The topology of the QDOT IRAS redshift survey

Abstract

We have used an all-sky redshift survey of galaxies detected by the IRAS satellite to investigate the topology of the Universe to a depth of 200 h–1 Mpc. Qualitatively, the distribution of galaxies out to this distance resembles a Gaussian density field with a sponge-like topology: high- and low-density regions are topologically similar and surfaces of constant density are interconnected. Quantitatively, we have used the genus-threshold density relation of Gott et al. 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–1 Mpc. To estimate random and systematic uncertainties in our analysis, we have used artificial ‘galaxy’ catalogues constructed from N-body simulations and a variety of Monte-Carlo techniques. We find that the observed genus curves are consistent with the Gaussian hypothesis. As an example of a non-Gaussian field, we have tested a Voronoi foam model with |$\sim 100 \enspace h^{-1}$| Mpc cells. We find that such a model can be ruled out at |$\sim 5 \sigma$|⁠. Our topological analysis is consistent with a power spectrum of galaxy fluctuations of the form |$P(k)\propto k^n$| with |$n \simeq -1$|⁠, over the full range of scales considered. On scales |$ \lesssim 15 \enspace h^{-1}$| Mpc, the QDOT power spectrum has a similar slope to that of the mass distribution in the standard cold dark matter model, but it falls off less steeply on larger scales; the maximum discrepancy occurs at |$ \sim 30 \enspace h^{-1}$| Mpc and is significant at about 2σ. Our power spectrum results are consistent with previous counts-in-cells analyses of the same survey, but the present method (which is sensitive to the slope of the spectrum rather than to its amplitude) weights the data quite differently.