How covariant is the galaxy luminosity function?

Monthly Notices of the Royal Astronomical Society (Impact Factor: 5.11). 05/2012; 426(1). DOI: 10.1111/j.1365-2966.2012.21745.x
Source: arXiv


We investigate the error properties of certain galaxy luminosity function
(GLF) estimators. Using a cluster expansion of the density field, we show how,
for both volume and flux limited samples, the GLF estimates are covariant. The
covariance matrix can be decomposed into three pieces: a diagonal term arising
from Poisson noise; a sample variance term arising from large-scale structure
in the survey volume; an occupancy covariance term arising due to galaxies of
different luminosities inhabiting the same cluster. To evaluate the theory one
needs: the mass function and bias of clusters, and the conditional luminosity
function (CLF). We use a semi-analytic model (SAM) galaxy catalogue from the
Millennium run N-body simulation and the CLF of Yang et al. (2003) to explore
these effects. The GLF estimates from the SAM and the CLF qualitatively
reproduce results from the 2dFGRS. We also measure the luminosity dependence of
clustering in the SAM and find reasonable agreement with 2dFGRS results for
bright galaxies. However, for fainter galaxies, L<L*, the SAM overpredicts the
relative bias by ~10-20%. We use the SAM data to estimate the errors in the GLF
estimates for a volume limited survey of volume V~0.13 [Gpc/h]^3. We find that
different luminosity bins are highly correlated: for L<L* the correlation
coefficient is r>0.5. Our theory is in good agreement with these measurements.
These strong correlations can be attributed to sample variance. For a
flux-limited survey of similar volume, the estimates are only slightly less
correlated. We explore the importance of these effects for GLF model parameter
estimation. We show that neglecting to take into account the bin-to-bin
covariances can lead to significant systematic errors in best-fit parameters.

10 Reads
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Using the technique of Angulo & White (2010) we scale the Millennium and Millennium-II simulations of structure growth in a LCDM universe from the cosmological parameters with which they were carried out (based on first-year results from the Wilkinson Microwave Anisotropy Probe, WMAP1) to parameters consistent with the seven-year WMAP data (WMAP7). We implement semi-analytic galaxy formation modelling on both simulations in both cosmologies to investigate how the formation, evolution and clustering of galaxies are predicted to vary with cosmological parameters. The increased matter density Omega_m and decreased linear fluctuation amplitude sigma8 in WMAP7 have compensating effects, so that the abundance and clustering of dark halos are predicted to be very similar to those in WMAP1 for z <= 3. As a result, local galaxy properties can be reproduced equally well in the two cosmologies by slightly altering galaxy formation parameters. The evolution of the galaxy populations is then also similar. In WMAP7, structure forms slightly later. This shifts the peak in cosmic star formation rate to lower redshift, resulting in slightly bluer galaxies at z=0. Nevertheless, the model still predicts more passive low-mass galaxies than are observed. For rp< 1Mpc, the z=0 clustering of low-mass galaxies is weaker for WMAP7 than for WMAP1 and closer to that observed, but the two cosmologies give very similar results for more massive galaxies and on large scales. At z>1 galaxies are predicted to be more strongly clustered for WMAP7. Differences in galaxy properties, including, clustering, in these two cosmologies are rather small up to redshift 3. Given that there are still considerable residual uncertainties in galaxy formation models, it is very difficult to distinguish WMAP1 from WMAP7 through observations of galaxy properties or their evolution.
    Monthly Notices of the Royal Astronomical Society 05/2012; 428(2). DOI:10.1093/mnras/sts115 · 5.11 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We quantify the accuracy with which the cosmological parameters characterizing the energy density of matter (\Omega_m), the amplitude of the power spectrum of matter fluctuations (\sigma_8), the energy density of neutrinos (\Omega_{\nu}) and the dark energy equation of state (w_0) can be constrained using data from large galaxy redshift surveys. We advocate a joint analysis of the abundance of galaxies, galaxy clustering, and the galaxy-galaxy weak lensing signal in order to simultaneously constrain the halo occupation statistics (i.e., galaxy bias) and the cosmological parameters of interest. We parameterize the halo occupation distribution of galaxies in terms of the conditional luminosity function and use the analytical framework of the halo model described in our companion paper (van den Bosch et al. 2012), to predict the relevant observables. By performing a Fisher matrix analysis, we show that a joint analysis of these observables, even with the precision with which they are currently measured from the Sloan Digital Sky Survey, can be used to obtain tight constraints on the cosmological parameters, fully marginalized over uncertainties in galaxy bias. We demonstrate that the cosmological constraints from such an analysis are nearly uncorrelated with the halo occupation distribution constraints, thus, minimizing the systematic impact of any imperfections in modeling the halo occupation statistics on the cosmological constraints. In fact, we demonstrate that the constraints from such an analysis are both complementary to and competitive with existing constraints on these parameters from a number of other techniques, such as cluster abundances, cosmic shear and/or baryon acoustic oscillations, thus paving the way to test the concordance cosmological model.
    Monthly Notices of the Royal Astronomical Society 06/2012; 430(2). DOI:10.1093/mnras/sts697 · 5.11 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We describe the construction of a suite of galaxy cluster mock catalogues from N-body simulations, based on the properties of the new ROSAT-ESO Flux-Limited X-Ray (REFLEX II) galaxy cluster catalogue. Our procedure is based on the measurements of the cluster abundance, and involves the calibration of the underlying scaling relation linking the mass of dark matter haloes to the cluster X-ray luminosity determined in the \emph{ROSAT} energy band $0.1-2.4$ keV. In order to reproduce the observed abundance in the luminosity range probed by the REFLEX II X-ray luminosity function ($0.01<L_{X}/(10^{44}{\rm erg}\,{\rm s}^{-1}h^{-2})<10$), a mass-X ray luminosity relation deviating from a simple power law is required. We discuss the dependence of the calibration of this scaling relation on the X-ray luminosity and the definition of halo masses and analyse the one- and two-point statistical properties of the mock catalogues. Our set of mock catalogues provides samples with self-calibrated scaling relations of galaxy clusters together with inherent properties of flux-limited surveys. This makes them a useful tool to explore different systematic effects and statistical methods involved in constraining both astrophysical and cosmological information from present and future galaxy cluster surveys.
    Monthly Notices of the Royal Astronomical Society 07/2012; 425(3). DOI:10.1111/j.1365-2966.2012.21685.x · 5.11 Impact Factor
Show more


10 Reads
Available from