Power spectrum analysis of the ESO Slice Project galaxy redshift survey

We measure the power spectrum of the galaxy distribution in the ESO Slice P roject (ESP) galaxy redshift survey. We develop a technique to describe the survey window function analytically, and then deconvolve it from the measu red power spectrum using a variant of the Lucy method. We test the whole de convolution procedure on ESP mock catalogues drawn from large N-body simula tions, and find that it is reliable for recovering the correct amplitude an d shape of P(k) at k > 0.065 h Mpc(-1). In general, the technique is applic able to any survey composed of a collection of circular fields with an arbi trary pattern on the sky, as typical of surveys based on fibre spectrograph s. The estimated power spectrum has a well-defined power-law shape k(n) wit h n similar or equal to -2.2 for k greater than or equal to 0.2 h Mpc(-1), and a smooth bend to a flatter shape (n similar or equal to -1.6) for small er k. The smallest wavenumber where a meaningful reconstruction can be perf ormed (k similar to 0.06 h Mpc(-1)) does not allow us to explore the range of scales where other power spectra seem to show a flattening and hint at a turnover. We also find, by a direct comparison of the Fourier transforms, that the estimate of the two-point correlation function xi (s) is much less sensitive to the effect of a problematic window function, such as that of the ESP, than the power spectrum. Comparison with other surveys shows an ex cellent agreement with estimates from blue-selected surveys. In particular, the ESP power spectrum is virtually indistinguishable from that of the Dur ham-UKST survey over the common range of k, an indirect confirmation of the quality of the deconvolution technique applied.