Optimal Surveys for Weak Lensing Tomography

TL;DR

This work addresses how to optimize future weak lensing surveys to constrain dark energy using a two-parameter w(a) model and power-spectrum tomography. It employs a Fisher-matrix framework for a seven-parameter cosmology to forecast constraints from tomographic $C_l^{ij}$, comparing ideal wide/deep surveys with degraded configurations and various systematics. The key results show that, at fixed observing time, wide-area surveys yield the strongest dark energy constraints, and photometric redshift calibration with $n_s$ around $10^4$–$10^5$ is sufficient to keep photo-z errors from dominating, while power-spectrum and theoretical uncertainties are the principal limiting factors. The authors also provide analytic scaling relations (FOM1 and FOM2) to guide survey design without full Fisher calculations, offering practical guidance for upcoming ground- and space-based imaging programs.

Abstract

Weak lensing surveys provide a powerful probe of dark energy through the measurement of the mass distribution of the local Universe. A number of ground-based and space-based surveys are being planned for this purpose. Here, we study the optimal strategy for these future surveys using the joint constraints on the equation of state parameter wn and its evolution wa as a figure of merit by considering power spectrum tomography. For this purpose, we first consider an `ideal' survey which is both wide and deep and exempt from systematics. We find that such a survey has great potential for dark energy studies, reaching one sigma precisions of 1% and 10% on the two parameters respectively. We then study the relative impact of various limitations by degrading this ideal survey. In particular, we consider the effect of sky coverage, survey depth, shape measurements systematics, photometric redshifts systematics and uncertainties in the non-linear power spectrum predictions. We find that, for a given observing time, it is always advantageous to choose a wide rather than a deep survey geometry. We also find that the dark energy constraints from power spectrum tomography are robust to photometric redshift errors and catastrophic failures, if a spectroscopic calibration sample of 10^4-10^5 galaxies is available. The impact of these systematics is small compared to the limitations that come from potential uncertainties in the power spectrum, due to shear measurement and theoretical errors. To help the planning of future surveys, we summarize our results with comprehensive scaling relations which avoid the need for full Fisher matrix calculations.

Figures (11)

• Figure 1: Dark energy constraints for a number of possible ideal surveys. The ideal survey covers half the sky (20,000 sq. degrees) with a median redshift of $z_m=1.23$ and 100 galaxies per amin$^2$. Also shown is a maximal ideal survey with $z_m=1.43$ and 260 galaxies per amin$^2$. Finally, a shallow survey is shown that has 35 galaxies per amin$^2$ and $z_m=0.9$
• Figure 2: Effect of survey geometry on the DE FOM. For each of the plots shown here only one survey property is varied at any time with others held fixed. Top: Figure of merit as a function of survey area. The symbols show the results of a Fisher calculation and the line shows a linear fit to the data. Middle: Figure of merit as a function of galaxy number density. The redshift distribution is the same for all the points with a median redshift of 1.23. Bottom: Dependence of the figure of merit on the median redshift of the lensed galaxies. The number density of galaxies has been fixed to 100 galaxies per square arc minute.
• Figure 3: Gains in FOM when time is dedicated to increasing one of the three parameters which impact the statistics of cosmic shear. We see that devoting observing time to increasing the area of the survey has the greatest impact on the FOM, while the change in median redshift lensed galaxies causes a minimal change in FOM. When performing a deep vs. wide trade-off study, these three factors fall into two groups. Increasing the area requires observing time being spent going wide, while the other two factors prefer a deep survey. Taking this into account, we see that the gains from increasing area out-weigh the combined gains of zm and ng.
• Figure 4: The results of a deep vs. wide trade-off study, given 3 years of observing time. The survey area, galaxy number counts and their median redshift are calculated by interpolating and extrapolating the results of 2004AJ....127.3089M. The three quantities are strongly correlated. Hence, a wide survey will have a lower galaxy number density and median redshift than a survey covering a small area. The upper panel shows the optimisation using the FOM, quantifying the error levels on a 2 parameter w model, and the lower panel shows the errors on the equation of state for a constant w model (i.e. a 1 parameter w model). As discussed in section \ref{['sec:theory_DEM']}, improvement as measured by the FOM is greater than the improvement from a 1 parameter w model.
• Figure 5: The upper panel shows the redshift distribution of galaxies, with $z_m=0.9$, divided into 10 redshift bins. The photometric redshifts are assumed to have $\delta_z=0.01$ and no catastrophic failures. The lower panel shows the distribution of the galaxies in the 8th redshift bin. The red curve shows this redshift slice for $\delta_z=0.1$, and the blue curve also has $\delta_z=0.1$ and $f_{\rm cat \it}=0.3$.