Quantifying cosmic variance

We determine an expression for the cosmic variance of any "normal" galaxy survey based on examination of M* +/- 1 mag galaxies in the SDSS DR7 data cube. We find that cosmic variance will depend on a number of factors principally: total survey volume, survey aspect ratio, and whether the area surveyed is contiguous or comprised of independent sight-lines. As a rule of thumb cosmic variance falls below 10% once a volume of 10^7h_0.7^-3Mpc^3 is surveyed for a single contiguous region with a 1:1 aspect ratio. Cosmic variance will be lower for higher aspect ratios and/or non-contiguous surveys. Extrapolating outside our test region we infer that cosmic variance in the entire SDSS DR7 main survey region is ~7% to z < 0.1. The equation obtained from the SDSS DR7 region can be generalised to estimate the cosmic variance for any density measurement determined from normal galaxies (e.g., luminosity densities, stellar mass densities and cosmic star-formation rates) within the volume range 10^3 to 10^7 h^-3_0.7Mpc^3. We apply our equation to show that 2 sightlines are required to ensure cosmic variance is <10% in any ASKAP galaxy survey (divided into dz ~0.1 intervals, i.e., ~1 Gyr intervals for z <0.5). Likewise 10 MeerKAT sightlines will be required to meet the same conditions. GAMA, VVDS, and zCOSMOS all suffer less than 10% cosmic variance (~3%-8%) in dz intervals of 0.1, 0.25, and 0.5 respectively. Finally we show that cosmic variance is potentially at the 50-70% level, or greater, in the HST Ultra Deep Field depending on assumptions as to the evolution of clustering. 100 or 10 independent sightlines will be required to reduce cosmic variance to a manageable level (<10%) for HST ACS or HST WFC3 surveys respectively (in dz ~ 1 intervals). Cosmic variance is therefore a significant factor in the z>6 HST studies currently underway.Comment: Accepted for publication in MNRA

The ugrizYJHK luminosity distributions and densities from the combined MGC, SDSS and UKIDSS LAS datasets

We combine data from the MGC, SDSS and UKIDSS LAS surveys to produce ugrizYJHK luminosity functions and densities from within a common, low redshift volume (z<0.1, ~71,000 h_1^-3 Mpc^3 for L* systems) with 100 per cent spectroscopic completeness. In the optical the fitted Schechter functions are comparable in shape to those previously reported values but with higher normalisations (typically 0, 30, 20, 15, 5 per cent higher phi*-values in u, g, r, i, z respectively over those reported by the SDSS team). We attribute these to differences in the redshift ranges probed, incompleteness, and adopted normalisation methods. In the NIR we find significantly different Schechter function parameters (mainly in the M* values) to those previously reported and attribute this to the improvement in the quality of the imaging data over previous studies. This is the first homogeneous measurement of the extragalactic luminosity density which fully samples both the optical and near-IR regimes. Unlike previous compilations that have noted a discontinuity between the optical and near-IR regimes our homogeneous dataset shows a smooth cosmic spectral energy distribution (CSED). After correcting for dust attenuation we compare our CSED to the expected values based on recent constraints on the cosmic star-formation history and the initial mass function.Comment: 17 pages, 13 figures, Accepted in MNRAS: 2010 January 18; in original form 2009 August 1

The GALEX-SDSS NUV & FUV Flux Density and Local Star-Formation Rate

We calculate the local UV flux density in the GALEX MIS FUV and NUV bands using redshifts provided by SDSS DR7. Luminosity functions are calculated for the overlapping MIS and SDSS sample, allowing flux densities to be measured and the local star formation rate (SFR) to be calculated using volumes much larger than previous FUV based estimates. We calculate flux densities for a dust corrected low redshift (0.013 < z < 0.1) sample of f[FUV] = 22.24 \pm 3.13 \times 10^25 h ergs s^-1 Hz^-1 Mpc^-3, f[NUV] = 38.54 \pm 5.30 \times 10^25 h ergs s^-1 Hz^-1 Mpc^-3. The star formation rate density found is 0.0312\pm0.0045 h M\odot yr^-1 Mpc^-3. This is larger than published rates recently found using the UV implied SFR, though the major discrepancy is the correction made for dust attenuation and once this is dealt with consistently the results agree well. These values are also consistent with recent Halpha derived SFRs. Once cosmic variance is taken into account most of the recent SFRs at low redshift (z < 0.3) found in the literature can be brought into agreement, however the lowest redshift values (z < 0.045) do appear to be significantly lower.Comment: 14 pages, 10 figures, accepted for publication in MNRA

Two-phase galaxy evolution: the cosmic star formation histories of spheroids and discs

From two very simple axioms: (1) that active galactic nucleus activity traces spheroid formation, and (2) that the cosmic star formation history is dominated by spheroid formation at high redshift, we derive simple expressions for the star formation histories of spheroids and discs, and their implied metal enrichment histories. Adopting a Baldry–Glazebrook initial mass function we use these relations and apply PEGASE.2 to predict the z = 0 cosmic spectral energy distributions (CSEDs) of spheroids and discs. The model predictions compare favourably to the dust-corrected CSED recently reported by the Galaxy And Mass Assembly team from the far-ultraviolet through to the K band. The model also provides a reasonable fit to the total stellar mass contained within spheroid and disc structures as recently reported by the Millennium Galaxy Catalogue team. Three interesting inferences can be made following our axioms: (1) there is a transition redshift at z ≈ 1.7 at which point the Universe switches from what we refer to as ‘hot mode evolution’ (i.e. spheroid formation/growth via mergers and/or collapse) to what we term ‘cold mode evolution’ (i.e. disc formation/growth via gas infall and minor mergers); (2) there is little or no need for any pre-enrichment prior to the main phase of star formation; (3) in the present Universe mass loss is fairly evenly balanced with star formation holding the integrated stellar mass density close to a constant value. The model provides a simple prediction of the energy output from spheroid and disc projenitors, the build-up of spheroid and disc mass and the mean metallicity enrichment of the Universe

The Millennium Galaxy Catalogue: the space density and surface brightness distribution(s) of galaxies

We recover the joint and individual space density and surface brightness distribution(s) of galaxies from the Millennium Galaxy Catalogue. The MGC is a local survey spanning 30.9 sq deg and probing approximately one--two mag/sq arcsec deeper than either the Two-Degree Field Galaxy Redshift Survey (2dFGRS) or the Sloan Digital Sky Survey (SDSS). The MGC contains 10,095 galaxies to B_mgc < 20 mag with 96 per cent spectroscopic completeness. We implement a joint luminosity-surface brightness step-wise maximum likelihood method to recover the bivariate brightness distribution (BBD) inclusive of most selection effects. Integrating the BBD over surface brightness we recover the following Schechter function parameters: phi* = (0.0177 +/- 0.0015) h^3 Mpc^{-3}, M_{B}* - 5 log h = (-19.60 +/- 0.04) mag and alpha =-1.13 +/- 0.02. Compared to the 2dFGRS (Norberg et al 2002) we find a consistent M* value but a slightly flatter faint-end slope and a higher normalisation, resulting in a final luminosity density j_{b_J} = (1.99 +/- 0.17) x 10^8 h L_{odot} Mpc^{-3}. The MGC surface brightness distribution is a well bounded Gaussian at the M* point with phi* = (3.5 +/- 0.1) x 10^{-2} h^3 Mpc^{-3}, mu^{e*} = (21.90 +/- 0.01) mag/sq arcsec and sigma_{ln R_e} = 0.35 +/- 0.01. The characteristic surface brightness for luminous systems is invariant to M_{B} - 5 log h ~ -19 mag faintwards of which it moves to lower surface brightness. Higher resolution (FWHM 26 mag/sq arcsec in the B-band) observations of the local universe are now essential to probe to lower luminosity and lower surface brightness levels. [abridged]Comment: Accepted for publication in MNRAS, 26 pages with 21 figures (some degraded). A full pdf version, along with MGC data release, is available from the MGC website at, http://www.eso.org/~jliske/mg

The nature of the dwarf population in Abell 868

We present the results of a study of the morphology of the dwarf galaxy population in Abell 868, a rich, intermediate redshift (z=0.154) cluster which has a galaxy luminosity function with a steep faint-end slope (alpha=-1.26 +/- 0.05). A statistical background subtraction method is employed to study the B-R colour distribution of the cluster galaxies. This distribution suggests that the galaxies contributing to the faint-end of the measured cluster LF can be split into three populations: dIrrs with B-R<1.4; dEs with 1.4<B-R<2.5; and contaminating background giant ellipticals (gEs) with B-R>2.5. The remvoal of the contribution of the background gEs from the counts only marginally lessens the faint-end slope (alpha=-1.22 +/- 0.16). However, the removal of the contribution of the dIrrs from the counts produces a flat LF (alpha=-0.91 +/- 0.16). The dEs and the dIrrs have similar spatial distributions within the cluster except that the dIrrs appear to be totally absent within a central projected radius of about 0.2 Mpc (Ho=75 km/s /Mpc). The number density of both dEs and dIrrs appear to fall off beyond a projected radius of about 0.35 Mpc. We suggest that the dE and dIrr populations of A868 have been associated with the cluster for similar timescales but that evolutionary processes such as `galaxy harassment' tend to fade the dIrr galaxies while having much less effect on the dE galaxies. The harassement would be expected to have the greatest effect on dwarfs residing in the central parts of the cluster.Comment: 6 pages, 6 figures To be published in The Monthly Notices of the Royal Astronomical Societ

Morphological Number Counts and Redshift Distributions to I = 25 from the Hubble Deep Fields: Constraints on Cosmological Models from Early Type Galaxies

We combine magnitude and photometric redshift data on galaxies in the Hubble Deep Fields with morphological classifications in order to separate out the distributions for early type galaxies. The updated morphological galaxy number counts down to I = 25 and the corresponding redshift distributions are used as joint constraints on cosmological models, in particular on the values of the density parameter Omega_{0} and normalised cosmological constant Lambda_{0}. We find that an Einstein - de Sitter universe with simple passive evolution gives an excellent fit to the counts and redshift data at all magnitudes. An open, low Omega_{0}, model with no net evolution (and conservation of the number of ellipticals), which fits the counts equally well, is somewhat less successful, predicting slightly lower mean redshifts and, more significantly, the lack of a high--z tail. A number conserving model with a dominant contribution from Lambda_{0}, on the other hand, is far less successful, predicting a much narrower distribution than seen. More complex models are obviously possible, but we conclude that if large scale transmutation between types does {\it not} occur, then the lambda-dominated models provide a very poor fit to the current data.Comment: Accepted for publication in MNRA

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

The Millennium Galaxy Catalogue (MGC) is a 37.5 deg^2, 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 (phi*) 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 phi* 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 \bj luminosity density of j_{b_J} = (1.986 +/- 0.031) x 10^8 h L_{\odot} Mpc^-3.Comment: 20 pages, LaTeX, 20 Postscript figures (some low resolution), MNRAS, in press; considerably revised versio

On the Continuous Formation of Field Spheroidal Galaxies in Hierarchical Models of Structure Formation

We re-examine the assembly history of field spheroidals as a potentially powerful discriminant of galaxy formation models. Whereas monolithic collapse and hierarchical, merger-driven, models suggest radically different histories for these galaxies, neither the theoretical predictions nor the observational data for field galaxies have been sufficiently reliable for precise conclusions to be drawn. A major difficulty in interpreting the observations, reviewed here, concerns the taxonomic definition of spheroidals in merger-based models. Using quantitative measures of recent star formation activity drawn from the internal properties of a sample of distant field galaxies in the Hubble Deep Fields, we undertake a new analysis to assess the continuous formation of spheroidal galaxies. Whereas abundances and redshift distributions of modelled spheroidals are fairly insensitive to their formation path, we demonstrate that the distribution and amount of blue light arising from recent mergers provides a more sensitive approach. With the limited resolved data currently available, the rate of mass assembly implied by the observed colour inhomogeneities is compared to that expected in popular Lambda-dominated cold dark matter models of structure formation. These models produce as many highly inhomogeneous spheroidals as observed, but underpredict the proportion of homogeneous, passive objects. We conclude that colour inhomogeneities, particularly when combined with spectroscopic diagnostics for large, representative samples of field spheroidals, will be a more valuable test of their physical assembly history than basic source counts and redshift distributions. Securing such data should be a high priority for the Advanced Camera for Surveys on Hubble Space Telescope.Comment: 14 pages, 7 figures, submitted to MNRA

The Luminosity Function of Low-Redshift Abell Galaxy Clusters

We present the results from a survey of 57 low-redshift Abell galaxy clusters to study the radial dependence of the luminosity function (LF). The dynamical radius of each cluster, r200, was estimated from the photometric measurement of cluster richness, Bgc. The shape of the LFs are found to correlate with radius such that the faint-end slope, alpha, is generally steeper on the cluster outskirts. The sum of two Schechter functions provides a more adequate fit to the composite LFs than a single Schechter function. LFs based on the selection of red and blue galaxies are bimodal in appearance. The red LFs are generally flat for -22 < M_Rc < -18, with a radius-dependent steepening of alpha for M_Rc > -18. The blue LFs contain a larger contribution from faint galaxies than the red LFs. The blue LFs have a rising faint-end component (alpha ~ -1.7) for M_Rc > -21, with a weaker dependence on radius than the red LFs. The dispersion of M* was determined to be 0.31 mag, which is comparable to the median measurement uncertainty of 0.38 mag. This suggests that the bright-end of the LF is universal in shape at the 0.3 mag level. We find that M* is not correlated with cluster richness when using a common dynamical radius. Also, we find that M* is weakly correlated with BM-type such that later BM-type clusters have a brighter M*. A correlation between M* and radius was found for the red and blue galaxies such that M* fades towards the cluster center.Comment: Accepted for publication in ApJ, 16 pages, 4 tables, 24 figure