3D Reconstruction of the Density Field: An SVD Approach to Weak Lensing Tomography

Abstract

We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares estimation) without a priori assumptions about the statistical nature of the signal. This singular value framework allows a quantitative comparison between different filtering methods: we evaluate our method beside the previously explored Wiener filter approaches. Our method yields near-optimal angular resolution of the lensing reconstruction and allows cluster sized halos to be de-blended robustly. It allows for mass reconstructions which are 2-3 orders-of-magnitude faster than the Wiener filter approach; in particular, we estimate that an all-sky reconstruction with arcminute resolution could be performed on a time-scale of hours. We find however that linear, non-parametric reconstructions have a fundamental limitation in the resolution achieved in the redshift direction.

11 pages, 6 figures. Accepted for publication in ApJ

References in corpus (3)

• A direct empirical proof of the existence of dark matter
• COSMOS: 3D weak lensing and the growth of structure
• The Virial Mass Function of Nearby SDSS Galaxy Clusters

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