Power spectrum analysis of the ESO Slice Project galaxy redshift survey

We measure the power spectrum of the galaxy distribution in the ESO Slice Project (ESP) galaxy redshift survey. We develop a technique to describe the survey window function analytically, and then deconvolve it from the measured power spectrum using a variant of the Lucy method. We test the whole deconvolution procedure on ESP mock catalogues drawn from large N ‐body simulations, and find that it is reliable for recovering the correct amplitude and shape of P ( k ) at k>0.065 h Mpc −1 . In general, the technique is applicable to any survey composed of a collection of circular fields with an arbitrary pattern on the sky, as typical of surveys based on fibre spectrographs. The estimated power spectrum has a well‐defined power‐law shape k n with n≃−2.2 for k≥0.2 h Mpc −1 , and a smooth bend to a flatter shape (n≃−1.6) for smaller k . The smallest wavenumber where a meaningful reconstruction can be performed (k∼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 ξ ( 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 excellent agreement with estimates from blue‐selected surveys. In particular, the ESP power spectrum is virtually indistinguishable from that of the Durham–UKST survey over the common range of k , an indirect confirmation of the quality of the deconvolution technique applied.