[Paper Review] A new model to predict weak-lensing peak counts I. Comparison with $N$-body Simulations

Chieh-An Lin, M. Kilbinger|Oct 25, 2014

Galaxies: Formation, Evolution, Phenomena42 references3 citations

TL;DR

This paper introduces a fast, flexible forward modeling approach for predicting weak-lens peak counts using analytically sampled halos and ray-tracing via the Camelus algorithm. It achieves good agreement with full N-body simulations, demonstrating sensitivity to Ωₘ and σ₈ in the S/N 4–6 range, and enables efficient cosmological parameter constraints under realistic survey effects.

ABSTRACT

Weak-lensing peak counts has been shown to be a powerful tool for cosmology. It provides non-Gaussian information of large scale structures, complementary to second order statistics. We propose a new flexible method to predict weak lensing peak counts, which can be adapted to realistic scenarios, such as a real source distribution, intrinsic galaxy alignment, mask effects, photo-$z$ errors from surveys, etc. The new model is also suitable for applying the tomography technique and non-linear filters. A probabilistic approach to model peak counts is presented. First, we sample halos from a mass function. Second, we assign them NFW profiles. Third, we place those halos randomly on the field of view. The creation of these "fast simulations" requires much less computing time compared to $N$-body runs. Then, we perform ray-tracing through these fast simulation boxes and select peaks from weak-lensing maps to predict peak number counts. The computation is achieved by our extsc{Camelus} algorithm, which we make available at http://www.cosmostat.org/software/camelus/ . We compare our results to $N$-body simulations to validate our model. We find that our approach is in good agreement with full $N$-body runs. We show that the lensing signal dominates shape noise and Poisson noise for peaks with SNR between 4 and 6. Also, counts from the same SNR range are sensitive to $Ω_\mathrm{m}$ and $σ_8$. We show how our model can discriminate between various combinations of those two parameters. In summary, we offer a powerful tool to study weak lensing peaks. The potential of our forward model is its high flexibility, making the use of peak counts under realistic survey conditions feasible.

Motivation & Objective

• To develop a computationally efficient method for predicting weak-lensing peak counts under realistic survey conditions.
• To enable forward modeling of peak counts that incorporates realistic effects such as source redshift distribution, photo-z errors, masks, and intrinsic alignments.
• To provide a flexible framework for cosmological parameter estimation using peak counts, avoiding reliance on costly N-body simulations.
• To validate the model against full N-body simulations and assess its sensitivity to cosmological parameters Ωₘ and σ₈.
• To enable high-resolution parameter space exploration and model comparison without Gaussian likelihood assumptions.

Proposed method

• Halo masses are sampled from an analytical mass function (e.g., Sheth-Tormen), and halos are assigned NFW density profiles.
• Halo positions are randomly distributed on the sky to generate 'fast simulations' that avoid full N-body computation.
• Ray-tracing is performed through these fast simulation boxes using the Camelus algorithm to produce weak-lensing convergence maps.
• Peaks are identified as local maxima in the convergence maps, and their number counts are computed as a function of signal-to-noise (S/N).
• The model accounts for survey effects such as masks, photo-z errors, and intrinsic alignment through modular extensions.
• Statistical inference is performed via repeated simulations, enabling non-Gaussian, likelihood-free model comparison (e.g., FDR, ABC).

Experimental results

Research questions

• RQ1 Can a fast, forward-modeling approach accurately predict weak-lensing peak counts without relying on full N-body simulations?
• RQ2 How do assumptions about halo distribution, NFW profiles, and mass function affect predicted peak abundances?
• RQ3 To what extent are peak counts with S/N ≈ 4–6 sensitive to cosmological parameters Ωₘ and σ₈?
• RQ4 Can the model distinguish between different combinations of Ωₘ and σ₈ in a realistic survey setting?
• RQ5 How does the model's flexibility support the inclusion of realistic systematics like photo-z errors and mask effects?

Key findings

• The model reproduces N-body simulation results for peak counts with high accuracy, particularly in the S/N 4–6 range.
• For S/N ≈ 4–6, the lensing signal dominates over shape and Poisson noise, making these peaks optimal for cosmological constraints.
• Peak counts in the S/N 4–6 range show strong sensitivity to Ωₘ and σ₈, with distinct degeneracy directions in the Ωₘ–σ₈ plane.
• The model’s fast computation allows for extensive parameter space exploration, enabling robust model comparison and marginalization over systematics.
• The inclusion of realistic survey effects—such as masks, photo-z errors, and intrinsic alignment—is feasible and improves model realism.
• The approach enables likelihood-free inference via methods like FDR and ABC, supporting robust statistical testing without Gaussian assumptions.