THE 3-DIMENSIONAL POWER SPECTRUM MEASURED FROM THE APM GALAXY SURVEY .1. USE OF THE ANGULAR-CORRELATION FUNCTION

We describe a method of recovering the three-dimensional power spectru m of galaxy clustering from measurements of the angular correlation fu nction w(theta). We apply the technique to w(theta) measured from the APM Galaxy Survey in the magnitude range 17 less-than-or-equal-to b(J) less-than-or-equal-to 20, using models for the redshift distribution of APM galaxies that reproduce the distributions measured in faint red shift surveys. The APM power spectrum is a power law at high wavenumbe rs, with slope P(k) is-proportional-to k-1.25, as expected from the po wer-law slope of the angular correlation function. The power spectrum rises above the power law at wavenumbers 0.08 h Mpc-1 less than or sim ilar to k less than or similar to 0.2 h Mpc-1. Systematic and random e rrors dominate the estimates of the power spectrum at wavenumbers smal ler than 0.05 h Mpc-1. Our results are compatible with the power spect ra measured from galaxy redshift surveys, but are more accurate. Our e stimates of P(k) for the APM survey are incompatible with the power sp ectrum of the standard OMEGA = 1 cold dark matter (CDM) model, but can fit modified CDM models in the region k approximately 0.1 h 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 hi gher wavenumbers, where the mass fluctuations are non-linear.