The galaxy power spectrum on the lightcone: deep, wide-angle redshift surveys and the turnover scale

We derive expressions for the survey-window convolved galaxy power spectrum in real space for a full sky and deep redshift survey, but taking into account the geometrical lightcone effect. We investigate the impact of using the standard mean redshift approximation as a function of survey depth, and show that this assumption can lead to both an overall amplitude suppression and scale-dependent error when compared to the 'true' spectrum. However, we also show that by using a carefully chosen 'effective fixed-time', one can find a range of scales where the approximation to the full model is highly accurate, but only on a more restricted set of scales. We validate the theory by constructing dark matter and galaxy lightcone mock surveys from a large N-body simulation with a high cadence of snapshots. We do this by solving the light cone equation exactly for every particle, where the particle worldlines are obtained in a piecewise fashion with cubic interpolation between neighbouring snapshots. We find excellent agreement between our measurements and the theory (~ ±5%) over scales (0.004 h Mpc-1 = k = 0.54 h Mpc-1) and for a variety of magnitude limits. Finally, we look to see how accurately we can measure the turnover scale of the galaxy power spectrum k 0. Using the lightcone mocks we show that one can detect the turnover scale with a probability P = 95% in an all-sky catalogue limited to an apparent magnitude m lim ~ 21. We also show that the detection significance would remain high for surveys with m lim ~ 22 and 20% sky coverage.