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What is a Power Spectrum?

Density fluctuations can be converted to power spectra by multiplying the square of the density fluctuation strength (dr/r)^2 by the volume over which the fluctuation is being sampled (L^3). When plotted against the length scale over which the fluctuations were detected--ranging from 10,000 to 10 Mpc--the result is a mountain-shaped curve which can be compared with actual distributions of galaxies, also represented in terms of their fluctuation strength. The shape of the power spectrum depends on the composition of dark matter dominating the universe: pure cold dark matter (represented by the green line), pure hot dark matter (the red line), or mixed cold and hot dark matter (the blue line).

The left end of the graph represents the power spectrum of density fluctuations over relatively large patches of sky (10,000 to 1,000 megaparsecs or Mpc), representing an era before galaxy formation. All three models produce power spectra compatible with fluctuations in the cosmic background radiation, but at small scal es--corresponding to galaxy formation--they differ.

A universe dominated by pure cold dark matter predicts fluctuations of greater strength, and therefore more and bigger clusters of galaxies than we observe; a pure hot dark matter-dominated universe predicts fluctuations of less strength, and thinner and smaller galaxy clusters than we observe. A model incorporating both cold and hot dark matter produces a power spectrum more similar to that predicted by the actual distribution of galaxies.

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NCSA. Last modified 10/7/95.