Maximum Likelihood Estimates of the Two- and Three-Dimensional Power Spectra of the APM Galaxy Survey

We estimate the two- and three-dimensional power spectra, P_2(K) and P_3(k), of the galaxy distribution by applying a maximum likelihood estimator to pixel maps of the APM Galaxy Survey. The analysis provides optimal estimates of the power spectra and of their covariance matrices if the fluctuations are assumed to be Gaussian. Our estimates of P_2(K) and P_3(k) are in good agreement with previous work but we find that the errors at low wavenumbers have been underestimated in some earlier studies. If the galaxy power spectrum is assumed to have the same shape as the mass power spectrum, then the APM maximum likelihood P_3(k) estimates at k < 0.19 h Mpc^-1 constrain the amplitude and shape parameter of a scale-invariant CDM model to lie within the 2 sigma ranges 0.78 < sigma_8_g < 1.18 and 0.05 < Gamma < 0.38. Using the Galactic extinction estimates of Schlegel, Finkbeiner and Davis, we show that Galactic obscuration has a negligible effect on galaxy clustering over most of the area of the APM Galaxy Survey.