Luminosity Distribution Of Galaxies Research Articles

A complex node of the cosmic web associated with the massive galaxy cluster MACS J0600.1-2008

ABSTRACT MACS J0600.1-2008 (MACS0600) is an X-ray-luminous, massive galaxy cluster at $z_{\mathrm{d}}=0.43$, studied previously by the REionization LensIng Cluster Survey and ALMA Lensing Cluster Survey projects which revealed a complex, bimodal mass distribution and an intriguing high-redshift object behind it. Here, we report on the results of a combined analysis of the extended strong lensing (SL), X-ray, Sunyaev–Zeldovich (SZ), and galaxy luminosity-density properties of this system. Using new JWST and ground-based Gemini-N and Keck data, we obtain 13 new spectroscopic redshifts of multiply-imaged galaxies and identify 12 new photometric multiple-image systems and candidates, including two multiply-imaged $z\sim 7$ objects. Taking advantage of the larger areal coverage, our analysis reveals an additional bimodal, massive SL structure which we measure spectroscopically to lie adjacent to the cluster and whose existence was implied by previous SL-modelling analyses. While based in part on photometric systems identified in ground-based imaging requiring further verification, our extended SL model suggests that the cluster may have the second-largest critical area and effective Einstein radius observed to date, $A_{\mathrm{crit}}\simeq 2.16\, \mathrm{arcmin}^2$ and $\theta _{\mathrm{E}}=49.7^{\prime \prime }\pm 5.0^{\prime \prime }$ for a source at $z_{\mathrm{s}}=2$, enclosing a total mass of $M(\lt \theta _{\mathrm{E}})=(4.7\pm 0.7)\times 10^{14}\, \mathrm{M}_{\odot }$. These results are also supported by the galaxy luminosity distribution, and the SZ and X-ray data. Yet another, probably related massive cluster structure, discovered in X-rays 5 arcmin (1.7 Mpc) further north, suggests that MACS0600 is part of an even larger filamentary structure. This discovery adds to several recent detections of massive structures around SL galaxy clusters and establishes MACS0600 as a prime target for future high-redshift surveys with JWST.

Non-universal stellar initial mass functions: large uncertainties in star formation rates at z ≈ 2–4 and other astrophysical probes

ABSTRACT We explore the assumption, widely used in many astrophysical calculations, that the stellar initial mass function (IMF) is universal across all galaxies. By considering both a canonical broken-power-law IMF and a non-universal IMF, we are able to compare the effect of different IMFs on multiple observables and derived quantities in astrophysics. Specifically, we consider a non-universal IMF that varies as a function of the local star formation rate, and explore the effects on the star formation rate density (SFRD), the extragalactic background light, the supernova (both core-collapse and thermonuclear) rates, and the diffuse supernova neutrino background. Our most interesting result is that our adopted varying IMF leads to much greater uncertainty on the SFRD at $z \approx 2-4$ than is usually assumed. Indeed, we find an SFRD (inferred using observed galaxy luminosity distributions) that is a factor of $\gtrsim 3$ lower than canonical results obtained using a universal IMF. Secondly, the non-universal IMF we explore implies a reduction in the supernova core-collapse rate of a factor of $\sim 2$, compared against a universal IMF. The other potential tracers are only slightly affected by changes to the properties of the IMF. We find that currently available data do not provide a clear preference for universal or non-universal IMF. However, improvements to measurements of the star formation rate and core-collapse supernova rate at redshifts $z \gtrsim 2$ may offer the best prospects for discernment.

The Host Galaxy of OJ 287 Revealed by Optical and Near-infrared Imaging

Abstract The BL Lacertae object OJ 287 (z = 0.306) has unique double-peaked optical outbursts every ∼12 yr, and it presents one of the best cases for a small-separation binary supermassive black hole (SMBH) system, with an extremely massive primary . However, the host galaxy is unresolved or only marginally detected in all optical studies so far, indicating a large deviation from the bulge mass—SMBH mass relation. We have obtained deep, high spatial resolution i-band and K-band images of OJ 287 when the target was in a low state, which enable us to detect the host galaxy. We find the broadband photometry of the host to be consistent with an early-type galaxy with M R = −22.5 and M K = −25.2, placing it in the middle of the host galaxy luminosity distribution of BL Lacertae objects. The central supermassive black hole is clearly overmassive for a host galaxy of that luminosity, but not unprecedented, given some recent findings of other “overmassive” black holes in nearby galaxies.

The XXL Survey

Context. The luminosity function (LF) is a powerful statistical tool used to describe galaxies and learn about their evolution. In particular, the LFs of galaxies inside clusters allow us to better understand how galaxies evolve in these dense environments. Knowledge of the LFs of galaxies in clusters is also crucial for clusters studies in the optical and near-infrared (NIR) as they encode, along with their density profiles, most of their observational properties. However, no consensus has been reached yet about the evolution of the cluster galaxy LF with halo mass and redshift. Aims. The main goal of this study is to investigate the LF of a sample of 142 X-ray selected clusters, with spectroscopic redshift confirmation and a well defined selection function, spanning a wide redshift and mass range, and to test the LF dependence on cluster global properties, in a homogeneous and unbiased way. Methods. Our study is based on the Canada–France–Hawaii Telescope Legacy Survey (CFHTLS) photometric galaxy catalogue, associated with photometric redshifts. We constructed LFs inside a scaled radius using a selection in photometric redshift around the cluster spectroscopic redshift in order to reduce projection effects. The width of the photometric redshift selection was carefully determined to avoid biasing the LF and depended on both the cluster redshift and the galaxy magnitudes. The purity was then enhanced by applying a precise background subtraction. We constructed composite luminosity functions (CLFs) by stacking the individual LFs and studied their evolution with redshift and richness, analysing separately the brightest cluster galaxy (BCG) and non-BCG members. We fitted the dependences of the CLFs and BCG distributions parameters with redshift and richness conjointly in order to distinguish between these two effects. Results. We find that the usual photometric redshift selection methods can bias the LF estimate if the redshift and magnitude dependence of the photometric redshift quality is not taken into account. Our main findings concerning the evolution of the galaxy luminosity distribution with redshift and richness are that, in the inner region of clusters and in the redshift-mass range we probe (about 0 < z < 1 and 1013 M⊙ < M500 < 5 × 1014 M⊙), the bright part of the LF (BCG excluded) does not depend much on mass or redshift except for its amplitude, whereas the BCG luminosity increases both with redshift and richness.

Probing cosmic velocity–density correlations with galaxy luminosity modulations

Abstract We study the possibility of using correlations between spatial modulations in the observed luminosity distribution of galaxies and the underlying density field as a cosmological probe. Considering redshift ranges, where magnification effects due to gravitational lensing may be neglected, we argue that the dipole part of such luminosity–density correlations traces the corresponding velocity–density signal which may thus be measured from a given galaxy redshift catalogue. Assuming an SDSS-like survey with mean density $\overline{n}=0.01 (h^{-1}$ Mpc)−3 and effective volume Veff = 0.2(h−1 Gpc)3 at a fiducial redshift $z$ = 0.1, we estimate that the velocity–density correlation function can be constrained with high signal-to-noise ratio ≳ 10 on scales 10–100 Mpc. Similar conclusions apply to the monopole which is sensitive to the environmental dependence of galaxy luminosities and relevant to models of galaxy formation.

Observing the very low surface brightness dwarfs in a deep field in the VIRGO cluster: constraints on dark matter scenarios

We report the discovery of 11 very faint (r< 23), low surface brightness ({\mu}_r< 27 mag/arcsec^2) dwarf galaxies in one deep field in the Virgo cluster, obtained by the prime focus cameras (LBC) at the Large Binocular Telescope (LBT). These extend our previous sample to reach a total number of 27 galaxies in a field of just of 0.17 deg^2 located at a median distance of 390 kpc from the cluster center. Their association with the Virgo cluster is supported by their separate position in the central surface brightness - total magnitude plane with respect to the background galaxies of similar total magnitude. For a significant fraction (26\%) of the sample the association to the cluster is confirmed by spectroscopic follow-up. We show that the mere abundance of satellite galaxies corresponding to our observed number in the target field provides extremely tight constraints on Dark Matter models with suppressed power spectrum compared to the Cold Dark Matter case, independently of the galaxy luminosity distribution. In particular, requiring the observed number of satellite galaxies not to exceed the predicted abundance of Dark Matter sub-halos yields a limit m_X >3 keV at 1-{\sigma} and m_X > 2.3 keV at 2-{\sigma} confidence level for the mass of thermal Warm Dark Matter particles. Such a limit is competitive with other limits set by the abundance of ultra-faint satellite galaxies in the Milky Way, is completely independent of baryon physics involved in galaxy formation, and has the potentiality for appreciable improvements with next observations. We extend our analysis to Dark Matter models based on sterile neutrinos, showing that our observations set tight constraints on the combination of sterile neutrino mass m_{\nu} and mixing parameter sin^2(2{\theta}). We discuss the robustness of our results with respect to systematics.

Recovering the tidal field in the projected galaxy distribution

We present a method to recover and study the projected gravitational tidal forces from a galaxy survey containing little or no redshift information. The method and the physical interpretation of the recovered tidal maps as a tracer of the cosmic web are described in detail. We first apply the method to a simulated galaxy survey and study the accuracy with which the cosmic web can be recovered in the presence of different observational effects, showing that the projected tidal field can be estimated with reasonable precision over large regions of the sky. We then apply our method to the 2MASS survey and present a publicly available full-sky map of the projected tidal forces in the local Universe. As an example of an application of these data we further study the distribution of galaxy luminosities across the different elements of the cosmic web, finding that, while more luminous objects are found preferentially in the most dense environments, there is no further segregation by tidal environment.

Properties of galaxies around AGNs with the most massive supermassive black holes revealed by clustering analysis

Abstract We present results of the clustering analysis between active galactic nuclei (AGNs) and galaxies at redshift 0.1–1.0, which was performed to investigate the properties of galaxies associated with the AGNs and reveal the nature of the fueling mechanism of supermassive black holes (SMBHs). We used 8059 AGNs/quasi-stellar objects (QSOs) for which virial masses of individual SMBHs were measured, and divided them into four mass groups.Cross-correlation analysis was performed to reconfirm our previous result that cross-correlation length increases with SMBH mass MBH; we obtained consistent results. A linear bias of AGN for each mass group was measured as 1.47 for MBH = 107.5–108.2 M⊙ and 3.08 for MBH = 109–1010 M⊙. The averaged color and luminosity distributions of galaxies around the AGNs/QSOs were also derived for each mass group. The galaxy color Dopt-IR was estimated from a spectral energy distribution (SED) constructed from a catalog derived by merging the Sloan Digital Sky Survey (SDSS) and the UKIRT Infrared Deep Sky Survey (UKIDSS) catalogs. The distributions of color and luminosity were derived by a subtraction method, which does not require redshift information of galaxies. The main results of this work are as follows. (1) A linear bias increases by a factor of two from the lower-mass group to the highest-mass group. (2) The environment around AGNs with the most massive SMBHs (MBH &amp;gt; 109 M⊙) is dominated by red sequence galaxies. (3) Marginal indication of decline in luminosity function at dimmer side of MIR &amp;gt; −19.5 is found for galaxies around AGNs with MBH = 108.2–109 M⊙ and nearest redshift group (z = 0.1–0.3). These results indicate that AGNs with the most massive SMBHs reside in haloes where a large fraction of galaxies have been transited to the red sequence. The accretion of hot halo gas as well as recycled gas from evolving stars can be one of the plausible mechanisms to fuel the SMBHs above ∼ 109 M⊙.

Growth Rate of Cosmological Perturbations at z∼0.1 from a New Observational Test.

Spatial variations in the distribution of galaxy luminosities, estimated from redshifts as distance proxies, are correlated with the peculiar velocity field. Comparing these variations with the peculiar velocities inferred from galaxy redshift surveys is a powerful test of gravity and dark-energy theories on cosmological scales. Using ∼2×10(5) galaxies from the SDSS Data Release 7, we perform this test in the framework of gravitational instability to estimate the normalized growth rate of density perturbations fσ8=0.37±0.13 at z∼0.1, which is in agreement with the cold dark matter model with a cosmological constant. This unique measurement is complementary to those obtained with more traditional methods, including clustering analysis. The estimated accuracy at z∼0.1 is competitive with other methods when applied to similar data sets.

THE GALAXY POPULATION IN VOIDS: ARE ALL VOIDS THE SAME?

The influence of under-dense environments on the formation and evolution of galaxies is studied by analysing the photometric properties of ~200 galaxies residing in voids, taken from our SDSS DR10 void catalogue up to z ~0.055. We split void galaxies into two subsamples based on the luminosity density contrast of their host voids: 'sparse void' {\delta}_s = {\delta} < -0.95 and 'populous void' {\delta}_p = {\delta} > -0.87. We find that galaxies in sparse voids are less massive than galaxies in populous voids. The luminosity distribution of galaxies in populous voids follows the same distribution observed across the SDSS survey in the same redshift range. Galaxies in the sparse voids are also bluer suggesting that they may be going through a relatively slow and continuous star formation. Additionally, we find that the luminosity function of galaxies in populous voids is represented with the Schechter function whereas the same does not hold for sparse voids. Our analysis suggests that the properties of a host void plays a significant role in the formation and evolution of the void galaxies and determining the large scale evolution of voids is an important step to understand what processes regulate the evolution of galaxies.

Large-scale peculiar velocities through the galaxy luminosity function at z ~ 0.1

AbstractPeculiar motion introduces systematic variations in the observed luminosity distribution of galaxies. This allows one to constrain the cosmic peculiar velocity field from large galaxy redshift surveys. Using around half a million galaxies from the SDSS Data Release 7 at z ~ 0.1, we demonstrate the applicability of this approach to large datasets and obtain bounds on peculiar velocity moments and σ8, the amplitude of the linear matter power spectrum. Our results are in good agreement with the ΛCDM model and consistent with the previously reported ~ 1% zero-point tilt in the SDSS photometry. Finally, we discuss the prospects of constraining the growth rate of density perturbations by reconstructing the full linear velocity field from the observed galaxy clustering in redshift space.

Distribution of Maximal Luminosity of Galaxies in the Sloan Digital Sky Survey

AbstractExtreme value statistics (EVS) is applied to the pixelized distribution of galaxy luminosities in the Sloan Digital Sky Survey (SDSS). We analyze the DR8 Main Galaxy Sample (MGS) as well as the Luminous Red Galaxy Sample (LRGS). A non-parametric comparison of the EVS of the luminosities with the Fisher-Tippett-Gumbel distribution (limit distribution for independent variables distributed by the Press-Schechter law) indicates a good agreement provided uncertainties arising both from the finite size of the samples and from the sample size distribution are accounted for. This effectively rules out the possibility of having a finite maximum cutoff luminosity.

DISTRIBUTION OF MAXIMAL LUMINOSITY OF GALAXIES IN THE SLOAN DIGITAL SKY SURVEY

Extreme value statistics (EVS) is applied to the distribution of galaxy luminosities in the Sloan Digital Sky Survey (SDSS). We analyze the DR8 Main Galaxy Sample (MGS), as well as the Luminous Red Galaxies (LRG). Maximal luminosities are sampled from batches consisting of elongated pencil beams in the radial direction of sight. For the MGS, results suggest a small and positive tail index $\xi$, effectively ruling out the possibility of having a finite maximum cutoff luminosity, and implying that the luminosity distribution function may decay as a power law at the high luminosity end. Assuming, however, $\xi=0$, a non-parametric comparison of the maximal luminosities with the Fisher-Tippett-Gumbel distribution (limit distribution for variables distributed by the Schechter fit) indicates a good agreement provided uncertainties arising both from the finite batch size and from the batch size distribution are accounted for. For a volume limited sample of LRGs, results show that they can be described as being the extremes of a luminosity distribution with an exponentially decaying tail, provided the uncertainties related to batch-size distribution are taken care of.

The environmental dependence of all the five band luminosities in the volume-limited main galaxy catalogs of the SDSS DR7

In this study, we performed a comparative study among all the five band luminosity distributions of galaxies in groups and isolated, to explore the environmental dependence of u-, g-, r-, i- and z-band luminosities. It is found that for r, i and z bands, isolated galaxies have a higher proportion of faint galaxies and a lower proportion of luminous galaxies than galaxy members of groups, for u-band an opposite trend can be observed. For the volume-limited Mr<−18 and Mr<−19 samples, we noted that the correlation between the u-band luminosity and the environment has two different trends in different luminosity regions. For the g-band, there are also the two different trends in different luminosity regions.

Subaru Weak Lensing Study of Seven Merging Clusters: Distributions of Mass and Baryons

Abstract We present and compare projected distributions of mass, galaxies, and the intracluster medium (ICM) for a sample of merging clusters of galaxies based on a joint weak-lensing, optical photometric, and X-ray analysis. Our sample comprised seven nearby Abell clusters, for which we had conducted systematic, deep imaging observations with Suprime-Cam on the Subaru Telescope. Our seven target clusters, representing various merging stages and conditions, allowed us to investigate in detail the physical interplay between dark matter, ICM, and galaxies associated with cluster formation and evolution. A 1750 and A 1758 are binary systems consisting of two cluster-sized components; A 520, A 754, A 1758N, A 1758S, and A 1914 are on-going cluster mergers; and A 2034 and A 2142 are cold-front clusters. In the binary clusters, the projected mass, optical light, and X-ray distributions are overall similar and regular without significant substructures. On-going and cold-front merging clusters, on the other hand, reveal highly irregular mass distributions. Overall, the mass distribution appears to be similar to the galaxy luminosity distribution, whereas their distributions are quite different from the ICM distribution in a various ways. We also measured for individual targets global cluster parameters, such as the cluster mass, the mass-to-light ratio, and the ICM temperature. A comparison of the ICM and the virial temperatures of merging clusters from X-ray and weak-lensing analyses, respectively, shows that the ICM temperature of on-going and cold-front clusters is significantly higher than the cluster virial temperature by a factor of $\sim 2$. This temperature excess in the ICM could be explained by the effects of merger boosts.

The metallicity dependence of the long-duration gamma-ray burst rate from host galaxy luminosities

We investigate the difference between the host galaxy properties of core-collapse supernovae (CC SNe) and long-duration gamma-ray bursts (LGRBs), and quantify a possible metallicity dependence of the efficiency of producing LGRBs. We use a sample of 16 CC SNe and 16 LGRBs from Fruchter et al. which have similar redshift distributions to eliminate galaxy evolution biases. We make a forward prediction of their host galaxy luminosity distributions from the overall cosmic metallicity distribution of star formation. The latter is based on luminosity functions, star formation rates (SFRs) and luminosity-metallicity (L-Z) relations of galaxies. This appioach is supported by the finding that LGRB hosts follow the L-Z relations of star-forming galaxies. We then compare predictions for metallicity-dependent event efficiencies with the observed host data. We find that ultraviolet-based SFR estimates predict the host distribution of CC SNe perfectly well in a metallicity-independent form. In contrast, LGRB hosts are on average fainter by one magnitude, almost as faint as the Large Magellanic Cloud. Assuming this to be a metallicity effect, the present data are insufficient to discriminate between a sharp cut-off and a soft decrease in efficiency towards higher metallicity. For a sharp cut-off, however, we find a best value for the cut-off metallicity, as reflected in the oxygen abundance, 12 + log (O/H) lim ≃ 8.7 ± 0.3 at 95 per cent confidence including systematic uncertainties, in the calibration of Asplund, Grevesse & Sauval. This value is somewhat lower than the traditionally quoted value for the Sun, but is comparable to the revised solar oxygen abundance. LGRB models that require sharp metallicity cut-offs well below approximately one-half the revised solar metallicity appear to be effectively ruled out, as they would require fainter LGRB hosts than those that are observed. We also discuss the likely implications of the still ongoing metallicity 'calibration debate'.

RASS-SDSS galaxy cluster survey

We explore the mass-to-light ratio in galaxy clusters and its relation to the cluster mass. We study the relations among the optical luminosity ($L_{op}$), the cluster mass ($M_{200}$) and the number of cluster galaxies within $r_{200}$ ($N_{gal}$) in a sample of 217 galaxy clusters with confirmed 3D overdensity. We correct for projection effects, by determining the galaxy surface number density profile in our cluster sample. This is best fitted by a cored King profile in low and intermediate mass systems. The core radius decreases with cluster mass, and, for the highest mass clusters, the profile is better represented by a generalized King profile or a cuspy Navarro, Frenk & White profile. We find a very tight proportionality between $L_{op}$ and $N_{gal}$, which, in turn, links the cluster mass-to-light ratio to the Halo Occupation Distribution $N_{gal}$ vs. $M_{200}$. After correcting for projection effects, the slope of the $L_{op}-M_{200}$ and $N_{gal}-M_{200}$ relations is found to be $0.92\pm0.03$, close, but still significantly less than unity. We show that the non-linearity of these relations cannot be explained by variations of the galaxy luminosity distributions and of the galaxy M/L with the cluster mass. We suggest that the nonlinear relation between number of galaxies and cluster mass reflects an underlying nonlinear relation between number of subhaloes and halo mass.

Where are z= 4 Lyman Break Galaxies? Results from conditional luminosity function models of luminosity-dependent clustering★

Using the conditional luminosity function (CLF) - the luminosity distribution of galaxies in a dark matter halo - as a way to model galaxy statistics, we study how z = 4 Lyman Break Galaxies (LBGs) are distributed in dark matter haloes. For this purpose, we measure luminosity-dependent clustering of LBGs in the Subaru/XMM-Newton Deep Field by separating a sample of 16 920 galaxies to three magnitude bins in i' band between 24.5 and 27.5. Our model fits to data show a possible trend for more-luminous galaxies to appear as satellites in more-massive haloes; the minimum halo mass in which satellites appear is 3.9 +4.1 -3.5 x 10 12 , 6.2 +3.8 -4.9 × 10 12 and 9.6 +7.0 -4.6 x 10 12 M ⊙ (1σ errors) for galaxies with 26.5 < i' < 27.5, 25.5 < i' < 26.5 and 24.5 < i' < 25.5 mag, respectively. The satellite fraction of galaxies at z = 4 in these magnitude bins is 0.13-0.3, 0.09-0.22 and 0.03-0.14, respectively, where the 1σ ranges account for differences coming from two different estimates of the z = 4 LF from the literature. To jointly explain the LF and the large-scale linear bias factor of z = 4 LBGs as a function of rest UV luminosity requires central galaxies to be brighter in UV at z = 4 than present-day galaxies in same dark matter mass haloes. Moreover, UV luminosity of central galaxies in haloes with total mass greater than roughly 10 12 M ⊙ must decrease from z = 4 to today by an amount more than the luminosity change for galaxies in haloes below this mass. This mass-dependent luminosity evolution is preferred at more than 3σ confidence level compared to a pure-luminosity evolution scenario where all galaxies decrease in luminosity by the same amount from z = 4 to today. The scenario preferred by the data is consistent with the 'downsizing' picture of galaxy evolution.

Halo model at its best: constraints on conditional luminosity functions from measured galaxy statistics

(Summary) Using the conditional luminosity function (CLF) -- the luminosity distribution of galaxies in a dark matter halo -- as the fundamental building block, we present an empirical model for the galaxy distribution. The model predictions are compared with the published luminosity function and clustering statistics from Sloan Digital Sky Survey (SDSS) at low redshifts, and galaxy correlation functions from COMBO-17 survey at a redshift of 0.6, DEEP2 survey at a redshift of unity, and Great Observatories Deep Origins Survey (GOODS) at a redshift around 3. The comparison with statistical measurements allows us to constrain certain parameters related to analytical descriptions that describe the relation between a dark matter halo and its central galaxy luminosity, its satellite galaxy luminosity, and the fraction of early- and late-type galaxies of that halo. The single parameter best constrained by clustering measurements is the total satellite galaxy luminosity averaged over the halo mass distribution probed by the galaxy sample. For SDSS, $ =(2.1^{+0.8}_{-0.4}) \times 10^{10}$ h${-2}$ L$_{\sun}$, while for GOODS at $z \sim 3$, $ < 2 \times 10^{11}$ h$^{-2}$ L$_{\sun}$. Quantities such as the fraction of satellite galaxies at a given galaxy luminosity are not strongly constrained with SDSS data. We use our CLFs to establish probability distribution of halo mass in which galaxies of a given luminosity could be found either at halo centers or as satellites. Finally, to help establish further properties of the galaxy distribution, we propose the measurement of cross-clustering between galaxies divided into two distinctly different luminosity bins.

Luminosity segregation in three clusters of galaxies (A119, A2443, A2218)

We use deep wide-field V-band imaging obtained with the Wide Field Camera at the prime focus of the Issac Newton Telescope to study the spatial and luminosity distribution of galaxies in three low redshift (0.04 < z < 0.2) clusters: Abell 119, Abell 2443 and Abell 2218. The absolute magnitude limits probed in these clusters are M V - 5 log h 0.7 = -13.3, -15.4 and -16.7 mag, respectively. The galaxy population, at all luminosities, along the line-of-sight to the clusters can be described by the linear combination of a King profile and a constant surface density of field galaxies. We find that, for these three clusters, the core radius is invariant with intrinsic luminosity of the cluster population to the above limits and thus there is no evidence for luminosity segregation in these clusters. The exception is the brightest galaxies in A2218 which exhibit a more compact spatial distribution. We find that the total projected luminosity distribution (within 1 h -1 0.7 Mpc of the cluster centre) can be well represented by a single Schechter function with moderately flat faint-end slopes: a = -1.22 +0.07 -0.06 (A119), a = -1.11 +0.10 -0.09 (A2443) and α = -1.14 +0.08 -0.07 (A2218). We perform a geometric deprojection of the cluster galaxy population and confirm that no 'statistically significant' evidence of a change in the shape of the luminosity distribution with cluster-centric radius exists. Again, the exception being A2218 which exhibits a core region with a flatter faint-end slope.