The power spectrum of galaxy clustering in the APM survey

We measure the power spectrum of galaxy clustering in real space from the APM Galaxy Survey. We present an improved technique for the numerical inversion of Limber's equation that relates the angular clustering of galaxies to an integral over the power spectrum in three dimensions. Our approach is underpinned by a large ensemble of mock galaxy catalogues constructed from the Hubble Volume N-body simulations. The mock catalogues are used to test for systematic effects in the inversion algorithm and to estimate the errors on our measurement. We find that we can recover the power spectrum to an accuracy of better than 15% over three decades in wavenumber. A key advantage of the use of mock catalogues to infer errors is that we can apply our technique on scales for which the density fluctuations are not Gaussian, thus probing the regime that offers the best constraints on models of galaxy formation. On large scales, our measurement of the power spectrum is consistent with the shape of the mass power spectrum in the popular ``concordance'' cold dark matter model. The galaxy power spectrum on small scales is strongly affected by nonlinear evolution of density fluctuations, and, to a lesser degree, by galaxy bias. The rms variance in the galaxy distribution, when smoothed in spheres of radius 8 h^(-1)Mpc, is sigma^g_8=0.96^(+0.17)_(-0.20) and the shape of the power spectrum on large scales is described by a simple fitting formula with parameter Gamma= 0.19^(+0.13)_(-0.04) (these errors are the 1-sigma ranges for a two parameter fit). We use our measurement of the power spectrum to estimate the galaxy two point correlation function; the results are well described by a power law with correlation length r_0 = 5.9 +- 0.7 h^(-1)Mpc and slope gamma = 1.61 +- 0.06 for pair separations in the range 0.1 < r/[h^(-1)Mpc] < 20.