What do cluster counts really tell us about the Universe?

Smith, R. E.; Marian, Laura

doi:10.1111/j.1365-2966.2011.19525.x

Cited by 16 publications

(21 citation statements)

References 55 publications

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“…For most of the range considered, the peak‐function derivatives are non‐zero, signifying that there is cosmological information in the high‐ peaks, as well as in the low‐ ones, as previously noticed by Dietrich & Hartlap (2010). This originates in a similar behaviour displayed by the halo mass function: in a previous work (Smith & Marian 2011), we found the derivatives of the latter with respect to the same parameters studied here to be non‐zero for a large range of halo masses, down to M = 10 13 h −1 M ⊙ (compare figs 6 and 7 in that work with Figs 4 and 5 in this work).…”

Section: Resultssupporting

confidence: 67%

Section: Resultssupporting

confidence: 66%

“…We show that the correlation matrix of ‐binned hierarchical peaks has strong off‐diagonal contributions for the small‐ bins, while being largely diagonal for the large‐ bins. The same applies to the mass‐binned correlation coefficient, and this behaviour is similar to that of haloes, as shown in Smith & Marian (2011). The high‐ single‐sized peaks are also reasonably described by the Poisson distribution, due to the fact that such peaks are usually quite massive and rare. The correlation matrix of these peaks seems slightly more correlated for than the hierarchical matrix.…”

Section: Resultssupporting

confidence: 64%

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Optimized detection of shear peaks in weak lensing maps

Marian

Smith

Hilbert

et al. 2012

Monthly Notices of the Royal Astronomical Society

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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-S/N peaks are included in the analysis (S/N ~ 3), the hierarchical method yields constraints significantly better than the single-sized filtering. For a large future survey such as Euclid or LSST, combined with information from a CMB experiment like Planck, the results for the hierarchical (single-sized) method are: \Delta n=0.0039 (0.004); \Delta \Omega m=0.002 (0.0045); \Delta \sigma 8=0.003 (0.006); \Delta w=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 S/N >= 6 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 S/N <= 6 and aperture mass of M < 3 x 1e+14 Ms/h, the higher bins being largely uncorrelated and therefore well described by a Poisson distribution.Comment: 17 pages, 13 figures, final version published in MNRA

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Section: Resultssupporting

confidence: 67%

Section: Resultssupporting

confidence: 66%

Section: Resultssupporting

confidence: 64%

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Optimized detection of shear peaks in weak lensing maps

Marian

Smith

Hilbert

et al. 2012

Monthly Notices of the Royal Astronomical Society

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“…The choice of a particular definition of the halo bias can in principle introduce a scale dependence in the bias measured from the simulations (Baumann et al 2013). This scale dependence introduces a few per cent difference between the measured bias that is defined by equation (10) and those defined by other bias definitions (Smith & Marian 2011;Pollack, Smith & Porciani 2012). This effect is much weaker compared to the strong scale dependence of the halo bias presented in this work and hence will be neglected.…”

Section: The Measured Biasmentioning

confidence: 99%

The clustering of dark matter haloes: scale-dependent bias on quasi-linear scales

Jose¹,

Lacey²,

Baugh³

2016

Mon. Not. R. Astron. Soc.

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“…In order to proceed further, we need to compute the expected number of clusters in the αth mass bin,

{〈N_{α}^{c}〉}_{normalP, normals}

. This may be done following the procedure described in Smith & Marian () (summarized in Appendix for convenience). Following this procedure gives

{(〈〉, N_{α}^{normalc})}_{P, s} = V_{normals} {\bar{n}}_{α},

where the number density of clusters in the αth mass bin is

{\bar{n}}_{α} \equiv \int_{M_{α} - Δ M_{α} / 2}^{M_{α} + Δ M_{α} / 2} d M n (M),

and where n ( M ) d M is the abundance of dark matter haloes in the mass interval [ M − d M /2, M + d M /2].…”

Section: Volume‐limited Galaxy Samplesmentioning

confidence: 99%

How covariant is the galaxy luminosity function?

Smith

2012

Monthly Notices of the Royal Astronomical Society

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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 h −3 Gpc 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-fit parameters. For Schechter function fits, the most strongly affected parameter is the characteristic luminosity L * , which can be significantly underestimated.

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What do cluster counts really tell us about the Universe?

Cited by 16 publications

References 55 publications

Optimized detection of shear peaks in weak lensing maps

Optimized detection of shear peaks in weak lensing maps

The clustering of dark matter haloes: scale-dependent bias on quasi-linear scales

How covariant is the galaxy luminosity function?

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