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Topology of the Universe  
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Introduction Galaxy bias and the cosmic variance: We use two large CDM simulations to study the statistical properties of biased "galaxy" distribution and to estimate the sample variance due to the choice of the observer position, socalled cosmic variance. For each simulations we employ two empirical bias schemes such that the lowest order statistical property (twopoint correlation function) of the "galaxies" closely resembles that of observed galaxies. We then use the Minkowski functionals to measure higherorder statistics.
Figure 1 Distribution of the model biased "galaxies"
Figure 2 Twopoint correlation functions of the biased "galaxies" Shown below are the computed twopoint correlation functions for our 4 biased "galaxy" samples. The observed correlation function (by APM galaxy survey) is plotted as open squares. Although all of our samples have similar values for this statistics, there is a significant difference in their higherorder statistics, see Figure 3 below. It is interesting that the 'galaxy' distributions look very different as shown in Figure 1.
Figure 3 The Minkowski functional (v1) measured for the biased "galaxies" The quantity v1 for the 'galaxy' distributions are
plotted against the "ball radii", bias L1 (solid lines) and
bias L2(dotted line).
Schmalzing, Yoshida, Diaferio, in preparation. Here is an example of proper credit for these Virgo data. Comments to: N. Yoshida naoki@mpagarching.mpg.de 