The dwarf galaxy population of the Coma cluster to MR=−11: a detailed description

We present the luminosity function and measurements of the scalelengths, colours and radial distribution of dwarf galaxies in the Coma cluster down to R =24. Our survey area is 674 arcmin²; this is the deepest and most detailed survey covering such a large area.
Our measurements agree with those of most previous authors at bright and intermediate magnitudes. The new results are as follows.
(1) Galaxies in the Coma cluster have a luminosity function φ( L )∝ L ^α that is steep (α∼−1.7) for −15< M_R <−11, and is shallower brighter than this. The curvature in the luminosity function at M_R ∼−15 is statistically significant.
(2) The galaxies that contribute most strongly to the luminosity function at −14< M_R <−12 have colours and scalelengths that are consistent with those of local dwarf spheroidal galaxies placed at the distance of Coma.
(3) These galaxies with −14< M_R <−12 have a colour distribution that is very strongly peaked at B − R =1.3. This is suggestive of a substantial degree of homogeneity in their star formation histories and metallicities.
(4) These galaxies with −14< M_R <−12 also appear to be more confined to the cluster core ( r ∼200 kpc) than the brighter galaxies. Alternatively, this observation may be explained in part or whole by the presence of an anomalously high number of background galaxies behind the cluster core. Velocity measurements of these galaxies would distinguish between these two possibilities.     

The galaxy luminosity function in clusters and the field

We present the results from a CCD survey of the B -band luminosity function of nine clusters of galaxies, and compare them to published photographic luminosity functions of nearby poor clusters like Virgo and Fornax, and also to the field luminosity function. We derive a composite luminosity function by taking the weighted mean of all the individual cluster luminosity functions; this composite luminosity function is steep at bright and faint magnitudes and is shallow in-between.
All clusters have luminosity functions consistent with this single composite function. This is true both for rich clusters like Coma and for poor clusters like Virgo.
This same composite function is also individually consistent with the deep field luminosity functions found by Cowie et al. and Ellis et al., and also with the faint end of the Las Campanas Redshift Survey R -band luminosity function, shifted by 1.5 mag. A comparison with the Loveday et al. field luminosity function, which is well determined at the bright end, shows that the composite function, which fits the field data well fainter than M _B=−19, drops too steeply between M _B=−19 and −22 to fit the field data there.     

The density of extremely red objects around high-z radio-loud active galactic nuclei

We present the results of a K -band imaging survey of 40 arcmin² in fields around 14 radio-loud active galactic nuclei (AGN), comprising six radio galaxies and eight quasars, with z >1.5. The survey, which is 80 per cent complete to K <19.2 mag and complemented by R -band imaging, aimed at investigating whether extremely red objects are present in excess around high- z AGN, and to study the environment of z >1.5 radio galaxies and radio-loud quasars. At 18< K <19 mag, the differential galaxy counts in our fields suggest a systematic excess over the general field counts. At K <19.2 mag we find an excess of galaxies with R − K >6 in comparison with the general field. Consistently, we also find that the R − K colour distribution of all the galaxies in the AGN fields is significantly redder than the colour distribution of the field galaxies. On the other hand, the distribution of the R − K colours is indistinguishable from that of galaxies taken from literature fields around radio-loud quasars at 1< z <2. We discuss the main implications of our findings and we compare the possible scenarios that could explain our results.     

Measurement of dwarf galaxies in the rich clusters Abell 665 and 963 at z=0.2

We show that the luminosity functions of the distant rich clusters Abell 665 ( z =0.182) and Abell 963 ( z =0.206) are flat or gradually rising down to M_R =−14, with α≈−1.2±0.4 [here α is the logarithmic slope of the luminosity function: φ( L )∝ L ^α at the faint end]. We do not confirm the steep luminosity functions (α≤−1.8) that have been recently proposed for these two clusters.
Several technical points are discussed in detail. In particular, we compute the corrections to the background contamination caused by gravitational lensing from the cluster dark matter, and show that the corrections are small unless we wish to determine variations in the luminosity function on small scales.
Recent observations have also shown that the field galaxy luminosity function at z ≈0.2 is also shallow between M_B =−19 and M_B =−13. Abell 665 and 963 are two of the richest clusters known at that redshift. We therefore propose that the galaxy luminosity function might be universal in this magnitude range at z =0.2.
The dwarf galaxies that we see in Abell 665 have a colour distribution that is strongly peaked at B − R =1.9. We compute K -corrections based on the spectral energy distributions of local galaxies, and show that these are probably dwarf spheroidal galaxies. This might suggest that the dwarf spheroidal population observed in Virgo already existed at z =0.2.     

The Norma cluster (ACO3627) – II. The near-infrared Ks -band luminosity function

A deep   K _s   -band photometric catalogue of galaxies at the core of the rich, nearby Norma cluster (ACO3627) is presented. The survey covers about  45 × 45 arcmin²  (slightly less than 1/3 Abell radius), which corresponds to  ∼0.8  h ⁻²₇₀ Mpc²  at the adopted distance  ( v _CMB/ H ₀)  of  70  h ⁻¹₇₀ Mpc  of this cluster. The survey is estimated to be complete to a magnitude of     . This extends into the dwarf regime, 6 mag below     . The catalogue contains 390 objects, 235 of which are classified as likely or definite galaxies and 155 as candidate galaxies. The   K _s   -band luminosity function (LF) is constructed from the photometric sample, using a spectroscopic subsample to correct for fore and background contamination. We fit a Schechter function with a characteristic magnitude of     and faint-end slope of  α=−1.26 ± 0.10  to the data. The shape of the LF is similar to those found in previous determinations of the cluster LF, in both optical and near-infrared. The Schechter parameters agree well with those of recent field LFs, suggesting that the shape of both the bright-end and the faint-end slopes are relatively insensitive to environment.     

The galaxy luminosity–size relation and selection biases in the Hubble Ultra Deep Field

We use the Hubble Ultra Deep Field to study the galaxy luminosity–size  ( M – R _e )  distribution. With a careful analysis of selection effects due to both detection completeness and measurement reliability, we identify bias-free regions in the   M – R _e   plane for a series of volume-limited samples. By comparison to a nearby survey also having well-defined selection limits, namely the Millennium Galaxy Catalogue, we present clear evidence for evolution in surface brightness since   z ∼ 0.7  . Specifically, we demonstrate that the mean, rest-frame B -band  〈μ〉 _e   for galaxies in a sample spanning 8 mag in luminosity between   M _B =−22  and −14 mag increases by ∼1.0 mag arcsec⁻² from   z ∼ 0.1  to 0.7. We also highlight the importance of considering surface brightness-dependent measurement biases in addition to incompleteness biases. In particular, the increasing, systematic underestimation of Kron fluxes towards low surface brightnesses may cause diffuse, yet luminous, systems to be mistaken for faint, compact objects.     

Depletion of background galaxies owing to the cluster lens CL0024+1654: U- and R-band observations

We have obtained U - and R -band observations of the depletion of background galaxies resulting from the gravitational lensing of the galaxy cluster CL0024+1654 ( z =0.39). The radial depletion curves show a significant depletion in both bands within a radius of 40–70 arcsec from the cluster centre. This is the first time that depletion is detected in the U band. This gives independent evidence for a break in the slope of the U -band luminosity function at faint magnitudes. The radially averaged R -band depletion curve is broader and deeper than in the U band. The differences can be attributed to the wavelength dependence of the slope of the luminosity function and to the different redshift distribution of the objects probed in the two bands. We estimate the Einstein radius, r _E, of a singular isothermal sphere lens model using maximum-likelihood analysis. Adopting a slope of the number counts of α =0.2 and using the background density found beyond r =150 arcsec, we find r _E=17±3 and 25±3 arcsec in the U and R bands, respectively. When combined with the redshift of the single background galaxy at z =1.675 seen as four giant arcs around 30 arcsec from the cluster centre, these values indicate a median redshift in the range 〈 z _S〉≈0.7 to 1.1 for the U _AB≥24 mag and R _AB≥24 mag populations.     

The surface brightness and colour–magnitude relations for Fornax cluster galaxies

We present BVI photometry of 190 galaxies in the central 4 ×3 deg² region of the Fornax cluster observed with the Michigan Curtis Schmidt Telescope. Results from the Fornax Cluster Spectroscopic Survey (FCSS) and the Flair-II Fornax Surveys have been used to confirm the membership status of galaxies in the Fornax Cluster Catalogue (FCC). In our catalogue of 213 member galaxies, 92 (43 per cent) have confirmed radial velocities.
In this paper, we investigate the surface brightness–magnitude relation for Fornax cluster galaxies. Particular attention is given to the sample of cluster dwarfs and the newly discovered ultracompact dwarf galaxies (UCDs) from the FCSS. We examine the reliability of the surface brightness–magnitude relation as a method for determining cluster membership and find that at surface brightnesses fainter than 22 mag arcsec⁻², it fails in its ability to distinguish between cluster members and barely resolved background galaxies. Cluster members exhibit a strong surface brightness–magnitude relation. Both elliptical (E) galaxies and dwarf elliptical (dE) galaxies increase in surface brightness as luminosity decreases. The UCDs lie off the locus of the relation.
  B − V   and   V − I   colours are determined for a sample of 113 cluster galaxies and the colour–magnitude relation is explored for each morphological type. The UCDs lie off the locus of the colour–magnitude relation. Their mean   V − I   colours (∼1.09) are similar to those of globular clusters associated with NGC 1399. The location of the UCDs on both surface brightness and colour–magnitude plots supports the 'galaxy threshing' model for infalling nucleated dwarf elliptical (dE, N) galaxies.     

The K-band luminosity function of nearby field galaxies

We present a measurement of the K -band luminosity function (LF) of field galaxies obtained from near-infrared imaging of a sample of 345 galaxies selected from the Stromlo-APM Redshift Survey. The LF is reasonably well fitted over the 10-mag range −26 M _K −16 by a Schechter function with parameters α =−1.16±0.19, M *=−23.58±0.42 and φ *=0.012±0.008 Mpc⁻³, assuming a Hubble constant of H ₀=100 km s⁻¹ Mpc⁻¹. We have also estimated the LF for two subsets of galaxies subdivided by the equivalent width of the H α emission line at EW(H α )=10 Å. There is no significant difference in LF shape between the two samples, although there is a hint (∼1 σ significance) that emission-line galaxies (ELGs) have M * roughly 1 mag fainter than non-ELGs. Contrary to the optical LF, there is no difference in faint-end slope α between the two samples.     

Evolution of the luminosity function and colours of galaxies in a Λ cold dark matter universe

The luminosity function of galaxies is derived from a cosmological hydrodynamic simulation of a Λ cold dark matter universe with the aid of a stellar population synthesis model. At     , the resulting B -band luminosity function has a flat faint-end slope of     with the characteristic luminosity and the normalization in fair agreement with observations, while the dark matter halo mass function is steep with a slope of     . The colour distribution of galaxies also agrees well with local observations. We also discuss the evolution of the luminosity function, and the colour distribution of galaxies from     to 5. A large evolution of the characteristic mass in the stellar mass function as a result of number evolution is compensated by luminosity evolution; the characteristic luminosity increases only by 0.8 mag from     to 2, and then declines towards higher redshift, while the B -band luminosity density continues to increase from     to 5 (but only slowly at     .     

The LBDS Hercules sample of mJy radio sources at 1.4 GHz – I. Multicolour photometry

The results are presented of an extensive programme of optical and infrared imaging of radio sources in a complete subsample of the Leiden–Berkeley Deep Survey. The LBDS Hercules sample consists of 72 sources observed at 1.4 GHz, with flux densities S _1.41.0 mJy, in a 1.2 deg² region of Hercules. This sample is almost completely identified in the g , r , i and K bands, with some additional data available at J and H . The magnitude distributions peak at r ≃22 mag, K ≃16 mag and extend down to r ≃26 mag, K ≃21 mag. The K -band magnitude distributions for the radio galaxies and quasars are compared with those of other radio surveys. At S _1.4 GHz≲1 Jy, the K -band distribution does not change significantly with radio flux density. The sources span a broad range of colours, with several being extremely red ( r − K ≳6). Though small, this is the most optically complete sample of mJy radio sources available at 1.4 GHz, and is ideally suited for studying the evolution of the radio luminosity function out to high redshifts.     

The cluster environments of the z ∼ 1 3CR radio galaxies

An analysis of the environments around a sample of 28 3CR radio galaxies with redshifts 0.6< z <1.8 is presented, based primarily upon K -band images down to K ∼20 taken using the UK Infrared Telescope (UKIRT). A net overdensity of K -band galaxies is found in the fields of the radio galaxies, with the mean excess counts being comparable to that expected for clusters of Abell Class 0 richness. A sharp peak is found in the angular cross-correlation amplitude centred on the radio galaxies that, for reasonable assumptions about the luminosity function of the galaxies, corresponds to a spatial cross-correlation amplitude between those determined for low-redshift Abell Class 0 and 1 clusters.
These data are complemented by J -band images also from UKIRT, and by optical images from the Hubble Space Telescope . The fields of the lower redshift ( z ≲0.9) radio galaxies in the sample generally show well-defined near-infrared colour–magnitude relations with little scatter, indicating a significant number of galaxies at the redshift of the radio galaxy; the relations involving colours at shorter wavelengths than the 4000 Å break show considerably greater scatter, suggesting that many of the cluster galaxies have low levels of recent or on-going star formation. At higher redshifts the colour–magnitude sequences are less prominent owing to the increased field galaxy contribution at faint magnitudes, but there is a statistical excess of galaxies with the very red infrared colours ( J − K ≳1.75) expected of old cluster galaxies at these redshifts.
Although these results are appropriate for the mean of all of the radio galaxy fields, there exist large field-to-field variations in the richness of the environments. Many, but certainly not all, powerful z ∼1 radio galaxies lie in (proto)cluster environments.     

The shapes of galaxies in the Sloan Digital Sky Survey

We determine the underlying shapes of spiral and elliptical galaxies in the Sloan Digital Sky Survey Data Release 6 (SDSS DR6) from the observed distribution of projected galaxy shapes, taking into account the effects of dust extinction and reddening. We assume that the underlying shapes of spirals and ellipticals are well approximated by triaxial ellipsoids. The elliptical galaxy data are consistent with oblate spheroids, with a correlation between luminosity and ellipticity: the mean values of minor to middle axis ratios are 0.41 ± 0.03 for   M _r ≈−18  ellipticals and 0.76 ± 0.04 for   M _r ≈−22.5  ellipticals. Ellipticals show almost no dependence of axial ratio on galaxy colour, implying a negligible dust optical depth.
There is a strong variation of spiral galaxy shapes with colour indicating the presence of dust. The intrinsic shapes of spiral galaxies in the SDSS DR6 are consistent with flat discs with a mean and dispersion of thickness to diameter ratio of (21 ± 2) per cent, and a face-on ellipticity, e , of  ln( e ) =−2.33 ± 0.79  . Not including the effects of dust in the model leads to discs that are systematically rounder by up to 60 per cent. More luminous spiral galaxies tend to have thicker and rounder discs than lower luminosity spirals. Both elliptical and spiral galaxies tend to be rounder for larger galaxies.
The marginalized value of the edge-on r -band dust extinction E ₀ in spiral galaxies is   E ₀≃ 0.45  mag for galaxies of median colours, increasing to   E ₀= 1  mag for   g − r > 0.9  and   E ₀= 1.9  for the luminous and most compact galaxies, with half-light radii  <2  h ⁻¹ kpc  .     

Luminosity and surface brightness distribution of K-band galaxies from the UKIDSS Large Area Survey

We present luminosity and surface-brightness distributions of 40 111 galaxies with K -band photometry from the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS), Data Release 3 and optical photometry from Data Release 5 of the Sloan Digital Sky Survey (SDSS). Various features and limitations of the new UKIDSS data are examined, such as a problem affecting Petrosian magnitudes of extended sources. Selection limits in K - and r -band magnitude, K -band surface brightness and K -band radius are included explicitly in the  1/ V _max  estimate of the space density and luminosity function. The bivariate brightness distribution in K -band absolute magnitude and surface brightness is presented and found to display a clear luminosity–surface brightness correlation that flattens at high luminosity and broadens at low luminosity, consistent with similar analyses at optical wavelengths. Best-fitting Schechter function parameters for the K -band luminosity function are found to be   M *− 5 log  h =−23.19 ± 0.04, α=−0.81 ± 0.04  and  φ*= (0.0166 ± 0.0008)  h ³ Mpc⁻³  , although the Schechter function provides a poor fit to the data at high and low luminosity, while the luminosity density in the K band is found to be   j = (6.305 ± 0.067) × 10⁸ L_⊙  h  Mpc⁻³  . However, we caution that there are various known sources of incompleteness and uncertainty in our results. Using mass-to-light ratios determined from the optical colours, we estimate the stellar mass function, finding good agreement with previous results. Possible improvements are discussed that could be implemented when extending this analysis to the full LAS.     

Evolution of the u-band luminosity function from redshift 1.2 to 0

We produce and analyse u -band (  λ≈ 355  nm) luminosity functions (LFs) for the red and blue populations of galaxies using data from the Sloan Digital Sky Survey (SDSS) u -band Galaxy Survey ( u GS) and Deep Evolutionary Exploratory Probe 2 (DEEP2) survey. From a spectroscopic sample of 41 575 SDSS u GS galaxies and 24 561 DEEP2 galaxies, we produce colour magnitude diagrams and make use of the colour bimodality of galaxies to separate red and blue populations. LFs for eight redshift slices in the range  0.01 < z < 1.2  are determined using the  1/ V _max  method and fitted with Schechter functions showing that there is significant evolution in   M *  , with a brightening of 1.4 mag for the combined population. The integration of the Schechter functions yields the evolution in the u -band luminosity density (LD) out to   z ∼ 1  . By parametrizing the evolution as  ρ∝ (1 + z )^β  , we find that  β= 1.36 ± 0.2  for the combined populations and  β= 2.09 ± 0.2  for the blue population. By removing the contribution of the old stellar population to the u -band LD and correcting for dust attenuation, we estimate the evolution in the star formation rate (SFR) of the Universe to be  β_SFR= 2.5 ± 0.3  . Discrepancies between our result and higher evolution rates measured using the infrared and far-UV can be reconciled by considering possibilities such as an underestimated dust correction at high redshifts or evolution in the stellar initial mass function.     

A comparative HST imaging study of the host galaxies of radio-quiet quasars, radio-loud quasars and radio galaxies – I

We present the first results from a major HST WFPC2 imaging study aimed at providing the first statistically meaningful comparison of the morphologies, luminosities, scalelengths and colours of the host galaxies of radio-quiet quasars, radio-loud quasars and radio galaxies. We describe the design of this study and present the images that have been obtained for the first half of our 33-source sample. We find that the hosts of all three classes of luminous AGN are massive elliptical galaxies, with scalelengths ≃10 kpc, and R − K colours consistent with mature stellar populations. Most importantly, this is first unambiguous evidence that, just like radio-loud quasars, essentially all radio-quiet quasars brighter than M _R =−24 reside in massive ellipticals. This result removes the possibility that radio 'loudness' is directly linked to host galaxy morphology, but is however in excellent accord with the black hole/spheroid mass correlation recently highlighted by Magorrian et al. We apply the relations given by Magorrian et al. to infer the expected Eddington luminosity of the putative black hole at the centre of each of the spheroidal host galaxies we have uncovered. Comparison with the actual nuclear R -band luminosities suggests that the black holes in most of these galaxies are radiating at a few per cent of the Eddington luminosity; the brightest host galaxies in our low- z sample are capable of hosting quasars with M _R ≃− 28, comparable to the most luminous quasars at z ≃3. Finally, we discuss our host-derived black hole masses in the context of the radio luminosity:black hole mass correlation recently uncovered for nearby galaxies by Franceschini et al., and consider the resulting implications for the physical origin of radio loudness.     

Globular cluster systems in nearby dwarf galaxies – I. HST/ACS observations and dynamical properties of globular clusters at low environmental density

We investigate the old globular cluster (GC) population of 68 faint  ( M _V > −16 mag)  dwarf galaxies located in the halo regions of nearby (≲12 Mpc) loose galaxy groups and in the field environment based on archival Hubble Space Telescope ( HST )/Advanced Camera for Surveys (ACS) images in F606W and F814W filters. The combined colour distribution of 175 GC candidates peaks at  ( V − I ) = 0.96 ± 0.07 mag  and the GC luminosity function turnover for the entire sample is found at   M _{V ,TO}=−7.6 ± 0.11 mag  , similar to the old metal-poor Large Magellanic Cloud (LMC) GC population. Our data reveal a tentative trend of   M _{V ,TO}  becoming fainter from late- to early-type galaxies. The luminosity and colour distributions of GCs in dIrrs show a lack of faint blue GCs (bGCs). Our analysis reveals that this might reflect a relatively younger GC system than typically found in luminous early-type galaxies. If verified by spectroscopy, this would suggest a later formation epoch of the first metal-poor star clusters in dwarf galaxies. We find several bright (massive) GCs which reside in the nuclear regions of their host galaxies. These nuclear clusters have similar luminosities and structural parameters as the peculiar Galactic clusters suspected of being the remnant nuclei of accreted dwarf galaxies, such as M54 and ωCen. Except for these nuclear clusters, the distribution of GCs in dIrrs in the half-light radius versus cluster mass plane is very similar to that of Galactic young halo clusters, which suggests comparable formation and dynamical evolution histories. A comparison with theoretical models of cluster disruption indicates that GCs in low-mass galaxies evolve dynamically as self-gravitating systems in a benign tidal environment.     

Near-infrared bulge–disc correlations of lenticular galaxies

We consider the luminosity and environmental dependence of structural parameters of lenticular galaxies in the near-infrared K band. Using a 2D galaxy image decomposition technique, we extract bulge and disc structural parameters for a sample of 36 lenticular galaxies observed by us in the K band. By combining data from the literature for field and cluster lenticulars with our data, we study correlations between parameters that characterize the bulge and the disc as a function of luminosity and environment. We find that scaling relations such as the Kormendy relation, photometric plane and other correlations involving bulge and disc parameters show a luminosity dependence. This dependence can be explained in terms of galaxy formation models in which faint lenticulars  ( M _T > −24.5)  formed via secular formation processes that likely formed the pseudo-bulges of late-type disc galaxies, while brighter lenticulars  ( M _T < −24.5)  formed through a different formation mechanism most likely involving major mergers. On probing variations in lenticular properties as a function of environment, we find that faint cluster lenticulars show systematic differences with respect to faint field lenticulars. These differences support the idea that the bulge and disc components fade after the galaxy falls into a cluster, while simultaneously undergoing a transformation from spiral to lenticular morphologies.     

The galaxy luminosity function from MR=−25 to MR=−9

Redshift surveys such as the Sloan Digital Sky Survey (SDSS) have given a very precise measurement of the galaxy luminosity function down to about   M_R =−17 (≈ M_B =−16)  . Fainter absolute magnitudes cannot be probed because of the flux limit required for spectroscopy. Wide-field surveys of nearby groups using mosaic CCDs on large telescopes are able to reach much fainter absolute magnitudes, about   M_R =−10  . These diffuse, spiral-rich groups are thought to be typical environments for galaxies, so their luminosity functions should be the same as the field luminosity function. The luminosity function of the groups at the bright end  ( M_R < −17)  is limited by Poisson statistics and is far less precise than that derived from redshift surveys. Here we combine the results of the SDSS and the surveys of nearby groups, and we supplement the results with studies of Local Group galaxies in order to determine the galaxy luminosity function over the entire range  −25 < M_R < −9  . The average logarithmic slope of the field luminosity function between   M_R =−19  and   M_R =−9  is  α=−1.26  , although a single power law is a poor fit to the data over the entire magnitude range. We also determine the luminosity function of galaxy clusters and demonstrate that it is different from the field luminosity function at a high level of significance; there are many more dwarf galaxies in clusters than in the field, due to a rise in the cluster luminosity function of  α∼−1.6  between   M_R =−17  and   M_R =−14  .     

Luminosity distributions within rich clusters — II. Demonstration and verification via simulation

We present detailed simulations of long-exposure CCD images. The simulations are used to explore the validity of the statistical method for reconstructing the luminosity distribution of galaxies within a rich cluster, i.e., by the subtraction of field number-counts from those of a sight-line through the cluster. In particular, we use the simulations to establish the reliability of our observational data to be presented in Paper III. Based on our intended CCD field-of-view (6.5 × 6.5 arcmin²) and a 1σ detection limit of 26 mag arcsec⁻², we conclude that the luminosity distribution can be robustly determined over a wide range of absolute magnitude (−23 <  M _R  < −16) provided: (a) the cluster has an Abell richness 1.5 or greater; (b) the redshift of the cluster lies in the range 0.1 <  z  < 0.3; (c) the seeing is better than FWHM 1.25 arcsec, and (d) the photometric zero-points are accurate to within Δ m  = ± 0.12. If these conditions are not met, then the recovered luminosity distribution is unreliable. Finally, although the method clearly has limitations, within these limitations the technique represents an extremely promising probe of galaxy evolution and environmental dependences.