The Multi-Tracer Optimal Estimator applied to VIPERS

Abstract

ABSTRACT We use mock galaxy data from the VIMOS Public Extragalactic Redshift Survey (VIPERS) to test the performance of the Multi-Tracer Optimal Estimator (MTOE) of Abramo et al. as a tool to measure the monopoles of the power spectra of multiple tracers of the large-scale structure, $P^{(0)}_\alpha (\mathbf {k})$. We show that MTOE provides more accurate measurements than the standard technique of Feldman, Kaiser & Peacock (FKP), independently of the tracer-selection strategy adopted, on both small and large scales. The largest improvements on individual $P^{(0)}_\alpha (\mathbf {k})$ are obtained on small scales, using a colour–magnitude selection, due to MTOE being naturally better equipped to deal with shot noise: we report an average error reduction with respect to FKP of $\sim 30{{\ \rm per\ cent}}$ at $0.3 \lt k \, [h$ Mpc−1] < 0.5, with improvements exceeding 40–50 ${{\ \rm per\ cent}}$ for some tracers. On large scales (k[h Mpc−1] ≲ 0.1), the gain in accuracy resulting from cosmic-variance cancellation is ∼10 ${{\ \rm per\ cent}}$ for the ratios of $P^{(0)}_\alpha (\mathbf {k})$. We have carried out a Markov chain Monte Carlo analysis to determine the impact of these gains on several quantities derived from $P^{(0)}_\alpha (\mathbf {k})$. If we pushthat the estimated power spectra are themselves the measurement to scales $0.3 \lt k \, [h$ Mpc−1] < 0.5, the average improvements are $\sim 30{{\ \rm per\ cent}}$ for the amplitudes of the monopoles, $\sim 75{{\ \rm per\ cent}}$ for the monopole ratios, and $\sim 20{{\ \rm per\ cent}}$ for the linear galaxy biases. Our results highlight the potential of MTOE to shed light upon the physics that operate both on large and small cosmological scales. The effect of MTOE on cosmological constraints using VIPERS data will be addressed in a separate paper.