THE 3-DIMENSIONAL POWER SPECTRUM MEASURED FROM THE APM GALAXY SURVEY .2. USE OF THE 2-DIMENSIONAL POWER SPECTRUM

We present the results of a Fourier transform analysis of galaxies from the APM Survey in the magnitude range 17 less-than-or-equal-to b(J) less-than-or-equal-to 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 approximately 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) is-proportional-to k-1.25, for wavenumbers k greater-than-or-equal-to 0. 2 h Mpc-1. It rises above this power law in the range 0.08 h Mpc-1 less-than-or-equal-to k less-than-or-equal-to 0.2 h Mpc-1. At wavenumbers smaller than approximately 0.01 h Mpc-1, systematic and random errors dominate our estimates of the power spectrum.