Pixelization Effects In Cosmic Shear Angular Power Spectra

We derive models that may bring residual biases to the percent stage on small scales. We elucidate the impression of aliasing and the various form of HEALPix pixels on Wood Ranger Power Shears shop spectra and present how the HEALPix pixel window function approximation is made within the discrete spin-2 setting. We propose a number of improvements to the standard estimator and its modelling, primarily based on the precept that supply positions and weights are to be thought of fixed. We show how empty pixels could be accounted for either by modifying the mixing matrices or applying correction factors that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and present that it could mitigate the results of aliasing. We introduce bespoke pixel window capabilities tailored to the survey footprint and show that, for band-restricted spectra, biases from utilizing an isotropic window operate can be successfully lowered to zero. This work partly intends to serve as a helpful reference for pixel-related effects in angular power spectra, Wood Ranger Power Shears shop that are of relevance for ongoing and forthcoming lensing and clustering surveys.



LambdaCDM and p.c stage constraints on the Dark Energy equation of state. The headline constraints from these surveys will likely be made from two-level statistics measured from catalogues of galaxy shapes and positions. The estimator proceeds by first constructing a map from the discrete set of points, taking the angular energy spectrum, after which decoding the consequence using mixing matrices constructed from weight maps that trace the survey footprint and other observational inhomogeneities in the info. Cosmic Microwave Background (CMB) knowledge (see Ref. These embody the truth that the enter information set is often within the form of catalogues, i.e. shear measurements at discrete samples throughout the survey footprint, rather than pixelized maps or time-ordered knowledge. Secondly, there isn't a analogue of the beam in CMB experiments and therefore the one small-scale filtering is due to the discrete sampling of the galaxy place discipline. Furthermore, weak lensing and galaxy clustering spectra have important energy on small scales, in contrast to in 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 extra inclined to aliasing and different pixelization results. That is exacerbated by the actual fact that most of the knowledge on cosmological parameters comes from small angular scales which have low statistical uncertainty, so explicit care must be taken to ensure that no biases come up because of insufficient understanding of the measurement course of. While pixel-associated results might be mitigated by utilizing maps at greater decision and truncating to scales far above the pixel scale, this increases the run-time of the estimator and can lead to empty pixels that must be accounted for in the interpretation of the facility spectra. In the previous case, the effect of pixelization is close to that of a convolution of the shear subject with the pixel window function, while in the latter case it is closer to some extent sampling. Since small-scale lensing analyses lie between these two regimes, Ref.



This paper has several objectives. Secondly, we elucidate the approximations that go into the HEALPix pixel window function when utilized to shear fields, which is a typical methodology 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 fashions for the affect of pixelization on shear power spectra and derive the HEALPix pixel window perform approximation for spin-2 fields. This part also presents derivations of energy spectrum biases as a result of finite pixel occupancy and stochasticity of the underlying supply galaxy quantity counts and their shear weights. In part 4 we take a look at our expressions towards simulated shear catalogues. In part 5 we explore an alternate to the usual estimator that doesn't normalize by the full weight in each pixel, and in section 6 we current an alternative measurement and testing process that considers the source galaxies and weights as fastened within the analysis. In section 7 we present a new methodology for estimating power spectra that roughly interlaces HEALPix grids.