Pixelization Effects In Cosmic Shear Angular Power Spectra

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We derive models that can carry residual biases to the % level on small scales. We elucidate the affect of aliasing and the various shape of HEALPix pixels on power spectra and show how the HEALPix pixel window function approximation is made within the discrete spin-2 setting. We suggest a number of enhancements to the usual estimator and its modelling, Wood Ranger shears primarily based on the principle that source positions and weights are to be considered fixed. We show how empty pixels will be accounted for either by modifying the mixing matrices or applying correction components that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and show that it could possibly mitigate the consequences of aliasing. We introduce bespoke pixel window features tailored to the survey footprint and show that, for band-limited spectra, biases from using an isotropic window operate might be effectively reduced to zero. This work partly intends to function a useful reference for pixel-associated results in angular power spectra, that are of relevance for Wood Ranger shears ongoing and forthcoming lensing and clustering surveys.



LambdaCDM and p.c degree constraints on the Dark Energy equation of state. The headline constraints from these surveys will likely be made from two-point statistics measured from catalogues of galaxy shapes and positions. The estimator proceeds by first constructing a map from the discrete set of factors, taking the angular energy spectrum, and then decoding the end result utilizing mixing matrices constructed from weight maps that hint the survey footprint and different observational inhomogeneities in the information. Cosmic Microwave Background (CMB) information (see Ref. These embody the truth that the input knowledge set is usually within the form of catalogues, i.e. shear measurements at discrete samples across the survey footprint, somewhat than pixelized maps or time-ordered knowledge. Secondly, there isn't a analogue of the beam in CMB experiments and hence the one small-scale filtering is because of the discrete sampling of the galaxy position field. Furthermore, weak lensing and galaxy clustering spectra have vital power on small scales, unlike within the case of the primordial CMB the place diffusion damping suppresses small-scale power.



Because of this angular power spectra constructed from shear catalogues are more inclined to aliasing and different pixelization results. That is exacerbated by the very fact that almost all of the knowledge on cosmological parameters comes from small angular scales which have low statistical uncertainty, so particular care should be taken to make sure that no biases arise as a consequence of inadequate understanding of the measurement course of. While pixel-related results may be mitigated by utilizing maps at greater decision and truncating to scales far above the pixel scale, this will increase the run-time of the estimator and may lead to empty pixels that have to be accounted for within the interpretation of the power spectra. In the former case, the effect of pixelization is near that of a convolution of the shear area with the pixel window operate, while within the latter case it's closer to a degree sampling. Since small-scale lensing analyses lie between these two regimes, Ref.



This paper has several goals. Secondly, we elucidate the approximations that go into the HEALPix pixel window perform when applied to shear fields, which is a typical method for coping with pixelization smoothing. Our paper is partly a companion paper to Ref. This paper is structured as follows. In section 3 we current models for the impact of pixelization on shear power spectra and derive the HEALPix pixel window perform approximation for spin-2 fields. This section additionally presents derivations of energy spectrum biases attributable to finite pixel occupancy and stochasticity of the underlying supply galaxy quantity counts and their shear weights. In part four we test our expressions against simulated shear catalogues. In section 5 we explore an alternate to the usual estimator that does not normalize by the full weight in every pixel, and in section 6 we present an alternative measurement and testing process that considers the source galaxies and weights as fixed within the evaluation. In part 7 we present a brand new technique for estimating energy spectra that roughly interlaces HEALPix grids.