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The fundamental plane of early-type galaxies in different environments

Abstract The study of Early-Type Galaxies (ETGs) in different environments is a strong tool to understand their star formation history and their evolution. The Fundamental Plane (FP) of ETGs has been studied in different environments in the nearby universe such as in groups, clusters and the field. We found that our sample of ETGs in different environments shows a good agreement with the FP of Coma cluster, except for a scatter of some galaxies. A major part of the scatter in the FP is due to variations in mass to light ratio as a result of metallicity or age trends in the stellar populations and structural or dynamical properties of galaxies. We noticed that the most deviant galaxies from the FP show many fine structures as tidal tails, shells, dust and a kinematically distinct core which indicates a past merger involving at least one gas-rich progenitor.


Introduction
Early-Type galaxies (ETGs) represent a group which includes both elliptical (E0-E7) and lenticular (S0) galaxies. They represent a class of well studied objects both because of their homogeneous properties and their high luminosities (À24 6 M B 6 À20) which allows to detect them at large distances. They are specifically important as they contain most of the visible mass in the universe (for a detailed review, see Renzini, 2006, and references therein). Therefore, by understanding their evolution, we can understand the evolution of galaxies in general, and the evolution of the universe as a whole.
Although ETGs seem to be a nearly homogeneous class, the data collected in the last 30 years showed that there are significant departures from the general properties found in the form of large quantities of gas and dust (Capaccioli and Longo, 1994;Goudfrooij et al., 1994aGoudfrooij et al., ,1994b, counter rotating nuclei and polar rings (Bender, 1988;Whitmore et al., 1987), shells, ripples, and disky or boxy components (e.g. Malin and Carter, 1980;Schweizer, 1980;Schweizer et al., 1990) and distinctive tidal tails (Fort et al., 1986;Schweizer and Seitzer, 1992;Michard and Prugniel, 2004;Bennert et al., 2008;Tal et al., 2009;Janowiecki et al., 2010). These morphological structures are explained in most of the theoretical models as a result of past merging in early stages of galaxy formation or of tidal interactions with close neighbors (e.g., de Zeeuw and Franx, 1989;. The role that environment plays in shaping the properties of ETGs is still an open issue in our understanding of galaxy formation and evolution (see Conselice et al., 2013 as a recent review). It is accepted that galaxy encounters, merging and interaction with inter cluster medium (ICM) are all processes that affect on the properties of galaxies to some extent. The influence of environment on the evolution of galaxies is testified by the presence of the well-known morphology-density relation (Dressler, 1980), according to which ETGs are preferred to be found in high density environments (Postman and Geller, 1984;Dressler et al., 1997;Postman et al., 2005;Bamford et al., 2009), while late-type galaxies are more found in low density environments. This distribution was proved in many studies: for example, Calvi et al. (2012) showed that there is a smooth increase in the fraction of ETGs when going from single galaxies, to pairs, to groups. Another relation that shows the influence of environment is the star formationdensity relation (Lewis et al., 2002;Go´mez et al., 2003;Haines et al., 2007).
The study of galaxies in different environments is a robust tool to understand their evolution and star formation history (e.g., Kuntschner et al., 2002;Sa´nchez-Bla´zquez et al., 2003Thomas et al., 2005;Collobert et al., 2006). ETGs display a relation in the 3-dimensional parameter space among their effective radius r e , the central velocity dispersion r o and the luminosity L (or equivalently the effective surface brightness expressed as I e in linear flux units, where I e = L/(2pr e 2 ), or l e in magnitudes). They are concentrated on a plane called the fundamental plane (FP, Dressler et al., 1987;Djorgovski and Davis, 1987) with, Which can be written as, where a and b are the slopes and c is the offset (intercept) of the FP. hl e i is the mean effective surface brightness enclosed by r e (simply referred to as the mean surface brightness). The exponents a and b depend on the specific band used for measuring the luminosity. This indicates that, besides being in virial equilibrium, ETGs show striking regularity in their structures and stellar populations (Renzini and Ciotti, 1993;Borriello et al., 2003). The FP can be understood as a demonstration of the virial plane predicted for relaxed systems (Binney and Tremaine, 2008), with assuming that galaxy mass-to-light ratios (M dyn / L) are constant or smoothly varying for galaxies. If M dyn /L is constant and if the structures were homologous for all ETGs, then the FP would be equivalent to the virial plane which takes the form r e / r 2 hl e i À1 with coefficients of a = 2 and b = À1 . Otherwise, the FP is rotated from the virial plane and the tilt of the FP is the difference between the observed coefficients of the plane, a and b, and those from the virial plane. Jørgensen et al. (1996) found that r e / r 1.24 I e À0.82 for the FP of local cluster ETGs. Also Pahre et al. (1998) found that the slopes, a $ 1.53 and b $ À0.79 for ellipticals observed in the near-infrared. The FP represents an important tool to study the properties of early type and dwarf galaxies and compute cosmological parameters. It is also an important diagnostic tool for galaxy evolution and mass-tolight (M/L) variations with redshift.
Although the FP relation is quite tight, there is a significant scatter around the plane and there is some contradiction in the literature regarding the source of this scatter. Some studies found that the scatter could be due to some reasons, such as variations in the formation times of galaxies, differences in the dark matter content of galaxies or metallicity trends in stellar populations. According to observations, the scatter around the FP is very low, and the position of a galaxy above or below the plane is independent of galaxy flattening, velocity anisotropy and isophotal twisting. Faber et al. (1987) found that deviations from the FP can be formed by M/L variation due to e.g. metallicity or age trends in stellar populations, dynamical or structural properties, and relative distribution of dark matter. In fact, each of these effects may also introduce a tilt into the FP if they represent a function of elliptical galaxy mass.
The origin of the scatter around the FP has been investigated by many authors. Jørgensen et al. (1996) could not reduce the scatter around the FP by introducing additional parameters, such as isophotal shape of the galaxies or ellipticity. Other studies found that variations in stellar populations in ETGs are partially responsible for the intrinsic scatter (e.g. Gregg, 1992;. Forbes et al. (1998) found that the scatter of the FP for a sample of non cluster galaxies is partly due to variation in galaxy age at a given mass, and to variations in the time of the last starburst. Also Reda et al. (2005) found the same results by studying a sample of isolated galaxies. They found that some galaxies deviate from the FP having lower M/L ratio and they explained this as due to younger stellar populations of those galaxies, probably induced by recent gaseous merger. Other studies showed that a major part of the scatter in the FP is due to variations in M/L ratio (e.g., Cappellari et al., 2006;Bolton et al., 2008;Auger et al., 2010;Cappellari et al., 2013).
On the other hand, some studies (e.g., Magoulas et al., 2012) found that the age of galaxies is the most important source of offset from the FP and may drive other trends through its correlation with environment, morphology and metallicity.
The FP appears to be the same in all environments (universal), in the sense that the coefficients are similar for galaxies in environments ranging from high density clusters to the lowdensity field (de la Rosa et al., 2001;Reda et al., 2005;Holden et al., 2010). On the other side, there are suggestions in the literatures that there are moderate, but significant, environmental variations (e.g. Lucey et al., 1991;de Carvalho and Djorgovski, 1992;Bernardi et al., 2003;La Barbera et al., 2010a, 2010bIbarra-Medel and Lo´pez-Cruz, 2011). On the other side, Cappellari et al. (2013) showed that the larger scatter in the FP is due to stellar population effects. They also confirmed that the deviation of the FP coefficients from the virial plane is due to M/L variation.
The aim of this study was to investigate the effect of local environment on the properties of early-type galaxies, in particular their scaling relations using a sample of ETGs in different environments such as in groups, clusters and in the field. In Section 2, we present the data used in this study that comes from photometric and spectroscopic observations of galaxies at 0 < z < 0.08. Section 3 presents our results concerning the fundamental plane, the Kormendy relation and the Faber-Jackson relation of ETGs. In Section 4, we discuss our results. Section 5 summarizes our main conclusions.

The data
In our study we used a sample consisting of 94 ETGs collected from different sources from literature as follows: 64 galaxies from Annibali et al. (2010, sample 1), 20 galaxies from Koleva et al. (2011, sample 2) and 10 galaxies from Ma´rmol-Queralto´et al. (2009, sample 3). Their effective radii (r 00 e ) and central velocity dispersions (r o ) are published by the authors. Their mean surface brightnesses hl e i B are calculated following Graham and Driver (2005). Effective radii were converted from arcsecond to parsec at the distance of the galaxy assuming that the Hubble constant H 0 = 75 km sec À1 Mpc À1 .
Sample 1 consists of 64 galaxies from Annibali et al. (2010), mostly located in low density environments (see Table 1). All galaxies in this sample belong to the Revised Shapley Ames Catalog of Bright Galaxies (RSA) (Sandage and Tammann, 1987) and have redshift lower than $5500 km s À1 . For this sample the effective radii in arcsec are obtained from RC3 (de Vaucouleurs et al., 1991) and the r o is from HyperLeda database (http://leda.univ-lyon1.fr/). The values of r o are obtained from apertures in r e /8 region.
Sample 2 consists of 20 galaxies from Koleva et al. (2011). Their basic properties are summarized in Table 2. Eight of these galaxies are in The Fornax cluster and 12 galaxies are in the Virgo cluster. For this sample the values of r o are from HyperLeda. For galaxies in the Fornax cluster, the velocity dispersion is overestimated in the external regions and more importantly, it is underestimated in the central regions.
Sample 3 consists of 10 galaxies (see Table 3). Two of them are in the Fornax cluster and 8 galaxies are in the field or low density environment. This sample is selected from Ma´rmol-Queralto´et al. (2009). Their r e values in arcsec in the B-band and their r o are obtained through private communication with Ma´rmol-Queralto´, where they collect them from the literature. Table 4 lists the calculated logarithmic values for the photometric and spectroscopic parameters of our samples in addition to the mean surface brightness hl e i B .

Results
3.1. The fundamental plane in log (r e ), hl e i, and log (r o ) space  Table 4. It is clear in this Figure that most of the deviant galaxies from the FP are those of sample 2 in Virgo and Fornax clusters which are located below it. As mentioned in Section 3, the values of r o for the Fornax galaxies are underestimated and this can be responsible for their direction of scatter relative to the FP. For the other galaxies, many different reasons can cause them to show such significant deviation.
For example, the projection effects can be reflected on a large spread in the measurement of r o . Also, r anomalies and the presence of inner subcomponents such as disks or central black holes (e.g., D'Onofrio et al., 1997;Goudfrooij et al., 2004) and the effects of aperture sizes must be taken into account.
In the next subsections we will analyze the available scaling relations such as the fundamental plane in j-space, the Kormendy relation and the Faber-Jackson relation to introduce some reasonable explanation for the observed scatter of our sample galaxies about the FP.
In Fig. 2, we performed fitting for our sample using the least square method and we obtained the parameters a, b and c of the FP as follows: a = 1.235 with error 0.608, b = 0.222 with error 0.107 and c = À3.983 with error 2.145. It is clear that the values of a and b of our fitting are close to those of the Coma cluster, while the value of parameter c is somehow different.

The fundamental plane in j-space
By a simple orthogonal coordinate transformation (i.e., a rotation), a different expression for the FP in terms of kappa (j) space was introduced by Bender et al. (1992). The axes of this coordinate system are directly proportional to the physical parameters of galaxies and defined as j 2 ¼ 2 logðrÞ þ 2 logðI e Þ À logðr e Þ ffiffi ffi 6 p ð4Þ where log I e = À0.4(hl e i À 27), j 1 is proportional to the logarithm of the mass, j 2 is proportional to the logarithm of (M/L) I 2 e and j 3 is proportional to the logarithm of M/L. The edge-on view of the FP is represented by j 1 and j 3 . In Fig. 3 we show the distribution of our sample of ETGs in j 1 -j 3 space. They show a similar tilt and dispersion to those of Virgo cluster galaxies from Bender et al. (1992). The galaxies that show deviation above the FP in Fig. 1 also show a tendency to have larger values of j 3 i.e. larger M/L ratios as expected for their old ages. On the other side, the galaxies that are deviated below the FP in Fig. 1 also show a tendency to have smaller values of j 3 which indicate lower M/L ratios. Previous studies (e.g. Forbes et al., 1998) show that there is a correlation between the residuals from the FP and the age of the central stellar populations of the galaxies. Table 5 shows the available published ages for some of our sample galaxies. These published ages are luminosity-weighted central ages based on Lick absorption lines and single stellar population models to break the age-metallicity degeneracy.   (Annibali et al., 2010). Col. (1) gives the galaxy identification; Col.

The Kormendy relation
(2) provides the galaxy morphological classification according to RC3 (Third Reference Catalog of bright galaxies, de Vaucouleurs et al., 1991); Col. (3) gives the effective radius r e in seconds of arc from RC3; Col. (4) gives the central velocity dispersion r o in km s À1 from HyperLeda (http:// leda.univ-lyon1.fr//); Col. (5) indicates the environment of the galaxy collected by us (when available, the name of the environment is mentioned): when the galaxy is a member of a well known cluster or group, their names are indicated; when the galaxies do not belong to a cluster or a group, it is labeled as field galaxy. The term ''low density" refers to the richness parameter of galaxies as clarified by Annibali et al. (2010).
shifted from V to the B-band assuming typical colors of BÀV = 0.9. We also transformed the surface brightness (l e ) at r e to hl e i using the relation of Graham and Colless (1997).
As clear in Fig. 4, most of the galaxies that are scattered from the FP also show deviation from the KR.  Fig. 5, most of our sample galaxies follow the FJR of ellipticals as the comparison sample in spite of some galaxies which are assigned in Fig. 1 to have significant scatter. We find that most of the galaxies which are scattered in Fig. 1 also show significant dispersion in this relation too.

The Faber-Jackson relation
Forbes and Ponman (1999) studied 5 galaxies of our sample. Those galaxies are NGC 4261, NGC 4697, FCC 021 (NGC 1316), FCC 170 (NGC 1381) and FCC 177 (NGC 1380A). They found that a galaxy's position relative to the FJR depends on its age. In particular, younger ellipticals are systematically brighter in M B and/or have lower central velocity dispersion (r o ).

Discussions
In Figs. 1 and 2 we have compared the FP for our sample of ETGs in different environments with that for the Coma cluster ETGs and isolated galaxies. We found that the FP of Coma cluster can fit well to some reasonable extent the galaxy samples taken from Annibali et al. (2010) and Ma´rmol-Queraltoé t al. (2009) as well as the comparison sample of isolated ETGs from Reda (2007). We noticed that the most deviant galaxies from the FP are from Koleva et al. (2011). For these galaxies, there are two possible reasons for their deviation from the FP. It is clear that they are also located below the hl e i Br e relation (see Fig. 4). Their positions in this KR indicate less hl e i than expected for their sizes. Possible reasons for such dimming measurements of hl e i B can be due to the presence of dust lanes or gas within the central regions of those galaxies. That is because of sensitivity of B-band to structures of galaxies. To explain the second reason for their deviation from the FP, we test the projection of the FP in j-space (see Fig. 3). These galaxies also tend to have smaller j 3 as clear in Fig. 3, which means that they have lower M/L ratios as expected for their young stellar populations (see Table 5). In Fig. 1 some galaxies deviate above the FP, which are NGC 2911, NGC 4261, NGC 4697, NGC 1533 and VCC 0828. In Fig. 3, the same five galaxies show a tendency to have larger j 3 values in the direction of higher M/L ratios which can be explained by the old ages of their stellar population. For example, NGC 1533 and NGC 4697 are old galaxies with ages 11.9 ± 6.9 and 10.10 ± 1.4 Gyr, respectively, while NGC 2911 has a moderate age of 5.7 ± 2 Gyr (see Table 5).
NGC 4697 has a dust lane and has a central supermassive black hole (SMBH) of mass 1.2 Â 10 8 M (Pinkney et al., 2000;Yuan et al., 2009). On the other side, many studies showed that this galaxy is candidate for a recent merger based on the presence of a central dusty disk (Pinkney et al., 2003;Sambhus et al., 2006;Bregman et al., 2006aBregman et al., , 2006bBregman et al., , 2008. From Fig. 1, it is noticed that NGC 4697 is highly deviated above the FP. This deviation could be attributed to the structures it has such as the central dust disk, the SMBH and its recent merger event. Also, its low mean effective surface brightness (21.40 mag/arcsec 2 ) may participate in its deviation from the FP while it is also deviated from the KR as shown in Fig. 4. Although KR indicates that larger galaxies have lower surface brightness, this galaxy is found to have much lower hl e i than expected for its size. On the other hand its central velocity dispersion is consistent with its total absolute magnitude (FJR, Fig. 5). We can conclude that its hl e i is likely to be the main reason of its deviation from the FP in Fig. 1. Such lower surface brightness affects the value of j 3 toward having high M/L ratio.
NGC 4261 is an old galaxy with age of 10:6 þ4:7 À4:7 , as measured by TF02 (see Table 5). This galaxy is a well known radio source in the Virgo cluster. It contains a well-defined disk of dust and gas which surrounds the unresolved nucleus. The structure and dynamics of this disk have been studied by Jaffe et al. (1993Jaffe et al. ( , 1996 and Ferrarese et al. (1996). In addition to this, the later authors detected a black hole with mass $5 Â 10 8 M . However, dust lanes were detected roughly along the major axis (Mahabal et al., 1996). Although KR indicates that larger galaxies have lower surface brightness, this galaxy is found to have much lower hl e i than expected for its size. On the other hand its central velocity dispersion is consistent with its total absolute magnitude (FJR, Fig. 5).  Rampazzo et al. (2013) where they took the group/cluster identification from Tully (1988).
From that we conclude that its hl e i might be the main reason of its deviation from the FP in Fig. 1. Such lower surface brightness affects the value of j 3 toward having high M/L ratio.
On the other hand, some galaxies are deviated below the FP as clear in Fig. 1. These galaxies are FCC 021, FCC 055, FCC 153, FCC 170, FCC 177, FCC 301, VCC 1231, NGC 1366 andNGC 4742. They also tend to have smaller j 3 as clear in Fig. 3, which means that they have lower M/L ratios as expected for their young stellar populations (see Table 5).
FCC 021 (NGC 1316) is deviated below the FP in Fig. 1. In Fig. 3, it shows smaller j 3 in the direction of smaller M/L ratio as expected for its young age of 3.4 Gyr as recorded by TF02 (see Table 5). This galaxy exhibits many unusual features for elliptical galaxies, such as dust patches, ripples and loops, Ha filaments (Schweizer 1980(Schweizer , 1981Carter et al., 1983) and it contains a complex net of dark, dust features. The presence  (Koleva et al., 2011). Col. (1) gives the galaxy name; Col. (2) states another name for the galaxy; Col. (3) gives type of the galaxy; Col (4) states the effective radius r e in seconds of arc; Col. (5) gives the central velocity dispersion r o in km s À1 from HyperLeda (http://leda.univ-lyon1.fr//); Col. (6) indicates the environment of the galaxy: when the galaxy is a member of a well known cluster, the cluster name is indicated; when the galaxy does not belong to a cluster or a group, it is labeled as field galaxy.   Kuntschner et al. (2002). Table 4 Structural properties of ETGs. The columns are as follows: identification of the galaxies, redshift for the galaxies from NED (Nasa Extragalactic Database), apparent magnitude in B-band from HyperLeda database, absolute magnitude in B-band from HyperLeda database, log of the effective radius in parsec, log of the central velocity dispersion in km/s, mean effective surface brightness in B-band, sample source: of these features strongly suggests that NGC 1316 is a merger remnant (Schweizer, 1980;Bosma et al., 1985) with a tidal-tail system. Also, On the other hand, D'Onofrio et al. (1995) noticed that the central velocity dispersion in NGC 1316 is lower than that expected for a galaxy of this luminosity from the FJR (260 versus 400 km/s). This action could be due to the presence of a dynamically cold disk-like component. Another evidence is presented by Nowak et al. (2008, their Figure 8), who found indications of a younger stellar component in the center of NGC 1316. All those characteristics mentioned above such as dust, shells, loops, ripples, and tails as previously found by D' Onofrio et al. (1997) together with a velocity dispersion which is lower than that of other elliptical galaxies of similar luminosity, cause NGC 1316 to lie far off the FP. FCC 170 (NGC 1381) is deviated below the FP in Fig. 1, while it shows smaller j 3 , in the direction of smaller M/L ratio as shown in Fig. 3. It has a luminosity weighted age of 6.6 Gyr as determined by TF02 (see Table 5). D' Onofrio et al. (1995) found that this galaxy has a small KDC inside r $ 6 00 . On the other hand, Silva et al. (2008) found that this S0 galaxy contains X-bulge isophotal pattern, which is related to a recent dynamical encounter or merger event. This galaxy is one of the most deviated galaxies below the FP as shown in Fig. 1. This behavior may be caused by its small values of the r e (4.3 00 ) and the r o (15 km/s). Also the structures it has such as the KDC, the bar and outer rings may contribute to this deviation.
It is found that some of the deviated galaxies were previously studied by Forbes et al. (1998). These galaxies are NGC 4261, NGC 4697, FCC 021 (NGC 1316), FCC 170 (NGC 1381. They showed that the scatter about the FP of those galaxies and others is correlated with age such that young galaxies have negative residuals from the FP, while old galaxies have positive residuals. On the other hand, Cappellari et al. (2013) constructed detailed dynamical Jeans Anisotropic models (JAM), based on the Jeans equations, for the volume limited and massselected ATLAS 3D sample of ETGs. We found that 27 of our galaxies are in their sample. They showed that the larger scatter in the FP is due to stellar population effects, variations in the M/L ratio (including trends in the stellar initial mass function [IMF]).

Conclusions
In this study we investigate the influence of environment on ETGs in groups, clusters and the field. We focus our study on the scaling relations of ETGs such as the FP, KR and FJR. We summarize our results as follows.
As for the FP, the deviation of some galaxies above the FP is due to their large values of M/L ratios as expected for their old ages. The deviation of some other galaxies below the FP is due to having lower M/L ratios as expected for their young ages.
We noticed that the most deviant galaxies from the FP are from Koleva et al. (2011). For these galaxies, there are two possible reasons for their deviation from the FP. It is clear that they are also located below the hl e i Br e relation toward less hl e i than expected for their sizes. Possible reasons for such dimming measurements of hl e i B can be due to the presence of dust lanes or gas within the central regions of those galaxies. That is because of the sensitivity of B-band to structures of galaxies. The second reason for their deviation from the FP comes from their tendency to have smaller j 3 , which means . Open circles are for the comparison sample of isolated early-type galaxies (Reda, 2007). The green solid line is the FP of galaxies in the Coma cluster from Jørgensen et al. (1993). The blue solid line represents best fitting of the sample using the least square method.

Figure 3
The edge-on view of the FP of the ETGs in different environments in the j 1 -j 3 space. Symbols are as shown in Fig. 1. The solid line is the FP for Virgo cluster galaxies from Bender et al. (1992). The short-dashed lines represent the typical observational errors added to the 1r intrinsic scatter of 0.05 in j 3 for Virgo cluster galaxies (Nipoti et al., 2003). The deviant galaxies above or below the FP in Fig. 1 show a tendency to have larger or smaller values of j 3 than the average. that they have lower M/L ratios as expected for their young stellar populations. Also these galaxies have underestimated values of the central velocity dispersions which might affect on their positions relative to the FP.
The scatter of ETGs about the FP is correlated with age. Thus, we can introduce strong support for the idea that the position of an elliptical galaxy with respect to the FP is dependent on the time since its last starburst.
We found that the scatter about FJR is correlated with the post-merger age of the galaxy. Young ellipticals are brighter in the B band and/or have lower central velocity dispersion than the mean relation. The mean relation corresponds to galaxies that are $10 Gyr old.

Figure 4
The Kormendy relation between the mean surface brightness hl e i B and effective radius r e in the B band for ETGs. The solid line represents the Hamabe and Kormendy (1987) relation. The zero-point of the original relation has been shifted from V to the B-band assuming typical colors of BÀV = 0.9. The symbols are as in Fig. 1.

Figure 5
The log r o versus B-band absolute magnitude relation for our samples of ETGs. The straight line is the Faber-Jackson relation (FJR) for normal elliptical galaxies (Faber and Jackson, 1976). The symbols are as in Fig. 1.