alleli28987821/2684wood-ranger-official
1
0
Code Issues Actions Packages Projects Wiki

Add Pixelization Effects In Cosmic Shear Angular Power Spectra

Eli Covey 2025-09-07 18:53:51 +08:00
parent 606a0a9b5c
commit 7c1ee7010b
1 changed files with 7 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

7
Pixelization-Effects-In-Cosmic-Shear-Angular-Power-Spectra.md Normal file

@ -0,0 +1,7 @@
<br>We derive fashions that may deliver residual biases to the % stage on small scales. We elucidate the influence of aliasing and the various shape of HEALPix pixels on energy spectra and present how the HEALPix pixel window perform approximation is made within the discrete spin-2 setting. We suggest several improvements to the usual estimator and its modelling, based on the precept that supply positions and weights are to be thought-about fastened. We show how empty pixels could be accounted for both by modifying the mixing matrices or making use of correction components that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and present that it may well mitigate the consequences of aliasing. We introduce bespoke pixel window features adapted to the survey footprint and show that, for band-limited spectra, biases from utilizing an isotropic window perform could be effectively diminished to zero. This work partly intends to function a helpful reference for pixel-related results in angular [buy Wood Ranger Power Shears](https://giteaismyownrepository.nosv.org/brunopugh47945) spectra, that are of relevance for ongoing and forthcoming lensing and clustering surveys.<br>
<br>LambdaCDM and percent degree constraints on the Dark Energy equation of state. The headline constraints from these surveys can be made from two-point statistics measured from catalogues of galaxy shapes and [buy Wood Ranger Power Shears](http://47.92.23.195:8418/aurorakorff121/1669079/wiki/Aoun+on+the+Making+of+%22Shears%22+-+Punk+Head.-) positions. The estimator proceeds by first constructing a map from the discrete set of factors, taking the angular energy spectrum, and then interpreting the result utilizing mixing matrices constructed from weight maps that hint the survey footprint and different observational inhomogeneities in the data. Cosmic Microwave Background (CMB) information (see Ref. These embody the truth that the enter data set is often in the form of catalogues, i.e. shear measurements at discrete samples throughout the survey footprint, quite than pixelized maps or time-ordered knowledge. Secondly, there isn't any analogue of the beam in CMB experiments and hence the one small-scale filtering is due to the discrete sampling of the galaxy position subject. Furthermore, weak lensing and galaxy clustering spectra have important power on small scales, unlike within the case of the primordial CMB the place diffusion damping suppresses small-scale power.<br>
<br>Because of this angular energy spectra constructed from shear catalogues are more inclined to aliasing and different pixelization results. This is exacerbated by the actual fact that the majority of the knowledge on cosmological parameters comes from small angular scales which have low statistical uncertainty, so particular care have to be taken to make sure that no biases come up as a consequence of inadequate understanding of the measurement course of. While pixel-associated effects will be mitigated through the use of 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 must be accounted for in the interpretation of the power spectra. In the previous case, the impact of pixelization is near that of a convolution of the shear discipline with the pixel window operate, while within the latter case it's nearer to a point sampling. Since small-scale lensing analyses lie between these two regimes, Ref.<br>
<br>This paper has a number of targets. Secondly, we elucidate the approximations that go into the HEALPix pixel window perform when utilized to shear fields, which is a common methodology for [Wood Ranger Power Shears coupon](https://git.jakubzabski.pl/twylabiggs429) Ranger Power Shears warranty coping with pixelization smoothing. Our paper is partly a companion paper to Ref. This paper is structured as follows. In part 3 we current fashions for [buy Wood Ranger Power Shears](https://ctpedia.org/index.php/Garden_Tool_Cutter_With_Precision_Bypass_Blade_Aluminum_Handles_:_Tools_House_Improvement) 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 power spectrum biases as a result of finite pixel occupancy and stochasticity of the underlying source galaxy quantity counts and their shear weights. In section 4 we test our expressions in opposition to simulated shear catalogues. In section 5 we discover an alternative to the standard estimator that does not normalize by the whole weight in each pixel, and in part 6 we present an alternate measurement and testing process that considers the supply galaxies and weights as mounted in the analysis. In part 7 we current a brand Wood Ranger Power Shears features new method for estimating power spectra that approximately interlaces HEALPix grids.<br>