Pixelization Effects In Cosmic Shear Angular Power Spectra

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We derive fashions that can bring residual biases to the p.c stage on small scales. We elucidate the influence of aliasing and the various form of HEALPix pixels on energy spectra and show how the HEALPix pixel window function approximation is made within the discrete spin-2 setting. We propose a number of improvements to the usual estimator and buy Wood Ranger Power Shears its modelling, based mostly on the precept that source positions and weights are to be thought-about fixed. We show how empty pixels might be accounted for both by modifying the mixing matrices or making use of correction factors that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and present that it will possibly mitigate the results of aliasing. We introduce bespoke pixel window capabilities adapted to the survey footprint and present that, for band-restricted spectra, biases from utilizing an isotropic window perform can be successfully lowered to zero. This work partly intends to serve as a helpful reference for pixel-related effects in angular energy spectra, buy Wood Ranger Power Shears which are of relevance for ongoing and forthcoming lensing and clustering surveys.



LambdaCDM and percent stage constraints on the Dark Energy equation of state. The headline constraints from these surveys might 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 buy Wood Ranger Power Shears spectrum, after which decoding the result using mixing matrices constructed from weight maps that hint the survey footprint and different observational inhomogeneities in the information. Cosmic Microwave Background (CMB) knowledge (see Ref. These include the fact that the input data set is usually in the form of catalogues, i.e. shear measurements at discrete samples across the survey footprint, reasonably than pixelized maps or time-ordered information. Secondly, there isn't any analogue of the beam in CMB experiments and hence the only small-scale filtering is because of the discrete sampling of the galaxy place subject. Furthermore, buy Wood Ranger Power Shears weak lensing and galaxy clustering spectra have important energy on small scales, not like in the case of the primordial CMB the place diffusion damping suppresses small-scale Wood Ranger Power Shears.



Which means that angular energy spectra constructed from shear catalogues are extra vulnerable to aliasing and different pixelization effects. 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 specific care must be taken to ensure that no biases arise resulting from insufficient understanding of the measurement process. While pixel-associated results will be mitigated through the use of maps at greater resolution and truncating to scales far above the pixel scale, this increases the run-time of the estimator and may result in empty pixels that must be accounted for within the interpretation of the electric power shears spectra. In the previous case, the effect of pixelization is close to that of a convolution of the shear subject with the pixel window operate, 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 a number of targets. Secondly, we elucidate the approximations that go into the HEALPix pixel window operate when utilized to shear fields, which is a common technique for coping with pixelization smoothing. Our paper is partly a companion paper to Ref. This paper is structured as follows. In section three we present fashions for the influence of pixelization on shear energy spectra and derive the HEALPix pixel window function approximation for spin-2 fields. This section additionally presents derivations of energy spectrum biases due to finite pixel occupancy and stochasticity of the underlying source galaxy number counts and buy Wood Ranger Power Shears their shear weights. In section 4 we check our expressions towards simulated shear catalogues. In part 5 we explore an alternative to the usual estimator that does not normalize by the total weight in every pixel, and in part 6 we present an alternate measurement and testing procedure that considers the supply galaxies and weights as mounted within the analysis. In section 7 we current a new methodology for estimating energy spectra that roughly interlaces HEALPix grids.

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