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

Abstract

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 ($\sim \pm 5\%$) over scales $(0.004h{\mathrm{Mpc}}^{-1}\le k\le 0.54h{\mathrm{Mpc}}^{-1})$ 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 $P\ge 95\%$ in an all-sky catalogue limited to an apparent magnitude $m_{\lim }\sim 21$. We also show that the detection significance would remain high for surveys with $m_{\lim }\sim 22$ and $20\%$ sky coverage.

31 + 11 pages, 12 figures. Closely matches version published in JCAP -- 2022JCAP...08..019P

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Cited by in corpus (2)

• Cosmological Analysis of Three-Dimensional BOSS Galaxy Clustering and Planck CMB Lensing Cross Correlations via Lagrangian Perturbation Theory
• Euclid preparation. The impact of relativistic redshift-space distortions on two-point clustering statistics from the Euclid wide spectroscopic survey