The three-dimensional power spectrum measured from the APM Galaxy Survey - I. Use of the angular correlation function

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We describe a method of recovering the three-dimensional power spectrum of galaxy clustering from measurements of the angular correlation function w(θ). We apply the technique to w(θ) measured from the APM Galaxy Survey in the magnitude range 17≤b J ≤20, using models for the redshift distribution of APM galaxies that reproduce the distributions measured in faint redshift surveys. The APM power spectrum is a power law at high wavenumbers, with slope P(k)∞k −1.25 , as expected from the power-law slope of the angular correlation fuction. The power spectrum rises above the power law at wavenumbers 0.08 h Mpc −1 ≤k≤0.2 h Mpc −1 . Systematic and random errors dominate the estimates of the power spectrum at wavenumbers smaller than 0.05 h Mpc −1