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.     

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  .     

Hα photometry of Abell 2390

We present the results of a search for strong H α emission line galaxies (rest frame equivalent widths greater than 50 Å) in the z ≈0.23 cluster Abell 2390. The survey contains 1189 galaxies over 270 arcmin², and is 50 per cent complete at M _r ≈−17.5+5 log  h . The fraction of galaxies in which H α is detected at the 2 σ level rises from 0.0 in the central regions (excluding the cD galaxy) to 12.5±8 per cent at R ₂₀₀. For 165 of the galaxies in our catalogue, we compare the H α equivalent widths with their [O  ii ] λ 3727 equivalent widths, from the Canadian Network for Observational Cosmology (CNOC1) spectra. The fraction of strong H α emission line galaxies is consistent with the fraction of strong [O  ii ] emission galaxies in the CNOC1 sample: only 2±1 per cent have no detectable [O  ii ] emission and yet significant (>2 σ ) H α equivalent widths. Dust obscuration, non-thermal ionization, and aperture effects are all likely to contribute to this non-correspondence of emission lines. We identify six spectroscopically 'secure' k+a galaxies [ W ₀(O  ii )<5 Å and W ₀(H δ )≳5 Å]; at least two of these show strong signs in H α of star formation in regions that are covered by the slit from which the spectra were obtained. Thus, some fraction of galaxies classified as k+a based on spectra shortward of 6000 Å are likely to be undergoing significant star formation. These results are consistent with a 'strangulation' model for cluster galaxy evolution, in which star formation in cluster galaxies is gradually decreased, and is neither enhanced nor abruptly terminated by the cluster environment.     

Radial and 2D colour properties of E+A galaxies

We investigated the radial colour gradient and two-dimensional (2D) colour properties of 22 E+A galaxies with  5.5 < Hδ equivalent width(EW) < 8.5 Å  and 49 normal early-type galaxies as a control sample at a redshift of <0.2 in the Second Data Release of the Sloan Digital Sky Survey. We found that a substantial number of E+A galaxies exhibit positive slopes of radial colour gradient (bluer gradients toward the centre) which are seldom seen in normal early-type galaxies. We found irregular 'colour morphologies'– asymmetrical and clumpy patterns – at the centre of g − r and r − i 2D colour maps of E+A galaxies with positive slopes of colour gradient. Kolomogorov–Smirnov two-sample tests show that g − r and r − i colour gradient distributions of E+A galaxies differ from those of early-type galaxies with a more than 99.99 per cent significance level. We also found a tight correlation between radial colour gradients and colours, and between radial colour gradients and the 4000-Å break in the E+A sample; E+A galaxies which exhibit bluer colour or weaker D ₄₀₀₀ tend to have positive slopes of radial colour gradient. We compared the GISSEL model and E+A observational quantities,  Hδ EW, D ₄₀₀₀  and u − g colour, and found that almost all our E+A galaxies are situated along a single evolutionary track. Therefore, these results are interpreted as E+A galaxies evolving from  Hδ EW ∼ 8 Å  to  Hδ EW ∼ 5 Å  , with colour gradients changing from positive to negative, and with the irregular 2D colour map becoming smoother, during a time-scale of ∼300 Myr. Our results favour the hypothesis that E+A galaxies are post-starburst galaxies caused by merger/interaction, having undergone a centralized violent starburst.     

The binary star population of the young cluster NGC 1818 in the Large Magellanic Cloud

We determine the binary star fraction as a function of radius in NGC 1818, a young rich cluster in the Large Magellanic Cloud, using Hubble Space Telescope images in bands F336W (∼ U ) and F555W (∼ V ). Our sample includes binaries with M _primary ∼ 2–5.5 M_⊙ and M _secondary ≳ 0.7 M_primary. The binary fraction increases towards the cluster centre, from ∼ 20 ± 5 per cent in the outer parts, to ∼ 35 ± 5 per cent inside the core. This increase is consistent with dynamical mass segregation and need not be primordial. We compare our results with expectations from N -body models, and discuss the implications for the formation and early evolution of such clusters.     

The black hole mass – spheroid luminosity relation

The differing   M _bh– L   relations presented in McLure & Dunlop, Marconi & Hunt and Erwin et al. have been investigated. A number of issues have been identified and addressed in each of these studies, including but not limited to the removal of a dependency on the Hubble constant, a correction for dust attenuation in the bulges of disc galaxies, the identification of lenticular galaxies previously treated as elliptical galaxies and the application of the same ( Y ∣ X ) regression analysis. These adjustments result in relations which now predict similar black hole masses. The optimal K -band relation is  log( M _bh/M_⊙) =−0.37(±0.04)( M _K + 24) + 8.29(±0.08)  , with a total (not intrinsic) scatter in log M _bh equal to 0.33 dex. This level of scatter is similar to the value of 0.34 dex from the     relation of Tremaine et al. and compares favourably with the value of 0.31 dex from the   M _bh– n   relation of Graham & Driver. Using different photometric data, consistent relations in the B and R band are also provided, although we do note that the small  ( N = 13)  R -band sample used by Erwin et al. is found here to have a slope of −0.30 ± 0.06. Performing a symmetrical regression on the larger K -band sample gives a slope of ∼−0.40, implying M _bh∝ L ^1.00. Implications for galaxy–black hole co-evolution, in terms of dry mergers, are briefly discussed, as are the predictions for intermediate mass black holes. Finally, as noted by others, a potential bias in the galaxy sample used to define the   M _bh– L   relations is shown and a corrective formula provided.     

BeppoSAX–ROSAT PSPC observations of the Shapley supercluster: A3562

We present a combined analysis of the BeppoSAX and ROSAT PSPC observation of the cluster of galaxies A3562, a massive member of the core of the Shapley supercluster. With a complex and interacting structure composed from two groups of galaxies and A3558 to the west, the surface brightness of A3562 shows excess in the sectors to east and south when compared with an azimuthally averaged model of the emission. The emission tends to be flatter, and the distribution of the gas broader, along the merging axis and in opposition to the two groups. We present the first determination of the gradients of the gas temperature and metallicity for a cluster in the Shapley region at large distance from the cluster centre. From an analysis of the BeppoSAX data in annuli and sectors, we observe both the profiles to be flat within 8 arcmin (∼0.62 Mpc), with emission-weighted values of kT =5.1±0.2 keV and Z =0.39±0.05 Z_⊙. The value of the temperature is consistent with recent ASCA measurements and is significantly higher than previous estimates obtained from ROSAT and EXOSAT . We discuss the possible reasons for this disagreement. Between 8 and 20 arcmin, the plasma temperature declines to about 3.2 keV. When a polytropic profile is used to represent the gas temperature profile, the best-fitting polytropic index is 1.16±0.03. These results imply a total mass within the virial radius of between 40 and 80 per cent lower than the optical estimate, and a gas mass fraction of about 30 per cent.     

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.     

Spiral galaxy distance indicators based on near-infrared photometry

We compare two methods of distance determination to spiral galaxies using optical/near-infrared (NIR) observations, the ( I − K ) versus M _K colour–absolute magnitude (CM) relation and the I - and K -band Tully–Fisher relation (TFR).
Dust-free colours and NIR absolute magnitudes greatly enhance the usefulness of the NIR CM relation as a distance indicator for moderately to highly inclined spiral galaxies in the field (inclinations between ∼80° and 90°); by avoiding contamination by dust the scatter in the CM relation is significantly reduced, compared with similar galaxy samples published previously. The CM relation can be used to determine distances to field spiral galaxies with M _K >−25.5, to at least M _K ≈−20.
Our results, supplemented with previously published observations for which we can – to some degree – control the effects of extinction, are consistent with a universal nature of the CM relation for field spiral galaxies.
High-resolution observations made with the Hubble Space Telescope can provide a powerful tool to calibrate the relation and extend the useful distance range by more than a factor of 2 compared with ground-based observations.
The intrinsic scatter in the NIR CM relation in the absolute K -band magnitudes is ∼0.5 mag, yielding a lower limit to the accuracy of distance determinations of the order of 25 per cent.
Although we find an unusually low scatter in the TFR (probably a statistical accident), a typical scatter in the TFR would yield distances to our sample galaxies with uncertainties of only ∼15 per cent. However, one of the main advantages of the use of the NIR CM relation is that we need only photometric data to obtain distance estimates; use of the TFR requires additional kinematic data, although it can be used to significantly greater distances.     

Keck spectroscopy of the faint dwarf elliptical galaxy population in the Perseus Cluster core: mixed stellar populations and a flat luminosity function

We present the result of a photometric and Keck low-resolution imaging spectrometer (LRIS) spectroscopic study of dwarf galaxies in the core of the Perseus Cluster, down to a magnitude of   M _B =−12.5  . Spectra were obtained for 23 dwarf-galaxy candidates, from which we measure radial velocities and stellar population characteristics from absorption line indices. From radial velocities obtained using these spectra, we confirm 12 systems as cluster members, with the remaining 11 as non-members. Using these newly confirmed cluster members, we are able to extend the confirmed colour–magnitude relation for the Perseus Cluster down to   M _B =−12.5  . We confirm an increase in the scatter about the colour–magnitude relationship below   M _B =−15.5  , but reject the hypothesis that very red dwarfs are cluster members. We measure the faint-end slope of the luminosity function between   M _B =−18  and −12.5, finding  α=−1.26 ± 0.06  , which is similar to that of the field. This implies that an overabundance of dwarf galaxies does not exist in the core of the Perseus Cluster. By comparing metal and Balmer absorption line indices with α-enhanced single stellar population models, we derive ages and metallicities for these newly confirmed cluster members. We find two distinct dwarf elliptical populations: an old, metal-poor population with ages ∼8 Gyr and metallicities  [Fe/H] < −0.33  , and a young, metal-rich population with ages <5 Gyr and metallicities  [Fe/H] > −0.33  . Dwarf galaxies in the Perseus Cluster are therefore not a simple homogeneous population, but rather exhibit a range in age and metallicity.     

The scatter in the near-infrared colour–magnitude relation in spiral galaxies

We have determined a dust-free colour–magnitude (CM) relation for spiral galaxies, by using I  −  K colours in edge-on galaxies above the plane. We find that the scatter in this relation is small and approximately as large as can be explained by observational uncertainties. The slope of the near-IR CM relation is steeper for spirals than for elliptical galaxies. We suggest two possible explanations. First, the difference could be caused by vertical colour gradients in spiral galaxies. In that case these gradients should be similar for all galaxies, on average ∼0.15 dex in [Fe/H] per scaleheight, and should increase for later galaxy types. The most likely explanation, however, is that spirals and ellipticals have intrinsically different CM relations. This means that the stars in spirals are younger than those in ellipticals. The age, however, or the fraction of young stars in spiral galaxies would be determined solely by the luminosity of the galaxy, and not by its environment.     

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.     

Quantifying dust and the ultraviolet radiation density in the local Universe

A sample of local galaxies for which far-infrared and ultraviolet fluxes are available is used to estimate the characteristic dust extinction in galaxies and to test whether standard dust properties are plausible. Assuming galaxies can be characterized by a single dust optical depth (certainly not valid for galaxies with a dominant starburst component), the infrared excess and ultraviolet colours of local galaxies are found to be consistent with normal Milky Way dust, with a mean value for   E ( B − V )  of 0.16. A significant fraction of the dust heating is caused by older, lower-mass stars, and this fraction increases towards earlier galaxy types.
Analysis of  ( F _FIR/ F _UV)  versus ultraviolet colour diagrams for starburst galaxies in terms of a simple screen dust model does not support a Calzetti (1997) rather than a Milky Way extinction law, though the absence of the expected strong 2200- Å feature in several galaxies with IUE spectra does show that more detailed radiative transfer models are needed – probably with nonspherical geometry.
A simple treatment in which the  100/60-μm  flux ratio is used to subtract the optically thick starburst contribution to the far-infrared radiation results in lower extinction estimates for the optically thin cirrus component, with a mean   E ( B − V )  of 0.10.
The ultraviolet luminosity density, corrected for dust extinction, is derived and a value for the local mean star formation rate inferred. This is consistent with previous estimates from ultraviolet surveys and from  Hα  surveys.     

Quantifying the coexistence of massive black holes and dense nuclear star clusters

In large spheroidal stellar systems, such as elliptical galaxies, one invariably finds a  10⁶–10⁹ M_⊙  supermassive black hole at their centre. In contrast, within dwarf elliptical galaxies one predominantly observes a  10⁵–10⁷ M_⊙  nuclear star cluster. To date, few galaxies have been found with both types of nuclei coexisting and even less have had the masses determined for both central components. Here, we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured. This doubles the known number of such hermaphrodite nuclei – which are expected to be fruitful sources of gravitational radiation. Over the host spheroid (stellar) mass range  10⁸–10¹¹ M_⊙  , we find that a galaxy's nucleus-to-spheroid (baryon) mass ratio is not a constant value but decreases from a few per cent to ∼0.3 per cent such that  log[( M _BH+ M _NC)/ M _sph]=−(0.39 ± 0.07) log[ M _sph/10¹⁰ M_⊙]− (2.18 ± 0.07)  . Once dry merging commences and the nuclear star clusters disappear, this ratio is expected to become a constant value.
As a byproduct of our investigation, we have found that the projected flux from resolved nuclear star clusters is well approximated with Sérsic functions having a range of indices from ∼0.5 to ∼3, the latter index describing the Milky Way's nuclear star cluster.     

Optical and infrared diagnostics of SDSS galaxies in the SWIRE survey

We present the rest-frame optical and infrared colours of a complete sample of  1114 z < 0.3  galaxies from the Spitzer Wide-Area Infrared Extragalactic (SWIRE) Legacy Survey and the Sloan Digital Sky Survey (SDSS). We discuss the optical and infrared colours of our sample and analyse in detail the contribution of dusty star-forming galaxies and active galactic nuclei (AGN) to optically selected red sequence galaxies.
We propose that the optical  ( g − r )  colour and infrared  log( L ₂₄/ L _3.6)  colour of galaxies in our sample are determined primarily by a bulge-to-disc ratio. The  ( g − r )  colour is found to be sensitive to the bulge-to-disc ratio for disc-dominated galaxies, whereas the  log( L ₂₄/ L _3.6)  colour is more sensitive for bulge-dominated systems.
We identify ∼18 per cent (195 sources) of our sample as having red optical colours and infrared excess. Typically, the infrared luminosities of these galaxies are found to be at the high end of star-forming galaxies with blue optical colours. Using emission-line diagnostic diagrams, 78 are found to have an AGN contribution and 117 are identified as star-forming systems. The red  ( g − r )  colour of the star-forming galaxies could be explained by extinction. However, their high optical luminosities cannot. We conclude that they have a significant bulge component.
The number densities of optically red star-forming galaxies are found to correspond to ∼13 per cent of the total number density of our sample. In addition, these systems contribute ∼13 per cent of the total optical luminosity density, and 28 per cent of the total infrared luminosity density of our SWIRE/SDSS sample. These objects may reduce the need for 'dry mergers'.     

Near-infrared luminosity function and colours of dwarf galaxies in the Coma cluster

We present K -band observations of the low-luminosity galaxies in the Coma cluster, which are responsible for the steep upturn in the optical luminosity function at M _R∼−16, discovered recently. The main results of this study are as follows.
(i) The optical–near-infrared colours of these galaxies imply that they are dwarf spheroidal galaxies. The median B − K colour for galaxies with −19.3< M_K <−16.3 is 3.6 mag.
(ii) The K -band luminosity function in the Coma cluster is not well constrained, because of the uncertainties due to the field-to-field variance of the background. However, within the estimated large errors, this is consistent with the R -band luminosity function, shifted by ∼3 mag.
(iii) Many of the cluster dwarfs lie in a region of the B − K versus B − R colour–colour diagram where background galaxies are rare ( B − K <5; 1.2< B − R <1.6). Local dwarf spheroidal galaxies lie in this region too. This suggests that a better measurement of the K -band cluster luminosity can be made if the field-to-field variance of the background can be measured as a function of colour, even if it is large.
(iv) If we assume that none of the galaxies in the region of the B − K versus B − R plane given in (iii) in our cluster fields are background, and that all the cluster galaxies with 15.5< K <18.5 lie in this region of the plane, then we measure α=−1.41^+0.34_−0.37 for −19.3< M_K −16.3, where α is the logarithmic slope of the luminosity function. The uncertainties in this number come from counting statistics.     

The environmental dependence of the chemical properties of star-forming galaxies

We use a  0.040 < z < 0.085  sample of 37 866 star-forming galaxies from the Fourth Data Release of the Sloan Digital Sky Survey to investigate the dependence of gas-phase chemical properties on stellar mass and environment. The local density, determined from the projected distances to the fourth and fifth nearest neighbours, is used as an environment indicator. Considering environments ranging from voids, i.e.  log Σ≲−0.8  , to the periphery of galaxy clusters, i.e.  log Σ≈ 0.8  , we find no dependence of the relationship between galaxy stellar mass and gas-phase oxygen abundance, along with its associated scatter, on local galaxy density. However, the star-forming gas in galaxies shows a marginal increase in the chemical enrichment level at a fixed stellar mass in denser environments. Compared with galaxies of similar stellar mass in low-density environments, they are enhanced by a few per cent for massive galaxies to about 20 per cent for galaxies with stellar masses  ≲10^9.5 M_⊙  . These results imply that the evolution of star-forming galaxies is driven primarily by their intrinsic properties and is largely independent of their environment over a large range of local galaxy density.     

Model-based pattern speed estimates for 38 barred galaxies

We have modelled 38 barred galaxies by using near-infrared and optical data from the Ohio State University Bright Spiral Galaxy Survey. We constructed the gravitational potentials of the galaxies from H -band photometry, assuming a constant mass-to-light ratio. The halo component we choose corresponds to the so-called universal rotation curve. In each case, we used the response of gaseous and stellar particle disc to rigidly rotating potential to determine the pattern speed.
We find that the pattern speed of the bar depends roughly on the morphological type. The average value of corotation resonance radius to bar radius,     , increases from 1.15 ± 0.25 in types SB0/a–SBab to 1.44 ± 0.29 in SBb and 1.82 ± 0.63 in SBbc–SBc. Within the error estimates for the pattern speed and bar radius, all galaxies of type SBab or earlier have a fast bar     , whereas the bars in later type galaxies include both fast and slow rotators. Of 16 later type galaxies with a nominal value of     , there are five cases, where the fast-rotating bar is ruled out by the adopted error estimates.
We also study the correlation between the parameter     and other galactic properties. The clearest correlation is with the bar size: the slowest bars are also the shortest bars when compared to the galaxy size. A weaker correlation is seen with bar strength in a sense that slow bars tend to be weaker. These correlations leave room for a possibility that the determined pattern speed in many galaxies corresponds to actually that of the spiral, which rotates more slowly than the bar. No clear correlation is seen with either the galaxy luminosity or the colour.     

The galaxy population of Cl 1601+42 at z=0.54

Photometric redshifts are used to determine the rest-frame luminosity function (LF) of both early- and late-type galaxies to  M_B∼−17.6  for the cluster Cl 1601+42 at  z=0.54  . The total LF shows a steep faint-end slope   α ∼−1.4  , indicating the existence of a population of numerous dwarf galaxies. Luminous galaxies, with  M_B≲−19.5  are mostly red, early-type galaxies, with a LF best described by a Gaussian. Faint galaxies are predominantly blue, late-type galaxies, well fitted by a Schechter function with   α ∼−1.7  . Compared with clusters at lower redshift, the steepening of the faint end starts at brighter magnitudes for Cl 1601+42, which may indicate a brightening of the present-day dwarf population relative to the giant population with increasing redshift. Early-type galaxies are centrally concentrated, and dominate the core region, implying that the radial gradient of early-type galaxies seen in local clusters is already established at  z∼0.5  . Bright, late-type galaxies are rare, consistent with a decrease in star formation in field galaxies as they are accreted on to the cluster, while faint, blue galaxies are evenly distributed across the cluster, except for a depletion in the core region. The blue fraction is  f_B∼0.15  , which is somewhat lower than the Butcher–Oemler average at  z∼0.5  . The value of f _B is found to increase with limiting magnitude and with radius from the centre.     

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.