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

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 $$17 \leq {b}_{J}\leq 20$$, 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 $$P(k)\propto {k}^{-1.25}$$, as expected from the power-law slope of the angular correlation function. The power spectrum rises above the power law at wavenumbers $$0.08 h\, \text {Mpc}^{-1}\lesssim k \lesssim 0.2 h\,\text {Mpc}^{-1}$$. Systematic and random errors dominate the estimates of the power spectrum at wavenumbers smaller than 0.05 h Mpc ^–1. Our results are compatible with the power spectra measured from galaxy redshift surveys, but are more accurate. Our estimates of P(k) for the APM survey are incompatible with the power spectrum of the standard Ω = 1 cold dark matter (CDM) model, but can fit modified CDM models in the region $$k\sim 0.1 h\, \text {Mpc}^{-1}$$ (e.g. low- density CDM models, or mixed dark matter models). It remains to be seen whether these models can explain the APM power spectrum at higher wavenumbers, where the mass fluctuations are non-linear.