From 214a2938596ca3bb418f99fe6498cccbeef76ced Mon Sep 17 00:00:00 2001 From: Abigail Lanning Date: Sat, 1 Nov 2025 02:33:02 +0800 Subject: [PATCH] Add 'Cosmic Shear Power Spectra In Practice' --- Cosmic-Shear-Power-Spectra-In-Practice.md | 9 +++++++++ 1 file changed, 9 insertions(+) create mode 100644 Cosmic-Shear-Power-Spectra-In-Practice.md diff --git a/Cosmic-Shear-Power-Spectra-In-Practice.md b/Cosmic-Shear-Power-Spectra-In-Practice.md new file mode 100644 index 0000000..5d1107c --- /dev/null +++ b/Cosmic-Shear-Power-Spectra-In-Practice.md @@ -0,0 +1,9 @@ +
Cosmic shear is probably the most powerful probes of Dark Energy, focused by several current and [Wood Ranger Tools](https://flensted-jensen.eu/hello-world/) future galaxy surveys. Lensing shear, nonetheless, is simply sampled on the positions of galaxies with measured shapes within the catalog, making its associated sky window function probably the most sophisticated amongst all projected cosmological probes of inhomogeneities, in addition to giving rise to inhomogeneous noise. Partly because of this, cosmic shear analyses have been largely carried out in real-house, making use of correlation features, as opposed to Fourier-space energy spectra. Since the usage of [Wood Ranger Power Shears USA](https://trevorjd.com/index.php/How_Do_You_Beat_The_Furry_Vengeance_Game_On_Poptropica) spectra can yield complementary data and has numerical advantages over real-space pipelines, it is very important develop a complete formalism describing the usual unbiased [buy Wood Ranger Power Shears](https://historydb.date/wiki/Shears_And_Cutting_Machines) spectrum estimators in addition to their associated uncertainties. Building on previous work, this paper comprises a examine of the main complications associated with estimating and decoding shear energy spectra, and presents quick and correct strategies to estimate two key portions wanted for their sensible utilization: the noise bias and the Gaussian covariance matrix, absolutely accounting for survey geometry, [Wood Ranger Tools](http://www.yangjisa.co.kr/bbs/board.php?bo_table=free&wr_id=214043) with some of these outcomes also applicable to different cosmological probes.
+ +
We show the efficiency of those methods by making use of them to the most recent public data releases of the Hyper Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence of systematics in our measurements and the validity of the covariance matrix estimate. We make the resulting energy spectra, covariance matrices, null exams and all associated knowledge crucial for a full cosmological evaluation publicly accessible. It therefore lies on the core of a number of present and [Wood Ranger Tools](https://45.76.249.136/index.php?title=Jake_Shears-Last_Man_Dancing-Album_Review) future surveys, including the Dark Energy Survey (DES)111https://www.darkenergysurvey.org., [Wood Ranger Tools](https://www.ge.infn.it/wiki//gpu/index.php?title=Pruners_Shears) the Hyper Suprime-Cam survey (HSC)222https://hsc.mtk.nao.ac.jp/ssp. Cosmic shear measurements are obtained from the shapes of individual galaxies and [Wood Ranger Tools](http://219.151.182.80:3000/ameliamacredie/wood-ranger-power-shears-shop1989/wiki/Power+Spectrum+Shears%25EF%2583%2581) the shear area can subsequently solely be reconstructed at discrete galaxy positions, making its related angular masks some of probably the most difficult amongst those of projected cosmological observables. That is in addition to the usual complexity of giant-scale structure masks because of the presence of stars and different small-scale contaminants. To this point, cosmic shear has due to this fact largely been analyzed in actual-space as opposed to Fourier-area (see e.g. Refs.
+ +
However, Fourier-house analyses offer complementary info and cross-checks in addition to a number of advantages, similar to simpler covariance matrices, and the possibility to use simple, interpretable scale cuts. Common to those strategies is that [Wood Ranger Power Shears USA](https://historydb.date/wiki/Eight_Best_Hair_Cutting_Shears_For_Professionals_And_Beginners) spectra are derived by Fourier reworking actual-area correlation capabilities, thus avoiding the challenges pertaining to direct approaches. As we'll focus on right here, these problems might be addressed precisely and analytically through the use of energy spectra. In this work, we construct on Refs. Fourier-area, particularly specializing in two challenges confronted by these strategies: the estimation of the noise [Wood Ranger Power Shears features](https://arvd.in/arvdwiki/index.php/User:RichHuntley) spectrum, or noise bias because of intrinsic galaxy shape noise and the estimation of the Gaussian contribution to the ability spectrum covariance. We current analytic expressions for each the shape noise contribution to cosmic shear auto-energy spectra and the Gaussian covariance matrix, which fully account for the consequences of advanced survey geometries. These expressions keep away from the need for potentially expensive simulation-based mostly estimation of those portions. This paper is organized as follows.
+ +
Gaussian covariance matrices within this framework. In Section 3, we current the information units used on this work and [Wood Ranger Tools](https://pipewiki.org/wiki/index.php/Discover_Precision_Cutting_With_Top-Quality_Fabric_Scissors) the validation of our outcomes utilizing these knowledge is offered in Section 4. We conclude in Section 5. Appendix A discusses the effective pixel window function in cosmic shear datasets, and Appendix B accommodates additional details on the null checks performed. In particular, we will focus on the issues of estimating the noise bias and disconnected covariance matrix within the presence of a complex mask, describing basic methods to calculate each precisely. We will first briefly describe cosmic shear and its measurement so as to provide a specific example for the era of the fields thought-about in this work. The following sections, describing energy spectrum estimation, make use of a generic notation applicable to the evaluation of any projected subject. Cosmic shear will be thus estimated from the measured ellipticities of galaxy images, however the presence of a finite level unfold function and noise in the pictures conspire to complicate its unbiased measurement.
+ +
All of these strategies apply different corrections for the measurement biases arising in cosmic shear. We refer the reader to the respective papers and Sections 3.1 and 3.2 for more details. In the best model, the measured shear of a single galaxy could be decomposed into the precise shear, a contribution from measurement noise and the intrinsic ellipticity of the galaxy. Intrinsic galaxy ellipticities dominate the observed [buy Wood Ranger Power Shears](https://nerdgaming.science/wiki/User:AngelicaThielen) and single object shear measurements are due to this fact noise-dominated. Moreover, intrinsic ellipticities are correlated between neighboring galaxies or with the massive-scale tidal fields, resulting in correlations not brought on by lensing, often referred to as "intrinsic alignments". With this subdivision, the intrinsic alignment signal must be modeled as a part of the theory prediction for cosmic shear. Finally we word that measured shears are prone to leakages because of the purpose unfold operate ellipticity and its related errors. These sources of contamination should be both saved at a negligible stage, or modeled and marginalized out. We observe that this expression is equal to the noise variance that may outcome from averaging over a large suite of random catalogs by which the unique ellipticities of all sources are rotated by impartial random angles.
\ No newline at end of file