Power Spectrum Tomography with Weak Lensing

TL;DR

The paper analyzes weak-lensing tomography by constructing convergence power spectra between redshift bins, $P^{\kappa}_{ij}(\ell)$, and including cross-bin correlations to trace the growth of structure in three dimensions. Using the Limber approximation and shot-noise corrected spectra $C_{ij}(\ell)=P^{\kappa}_{ij}(\ell)+\langle\gamma_{\rm int}^2\rangle\delta_{ij}/\bar{n}_i$, it demonstrates how photometric redshift binning enhances information about cosmological parameters. A Fisher-matrix analysis for correlated power spectra shows that crude two-bin division can dramatically improve constraints (e.g., factors of 2–7 on $\Omega_\Lambda$, $\Omega_K$, $m_\nu$, $\ln A$) with modest gains from a third bin, and even larger improvements for wider redshift distributions. The findings highlight the feasibility and value of weak-lensing tomography for probing the growth of structure and testing the adiabatic CDM paradigm, while also addressing practical concerns from photometric redshift errors and biases.

Abstract

Upcoming weak lensing surveys on wide fields will provide the opportunity to reconstruct the structure along the line of sight tomographically by employing photometric redshift information about the source distribution. We define power-spectrum statistics, including cross correlation between redshift bins, quantify the improvement that redshift information can make in cosmological parameter estimation, and discuss ways to optimize the redshift binning. We find that within the adiabatic cold dark matter class of models, crude tomography using two or three redshift bins is sufficient to extract most of the information and improve the measurements of cosmological parameters that determine the growth rate of structure by up to an order of magnitude.

Figures (3)

• Figure 1: Subdividing the source population. Partitioning the galaxies by the median redshift (or distance $D$) yields lensing efficiencies with strong overlap.
• Figure 2: Power spectra and cross correlation for a subdivision in two across the median redshift $z_{\rm median}=1$ and errors for a survey of $5^{\circ}$ on the side, $\left< \gamma_{\rm int}^2 \right>^{1/2}=0.4$, and $\bar{n} = 2 \times 10^5$ deg$^{-2}$. Note the strong correlation ${\bf R}_{ij}$ between the two power spectra make the combination of the power spectra less constraining than a naive interpretation of the individual errors would imply.
• Figure 3: Tomographic error improvements on $\Omega_\Lambda$ for $z_{\rm median}=1$. Upper panel: improvement as a function of the fraction of galaxies in the upper redshift bin for 2 bins versus 3 bins (same fraction in upper two bins). Lower panel: redshift corresponding to the upper division.