Luminous early-type field galaxies at z∼0.4– I. Observations and redshift catalogue of 581 galaxies

We have compiled a sample of ∼ 9600 bright, i ≤18.95 , red, b _J− r >2 , candidate galaxies in an area of 220 deg². These are luminous, L > L * , field early-type galaxies with redshifts 0.3≲ z ≲0.6 . We present a redshift catalogue of a subsample of 581 targets. The galaxies were selected according to their broad-band b _J ri colours from United Kingdom Schmidt Telescope plates, and have a surface density on the sky of only ∼ 50 deg⁻². Such luminous field galaxies are virtually absent from published redshift surveys and the catalogue provides a large sample of the most luminous normal galaxies, at cosmological distances. The statistical properties of the galaxy spectra, including absorption-line and emission-line measures, are presented and a composite spectrum constructed. The nature of the sample, combined with the relatively bright apparent magnitudes, makes the galaxies suitable targets for several key investigations in galaxy evolution and cosmology.     

The 2dF Galaxy Redshift Survey: luminosity functions by density environment and galaxy type

We use the 2dF Galaxy Redshift Survey to measure the dependence of the b _J-band galaxy luminosity function on large-scale environment, defined by density contrast in spheres of radius  8  h ⁻¹ Mpc  , and on spectral type, determined from principal component analysis. We find that the galaxy populations at both extremes of density differ significantly from that at the mean density. The population in voids is dominated by late types and shows, relative to the mean, a deficit of galaxies that becomes increasingly pronounced at magnitudes brighter than   M _{b J}−5log₁₀ h ≲−18.5  . In contrast, cluster regions have a relative excess of very bright early-type galaxies with   M _{b J}−5log₁₀ h ≲−21  . Differences in the mid- to faint-end population between environments are significant: at   M _{b J}−5log₁₀ h =−18  early- and late-type cluster galaxies show comparable abundances, whereas in voids the late types dominate by almost an order of magnitude. We find that the luminosity functions measured in all density environments, from voids to clusters, can be approximated by Schechter functions with parameters that vary smoothly with local density, but in a fashion that differs strikingly for early- and late-type galaxies. These observed variations, combined with our finding that the faint-end slope of the overall luminosity function depends at most weakly on density environment, may prove to be a significant challenge for models of galaxy formation.     

The 2dF Galaxy Redshift Survey: galaxy luminosity functions per spectral type

We calculate the optical b _J luminosity function (LF) of the 2dF Galaxy Redshift Survey (2dFGRS) for different subsets defined by their spectral properties. These spectrally selected subsets are defined using a new parameter, η , which is a linear combination of the first two projections derived from a Principal Component Analysis. This parameter η identifies the average emission- and absorption-line strength in the galaxy rest frame spectrum, and hence is a useful indicator of the present star formation. We use a total of 75 000 galaxies in our calculations, chosen from a sample of high signal-to-noise ratio, low-redshift galaxies observed before 2001 January. We find that there is a systematic steepening of the faint-end slope ( α ) as one moves from passive  ( α =-0.54)  to active  ( α =-1.50)  star-forming galaxies, and that there is also a corresponding faintening of the rest frame characteristic magnitude   M *-5 log₁₀( h )  (from −19.6 to −19.2). We also show that the Schechter function provides a poor fit to the quiescent (Type 1) LF for very faint galaxies  [ M _{b J}-5 log₁₀( h )  fainter than −16.0], perhaps suggesting the presence of a significant dwarf population. The LFs presented here give a precise confirmation of the trends seen previously in a much smaller preliminary 2dFGRS sample, and in other surveys. We also present a new procedure for determining self-consistent k -corrections, and investigate possible fibre-aperture biases.     

Globular cluster systems in low-luminosity early-type galaxies near the Fornax cluster centre

We present a photometric study of the globular cluster systems (GCSs) of the Fornax cluster galaxies NGC 1374, NGC 1379 and NGC 1387. The data consist of images from the wide-field MOSAIC imager of the Cerro Tololo Inter-American Observatory (CTIO) 4-m telescope, obtained with Washington C and Kron–Cousins R filters. The images cover a field of  36 × 36 arcmin²  , corresponding to  200 × 200 kpc²  at the Fornax distance. Two of the galaxies, NGC 1374 and NGC 1379, are low-luminosity ellipticals while NGC 1387 is a low-luminosity lenticular. Their cluster systems are still embedded in the cluster system of NGC 1399. Therefore, the use of a large field is crucial and some differences to previous work can be explained by this. The colour distributions of all GCSs are bimodal. NGC 1387 presents a particularly distinct separation between red and blue clusters and an overproportionally large population of red clusters. The radial distribution is different for blue and red clusters, red clusters being more concentrated towards the respective galaxies. The different colour and radial distributions point to the existence of two globular cluster subpopulations in these galaxies. Specific frequencies are in the range   S_N = 1.4–2.4  , smaller than the typical values for elliptical galaxies. These galaxies might have suffered tidal stripping of blue globular clusters by NGC 1399.     

Spin vector orientation of galaxies in the region 15h 48m≤α(2000) ≤ 19h 28m, −68°≤δ(2000) ≤−62°

We present an analysis of the orientations of 1433 galaxies found in the region  15^h 48^m≤α(2000) ≤ 19^h 28^m, −68°≤δ(2000) ≤−62°  . In this region we investigated three Abell clusters (S0794, S0797, S0805) of richness Class 0 and the Triangulum Australis cluster. Our aim is to examine non-random effects in galaxy orientations in clusters. In addition, we classified the investigated galaxies into subsamples on the basis of their axial ratio, major diameter and morphology. The spin vector orientations of total galaxies in the investigated region is found to be random. No preferred orientation is found in the clusters. We could not note any morphological dependence of the galaxy orientations in our samples. No preferred orientations can be seen for the spiral galaxies. The morphologically unidentified galaxies, galaxies having major diameters of <47 arcsec, and the nearly edge-on galaxies  ( b / a < 0.5, 0.4 < b / a ≤ 0.5)  show anisotropy: spin vectors of galaxies tend to be oriented perpendicular to the Local Supercluster plane and spin vector projections tend to point radially with respect to the Virgo cluster centre.     

A top-heavy stellar initial mass function in starbursts as an explanation for the high mass-to-light ratios of ultra-compact dwarf galaxies

It has been recently shown that the dynamical V -band mass-to-light ratios of compact stellar systems with masses from 10⁶ to  10⁸ M_⊙  are not consistent with the predictions from simple stellar population models. Top-heavy stellar initial mass functions (IMFs) in these so-called ultra-compact dwarf galaxies (UCDs) offer an attractive explanation for this finding, the stellar remnants and retained stellar envelopes providing the unseen mass. We therefore construct a model which quantifies by how much the IMFs of UCDs would have to deviate in the intermediate- and high-mass range from the canonical IMF in order to account for the enhanced   M / L_V   ratio of the UCDs. The deduced high-mass IMF in the UCDs depends on the age of the UCDs and the number of faint products of stellar evolution retained by them. Assuming that the IMF in the UCDs is a three-part power law equal to the canonical IMF in the low-mass range and taking 20 per cent as a plausible choice for the fraction of the remnants of high-mass stars retained by UCDs, the model suggests the exponent of the high-mass IMF to be ≈1.6 if the UCDs are  13 Gyr  old (i.e. almost as old as the Universe) or ≈1.0 if the UCDs are  7 Gyr  old, in contrast to 2.3 for the Salpeter–Massey IMF. If the IMF was as top heavy as suggested here, the stability of the UCDs might have been threatened by heavy mass loss induced by the radiation and evolution of massive stars. The central densities of UCDs must have been in the range  10⁶ to 10⁷ M_⊙ pc⁻³  when they formed with star formation rates of  10 to 100 M_⊙ yr⁻¹  .     

The early-type galaxies NGC 1407 and NGC 1400 – II. Star formation and chemical evolutionary history

We present a possible star formation and chemical evolutionary history for two early-type galaxies NGC 1407 and NGC 1400. They are the two brightest galaxies of the NGC 1407 (or Eridanus-A) group, one of the 60 groups studied as part of the Group Evolution Multi-wavelength Study.
Our analysis is based on new high signal-to-noise ratio spatially resolved integrated spectra obtained at the ESO 3.6-m telescope, out to ∼0.6 (NGC 1407) and ∼1.3 (NGC 1400) effective radii. Using Lick/IDS indices, we estimate luminosity-weighted ages, metallicities and α-element abundance ratios. Colour radial distributions from HST /ACS and Subaru Suprime-Cam multiband wide-field imaging are compared to colours predicted from spectroscopically determined ages and metallicities using single stellar population (SSP) models. The galaxies formed over half of their mass in a single short-lived burst of star formation  (≥100 M_⊙ yr⁻¹)  at redshift z ≥ 5. This likely involved an outside–in mechanism with supernova-driven galactic winds, as suggested by the flatness of the α-element radial profiles and the strong negative metallicity gradients. Our results support the predictions of the revised version of the monolithic collapse model for galaxy formation and evolution. We speculate that, since formation, the galaxies have evolved quiescently and that we are witnessing the first infall of NGC 1400 in the group.     

The 6dF Galaxy Survey: final redshift release (DR3) and southern large-scale structures

We report the final redshift release of the 6dF Galaxy Survey (6dFGS), a combined redshift and peculiar velocity survey over the southern sky  (| b | > 10°)  . Its 136 304 spectra have yielded 110 256 new extragalactic redshifts and a new catalogue of 125 071 galaxies making near-complete samples with  ( K , H , J , r _F, b _J) ≤ (12.65, 12.95, 13.75, 15.60, 16.75)  . The median redshift of the survey is 0.053. Survey data, including images, spectra, photometry and redshifts, are available through an online data base. We describe changes to the information in the data base since earlier interim data releases. Future releases will include velocity dispersions, distances and peculiar velocities for the brightest early-type galaxies, comprising about 10 per cent of the sample. Here we provide redshift maps of the southern local Universe with   z ≤ 0.1  , showing nearby large-scale structures in hitherto unseen detail. A number of regions known previously to have a paucity of galaxies are confirmed as significantly underdense regions. The URL of the 6dFGS data base is http://www-wfau.roe.ac.uk/6dFGS .     

Dry mergers: a crucial test for galaxy formation

We investigate the role that dry mergers play in the build-up of massive galaxies within the cold dark matter paradigm. Implementing an empirical shut-off mass scale for star formation, we find a nearly constant dry merger rate of  ∼6 × 10⁻⁵ Mpc⁻³ Gyr⁻¹  at   z ≤ 1  and a steep decline at larger z . Less than half of these mergers are between two galaxies that are morphologically classified as early-types, and the other half is mostly between an early- and late-type galaxy. Latter are prime candidates for the origin of tidal features around red elliptical galaxies. The introduction of a transition mass scale for star formation has a strong impact on the evolution of galaxies, allowing them to grow above a characteristic mass scale of   M _{*, c} ∼ 6.3 × 10¹⁰ M_⊙  by mergers only. As a consequence of this transition, we find that around   M _{*, c}   , the fraction of 1:1 mergers is enhanced with respect to unequal mass major mergers. This suggests that it is possible to detect the existence of a transition mass scale by measuring the relative contribution of equal mass mergers to unequal mass mergers as a function of galaxy mass. The evolution of the high-mass end of the luminosity function is mainly driven by dry mergers at low z . We however find that only 10–20 per cent of galaxies more massive than   M _{*, c}   experience dry major mergers within their last Gyr at any given redshift   z ≤ 1  .     

Exploring disc galaxy dynamics using integral field unit data

In order to test the basic equations believed to dictate the dynamics of disc galaxies, we present and analyse deep two-dimensional spectral data obtained using the PPAK integral field unit for the early-type spiral systems NGC 2273, NGC 2985, NGC 3898 and NGC 5533. We describe the care needed to obtain and process such data to a point where reliable kinematic measurements can be obtained from these observations, and a new more optimal method for deriving the rotational motion and velocity dispersions in such disc systems. The data from NGC 2273 and NGC 2985 show systematic variations in velocity dispersion with azimuth, as one would expect if the shapes of their velocity ellipsoids are significantly anisotropic, while the hotter discs in NGC 3898 and NGC 5533 appear to have fairly isotropic velocity dispersions. Correcting the rotational motion for asymmetric drift using the derived velocity dispersions reproduces the rotation curves inferred from emission lines reasonably well, implying that this correction is quite robust, and that the use of the asymmetric drift equation is valid. NGC 2985 is sufficiently close to face on for the data, combined with the asymmetric drift equation, to determine all three components of the velocity ellipsoid. The principal axes of this velocity ellipsoid are found to be in the ratio  σ _z : σ_φ : σ _R ≈ 0.7 : 0.7 : 1  , which shows unequivocally that this disc distribution function respects a third integral of motion. The ratio is also consistent with the predictions of epicyclic theory, giving some confidence in the application of this approximation to even fairly early-type disc galaxies.     

Massive dark matter haloes around bright isolated galaxies in the 2dFGRS

We identify a large sample of isolated bright galaxies and their fainter satellites in the 2dF Galaxy Redshift Survey (2dFGRS). We analyse the dynamics of ensembles of these galaxies selected according to luminosity and morphological type by stacking the positions of their satellites and estimating the velocity dispersion of the combined set. We test our methodology using realistic mock catalogues constructed from cosmological simulations. The method returns an unbiased estimate of the velocity dispersion provided that the isolation criterion is strict enough to avoid contamination and that the scatter in halo mass at fixed primary luminosity is small. Using a maximum likelihood estimator that accounts for interlopers, we determine the satellite velocity dispersion within a projected radius of 175  h ⁻¹ kpc. The dispersion increases with the luminosity of the primary and is larger for elliptical galaxies than for spiral galaxies of similar b _J luminosity. Calibrating the mass–velocity dispersion relation using our mock catalogues, we find a dynamical mass within 175  h ⁻¹ kpc of     for elliptical galaxies and     for spiral galaxies. Finally, we compare our results with recent studies and investigate their limitations using our mock catalogues.     

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.     

Galaxy groups at 0.3 ≤z≤ 0.55 – II. Evolution to z∼ 0

We compare deep Magellan spectroscopy of 26 groups at  0.3 ≤ z ≤ 0.55  , selected from the Canadian Network for Observational Cosmology 2 field survey, with a large sample of nearby groups from the 2PIGG catalogue. We find that the fraction of group galaxies with significant [O  ii ]λ3727 emission (≥5 Å) increases strongly with redshift, from ∼29 per cent in 2dFGRS to ∼58 per cent in CNOC2, for all galaxies brighter than  ∼ M _*+ 1.75  . This trend is parallel to the evolution of field galaxies, where the equivalent fraction of emission-line galaxies increases from ∼53 to ∼75 per cent. The fraction of emission-line galaxies in groups is lower than in the field, across the full redshift range, indicating that the history of star formation in groups is influenced by their environment. We show that the evolution required to explain the data is inconsistent with a quiescent model of galaxy evolution; instead, discrete events in which galaxies cease forming stars (truncation events) are required. We constrain the probability of truncation ( P _trunc) and find that a high value is required in a simple evolutionary scenario neglecting galaxy mergers  ( P _trunc≳ 0.3 Gyr⁻¹)  . However, without assuming significant density evolution, P _trunc is not required to be larger in groups than in the field, suggesting that the environmental dependence of star formation was embedded at redshifts   z ≳ 0.45  .     

Galaxy groups at 0.3 ≤z≤ 0.55 – I. Group properties

The evolution of galaxies in groups may have important implications for the evolution of the star formation history of the Universe, since many processes which operate in groups may suppress star formation and the fraction of galaxies in bound groups grows rapidly between   z = 1  and the present day. In this paper, we present an investigation of the properties of galaxies in galaxy groups at intermediate redshift  ( z ∼ 0.4)  . The groups were selected from the Canadian Network for Observational Cosmology Redshift Survey (CNOC2) redshift survey as described by Carlberg et al., with further spectroscopic follow-up undertaken at the Magellan telescope in order to improve the completeness and depth of the sample. We present the data for the individual groups, and find no clear trend in the fraction of passive galaxies with group velocity dispersion and group concentration. We stack the galaxy groups in order to compare the properties of group galaxies with those of field galaxies at the same redshift. The groups contain a larger fraction of passive galaxies than the field, this trend being particularly clear for galaxies brighter than   M _{B J} < −20  in the higher velocity dispersion groups. In addition, we see evidence for an excess of bright passive galaxies in the groups relative to the field. In contrast, the luminosity functions of the star-forming galaxies in the groups and the field are consistent. These trends are qualitatively consistent with the differences between group and field galaxies seen in the local Universe.     

Detection of candidate Lyα-emitting galaxies at z=5.7

We report the detection of seven candidate Lyα-emitting galaxies which have been found during the preliminary phase of the 'Calar Alto Deep Imaging Survey' (CADIS). They are selected from 147 emission-line galaxies detected in a field of 60 arcmin² with a Fabry–Pérot interferometer, following the exclusion of 140 sources identified as foreground galaxies by a combination of broad- and narrow-band filters. Although no conclusive spectroscopic confirmation is yet available, we expect from an analysis of possible residual contamination by foreground objects that two or more of the candidates will turn out to be genuine Lyα-emitting primeval galaxies at a redshift of z =5.7. For a flat universe ( q ₀=0.5) this would be in perfect agreement with refined predictions of the abundance of primeval galaxies and various recent results on the space density of young galaxies at z ≤4.5.     

Scaling relations of the colour-detected cluster RzCS 052 at z= 1.016 and some other high-redshift clusters

This paper investigates the possibility that ultra-compact dwarf (UCD) galaxies in the Fornax cluster are formed by the threshing of nucleated, early-type dwarf galaxies (hereafter dwarf galaxies).
Similar to the results of Côté et al. for the Virgo cluster, we show that the Fornax cluster observations are consistent with a single population in which all dwarfs are nucleated, with a ratio of nuclear to total magnitude that varies slowly with magnitude. Importantly, the magnitude distribution of the UCD population is similar to that of the dwarf nuclei in the Fornax cluster.
The joint population of UCDs and the dwarfs from which they may originate is modelled and shown to be consistent with a Navarro, Frenk & White (NFW) profile with a characteristic radius of 5 kpc. Furthermore, a steady-state dynamical model reproduces the known mass profile of Fornax. However, there are a number of peculiarities in the velocity dispersion data that remain unexplained.
The simplest possible threshing model is tested, in which dwarf galaxies move on orbits in a static cluster potential and are threshed if they pass within a radius at which the tidal force from the cluster exceeds the internal gravity at the core of their dark matter halo. This fails to reproduce the observed fraction of UCDs at radii greater than 30 kpc from the core of Fornax.     

Morphological classification of nearby galaxies based on asymmetry and luminosity concentration

We investigate the behaviour of the asymmetry parameter A as a morphological parameter using a 'volume-limited' sample of 349 galaxies  (distance ≤25 Mpc,  M_V ≤−18.5 mag)  and a larger magnitude-limited sample of 707 nearby galaxies. We confirm the correlation of A with morphological type. The late-type galaxies (Sdm, Sm and Im) have larger A than early-type galaxies, and they tend to have larger A than spiral galaxies. We investigate the usefulness of the A versus concentration index C _in diagram as a tool for the regular–irregular and early–late classification. The diagram is not very useful to the regular versus late-type irregular classification, as inferred previously, but it is found to be useful to the early–late classification.     

The anatomy of the NGC 5044 group – II. Stellar populations and star formation histories

The distribution of galaxy properties in groups and clusters holds important information on galaxy evolution and growth of structure in the Universe. While clusters have received appreciable attention in this regard, the role of groups as fundamental to formation of the present-day galaxy population has remained relatively unaddressed. Here, we present stellar ages, metallicities and α-element abundances derived using Lick indices for 67 spectroscopically confirmed members of the NGC 5044 galaxy group with the aim of shedding light on galaxy evolution in the context of the group environment.
We find that galaxies in the NGC 5044 group show evidence for a strong relationship between stellar mass and metallicity, consistent with their counterparts in both higher and lower mass groups and clusters. Galaxies show no clear trend of age or α-element abundance with mass, but these data form a tight sequence when fitted simultaneously in age, metallicity and stellar mass. In the context of the group environment, our data support the tidal disruption of low-mass galaxies at small group-centric radii, as evident from an apparent lack of galaxies below  ∼10⁹ M_⊙  within ∼100 kpc of the brightest group galaxy. Using a joint analysis of absorption- and emission-line metallicities, we are able to show that the star-forming galaxy population in the NGC 5044 group appears to require gas removal to explain the ∼1.5 dex offset between absorption- and emission-line metallicities observed in some cases. A comparison with other stellar population properties suggests that this gas removal is dominated by galaxy interactions with the hot intragroup medium.     

Compact stellar systems around NGC 1399

We have obtained spectroscopic redshifts of colour-selected point sources in four wide area VLT-FLAMES (Very Large Telescope-Fibre Large Array Multi Element Spectrograph) fields around the Fornax cluster giant elliptical galaxy NGC 1399, identifying as cluster members 27 previously unknown faint     compact stellar systems (CSS), and improving redshift accuracy for 23 previously catalogued CSS.
By amalgamating our results with CSS from previous 2dF observations and excluding CSS dynamically associated with prominent (non-dwarf) galaxies surrounding NGC 1399, we have isolated 80 'unbound' systems that are either part of NGC  1399's globular cluster (GC) system or intracluster GCs. For these unbound systems, we find (i) they are mostly located off the main stellar locus in colour–colour space; (ii) their projected distribution about NGC  1399 is anisotropic, following the Fornax cluster galaxy distribution, and there is weak evidence for group rotation about NGC  1399; (iii) their completeness-adjusted radial surface density profile has a slope similar to that of NGC  1399's inner GC system; (iv) their mean heliocentric recessional velocity is between that of NGC  1399's inner GCs and that of the surrounding dwarf galaxies, but their velocity dispersion is significantly lower; (v) bright CSS  ( M _V < −11)  are slightly redder than the fainter systems, suggesting they have higher metallicity; (vi) CSS show no significant trend in   g '− i '  colour index with radial distance from NGC  1399.     

The Millennium Galaxy Catalogue: 16 ≤BMGC < 24 galaxy counts and the calibration of the local galaxy luminosity function

The Millennium Galaxy Catalogue (MGC) is a 37.5 deg², medium-deep, B -band imaging survey along the celestial equator, taken with the Wide Field Camera on the Isaac Newton Telescope. The survey region is contained within the regions of both the Two Degree Field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey Early Data Release (SDSS-EDR). The survey has a uniform isophotal detection limit of 26 mag arcsec⁻² and it provides a robust, well-defined catalogue of stars and galaxies in the range  16 ≤ B _MGC < 24 mag  .
Here we describe the survey strategy, the photometric and astrometric calibration, source detection and analysis, and present the galaxy number counts that connect the bright and faint galaxy populations within a single survey. We argue that these counts represent the state of the art and use them to constrain the normalizations (φ*) of a number of recent estimates of the local galaxy luminosity function. We find that the 2dFGRS, SDSS Commissioning Data (CD), ESO Slice Project, Century Survey, Durham/UKST, Mt Stromlo/APM, SSRS2 and NOG luminosity functions require a revision of their published φ* values by factors of  1.05 ± 0.05, 0.76 ± 0.10, 1.02 ± 0.22, 1.02 ± 0.16, 1.16 ± 0.28, 1.75 ± 0.37, 1.40 ± 0.26  and  1.01 ± 0.39  , respectively. After renormalizing the galaxy luminosity functions we find a mean local b _J luminosity density of     . ¹