From 630795fc57a206fa3b216011cef3c5eaee2f5dc2 Mon Sep 17 00:00:00 2001 From: trenthay059976 Date: Fri, 24 Oct 2025 20:42:52 +0800 Subject: [PATCH] Add 'Pixelization Effects In Cosmic Shear Angular Power Spectra' --- ...zation-Effects-In-Cosmic-Shear-Angular-Power-Spectra.md | 7 +++++++ 1 file changed, 7 insertions(+) create mode 100644 Pixelization-Effects-In-Cosmic-Shear-Angular-Power-Spectra.md 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..c4a1d29 --- /dev/null +++ b/Pixelization-Effects-In-Cosmic-Shear-Angular-Power-Spectra.md @@ -0,0 +1,7 @@ +
We derive models that may convey residual biases to the percent level 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 operate approximation is made in the discrete spin-2 setting. We suggest a number of enhancements to the standard estimator and its modelling, based mostly on the precept that supply positions and weights are to be thought of fixed. We show how empty pixels might be accounted for either 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 show that it could mitigate the effects of aliasing. We introduce bespoke pixel window functions adapted to the survey footprint and show that, for band-limited spectra, biases from using an isotropic window perform can be effectively lowered to zero. This work partly intends to serve as a helpful reference for pixel-related effects in angular power spectra, which are of relevance for [Wood Ranger official](https://wiki.lerepair.org/index.php/James_Shears_And_Sons) ongoing and forthcoming lensing and clustering surveys.
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LambdaCDM and % stage constraints on the Dark Energy equation of state. The headline constraints from these surveys might be made from two-point statistics measured from catalogues of galaxy shapes and positions. The estimator proceeds by first constructing a map from the discrete set of factors, taking the angular power spectrum, and then decoding the consequence utilizing mixing matrices constructed from weight maps that hint the survey footprint and other observational inhomogeneities in the data. Cosmic Microwave Background (CMB) information (see Ref. These embody the fact that the enter information set is usually in the form of catalogues, i.e. shear measurements at discrete samples throughout the survey footprint, relatively than pixelized maps or [Wood Ranger official](https://3ii.de/brandiekeen197) time-ordered knowledge. Secondly, there is no analogue of the beam in CMB experiments and therefore the one small-scale filtering is due to the discrete sampling of the galaxy position discipline. Furthermore, weak lensing and galaxy clustering spectra have vital energy on small scales, not like in the case of the primordial CMB where diffusion damping suppresses small-scale power.
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Because of this angular energy spectra constructed from shear catalogues are extra vulnerable to aliasing and other pixelization results. That is exacerbated by the fact that the majority of the knowledge on cosmological parameters comes from small angular scales which have low statistical uncertainty, so particular care should be taken to ensure that no biases arise resulting from insufficient understanding of the measurement process. While pixel-related results will be mitigated through the use of maps at greater resolution and truncating to scales far above the pixel scale, this will increase the run-time of the estimator and might lead to empty pixels that have to be accounted for within the interpretation of the facility spectra. In the previous case, the effect of pixelization is near that of a convolution of the shear discipline with the pixel window operate, while in the latter case it's closer 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 goals. Secondly, electric power shears we elucidate the approximations that go into the HEALPix pixel window function when utilized 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 current fashions for the affect of pixelization on shear energy spectra and [Wood Ranger official](http://shinhwaspodium.com/bbs/board.php?bo_table=free&wr_id=4286673) derive the HEALPix pixel window operate approximation for spin-2 fields. This part also presents derivations of energy spectrum biases due to finite pixel occupancy and stochasticity of the underlying source galaxy number counts and their shear weights. In part 4 we check our expressions against simulated shear catalogues. In part 5 we discover an alternate to the usual estimator that doesn't normalize by the full weight in each pixel, [Wood Ranger Power Shears manual](https://utelectra.com/efrenwebre8829) Ranger Power Shears price and in part 6 we present an alternate measurement and testing process that considers the supply galaxies and weights as fixed within the evaluation. In part 7 we present a brand new method for estimating energy spectra that approximately interlaces HEALPix grids.
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