A&A 425, 797-812 (2004)
F. La Barbera - P. Merluzzi - G. Busarello - M. Massarotti - A. Mercurio
INAF, Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli, Italy
Received 28 January 2004 / Accepted 10 June 2004
We present a detailed analysis of the photometric properties of galaxies in the cluster A 2163B at redshift . R-, I- and K-band structural parameters, (half light radius , mean surface brightness within and Sersic index n) are derived for galaxies, and are used to study their internal colour gradients. For the first time, we use the slopes of optical-NIR Kormendy relations to study colour gradients as a function of galaxy size, and we derive the Photometric Plane at in the K band. Colour gradients are negligible at optical wavelengths, and are negative in the optical-NIR, amounting on average to . This result is in agreement with our previous measurements of colour gradients at intermediate redshifts, and imply a metallicity gradient in galaxies of per radial decade. The analysis of the Kormendy relation suggests that its slope increases from the optical to the NIR, implying that colour gradients do not vary or even do become less steep in more massive galaxies. Such a result is not simply accomodated within a monolithic collapse scenario, while it can be well understood within a hierarchical merging framework. Finally, we derive the first NIR Photometric Plane at , accounting for both the correlations on the measurement uncertainties and the selection effects. The Photometric Plane at is consistent with that at , with an intrinsic scatter significantly smaller than the Kormendy relation but larger than the Fundamental Plane.
Key words: galaxies: clusters: individual: A 2163B - galaxies: photometry - galaxies: fundamental parameters - galaxies: evolution
Studies of galaxy populations in clusters at intermediate redshifts have been proved to be an effective tool to constrain the mechanisms underlying their formation and evolution. A pure photometric approach involves the analysis of galaxy Luminosity Functions (LFs), of galaxy colours, mainly via the colour magnitude (CM) diagrams, and of the internal light distribution of galaxies, i.e. their structural parameters.
The galaxy LF and its dependence on the waveband carry information both on the stellar processes occurring in galaxies and on the cosmological processes which determine their mass function. Since Press & Schechter (1974), the shape of the LF has been seen as a basic test of theories of structure formation and evolution. The luminosities of early-type galaxies are also tightly correlated with their colours, through the colour magnitude (CM) relation (Visvanathan & Sandage 1977; Bower et al. 1992). The slope of this relation shows little evolution with redshift up to , while its zeropoint changes according to what is expected for an old passively evolving stellar population (e.g. Stanford et al. 1998, Kodama et al. 1998, hereafter KAB98). As shown by KAB98 (see also Merluzzi et al. 2003), the evolution of the CM sequence with redshift sets strong constraints on the origin of this relation, resolving the well known age-metallicity degeneracy (Worthey et al. 1996).
The structural properties of galaxies at different redshifts provide a wealth of information by which galaxy evolution can be investigated, both through the study of the correlations and through the analysis of the waveband dependence of such quantities. The NIR light, in fact, is less sensitive to more recent star formation, to metallicity effects (though line blanketing) and to dust absorption, following more closely the luminous matter distribution.
The multi-waveband analysis gives information on the internal colour gradients (CGRs) of galaxies, and therefore on the radial gradients of the properties of their stellar populations (SPs), such as age, metallicity and dust content. Nearby galaxies have on average negative CGRs, their SPs becoming bluer toward the periphery (Peletier et al. 1990a, b). Due to the low evolution of colour gradients with redshift, metallicity seems to be the primary driver of the SP gradients in spheroidal galaxies, as demonstrated both by optical-optical studies (e.g. Tamura & Ohta 2000; Saglia et al. 2000) and by optical-NIR CG measurements (La Barbera et al. 2003a,2002, hereafter LBM02 and LBM03a). Age gradients, however, are not fully ruled out by the present data (Saglia et al. 2000, LBM03a), while the effects of dust absorption still remain substantially unresolved. The presence of metallicity gradients can be well explained in the monolithic formation scenario of early-type galaxies (Larson 1974), due to the later beginning of a galactic wind in the inner galaxy regions. However, it can also be accommodated within the hierarchical merging framework, since metallicity gradients are settled in disk galaxies at high redshifts, and more massive early-types form on average from the merging of larger disks (Kauffmann 1996).
Structural parameters, such as the effective (half-light) radius , the mean surface brightness within and the Sersic index n, are correlated by various relations, whose physical origins reside both in the properties of the SPs of galaxies and in the dynamical structure of these systems. For the early-type galaxies, one of these correlations is that between and , also known as the Kormendy relation (KR). As shown by Capaccioli, Caon and D'Onofrio (1992), form two distinct families in the plane of effective parameters: that of the bright early-types, following the KR, and another "ordinary'' family, whose properties are more disperse and heterogeneous. Recently, Graham & Guzmàn (2003) showed that a real dichotomy does not exist between the two families, but their observed properties are well explained by a systematic change in the profile shape with galaxy luminosity. The evolution of the zeropoint of the KR has been largely investigated at optical wavebands to constrain the major formation epoch of galaxy SPs and to perform the Tolman test for the cosmological expansion (Lubin & Sandage 2001; Sandage & Perelmuter 1991; Barger et al. 1998; Sandage & Lubin 2001; Ziegler et al. 1999; Pahre et al. 1996). On the other hand, the slope of the KR is an interesting tool to gain insight into the properties of the galaxy SPs as a function of galaxy size (Ziegler et al. 1999; La Barbera et al. 2003b, hereafter LBM03b), which is a crucial prediction of hierarchical merging scenarios. As recently shown by Graham (2002, hereafter GRA02), early-type galaxies also follow a three-dimensional relation between , and , which is similar to the spectroscopic Fundamental Plane (FP), once velocity dispersions are replaced by Sersic indices. This "photometric plane'' (hereafter PHP) has an observed scatter comparable to that of the Fundamental Plane (FP) relation, and carries interesting information on the physical properties of galaxies and their origin.
In the framework of a project aimed at investigating the optical-NIR photometric properties of galaxies in the fields of ROSAT PSPC extended sources, we have obtained multi-waveband data (BVRIK) for a field of centered at and , at about 6.5' North ( at with , and ) of the Abell cluster A 2163 at redshift z=0.201 (Arnaud et al. 1994). The coordinates of this field correspond to the center of a secondary extended emission in the X-ray map of A 2163, known as A 2163B (Elbaz et al. 1995, hereafter EAB95), with an X-ray temperature . The cluster A 2163 ( , ) is a very rich and complex structure of galaxies, which has been extensively studied for its exceptionally hot X-ray temperature, (see Markevitch et al. 1996, and references therein), and for its huge radio halo, one of the most powerful known so far (Feretti et al. 2001, hereafter FFG01). Our data show the presence of a significant excess of galaxies at redshift in the field of A 2163B, with a NIR spatial distribution typical for a cluster of galaxies, with a main central overdensity and a secondary structure at in the North-East direction.
In the present work, we study the photometric and structural properties of the galaxy population of A 2163B, by discussing the constraints implied by our results on different galaxy evolution scenarios.
The layout of the paper is as follows. The data are presented in Sect. 2, while the luminosity density map, the colour magnitude relations and the K-band LF of A 2163B are studied in Sect. 3. Cluster members are then selected by the photometric redshift technique, as described in Sect. 4. The derivation of structural parameters is outlined in Sect. 5. Section 6 deals with the comparison of structural parameters and with the analysis of the internal colour gradients of galaxies. Sections 7 and 8 deal with the correlations between the structural parameters. In Sect. 7, we attempt for the first time to perform an optical/NIR comparative study of the - relation, while in Sect. 8 we use the K-band data to analyze the PHP for the population of spheroids in A 2163B. Discussion and conclusions follow in Sect. 9. Details on data reduction are given in Appendix A, while the estimate of the cluster redshift from the optical-NIR CM relations is detailed in Appendix B. The catalogue, including all the photometric properties of galaxies in the field of A 2163B, that is BVRIK total magnitudes, colours, photometric redshifts and RIK structural parameters, is described in Sect. 2.3.
During three nights of run I, we obtained K-band imaging with the SOFI instrument (pixel scale ) for a field of . The sky conditions were photometric for two nights and non photometric for the third night. A total of 120 exposures were collected, with a DIT of , , and a dithering box of . Due to the non photometric conditions, only 85 exposures were retained, resulting in a total integration time of . Standard stars from Persson et al. (1998) were observed during each night, each at five different positions on the chip. In order to perform the illumination correction (see Sect. A.2), we also observed a standard star at different positions on a grid across the frame. In the same period, we also obtained V-, R-, and I-band photometry with the EMMI instrument for a region of (pixel scale ), under non photometric conditions. On April 2002, the field A 2163B was re-observed in B, V, R and I band with EMMI under photometric conditions. The relevant information on the observations are summarized in Table 1. The total exposure times amount to 600, 3000, 1200 and for the B, V, R and I bands, respectively.
Table 1: Observations. The notes refer to the sky conditions: and denote non-photometric and photometric conditions, respectively.
|Figure 1: K-band image ( left panel) and luminosity-weighted map ( right panel) for the field of galaxies A 2163B. The image is centered at and , and was smoothed for the plot by a Gaussian convolution. The scale and the orientation of the image are shown in the lower left corner of the left panel. In the same panel, the crosses indicates the positions of the radio sources in the field. In the right plot, the circles enclose the regions that were used to calculate the LF in the higher density environment (see Sect. 3.2).|
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The BVRIK photometric catalogue for the N=131 galaxies with photometric redshift estimate (see Sect. 4) is shown in Table 2.
The catalogue is organized as follows. Two rows correspond to each galaxy. The first one provides the measured quantities, while the second one gives the relative uncertainties (one sigma standard intervals). All the photometric quantities have been corrected for galactic extinction by using the photometric redshift estimates and adopting E(B-V)=0.415, with the extinction law from SFD98. The typical uncertainties on the structural parameters are discussed in Sect. 6.1.
Column 1: running number of the catalogue.
Column 2: photometric redshift.
Columns 3, 4: right ascension and declination referred to J2000. The astrometric solution was computed by using a list of stars from the USNO catalogue. The rms of the residuals to the astrometric solution is .
Columns 5-9: B-, V-, R-, I- and K-band total magnitudes.
Columns 10-13: optical-NIR galaxy colours in the aperture of 3.5'' corrected for seeing effects.
Columns 14-16: mean surface brightness within the effective radius , logarithm of (in arcsec) and Sersic index n for the R-band.
Columns 17-19: the same of Cols. 14-16 for the I-band.
Columns 20-22: the same of Cols. 14-16 for the K-band.
Columns 23, 24: axis ratio and position angle in degrees obtained from the K-band surface photometry.
|Figure 2: Optical-NIR CM diagrams for galaxies in the field of A 2163B. For each panel, the slope and zeropoint of the CM relations are shown in the lower left corner, while the error bars from the left to the right denote the averaged uncertainties on colours and magnitudes at and , respectively.|
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In order to derive the redshift of the galaxy population of A 2163B we compared the BVRIK photometry with predictions of stellar population models from the GISSEL00 code (Bruzual & Charlot 1993). In particular, we used (1) the optical-NIR colour magnitude (hereafter CM) relations (Sect. 3.1); (2) the K-band LF (Sect. 3.2) and (3) the photometric redshift technique (Sect. 4). We point out that, although it is known that broad-band colours are degenerate in age, metallicity and redshift, and that uncertainties exist among stellar population models (e.g. Charlot et al. 1996), the large wavelength baseline provided by our photometry (from U to NIR restframe) and the use of the GISSEL synthesis code allow to obtain a reliable redshift estimate of galaxies at intermediate redshifts by using purely photometric techniques, as shown by other studies (e.g., de Propris & Pritchet 1998; Busarello et al. 2002; La Barbera et al. 2003c). Another important point for estimating is the effect of the galactic reddening E(B-V). The main sources for the reddening of the Milky Way are based on measurements from Burstein & Heiles (1984, hereafter BH84) and on COBE/DIRBE and IRAS/ISSA FIR data from Schlegel et al. (1998, hereafter SFD98). Generally, the estimates of E(B-V) from SFD98 are systematically higher than those of BH84. For A 2163B, BH84 and SFD98 predict very different extinction values, E(B-V)=0.18 and E(B-V)=0.415, respectively. In the next section, we obtain a simultaneous estimate of the galactic reddening as well as of the cluster redshift from the optical-NIR colour magnitude relations. This procedure gives an extinction value which is in remarkable agreement with that of SFD98 and a redshift estimate of , which concides within the uncertainties with that obtained from the K-band LF (Sect. 3.2), for which extinction effects are negligible. The difference between BH84 and SFD98 reddening values, therefore, does not affect the present analysis.
The zeropoints of the CM relation were used to obtain a simultaneous estimate of the cluster redshift and of the galactic reddening in the direction of A 2163, fitting the values of with the colours expected from old stellar population models (see Appendix B for details). In this approach, we took into account the degeneracy among metallicity and the other stellar population parameters exploiting the fact that the CM relation mainly origins from a mass-metallicity relation (see Merluzzi et al. 2003 and references therein). This procedure gives and . It is quite remarkable that (1) the estimate of E(B-V) is in very good agreement with that of SFD98, E(B-V)=0.415; and (2) the value of coincides with that obtained from the K-band LF, which is virtually unaffected by galactic reddening. For this reason, we adopted in the following E(B-V)=0.415, and applied the corresponding absorption corrections to our photometry. Repeating the zeropoint fitting with E(B-V)=0.415gives , which is fully consistent with the redshift of the main cluster structure (A 2163 ) at .
We used these results in order to obtain a further estimate of the
redshift of A 2163B. The K-band LF was obtained by correcting our
number counts with field galaxy counts from the Calar Alto Deep
Imaging Survey (CADIS, see Huang et al. 2001), which is the largest
medium deep K-band survey to date, with a total area of
and a completeness magnitude of
K-band photometry is complete down to
Sect. 2.2), the CADIS data are the most suitable dataset for
the estimate of field galaxy counts. The LF of A 2163B is shown in
Fig. 3. The error bars take into account Poissonian
uncertainties on both field and cluster counts, while the different
curves show the SF fits of the LF. In order to account for the finite
size of the magnitude bins, the fits were performed by the convolution
of a SF with the bin size. Following dPS99 and de Propris & Pritchet (1998, hereafter
dPP98), we fitted the galaxy counts down to
see below) by a SF with
three brightest cluster galaxies. The fit provided a good description
of the counts of bright galaxies,
giving the following estimate of the characteristic magnitude:
In order to estimate ,
minimized the function:
|Figure 3: K-band LF of A 2163B. The two curves indicate the best-fit Schecter functions obtained by fitting both and K* (solid line) and by fitting only K* with fixed to -0.9 (dashed line). In the last case, the three brightest cluster galaxies were excluded from the fit: the first bin was not considered while the galaxy counts for the second bin are marked by the empty circle. Contours in the smaller panel denote , and probability levels, respectively.|
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In order to study the faint end of the LF, we performed a SF fit for by treating both and K* as free parameters. As shown in Fig. 3, the SF, whose best-fit parameters are and , provides a good description of the LF of A 2163B. The cluster counts show some deviation from the SF fit only for the two bins at and . Although this could be an indication of a bimodal behaviour of the LF, as found by previous studies (see Mercurio et al. 2003, and references therein), the deviations are only at the levels of and , respectively, and are therefore not very significant. The value of is in very good agreement with the value of -1.18 found by Andreon (2001) for a rich cluster of galaxies at z=0.3 in an area of , which is similar to that analyzed in the present study ( ), and is also consistent with values of the faint end slope of the NIR LF for the Coma cluster, (dPP98) and (Andreon & Pellò 2000), and for field galaxies, (Kochanek et al. 2001). We also analyzed the dependence of the LF of A 2163B on environment, by performing the SF fits separately for the galaxies inside the higher density region, defined by the circles in Fig. 1, and for the galaxies outside that region. The two LFs are shown in Fig. 4 with the corresponding SF fits. Interestingly, we found that the values of vary from (higher density) to (lower density), implying a steepening of the faint end slope at lower densities, in agreement with the findings of other studies (see Haines et al. 2004, and references therein). This steepening is due to the fact that, as shown in Fig. 4, the lower density environment is characterized by a higher fraction of faint galaxies, with a significant difference ( ) in the low- and high- density counts at .
|Figure 4: K-band LF of A 2163B in the low- and high- density environments. The points and the error bars corresponding to the high density region have been shifted by for sake of semplicity. The curves show the best fitting Schechter functions.|
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In order to select cluster members, we used the photometric redshift technique, which has been proven to be an effective tool to estimate the redshift of cluster galaxies at intermediate redshifts (e.g. Busarello et al. 2002; La Barbera et al. 2003c, and references therein). Photometric redshifts were estimated according to the Spectral Energy Distribution fitting method (see Massarotti et al. 2001a,b, and references therein). In order to achieve a reasonable accuracy, we considered galaxies with signal-to-noise ratio in at least three bands, limiting the sample to the N=131 galaxies brighter than . Since the percentage of galaxies at redshift z > 1 with K < 17.5 is expected to be negligible (), we looked for redshifts in the range with a step of 0.01, imposing that at a given redshift galaxy templates were younger than the age of the universe in the adopted cosmology. We used the GISSEL00 code in order to produce galaxy templates with a Scalo IMF and an exponential SFR . The colours of E/S0, Sa/Sb, and Sc/Sd spectra were modeled by choosing and , respectively, while early-type galaxies with different metallicities were described by using E/S0 models with , 0.4, 1 and 2.5. The differential dust extinction of the Milky Way was included in the computation of model colours by adopting the extinction curve of Cardelli et al. (1989) and a colour excess of E(B-V)=0.415 (see Sect. 3.1). The uncertainty on the photometric redshift was estimated by performing numerical simulations, taking into account the measurement errors on galaxy colours. The mean value of is , varying from at to at .
|Figure 5: Distribution of photometric redshifts. The solid line and thedashed region indicate the estimate of the cluster redshift, , and the relative uncertainty ( standard interval). Dashed lines enclosethe range of z, , used to select cluster members.|
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As shown in Fig. 5, the distribution of photometric redshifts is dominated by the peak around , indicating that most galaxies with are actually cluster members. Applying the bi-weight statistics, we obtained the following estimate of the cluster redshift: , in agreement with the values obtained in Sects. 3.1 and 3.2. Galaxies with photometric redshift in a range of around were defined as cluster members, resulting in a final list of N=102 objects. This value is in good agreement with that predicted from the LF of cluster galaxies, N=112 (see Sect. 3.2).
Surface photometry was derived for all the galaxies brighter than in the R and I bands, and for the galaxies brighter than in the K band. These selection criteria were chosen in order to obtain reliable structural parameters from the A 2163B photometry, and were the results of numerical simulations performed as described in LBM02. A further selection was performed a posteriori by excluding few faint galaxies in the I and K bands because of the strong contamination from close stars. The resulting samples include N=64, 62 and 58 galaxies for the R, I and K bands, respectively, with N=62 objects in common between the Rand I bands, and N=58 galaxies in common between the R and K bands. Structural parameters for these galaxies are given in the catalogue (see Sect. 2.3).
Galaxy images were fitted with 2D models convolved with the PSF, as
detailed in LBM02. As shown in that paper, the 2D approach allows
reliable structural parameters to be obtained for galaxies at
intermediate redshifts (
from ground based data taken
under ordinary observing conditions (seeing
Galaxy models were parametrized by the Sersic law:
|Figure 6: 2D fits of galaxies in the K-band image. For each plot, from left to right, the galaxy image, the 2D model and the residual map are shown. The size of the horizontal white bar is 5''.|
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plots, as an example, the K-band 2D fitting of some galaxies in the
cluster field. The models turned out to give a very good description
of the galaxy images.
|Figure 7: Comparison of structural parameter in the optical. For each panels, differences are computed between R and I bands. The correlation between effective parameters is shown inside the lower right panel.|
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Differences between R- and K-band structural parameters are shown in
Fig. 8. We note that the differences of mean surface
were obtained by
subtracting the R-K galaxy colours, that is:
The mean values of the distributions show that cluster galaxies are
more concentrated in the NIR than in the optical, having NIR effective
radii which are on average
smaller than in the R-band
), and Sersic indices slightly
larger in the K band, although the last difference is not very
significant. The mean difference of
can be fully explained by using the definition of total magnitude
computing the difference between R- and K-band total magnitudes:
The dispersion of the distributions in Fig. 8 is due (1) to the uncertainties on both the R- and K-band parameters; and (2) to the intrinsic scatter of the optical-NIR properties of galaxies. We verified by numerical simulations (performed as described in LBM02) that the uncertainties on the K-band structural parameters are as large as or smaller than those estimated for the optical wavebands. This suggests that the dispersions of the histograms in Fig. 8 have mainly an intrinsic origin. In Sects. 7 and 8, in order to describe the uncertainties on , and , we adopted the same covariance matrix for both the optical and the NIR data. By looking at Fig. 8, we stress again the small dispersion in the variable, that amounts to .
The distributions of colour gradients for the galaxies of A 2163B
are shown in Fig. 9, we wrote the R-I and R-K colour gradients as V-R and V-K restframe gradients,
respectively. By using different galaxy templates from the GISSEL00
code, we verified, in fact, that the conversion from R-I (R-K) at z=0.2 into V-R (V-K) at z=0 is
independent of the spectral type (for ), with variations of 0.01 and
between different spectral
models for the optical-optical and the optical-NIR colours,
respectively. As expected on the basis of the structural parameters,
galaxies show optical-optical colour gradients which are fully
consistent with zero, while the V-K colour gradients are negative for
most galaxies, implying that their SPs are on average redder in the
center. The mean value of the optical-NIR gradient is -0.48, which
implies that galaxies become
bluer per decade of
radius toward the periphery. The value of grad(V-K) is fully
consistent with the colour gradient estimate of LBM03a (
|Figure 9: Distributions of V-R and V-K colour gradients. The mean values are marked by a solid line.|
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|Figure 10: Kormendy relations in R and K bands. Dashed lines mark the completeness magnitudes and the surface brightness cut ( right panel) of each sample. The typical uncertainties on the effective parameters are indicated by the ellipses in the lower left corner of each panel. The ellipses mark the contours that enclose a probability of for a 2D normal deviate.|
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diagrams for the galaxies of A 2163B are shown in
Fig. 10 for the R and K bands. We note that the I-band data
provide almost the same spectral information as the R-band photometry,
and therefore are not discussed in the following. For each band, we
excluded the disks (n < 2) and the galaxies for which the total
magnitude estimated by the structural parameters is fainter than the
completeness magnitude. This selection results in N=52 and N=53 galaxies in the R and K bands, respectively. For what concerns
the NIR data, we also excluded two galaxies that have small radii and
low surface brightness and for which, therefore, structural parameters
are possibly affected by a larger uncertainty. The K-band sample
consists of N=51 objects.
In order to describe the
sequence, we consider the
following equation for each waveband :
|Figure 11: Ratios of optical to NIR effective radii and colour gradients are plotted versus the logarithm of the K-band effective radius. The dashed lines mark the mean values of and grad(V-K) in the left and right panels, respectively. Data were binned in order to have the same number of points in each bin. The solid lines mark the best-fits to the data, while the dot-dashed lines indicate the confidence intervals.|
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|Figure 12: Distribution of galaxies in the space of structural parameters. Upper-left: - relation. The ellipses is in the upper plots are the probability contours. The solid and dot-dashed lines are the best-fit and the confidence lines, respectively. The region affected by the magnitude selection is filled by a dashed pattern. Upper-right: edge-on projection of the PHP with the best-fit relation marked by a solid line. Lower-left: "long'' edge-on projection of the PHP. Lower-right: face-on view of the PHP. The shaded region is delimited on the right by the line that results from the intersection of the plane with a plane parallel to the PHP but with zeropoint .|
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other panels of Fig. 12 show different projections of the
so-called Photometric Plane (PHP). For comparison with GRA02, we
adopted the following representation of the PHP:
The slopes and the scatter of the NIR PHP at turn out to be in remarkable agreement with those derived by GRA02 for galaxies in the Fornax and Virgo clusters: , and . We point out that the magnitude selection significantly affects the coefficient and that, therefore, it would be very interesting to use a sample of galaxies spanning a larger magnitude range in order to better constrain this coefficient. The selection effects can be further illustrated by looking at the face-on projection of the PHP in Fig. 12d. Due to the finite dispersion of the galaxies around the PHP, its intersection with the plane results in a "strip'', whose "upper'' border marks the limits of the dashed area in Fig. 12d. As consequence, the distribution of galaxies in this area is not "complete''.
In order to estimate the intrinsic dispersions of the - relation and of the PHP, we subtracted to the observed dispersion in the amount of scatter expected from the measurement errors on the observed parameters, taking into account the covariance terms between the uncertainties on , and . The intrinsic dispersions of the - relation and of the PHP turn out to be and , respectively. Interestingly, we find that the measurement errors account only for few percents of the observed dispersion around the PHP, because, as shown in Fig. 12b, their correlation is almost parallel to the plane, in the same way as for the KR.
The K-band luminosity density map of A 2163B presents a main central overdensity of radius , and a secondary structure from the center. The colour-magnitude diagrams show a sharp red sequence whose slope flattens at longer wavelengths: galaxy colours become bluer by per magnitude in the B-K vs. diagrams, and by in the I-K vs. plane. These values agree with the predictions of a mass-metallicity model of the CM relation (KAB98). By introducing a suitable procedure to account for the Milky Way reddening, we find that the zeropoints of the CM sequence are consistent with those expected for a red galaxy population at redshift , implying that A 2163B is a cluster of galaxies likely involved in a merging event with A 2163. The value of is also confirmed by the analysis of the K-band LF and by the photometric redshift technique, which is used to select cluster members. The luminosity segregation of A 2163B is investigated by means of the K-band LF. The global LF is well described by a single Schecter function with a faint end slope of , in agreement with other studies of the NIR LF both in clusters and in the field (e.g. Andreon 2001; Kochanek et al. 2001). On the other hand, the faint end slope depends on environment, varying from about -1 in the two higher density clumps, to about -1.4 into the outer region, implying that the population of dwarf galaxies is less abundant in the denser environments. This behaviour of the LF suggests that some mechanism, such as tidal disruption or cannibalism, is working in the higher density environments, decreasing the number of faint galaxies (Haines et al. 2004).
Surface photometry has been derived in the R, I and K bands for cluster galaxies, and has been used:
The population of spheroids in A 2163B has null colour gradients at optical wavelengths (V-Rrestframe) and optical-NIR gradients that are significantly negative ( ), consistently with the quoted differences among the effective radii. As shown by LBM03a, the optical-NIR gradients do not evolve significantly with redshift, amounting to . As detailed in that work, the redshift dependence of both optical-NIR and UV-optical colour gradients strongly constrains the age and metallicity of the inner and outer galaxy stellar populations. Using the colour gradient model of LBM03a (see model Z1, Table 6), the quoted colour gradients imply a metallicity gradient in spheroids of per decade of radius. This result is in agreement with that reported from other studies of colour gradients for both nearby and intermediate redshift galaxies (Idiart et al. 2002; Saglia et al. 2000).
Monolithic collapse models predict that early-type galaxies are more metal rich in the center than in the outskirts. During galaxy formation, the gas dissipates its kinetic energy carrying the heavy elements ejected from the evolved stars into the inner region (Larson 1974). Numerical simulations predict a metal abundance gradient of about -0.5 (e.g. Carlberg 1984; Kawata 2001, see their models B1/B2 which correspond to the magnitude range of our samples). This value is not consistent with our results, although some caution is needed due to scatter present both in the observed data and in the simulation results (see Kawata 2001). The difference of observed and predicted metallicity gradients suggests that gas dissipation has a minor role in monolithic collapse models. We note, however, that dissipation is required in order to reproduce the mass-metallicity relation of early-type galaxies and their moderate orbital anisotropies. We argue, therefore, that some tuning of the parameters driving the physics of gas dissipation would be required in order to fit all the observed properties into the monolithic scenario. A likely explanation of the observed metallicity gradients resides in the merging processes, which mix the SPs inside galaxies. It has been shown that both dissipationless merging of spheroidal systems (White 1980) and dissipative merging of disk galaxies (Bekki & Shioya 2001) produce more shallow stellar population gradients.
The slope and the zeropoint of the optical - relation are consistent with those obtained in LBM03b. For what concerns the NIR KR, we compared its slope and zeropoint with the optical values by taking into account (i) the colour magnitude relation; and (ii) the mean value of the ratio of optical/NIR effective radii. These factors fully explain the difference among the optical and NIR zeropoints. The most interesting result is that the slope of the R-band KR, corrected for the effects (i) and (ii), is lower by than the K-band value. We show that this difference can be explained if the ratio of optical to NIR effective radii (the optical/NIR colour gradient) decreases (flattens) for larger galaxies. A direct inspection of the and the grad(V-K) vs. diagrams shows that such trend exists. Our data do not favour a steepening of colour gradients with galaxy size, that would imply a larger discrepancy between the R- and K-band KR slopes. A steepening of colour gradients with galaxy luminosity (size) is a natural expectation of the monolithic collapse model, due to the galactic wind mechanism (Larson 1974). The galactic wind blows early in less massive galaxies, preventing gas dissipation to carry heavy metals in the center, and producing, therefore, a less steep gradient in these systems. A steepening of colour gradients with galaxy luminosity has been unfruitfully looked for by various studies (e.g. Peletier et al. 1990a; Bartholomew et al. 2001). Recently, Tamura & Ohta (2003) measured the optical colour gradients for N=36 galaxies at . They found that the optical colour gradient of very bright early-types ( ) can steepen with galaxy luminosity, while an opposite trend was suggested for fainter galaxies. A similar bimodal behaviour was found by (Balcells & Peletier 1994) for the colour gradients of early-type spiral bulges. We note that our data do not allow us to distinguish the behaviour of colour gradients for the very bright early-types, while they allow a larger magnitude range in both optical and NIR to be analyzed. In hierarchical merging models, more massive galaxies form from larger disk systems, which have stronger internal gradients. Since merging dilutes the stellar population gradients (White 1980), if galaxies with larger size have experienced a higher merging rate (Capaccioli et al. 1992), their colour profile can be as flat as or even less steep than those of smaller systems. The data of A 2163B seem to favour this interpretation.
Finally, we have analyzed the so-called Photometric Plane (PHP) of spheroids at . We find that galaxies follow a bivariate relation between K-band effective parameters and the logarithm of the Sersic index: . Accounting for the correlations among the uncertainties on structural parameters as well as for the selection effects, we find and , and an observed dispersion of in . These values are consistent with the optical PHP coefficients found by GRA02 for early-types in the Fornax and Coma clusters. We have discussed how the magnitude cut affects the distribution of galaxies in the space of the structural parameters: the term of the PHP turns out to be significantly affected by the magnitude selection, indicating that it would be very interesting to analyze a larger, deeper sample of galaxies to further constrain the coefficients of this relation. Interestingly, we find that the correlation of the uncertainties on the structural parameters is almost parallel to the PHP, analogously to what happens for the KR. This implies that the intrinsic scatter of the PHP amounts to about , which is only few percents smaller than the observed scatter, but lower than that of the KR ( ). Therefore, although the observed scatter around the plane seems to be similar to that of the spectroscopic Fundamental Plane ( ) as found by GRA02, the present data indicate that its intrinsic dispersion can be significantly larger. This point will have to be further analyzed by studying samples of galaxies for which both velocity dispersions and Sersic indices are available.
Instrumental magnitudes for the Landolt stars were computed within an aperture of diameter 10'' by means of S-Extractor (Bertin & Arnout 1996). For each band, in order to obtain the zeropoint and the colour term of the photometric calibration, we performed a robust least square fit. Colour terms were found to be small and were neglected, while the zeropoints turned out to be , , , (scaled to 1 s exposure time).