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Smith R.E.,University of Zurich | Smith R.E.,Argelander Institute for Astronomy
Monthly Notices of the Royal Astronomical Society | Year: 2012

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 and 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. to explore these effects. The GLF estimates from the SAM and the CLF qualitatively reproduce results from the two degree Field Galaxy Redshift Survey (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 per cent. We use the SAM data to estimate the errors in the GLF estimates for a volume-limited survey of volume V ∼ 0.13h -3Gpc 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, induced by the large-scale structures in the survey, can lead to significant systematic errors in best-fitting parameters. For Schechter function fits, the most strongly affected parameter is the characteristic luminosity L *, which can be significantly underestimated. © 2012 The Author Monthly Notices of the Royal Astronomical Society © 2012 RAS.

Marian L.,Argelander Institute for Astronomy | Smith R.E.,Argelander Institute for Astronomy | Smith R.E.,University of Zurich | Hilbert S.,Argelander Institute for Astronomy | And 3 more authors.
Monthly Notices of the Royal Astronomical Society | Year: 2012

We present a new method to extract cosmological constraints from weak lensing (WL) peak counts, which we denote as 'the hierarchical algorithm'. The idea of this method is to combine information from WL maps sequentially smoothed with a series of filters of different size, from the largest down to the smallest, thus increasing the cosmological sensitivity of the resulting peak function. We compare the cosmological constraints resulting from the peak abundance measured in this way and the abundance obtained by using a filter of fixed size, which is the standard practice in WL peak studies. For this purpose, we employ a large set of WL maps generated by ray tracing through N-body simulations, and the Fisher matrix formalism. We find that if low signal-to-noise ratio peaks are included in the analysis, the hierarchical method yields constraints significantly better than the single-sized filtering. For a large future survey such as Euclid or Large Synoptic Survey Telescope, combined with information from a cosmic microwave background experiment like Planck, the results for the hierarchical (single-sized) method are Δn s= 0.0039(0.004),ΔΩ m= 0.002(0.0045),Δσ 8= 0.003(0.006) and Δw= 0.019(0.0525). This forecast is conservative, as we assume no knowledge of the redshifts of the lenses, and consider a single broad bin for the redshifts of the sources. If only peaks with are considered, then there is little difference between the results of the two methods. We also examine the statistical properties of the hierarchical peak function: Its covariance matrix has off-diagonal terms for bins with and aperture mass of M < 3 × 10 14h -1M ⊙, the higher bins being largely uncorrelated and therefore well described by a Poisson distribution. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.

Smith R.E.,University of Zurich | Smith R.E.,Argelander Institute for Astronomy | Marian L.,Argelander Institute for Astronomy
Monthly Notices of the Royal Astronomical Society | Year: 2011

We study the covariance matrix of the cluster mass function in cosmology. We adopt a two-line attack: first, we employ the counts-in-cells framework to derive an analytic expression for the covariance of the mass function. Secondly, we use a large ensemble of N-body simulations in the Λ cold dark matter framework to test this. Our theoretical results show that the covariance can be written as the sum of two terms: a Poisson term, which dominates in the limit of rare clusters; and a sample variance term, which dominates for more abundant clusters. Our expressions are analogous to those of Hu & Kravtsov for multiple cells and a single mass tracer. Calculating the covariance depends on: the mass function and bias of clusters, and the variance of mass fluctuations within the survey volume. The predictions show that there is a strong bin-to-bin covariance between measurements. In terms of the cross-correlation coefficient, we find r≳ 0.5 for haloes with M≲ 3 × 1014h-1M⊙ at z= 0. Comparison of these predictions with estimates from simulations shows excellent agreement. We use the Fisher matrix formalism to explore the cosmological information content of the counts. We compare the Poisson likelihood model, with the more realistic likelihood model of Lima & Hu, and all terms entering the Fisher matrices are evaluated using the simulations. We find that the Poisson approximation should only be used for the rarest objects, M≳ 5 × 1014h-1M⊙, otherwise the information content of a survey of size V∼ 13.5h-3Gpc3 would be overestimated, resulting in errors that are nearly two times smaller. As an auxiliary result, we show that the bias of clusters, obtained from the cluster-mass cross-variance, is linear on scales >50h-1Mpc, whereas that obtained from the auto-variance is non-linear. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.

Ngeow C.-C.,National Central University | Neilson H.R.,Argelander Institute for Astronomy | Nardetto N.,French National Center for Scientific Research | Marengo M.,Iowa State University
Astronomy and Astrophysics | Year: 2012

Context. The projection factor (p), which converts the radial velocity to pulsational velocity, is an important parameter in the Baade-Wesselink (BW) type analysis and distance scale work. The p-factor is either adopted as a constant or linearly depending on the logarithmic of pulsating periods. Aims. The aim of this work is to calibrate the p-factor if a Cepheid has both the BW distance and an independent distance measurement, and examine the p-factor for δ Cephei-the prototype of classical Cepheids. Methods. We calibrated the p-factor for several Galactic Cepheids that have both the latest BW distances and independent distances either from Hipparcos parallaxes or main-sequence fitting distances to Cepheid-hosted stellar clusters. Results. Based on 25 Cepheids, the calibrated p-factor relation is consistent with latest p-factor relation in literature. The calibrated p-factor relation also indicates that this relation may not be linear and may exhibit an intrinsic scatter. We also examined the discrepancy of empirical p-factors for δ Cephei, and found that the reasons for this discrepancy include the disagreement of angular diameters, the treatment of radial velocity data, and the phase interval adopted during the fitting procedure. Finally, we investigated the impact of the input p-factor in two BW methodologies for δ Cephei, and found that different p-factors can be adopted in these BW methodologies and yet result in the same angular diameters. © 2012 ESO.

Schneider A.,University of Zurich | Smith R.E.,University of Zurich | Smith R.E.,Argelander Institute for Astronomy | MacCio A.V.,Max Planck Institute for Astronomy | Moore B.,University of Zurich
Monthly Notices of the Royal Astronomical Society | Year: 2012

The dark energy dominated warm dark matter (WDM) model is a promising alternative cosmological scenario. We explore large-scale structure formation in this paradigm. We do this in two different ways: with the halo model approach and with the help of an ensemble of high-resolution N-body simulations. Combining these quasi-independent approaches leads to a physical understanding of the important processes which shape the formation of structures. We take a detailed look at the halo mass function, the concentrations and the linear halo bias of WDM. In all cases we find interesting deviations with respect to cold dark matter (CDM). In particular, the concentration-mass relation displays a turnover for group scale dark matter haloes, for the case of WDM particles with masses of the order of m WDM∼ 0.25keV. This may be interpreted as a hint for top-down structure formation on small scales. We implement our results into the halo model and find much better agreement with simulations. On small scales, the WDM halo model now performs as well as its CDM counterpart. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.

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