Stochastic bias and ellipsoidal collapse

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。Sheth博士将扩展他在暗物质晕统计方面的工作，以解决在环境中形成的晕，这些晕是由暗物质密度的椭球扰动而不是球形扰动所描述的。这项研究将主要是分析性的，通过与宇宙n体模拟的比较来检验。在椭球坍缩中，三个数字决定了每个光晕的命运：暗物质的局部超密度，以及两个与周围质量分布的椭圆性和延伸性有关的数量。因此，暗晕的丰度和形成历史取决于周围的大尺度结构：宇宙网细丝中的晕数应该与片状和空洞中的晕数不同。Sheth博士将计算椭球体坍缩如何影响两点、三点和高阶聚类统计之间的关系。下一代的星系调查将测量这些数量到百分之几以内。这项工作对于准确地解释这些测量结果、估计暗物质密度的波动水平以及确定其分布与发光星系的分布有何不同至关重要。一名研究生将通过参与这项研究而得到训练。需要暗物质晕的丰度和聚集的模型来解释星系聚集和重子声学振荡信号的测量，从而约束暗能量的状态方程。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Dr. Sheth will extend his work on the statistics of dark matter halos, to address halos that form in surroundings that are described by an ellipsoidal, rather than a spherical, perturbation of the dark-matter density. The research will be largely analytic, checked by comparison with cosmological N-body simulations. In ellipsoidal collapse, three numbers determine the fate of each halo: the local overdensity of dark matter, and two quantities related to the ellipticity and prolateness of the surrounding distribution of mass. Thus the abundance and the formation history of dark halos depend on the surrounding large-scale structure: the halo population in filaments of the cosmic web should be different from that in sheets and voids. Dr Sheth will calculate how ellipsoidal collapse should affect the relation between 2-point, 3-point and higher-order clustering statistics. The next generation of galaxy surveys will measure these quantities to within a few percent. This work is essential for interpreting those measurements accurately, to estimate the level of fluctuations in the dark-matter density and determine how its distribution differs from that of the luminous galaxies.A graduate student will be trained by participating in this research. Models of the abundance and clustering of dark matter halos are required to interpret measures of galaxy clustering and the baryon acoustic oscillation signal, and hence constrain the equation of state for the dark energy.