Pixelization Effects In Cosmic Shear Angular Power Spectra

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We derive fashions that can deliver residual biases to the percent level on small scales. We elucidate the impression of aliasing and the various shape of HEALPix pixels on energy spectra and present how the HEALPix pixel window function approximation is made in the discrete spin-2 setting. We propose several enhancements 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 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 show that it may well 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 perform might be effectively reduced to zero. This work partly intends to serve as a useful reference for pixel-associated results in angular energy spectra, which are of relevance for 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 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 result using mixing matrices constructed from weight maps that trace the survey footprint and different observational inhomogeneities in the data. Cosmic Microwave Background (CMB) data (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 throughout the survey footprint, rather than pixelized maps or time-ordered information. Secondly, there is no analogue of the beam in CMB experiments and therefore the only small-scale filtering is due to the discrete sampling of the galaxy position subject. Furthermore, weak lensing and galaxy clustering spectra have important Wood Ranger Power Shears official site on small scales, in contrast to within the case of the primordial CMB the place diffusion damping suppresses small-scale energy.



This means that angular energy spectra constructed from shear catalogues are more susceptible to aliasing and other pixelization results. That is exacerbated by the actual fact that most of the data on cosmological parameters comes from small angular scales which have low statistical uncertainty, so specific care have to be taken to make sure that no biases come up as a consequence of inadequate understanding of the measurement process. While pixel-associated results will be mitigated through the use of maps at larger resolution and Wood Ranger Power Shears manual Wood Ranger Power Shears manual Power Shears warranty truncating to scales far above the pixel scale, this will increase the run-time of the estimator and might result in empty pixels that should be accounted for in the interpretation of the Wood Ranger Power Shears for sale spectra. In the former case, the effect of pixelization is near that of a convolution of the shear area with the pixel window function, while within the latter case it is nearer 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 perform when applied to shear fields, which is a typical technique for dealing with pixelization smoothing. Our paper is partly a companion paper to Ref. This paper is structured as follows. In part 3 we present fashions for the affect of pixelization on shear energy spectra and derive the HEALPix pixel window perform approximation for spin-2 fields. This part additionally presents derivations of power spectrum biases on account of finite pixel occupancy and stochasticity of the underlying source galaxy number counts and their shear weights. In section 4 we test our expressions in opposition to simulated shear catalogues. In section 5 we discover another to the standard estimator that doesn't normalize by the overall weight in every pixel, and in section 6 we present another measurement and testing process that considers the source galaxies and weights as mounted within the analysis. In section 7 we present a new technique for estimating power spectra that roughly interlaces HEALPix grids.