The three-dimensional power spectrum measured from the APM Galaxy Survey - II. Use of the two-dimensional power spectrum

We present the results of a Fourier transform analysis of galaxies from the APM Survey in the magnitude range |17≤ b_ J≤ 20|⁠. The two-dimensional power spectrum of galaxy clustering is found to obey a power law with |K-1.33|⁠, displaying a break at |K~ 30|⁠, where K is the physical wavenumber on the plane of the sky and has units of inverse radians. We compare this with the power spectrum of the Lick Survey using a scaling relationship. We then recover the three-dimensional power spectrum from the two-dimensional power spectrum and reproduce results that we have previously obtained using the angular correlation function. The APM power spectrum in three dimensions is a power law, |P(k) ∝ k-1.25|⁠, for wavenumbers |k ≥ 0.2 h⁻¹|⁠. It rises above this power law in the range |0.08 h⁻¹ ≤ k ≤ 0.2 h⁻¹|⁠. At wavenumbers smaller than approximately |~ 0.01 h Mpc⁻¹|⁠, systematic and random errors dominate our estimates of the power spectrum.