TY - JOUR
T1 - Shapefinders
T2 - A new shape diagnostic for large-scale structure
AU - Sahni, Varun
AU - Sathyaprakash, B. S.
AU - Shandarin, Sergei F.
N1 - Funding Information:
The statistic suggested by us could also be used to study more general shapes than those appearing in large-scale structure. For instance, one could use them to study the shapes of concentrated cosmic magnetic fields, which might have important astrophysical consequences (Biermann et al. 1997). Finally, the two-dimensional shapefinders H1 = S/L, H2 = L, and K = (H2 − H1)/(H2 + H1) (L is the circumference of a curve bounding a two-dimensional area S), combined with the two-dimensional genus, could prove useful when studying shapes and topologies of two-dimensional contours defining “hot and cold spots” in the cosmic microwave background or isodensity surfaces in projection data. (Values of K range from zero, for a circle, to unity, for a filament.) We acknowledge stimulating discussions with Sanjeev Dhurandhar and Somak Raychaudhury. S. F. S. acknowledges financial support from the NSF-EPSCoR program and NASA grant NAG5-4039.
PY - 1998
Y1 - 1998
N2 - We construct a set of shapefinders used to determine the shapes of compact surfaces (isodensity surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations, as has been done earlier. The new indicators, based on the Minkowski functionals, arise from simple, geometrical considerations and are derived from the fundamental properties of a surface such as its volume, surface area, integrated mean curvature, and connectivity characterized by the genus. These "shapefinders" could be used to diagnose the presence of filaments, pancakes, and ribbons in large-scale structure. Their lower dimensional generalization may be useful for the study of two-dimensional distributions such as temperature maps of the cosmic microwave background.
AB - We construct a set of shapefinders used to determine the shapes of compact surfaces (isodensity surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations, as has been done earlier. The new indicators, based on the Minkowski functionals, arise from simple, geometrical considerations and are derived from the fundamental properties of a surface such as its volume, surface area, integrated mean curvature, and connectivity characterized by the genus. These "shapefinders" could be used to diagnose the presence of filaments, pancakes, and ribbons in large-scale structure. Their lower dimensional generalization may be useful for the study of two-dimensional distributions such as temperature maps of the cosmic microwave background.
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U2 - 10.1086/311214
DO - 10.1086/311214
M3 - Article
AN - SCOPUS:0004987653
SN - 0004-637X
VL - 495
SP - L5-L8
JO - Astrophysical Journal
JF - Astrophysical Journal
IS - 1 PART II
ER -