6.1 1.5 5.9 3.9 2.4 2.0 6.3 5.3 5.1 5.0 3.5 3.6 4.2 1.9 3.7 3.5 5.7 4.0 1.4 6.5

21.42 21.04 20.84 19.63 18.99 18.39 20.24 19.72 19.43 20.07 20.18 20.46 19.36 20.73 19.40 19.39 21.90 20.35 20.99 20.83 20.32 19.37 19.62 20.60 20.12 20.12 19.78 19.72 20.24 20.67 19.21 19.28 19.92 19.95 20.21 20.98 19.74 20.74 19.73 19.45 19.57 20.14 21.16 20.06 20.61 19.76 19.82 18.58 20.41 21.09 21.01 20.08 21.09 19.78 19.34 20.11 18.32 21.05

14.3 6.9 3.3 1.7 1.9 1.1 2.5 2.1 1.6 2.4 1.9 3.3 1.4 3.6 1.8 2.0 7.6 3.7 4.2 2.6 3.1 1.7 1.6 3.2 3.7 3.7 2.1 3.1 2.9 2.9 2.0 1.6 2.0 2.8 4.6 2.5 2.6 2.2 1.9 1.7 1.5 2.5 7.2 2.4 3.0 1.7 2.0 1.3 2.6 4.3 2.6 3.0 1.8 1.8 1.5 2.3 1.1 2.6

-23.91 -24.29 -24.22 -23.54 -25.04 -23.31 -24.87 -23.68 -24.66 -23.69 -22.77 -24.73 -23.95 -25.48 -22.54 -23.98 -24.97 -23.26 -24.88 -24.48 -24.91 -23.94 -23.32 -24.58 -25.03 -24.86 -23.45 -24.87 -24.74 -22.80 -24.89 -24.36 -22.39 -24.29 -24.69 -24.04 -24.50 -24.01 -23.71 -23.53 -23.16 -23.49 -25.05 -24.18 -24.52 -24.07 -24.12 -24.25 -23.61 -24.05 -23.86 -23.79 -23.94 -23.21 -23.34 -24.59 -21.96 -24.21

-23.84 -22.66 -21.25 -21.07 -21.86 -21.09 -21.43 -21.58 -21.04 -20.92 -20.87 -21.70 -20.76 -21.57 -21.47 -21.50 -22.07 -22.01 -22.32 -20.85 -21.82 -21.24 -20.84 -21.57 -22.43 -22.43 -21.42 -22.19 -21.71 -21.10 -21.35 -21.22 -21.08 -21.86 -21.62 -20.52 -21.79 -20.50 -20.90 -21.26 -20.65 -21.40 -22.70 -21.37 -21.22 -20.79 -20.96 -21.61 -21.30 -21.66 -20.43 -21.93 -19.82 -21.00 -20.89 -21.24 -21.20 -20.55

-24.63 -24.51 -24.29 -23.65 -25.10 -23.44 -24.91 -23.82 -24.70 -23.77 -22.95 -24.79 -24.01 -25.51 -22.88 -24.09 -25.05 -23.56 -24.98 -24.52 -24.97 -24.03 -23.42 -24.65 -25.13 -24.97 -23.61 -24.96 -24.80 -23.00 -24.93 -24.42 -22.68 -24.40 -24.75 -24.08 -24.58 -24.05 -23.79 -23.66 -23.26 -23.64 -25.17 -24.25 -24.57 -24.12 -24.18 -24.34 -23.73 -24.16 -23.91 -23.97 -23.97 -23.34 -23.45 -24.63 -22.40 -24.25

0.935 0.222 0.065 0.102 0.053 0.130 0.042 0.144 0.036 0.078 0.173 0.061 0.053 0.027 0.375 0.101 0.069 0.316 0.095 0.035 0.058 0.083 0.102 0.062 0.091 0.107 0.154 0.085 0.062 0.210 0.038 0.055 0.299 0.106 0.059 0.039 0.083 0.039 0.075 0.123 0.099 0.145 0.115 0.075 0.048 0.049 0.055 0.088 0.120 0.111 0.042 0.180 0.022 0.130 0.105 0.046 0.495 0.034

24


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

e/S (10)


24.79 25.12 21.93 21.45 22.83 24.64 24.13 21.95 24.34 23.72 23.59 23.91 23.22 27.15 24.65 23.96 23.73 24.18 22.43 24.80 25.46 27.66 28.07 22.94 23.02 22.23 24.12 23.92 22.72 24.38 23.62 25.34 24.65 25.41 26.55 23.84 23.20 23.14 28.80 26.02 22.92 22.92 26.93 23.03 21.19 25.01 23.54 23.39 25.48 21.68 23.70 23.75 23.50 22.94 23.03 21.99 23.17 22.61

77.1 137.6 14.6 12.3 22.4 85.8 41.4 17.1 42.5 43.6 35.7 47.2 31.5 354.7 76.6 63.7 45.6 44.1 19.8 65.6 100.1 561.3 691.6 25.4 26.1 23.8 58.2 31.3 31.0 51.1 35.0 64.3 71.8 86.2 144.4 30.6 25.6 41.4 602.5 131.5 19.5 29.0 283.2 22.8 5.5 64.9 40.8 36.5 127.8 9.0 35.1 25.0 18.1 37.7 12.8 11.1 17.9 15.0

4.0 2.4 1.7 1.0 1.5 4.2 5.5 1.5 7.3 1.0 3.6 2.3 1.5 6.2 3.8 3.0 3.6 2.1 1.0 3.7 6.2 5.0 5.8 2.1 3.8 2.6 2.9 4.0 1.7 3.2 3.0 7.2 4.8 4.6 7.5 4.1 2.3 2.2 9.1 5.2 1.4 2.3 7.8 2.0 1.4 6.5 2.6 1.8 3.9 1.4 4.1 3.6 3.2 4.1 3.7 3.5 1.0 1.3

19.18 20.74 19.19 19.65 19.88 19.94 20.55 19.36 19.86 20.55 19.78 20.27 20.76 20.98 20.12 20.23 19.97 20.01 19.98 19.72 21.10 19.87 21.17 19.55 19.33 19.21 21.38 19.46 20.71 20.32 19.58 20.68 20.76 19.83 19.60 20.70 20.34 20.31 19.36 19.25 20.52 19.18 19.56 19.69 17.45 20.11 19.84 19.73 22.45 19.09 19.77 20.30 19.73 18.62 19.62 18.84 20.47 19.73

2.2 4.8 1.9 1.6 2.7 2.8 3.1 2.0 1.8 5.2 2.9 3.4 5.3 3.5 3.5 2.7 2.3 2.8 3.2 2.5 3.8 2.2 5.5 1.9 1.9 2.6 5.6 1.9 1.9 1.8 2.8 3.7 3.8 2.6 2.2 2.8 2.9 2.5 2.2 2.3 1.7 0.8 1.7 1.7 0.5 1.7 2.8 2.0 8.1 1.8 2.2 2.4 1.6 1.8 1.6 1.4 3.7 2.6

-24.66 -25.57 -23.77 -23.68 -23.68 -25.31 -24.41 -24.04 -24.36 -24.06 -24.34 -24.47 -24.04 -26.09 -25.03 -25.23 -24.82 -23.97 -23.56 -24.45 -25.06 -26.34 -26.45 -23.77 -24.02 -24.37 -24.50 -23.72 -24.58 -24.35 -24.14 -24.22 -24.93 -24.71 -24.92 -23.95 -23.95 -24.92 -25.67 -24.84 -23.22 -24.40 -25.77 -23.77 -22.11 -24.49 -24.57 -24.16 -25.27 -22.64 -24.28 -23.42 -22.93 -24.78 -22.70 -23.15 -22.68 -22.94

-21.86 -22.23 -21.87 -21.09 -21.86 -21.86 -21.50 -21.76 -20.91 -22.62 -22.07 -22.00 -22.42 -21.33 -22.16 -21.54 -21.43 -21.75 -22.08 -21.81 -21.37 -21.29 -21.97 -21.20 -21.31 -22.11 -21.64 -21.39 -20.22 -20.52 -22.15 -21.67 -21.66 -21.90 -21.73 -21.19 -21.68 -21.29 -21.82 -21.95 -20.17 -19.93 -21.01 -21.19 -20.30 -20.51 -21.99 -21.29 -21.62 -21.51 -21.48 -21.13 -20.92 -21.80 -20.92 -21.16 -21.95 -21.91

-24.73 -25.62 -23.95 -23.78 -23.87 -25.36 -24.48 -24.17 -24.41 -24.32 -24.46 -24.58 -24.26 -26.11 -25.11 -25.27 -24.86 -24.10 -23.81 -24.54 -25.09 -26.35 -26.47 -23.87 -24.11 -24.50 -24.57 -23.84 -24.60 -24.38 -24.30 -24.32 -24.98 -24.79 -24.98 -24.03 -24.07 -24.96 -25.70 -24.91 -23.28 -24.41 -25.78 -23.87 -22.29 -24.52 -24.67 -24.24 -25.30 -22.96 -24.36 -23.54 -23.08 -24.85 -22.89 -23.31 -23.13 -23.30

0.076 0.046 0.172 0.092 0.187 0.042 0.069 0.122 0.042 0.266 0.124 0.102 0.224 0.012 0.071 0.033 0.044 0.130 0.255 0.088 0.033 0.010 0.016 0.093 0.083 0.125 0.072 0.117 0.018 0.029 0.160 0.095 0.049 0.075 0.053 0.079 0.124 0.035 0.029 0.070 0.060 0.016 0.012 0.093 0.190 0.026 0.092 0.071 0.035 0.355 0.076 0.122 0.158 0.064 0.195 0.159 0.508 0.389

25


µe (2)

re (3)

n (4)

µ0 (5)

r0 (6)

MSersic (7)

Mexp (8)

MT (9)

e/S (10)

A3104 A3107 A3110 A3111 A3112 A3120 A3122 A3123 A3125 A3142 A3223 A3225 A3266 A3301 A3332 A3336 A3341 A3354 A3374 A3376 A3380 A3390 A3408 A3420 A3528 A3530 A3531 A3532 A3554 A3559 A3562 A3574 A3605 A3667 A3703 A3716 A3731 A3733 A3741 A3782 A3796 A3806 A3825 A3844 A3851 A3879 A3897 A3912 A4049

23.26 25.84 22.02 23.57 23.91 24.82 24.29 21.98 22.59 24.48 23.05 22.16 22.83 26.53 28.15 24.45 24.76 26.09 20.79 25.10 28.80 24.31 25.06 23.56 24.78 24.04 24.96 28.22 23.45 22.75 28.77 23.36 27.28 28.77 25.45 23.49 25.84 23.48 25.47 26.04 24.66 25.01 22.15 26.38 22.90 23.17 24.94 23.93 23.85

36.3 75.1 18.5 33.6 74.2 74.4 44.8 11.5 11.8 47.9 23.3 12.9 43.6 240.0 326.5 61.0 57.7 80.0 6.5 85.9 593.9 39.8 82.1 19.3 92.0 67.3 56.2 728.6 41.2 29.3 1160.1 48.2 305.7 812.0 101.2 40.6 94.8 24.2 86.1 130.0 54.6 81.3 6.8 66.8 21.1 18.3 67.7 30.6 31.5

1.3 4.5 0.9 2.9 2.5 3.9 6.0 1.3 0.9 4.8 2.8 1.1 1.3 5.2 9.2 2.8 4.5 6.8 1.0 5.2 7.4 4.2 5.1 2.8 3.8 3.2 3.2 6.5 2.5 2.0 6.9 3.3 4.1 8.6 3.6 2.6 7.1 1.9 3.4 6.8 3.6 4.9 0.7 3.7 1.9 3.1 3.8 1.4 4.4

19.82 20.61 19.93 20.66 21.08 20.58 19.48 18.95 19.85 20.69 20.35 19.58 19.92 20.89 20.84 21.20 19.29 20.56 17.99 20.43 20.62 19.74 20.16 20.43 19.92 19.93 19.73 20.37 19.18 18.85 21.30 18.52 21.47 21.39 21.19 19.79 20.15 20.17 21.18 20.76 20.77 21.63 19.41 20.79 20.12 19.24 19.84 21.46 19.63

2.7 2.9 5.0 2.7 4.2 2.8 2.3 1.7 2.6 2.7 3.5 2.3 3.1 5.2 3.7 5.0 1.4 3.4 0.6 3.3 3.3 1.6 2.8 2.7 2.7 2.1 1.2 2.8 1.3 1.9 5.1 1.0 8.2 5.8 4.3 2.1 2.7 2.3 3.9 2.7 3.1 6.7 1.5 3.0 3.1 1.7 2.6 7.6 1.8

-24.25 -23.85 -23.84 -24.18 -25.48 -24.64 -24.43 -22.97 -22.25 -24.26 -23.83 -22.93 -25.01 -25.70 -25.16 -24.60 -24.22 -23.93 -22.72 -24.89 -25.57 -23.84 -24.78 -22.91 -25.30 -25.25 -23.85 -26.64 -24.60 -24.45 -27.08 -24.53 -25.42 -26.37 -24.78 -24.49 -24.53 -23.18 -24.40 -25.02 -24.25 -24.93 -21.23 -22.96 -23.54 -23.26 -24.55 -23.20 -23.77

-21.94 -21.24 -23.13 -21.07 -21.62 -21.07 -21.85 -21.74 -21.74 -21.05 -21.86 -21.75 -22.04 -22.20 -21.63 -21.89 -20.80 -21.63 -20.43 -21.63 -21.44 -20.68 -21.52 -21.29 -21.83 -21.28 -20.09 -21.44 -20.96 -22.08 -21.77 -20.40 -22.67 -21.91 -21.54 -21.31 -21.47 -21.08 -21.35 -20.88 -21.24 -22.09 -20.85 -21.15 -21.83 -21.49 -21.88 -22.49 -21.03

-24.37 -23.94 -24.30 -24.24 -25.51 -24.68 -24.53 -23.27 -22.78 -24.32 -23.99 -23.24 -25.08 -25.74 -25.20 -24.69 -24.26 -24.05 -22.85 -24.95 -25.60 -23.89 -24.84 -23.13 -25.34 -25.28 -23.88 -26.65 -24.64 -24.56 -27.09 -24.55 -25.51 -26.39 -24.83 -24.55 -24.59 -23.33 -24.47 -25.04 -24.32 -25.01 -21.81 -23.15 -23.75 -23.45 -24.64 -23.65 -23.86

0.119 0.091 0.518 0.057 0.028 0.037 0.093 0.322 0.625 0.052 0.164 0.337 0.064 0.040 0.039 0.082 0.043 0.121 0.121 0.050 0.022 0.055 0.049 0.224 0.041 0.026 0.031 0.008 0.035 0.113 0.007 0.022 0.079 0.016 0.051 0.053 0.060 0.144 0.060 0.022 0.062 0.073 0.699 0.188 0.206 0.196 0.085 0.518 0.080

Note.—Col. (1), Abell Cluster; col (2), effective surface magnitude; col. (3), effective radius (kpc); col. (4), n parameter; col. (5), central surface magnitude; col. (6), scale length (kpc); col. (7),Sersic absolute magnitude; col. (8), exponential absolute magnitude; col. (9), total absolute magnitude; col. (10), exponential/S´ ersic ratio.

26