diff --git a/Pixelization-Effects-In-Cosmic-Shear-Angular-Power-Spectra.md b/Pixelization-Effects-In-Cosmic-Shear-Angular-Power-Spectra.md new file mode 100644 index 0000000..be6ef55 --- /dev/null +++ b/Pixelization-Effects-In-Cosmic-Shear-Angular-Power-Spectra.md @@ -0,0 +1,7 @@ +
We derive fashions that can convey residual biases to the percent level on small scales. We elucidate the impression of aliasing and the various shape of HEALPix pixels on power spectra and present how the HEALPix pixel window operate approximation is made in the discrete spin-2 setting. We suggest several improvements to the usual estimator and its modelling, primarily based on the precept that supply positions and weights are to be thought-about fastened. We present how empty pixels may be accounted for both by modifying the mixing matrices or [Wood Ranger shears](https://granadapedia.wikanda.es/wiki/Usuario:IlaOko396068237) applying correction elements that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and present that it could mitigate the effects of aliasing. We introduce bespoke pixel window features adapted to the survey footprint and present that, for band-limited spectra, biases from utilizing an isotropic window perform might be successfully reduced to zero. This work partly intends to serve as a useful reference for [Wood Ranger shears](https://pdffilesportal.com/2025/09/23/the-ultimate-guide-to-wood-ranger-power-shears-and-garden-pruning-tools-7/) pixel-related effects in angular energy spectra, that are of relevance for ongoing and forthcoming lensing and clustering surveys.
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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 wood shears positions. The estimator proceeds by first constructing a map from the discrete set of factors, taking the angular power spectrum, and then interpreting the result 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 embrace the fact that the input data set is normally in the type of catalogues, i.e. shear measurements at discrete samples across the survey footprint, somewhat than pixelized maps or time-ordered knowledge. Secondly, there is no analogue of the beam in CMB experiments and therefore the one small-scale filtering is as a result of discrete sampling of the galaxy position discipline. Furthermore, weak lensing and galaxy clustering spectra have important power on small scales, unlike within the case of the primordial CMB where diffusion damping suppresses small-scale power.
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Which means that angular power spectra constructed from shear catalogues are more prone to aliasing and other pixelization results. This is exacerbated by the 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 arise as a consequence of insufficient understanding of the measurement course of. While pixel-associated effects might be mitigated through the use of maps at higher resolution and truncating to scales far above the pixel scale, this will increase the run-time of the estimator and might result in empty pixels that have to be accounted for within the interpretation of the power spectra. In the previous case, the impact of pixelization is close to that of a convolution of the shear subject with the pixel window perform, while in the latter case it is nearer to a point sampling. Since small-scale lensing analyses lie between these two regimes, Ref.
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This paper has a number of targets. Secondly, [Wood Ranger shears](http://taxwiki.us/index.php/Wish_To_Spruce_Up_Your_Wardrobe) we elucidate the approximations that go into the HEALPix pixel window perform when applied to shear fields, which is a common method for dealing 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 energy spectra and [Wood Ranger Power Shears price](https://git.autotion.net/rochellefortin) derive the HEALPix pixel window function approximation for spin-2 fields. This part also 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 part four we test our expressions towards simulated shear catalogues. In part 5 we explore another to the usual estimator [Wood Ranger shears](http://guilairo520.gain.tw/viewthread.php?tid=52320&extra=) that does not normalize by the whole weight in every pixel, and in section 6 we present an alternative measurement and testing procedure that considers the source galaxies and weights as fastened within the evaluation. In section 7 we present a brand new technique for estimating energy spectra that roughly interlaces HEALPix grids.
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