TY - JOUR
T1 - Filament and shape statistics
T2 - A quantitative comparison of cold + hot and cold dark matter cosmologies versus CfA1 data
AU - Davé, Romeel
AU - Hellinger, Doug
AU - Primack, Joel
AU - Nolthenius, Richard
AU - Klypin, Anatoly
PY - 1997
Y1 - 1997
N2 - A new class of geometric statistics for analysing galaxy catalogues is presented. Filament statistics quantify filamentarity and planarity in large-scale structure in a manner consistent with catalogue visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsion. Filament statistics are applied to cold dark matter (CDM) and cold + hot dark matter (CHDM) (Ω=0.3) simulations of Klypin et al., the CfA1-like mock redshift catalogues of Nolthenius, Klypin & Primack, and the CfA1 catalogue. We also apply the moment-based shape statistics developed by Babul & Starkman, Luo & Vishniac and Robinson & Albrecht to these same catalogues, and compare their robustness and discriminatory power versus filament statistics. For 100-Mpc periodic simulation boxes (H0=50 km s-1 Mpc-1), we find discrimination of ∼4σ (where σ represents resampling errors) between CHDM and CDM for selected filament statistics and shape statistics, including variations in the galaxy identification scheme. Comparing the CfA1 data versus the models does not yield a conclusively favoured model; no model is excluded at more than a ∼ 2σ level for any statistic, not including cosmic variance which could further degrade the discriminatory power. We find that CfA1 discriminates poorly between models, mainly because of its sparseness and small number of galaxies, not as a result of redshift distortion, magnitude limiting or geometrical effects. We anticipate that the proliferation of large redshift surveys and simulations will enable the statistics presented here to provide robust discrimination between large-scale structure in various cosmological models.
AB - A new class of geometric statistics for analysing galaxy catalogues is presented. Filament statistics quantify filamentarity and planarity in large-scale structure in a manner consistent with catalogue visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsion. Filament statistics are applied to cold dark matter (CDM) and cold + hot dark matter (CHDM) (Ω=0.3) simulations of Klypin et al., the CfA1-like mock redshift catalogues of Nolthenius, Klypin & Primack, and the CfA1 catalogue. We also apply the moment-based shape statistics developed by Babul & Starkman, Luo & Vishniac and Robinson & Albrecht to these same catalogues, and compare their robustness and discriminatory power versus filament statistics. For 100-Mpc periodic simulation boxes (H0=50 km s-1 Mpc-1), we find discrimination of ∼4σ (where σ represents resampling errors) between CHDM and CDM for selected filament statistics and shape statistics, including variations in the galaxy identification scheme. Comparing the CfA1 data versus the models does not yield a conclusively favoured model; no model is excluded at more than a ∼ 2σ level for any statistic, not including cosmic variance which could further degrade the discriminatory power. We find that CfA1 discriminates poorly between models, mainly because of its sparseness and small number of galaxies, not as a result of redshift distortion, magnitude limiting or geometrical effects. We anticipate that the proliferation of large redshift surveys and simulations will enable the statistics presented here to provide robust discrimination between large-scale structure in various cosmological models.
KW - Cosmology: theory
KW - Dark matter
KW - Large-scale structure of universe
KW - Methods: data analysis
KW - Methods: numerical
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U2 - 10.1093/mnras/284.3.607
DO - 10.1093/mnras/284.3.607
M3 - Article
AN - SCOPUS:0010164317
VL - 284
SP - 607
EP - 626
JO - Monthly Notices of the Royal Astronomical Society
JF - Monthly Notices of the Royal Astronomical Society
SN - 0035-8711
IS - 3
ER -