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

TL;DR

This paper develops a model for the galaxy power spectrum on the lightcone, accounting for survey geometry and depth, and validates it with simulations to assess the detection of the turnover scale in galaxy surveys.

Contribution

It introduces a full-sky, deep redshift survey model for the galaxy power spectrum that includes lightcone effects and validates it with N-body simulations.

Findings

The model agrees with simulations within ±5% over relevant scales.

Using an effective fixed-time approximation can be highly accurate on certain scales.

The galaxy power spectrum turnover scale can be detected with >95% probability in large surveys.

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 $(0.004 h{\rm Mpc}^{-1} \leq k \leq 0.54 h {\rm Mpc}^{-1})$ 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 $P \geq 95\%$ in an all-sky catalogue limited to an apparent magnitude $m_{\rm lim}\sim 21$. We also show that the detection significance would remain high for surveys with $m_{\rm lim}\sim22$ and $20\%$ sky coverage.