Sample Variance Considerations for Cluster Surveys

By Wayne Hu, Andrey V. Kravtsov. 2002

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We present a general statistical framework for describing the effect of sample variance in the number counts of virialized objects and examine its effect on cosmological parameter estimation. Specifically, we consider effects of sample variance on the power spectrum normalization and properties of dark energy extracted from current and future local and high-redshift samples of clusters. We show that for future surveys that probe ever lower cluster masses and temperatures, sample variance is generally comparable to or greater than shot noise and thus cannot be neglected in deriving precision cosmological constraints. For example, sample variance is usually more important than shot variance in constraints on the equation of state of the dark energy from z < 1 clusters. Although we found that effects of sample variance on the σ8-Ωm constraints from the current flux- and temperature-limited X-ray surveys are not significant, they may be important for future studies utilizing the shape of the temperature function to break the σ8-Ωm degeneracy. We also present numerical tests clarifying the definition of cluster mass employed in cosmological modeling and an accurate fitting formula for the conversion between different definitions of halo mass (e.g., virial vs. fixed overdensity).

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7778350d2a1a5a2b5e165bc9d585a7f9f377b670

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Citations in the corpus

Evidence for Significant Growth in the Stellar Mass of Brightest Cluster Galaxies over the Past 10 Billion Years (2012, methodology): “For the conversion, we use the formulae listed in appendix C of Hu & Kravtsov (2003).”
COSMOLOGICAL CONSTRAINTS FROM GALAXY CLUSTERS IN THE 2500 SQUARE-DEGREE SPT-SZ SURVEY (2016, methodology): “As is appropriate for a cluster abundance measurement (Hu & Kravtsov 2003; Holder 2006), we start with the binned Poisson statistic.”
Observational probes of cosmic acceleration (2012, background): “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), (∆N)2 = N + b̄2N2σ2(V ).”
Satellite kinematics – III. Halo masses of central galaxies in SDSS (2010, positive): “In particular, we follow Hu & Kravtsov (2003) to convert between different definitions of halo mass and use the results of Bell et al. (2003) and Borch et al. (2006) to convert stellar masses to the Kroupa (2001) initial mass function adopted here.”
New constraints on dark energy from the observed growth of the most X-ray luminous galaxy clusters (2007, methodology): “Given that our sample covers a very wide survey area (∼ 2/3 of the sky) and includes only the most luminous, and therefore rare, objects, the clustering term is negligible compared to the pure Poisson term (e.g. Hu & Kravtsov 2003).”
Self-Calibration in Cluster Studies of Dark Energy: Combining the Cluster Redshift Distribution, the Power Spectrum, and Mass Measurements (2003, background): “Since then, a series of papers has focused on the prospects of high yield cluster surveys as probes of dark energy (Holder et al. 2001; Weller et al. 2001; Levine et al. 2002; Hu & Kravtsov 2003; Majumdar & Mohr 2003; Hu 2003).”
Detailed cluster lensing profiles at large radii and the impact on cluster weak lensing studies (2011, methodology): “For a given set of Mvir and cvir, we compute the mass for ∆ = 800 assuming the NFW profile (see, e.g., Hu & Kravtsov 2003).”
The Observed Growth of Massive Galaxy Clusters I: Statistical Methods and Cosmological Constraints (2009, methodology): “…of sources is unimportant compared with the pure Poisson nature of their occurrence, which is justified for current all-sky surveys of very massive clusters (i.e. where the survey dimensions are large compared with the correlation length), as in this study (Hu & Kravtsov 2003; Holder 2006).”
SIMULATIONS OF WIDE-FIELD WEAK LENSING SURVEYS. I. BASIC STATISTICS AND NON-GAUSSIAN EFFECTS (2009, background): “As first pointed out in Hu & Kravtsov (2003), the halo clustering causes additional sampling variance to the covariance due to the statistical fluctuations in the number of halos sampled by a finite survey volume (also see Takada & Bridle 2007; Neyrinck et al. 2006; Zhang & Sheth 2007; Reid &…”
MASS FUNCTION PREDICTIONS BEYOND ΛCDM (2010, methodology): “The results can be directly compared to simple estimates of the variance using the halo model following Hu & Kravtsov (2003).”
CONSTRAINING THE SCATTER IN THE MASS–RICHNESS RELATION OF maxBCG CLUSTERS WITH WEAK LENSING AND X-RAY DATA (2008, methodology): “They find 〈M200b|N〉 1014 h−1M⊙ = exp(0.45±0.08)(N/20)1.15±0.14 (A10) To compare against the Johnston et al. (2007) values, we use the Hu & Kravtsov (2003) mass conversion formulae to find an approximate power law relation betweenM200b andM180b over the range 5× 1014 M⊙ ≤ M200b ≤ 1015 M⊙.”
Simulating the Universe with MICE: The abundance of massive clusters (2009, background): “More importantly, the abundance and clustering of clusters are complementary to other large-scale structure probes such as the clustering of galaxies, weak lensing and supernovae (see e.g. Hu & Kravtsov 2003; Cunha 2009; Cunha, Huterer & Frieman 2009; Estrada, Sefusatti & Frieman 2009).”
CLASH: JOINT ANALYSIS OF STRONG-LENSING, WEAK-LENSING SHEAR, AND MAGNIFICATION DATA FOR 20 GALAXY CLUSTERS (2015, neutral): “The covariance matrix Cov[N(θm), N(θn)] ≡ (CN )mn of the source counts includes the clustering and Poisson contributions (Hu & Kravtsov 2003) as (CN )mn = (Nµ)2ωmn + δmnNµ(θm), with ωmn the cell-averaged angular correlation function of source galaxies (see Equation (14) of Umetsu et al. 2015).”
ERRATUM: “CHANDRA SAMPLE OF NEARBY RELAXED GALAXY CLUSTERS: MASS, GAS FRACTION, AND MASS–TEMPERATURE RELATION” (2006, ApJ, 640, 691) (2005, methodology): “Note that we converted the concentrations and masses from the definitions used by Dolag et al. to c500 andM500 used in our analysis (e.g., Hu & Kravtsov 2003).”