The topology of the QDOT IRAS redshift survey

An all-sky redshift survey of galaxies detected by the IRAS satellite is used to investigate the topology of the universe to a depth of 200/h Mpc. Qualitatively, the distribution of galaxies out to this distance resembles a Gaussian density field with a spongelike topology: high- and low-density regions are topologically similar, and surfaces of constant density are interconnected. Quantitatively, the genus-threshold density relation of Gott et al. (1986, 1987) is used to test the hypothesis that the galaxy distribution grew out of initially Gaussian density fluctuations and to measure the effective slope of the power spectrum of fluctuations over a range of length-scales between 10 and 50/h Mpc. The observed genus curves are found to be consistent with the Gaussian hypothesis. A Voronoi foam model with about 100/h Mpc cells is tested as an example. It is found that such a model can be ruled out at about 5 sigma. On scales less than about 15/h Mpc, the QDOT power spectrum has a similar slope to that of the mass distribution in the standard dark cold matter model, but it falls off less steeply on larger scales; the maximum discrepancy occurs at about 30/h Mpc and is significant at about 2 sigma.