Sample Variance Considerations for Cluster Surveys

Hu, Wayne; Kravtsov, Andrey V.

doi:10.1086/345846

Cited by 438 publications

(574 citation statements)

References 48 publications

(90 reference statements)

Supporting

Mentioning

552

Contrasting

Unclassified

Order By: Relevance

“…As explained above, this study is motivated by the need for such covariance matrices to compare any survey with theory. This extends over some previous works, which only considered the sample variance of number counts (Hu & Kravtsov 2003) or neglected high-order or non-Gaussian terms in the sample variance of estimators for two-point correlations or power spectra (Feldman et al 1994;Majumdar & Mohr 2004;Eisenstein et al 2005;Cohn 2006;Crocce et al 2011). Indeed, while the sample variance of number counts (i.e., the mean number of objects per unit volume) only involves the twopoint correlation of the objects, the sample variance of estimators of the two-point correlation itself also involves the threeand four-point correlations (and so on for estimators of higher order correlation functions) (Bernstein 1994).…”

Section: Introductionsupporting

confidence: 70%

Covariance matrices for halo number counts and correlation functions

Valageas

Clerc

Pacaud

et al. 2011

A&A

View full text Add to dashboard Cite

Aims. We study the mean number counts and two-point correlation functions, along with their covariance matrices, of cosmological surveys such as for clusters. In particular, we consider correlation functions averaged over finite redshift intervals, which are well suited to cluster surveys or populations of rare objects, where one needs to integrate over nonzero redshift bins to accumulate enough statistics. Methods. We develop an analytical formalism to obtain explicit expressions of all contributions to these means and covariance matrices, taking into account both shot-noise and sample-variance effects. We compute low-order as well as high-order (including non-Gaussian) terms. Results. We derive expressions for the number counts per redshift bins both for the general case and for the small window approximation. We estimate the range of validity of Limber's approximation and the amount of correlation between different redshift bins. We also obtain explicit expressions for the integrated 3D correlation function and the 2D angular correlation. We compare the relative importance of shot-noise and sample-variance contributions, and of low-order and high-order terms. We check the validity of our analytical results through a comparison with the Horizon full-sky numerical simulations, and we obtain forecasts for several future cluster surveys.

show abstract

Section: Introductionsupporting

confidence: 70%

Covariance matrices for halo number counts and correlation functions

Valageas

Clerc

Pacaud

et al. 2011

A&A

View full text Add to dashboard Cite

show abstract

“…Assuming halo masses can be adequately measured, the statistical error in cluster abundances is the sum in quadrature of Poisson noise and sample variance (Hu and Kravtsov, 2003),…”

Section: Expected Numbers and Cosmological Sensitivitymentioning

confidence: 99%

Observational probes of cosmic acceleration

et al. 2013

View full text Add to dashboard Cite

The accelerating expansion of the universe is the most surprising cosmological discovery in many decades, implying that the universe is dominated by some form of "dark energy" with exotic physical properties, or that Einstein's theory of gravity breaks down on cosmological scales. The profound implications of cosmic acceleration have inspired ambitious efforts to understand its origin, with experiments that aim to measure the history of expansion and growth of structure with percent-level precision or higher. We review in detail the four most well established methods for making such measurements: Type Ia supernovae, baryon acoustic oscillations (BAO), weak gravitational lensing, and the abundance of galaxy clusters. We pay particular attention to the systematic uncertainties in these techniques and to strategies for controlling them at the level needed to exploit "Stage IV" dark energy facilities such as BigBOSS, LSST, Euclid, and WFIRST. We briefly review a number of other approaches including redshift-space distortions, the Alcock-Paczynski effect, and direct measurements of the Hubble constant H 0 . We present extensive forecasts for constraints on the dark energy equation of state and parameterized deviations from General Relativity, achievable with Stage III and Stage IV experimental programs that incorporate supernovae, BAO, weak lensing, and cosmic microwave background data. We also show the level of precision required for clusters or other methods to provide constraints competitive with those of these fiducial programs. We emphasize the value of a balanced program that employs several of the most powerful methods in combination, both to cross-check systematic uncertainties and to take advantage of complementary information. Surveys to probe cosmic acceleration produce data sets that support a wide range of scientific investigations, and they continue the longstanding astronomical tradition of mapping the universe in ever greater detail over ever larger scales.

show abstract

“…By assuming a specific form of halo density profiles, we can rescale mass definitions from the virial mass M vir to M 200 , the mass definition used in the simulation measurements, as outlined in [32] (again, all overdensities are referred to the background matter density). We use this approach to compare the scaling relation predictions to the simulations in §V.…”

Section: Halo Model Predictionsmentioning

confidence: 99%

Spherical collapse and the halo model in braneworld gravity

2010

Self Cite

View full text Add to dashboard Cite

We present a detailed study of the collapse of a spherical perturbation in DGP braneworld gravity for the purpose of modeling simulation results for the halo mass function, bias and matter power spectrum. The presence of evolving modifications to the gravitational force in form of the scalar brane-bending mode lead to qualitative differences to the collapse in ordinary gravity. In particular, differences in the energetics of the collapse necessitate a new, generalized method for defining the virial radius which does not rely on strict energy conservation. These differences and techniques apply to smooth dark energy models with w = −1 as well. We also discuss the impact of the exterior of the perturbation on collapse quantities due to the lack of a Birkhoff theorem in DGP. The resulting predictions for the mass function, halo bias and power spectrum are in good overall agreement with DGP N-body simulations on both the self-accelerating and normal branch. In particular, the impact of the Vainshtein mechanism as measured in the full simulations is matched well. The model and techniques introduced here can serve as practical tools for placing consistent constraints on braneworld models using observations of large scale structure.

show abstract

Sample Variance Considerations for Cluster Surveys

Cited by 438 publications

References 48 publications

Covariance matrices for halo number counts and correlation functions

Covariance matrices for halo number counts and correlation functions

Observational probes of cosmic acceleration

Spherical collapse and the halo model in braneworld gravity

Contact Info

Product

Resources

About