apriltgv96581/9270297
1
0
Code Issues Actions Packages Projects Wiki

Add Pixelization Effects In Cosmic Shear Angular Power Spectra

April Jury 2025-08-13 22:41:26 +00:00
parent b3a679d4f2
commit aa2b194c3e
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 convey residual biases to the percent degree 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 perform approximation is made in the discrete spin-2 setting. We propose several improvements to the usual estimator and its modelling, based mostly on the principle that source positions and [Wood Ranger Power Shears specs](http://wiki.die-karte-bitte.de/index.php/Used_Metal_Shears_For_Sale) weights are to be thought of fixed. We show how empty pixels may 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 present that it may well mitigate the results of aliasing. We introduce bespoke pixel window features adapted to the survey footprint and [Wood Ranger Power Shears specs](http://wiki.die-karte-bitte.de/index.php/No_Squeezing_Of_The_Handles_Needed) show that, for band-limited spectra, biases from utilizing an isotropic window operate can be effectively diminished to zero. This work partly intends to serve as a useful reference for pixel-associated effects in angular energy spectra, which are of relevance for ongoing and forthcoming lensing and clustering surveys.<br>
<br>LambdaCDM and p.c stage constraints on the Dark Energy equation of state. The headline constraints from these surveys will probably be made from two-level statistics measured from catalogues of galaxy shapes and positions. The estimator [Wood Ranger Power Shears specs](https://bbarlock.com/index.php/Are_You_Able_To_Name_All_Of_Those_Sewing_Terms) proceeds by first constructing a map from the discrete set of points, taking the angular energy spectrum, and then interpreting the outcome using mixing matrices constructed from weight maps that hint the survey footprint and different observational inhomogeneities in the data. Cosmic Microwave Background (CMB) knowledge (see Ref. These include the fact that the enter information set is normally within the form of catalogues, i.e. shear measurements at discrete samples across the survey footprint, reasonably than pixelized maps or [Wood Ranger Power Shears specs](http://kmelec.com/bbs/board.php?bo_table=free&wr_id=289015) time-ordered knowledge. Secondly, there is no analogue of the beam in CMB experiments and therefore the one small-scale filtering is because of the discrete sampling of the galaxy place subject. Furthermore, weak lensing and galaxy clustering spectra have vital energy on small scales, not like 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 other pixelization effects. This is exacerbated by the very fact that almost all of the data on cosmological parameters comes from small angular scales which have low statistical uncertainty, so specific care must be taken to ensure that no biases come up attributable to insufficient understanding of the measurement course of. While pixel-related effects might be mitigated by utilizing maps at increased resolution and [Wood Ranger Power Shears manual](https://rentry.co/53322-case-study-wood-ranger-power-shears---the-ultimate-tool-for-gardeners-and-landscapers) Ranger Power Shears truncating to scales far above the pixel scale, this increases the run-time of the estimator and can lead to empty pixels that have to be accounted for in the interpretation of the power spectra. In the former case, the impact of pixelization is near that of a convolution of the shear subject with the pixel window function, while in 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 objectives. Secondly, we elucidate the approximations that go into the HEALPix pixel window operate when utilized to shear fields, which is a common technique for coping with pixelization smoothing. Our paper is partly a companion paper to Ref. This paper is structured as follows. In section 3 we current models for [Wood Ranger Power Shears specs](http://wiki.die-karte-bitte.de/index.php/Benutzer_Diskussion:JHDSanto215151) the influence of pixelization on shear [Wood Ranger Power Shears specs](http://blueroses.top:8888/deonstepp0575) spectra and derive the HEALPix pixel window function approximation for spin-2 fields. This section also presents derivations of power spectrum biases because of finite pixel occupancy and stochasticity of the underlying supply galaxy number counts and their shear weights. In part four we take a look at our expressions towards simulated shear catalogues. In part 5 we explore an alternative to the usual estimator that doesn't normalize by the entire weight in each pixel, and in part 6 we current an alternate measurement and testing procedure that considers the source galaxies and weights as mounted within the evaluation. In part 7 we present a brand new technique for estimating energy spectra that approximately interlaces HEALPix grids.<br>