2017/11/30 by Fabien Lacasa
Engineering · Physics and Astronomy · #Astronomy and Astrophysical Research #Computation #Covariance #Galaxies: Formation, Evolution, Phenomena #Galaxy #Halo #Observable #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Space Technology and Applications #Spectral density #astro-ph.CO
paper · pdf · doi:10.1051/0004-6361/201732343
published as A&A 615, A1 (2018) · 18+17 pages, 3+4 figures. Updated to match version published in Astronomy & Astrophysics
openalex created_date 2017/12/04 · openalex publication_date 2018/01/24 · arxiv created 2018/07/11 · arxiv updated 2018/07/12 · openalex updated_date 2026/08/05
As the determination of density fluctuations becomes more precise with larger surveys, it becomes more important to account for the increased covariance due to the non-linearity of the field. Here I have focussed on the galaxy density, with analytical prediction of the non-Gaussianity using the halo model coupled with standard perturbation theory in real space. I carried out an exact and exhaustive derivation of all tree-level terms of the non-Gaussian covariance of the galaxy C ℓ , with the computation developed up to the third order in perturbation theory and local halo bias, including the non-local tidal tensor effect. A diagrammatic method was used to derive the involved galaxy 3D trispectra, including shot-noise contributions. The projection to the angular covariance was derived in all trispectra cases with and without Limber’s approximation, with the formulae being of potential interest for other observables than galaxies. The effect of subtracting shot-noise from the measured spectrum is also discussed, and does simplify the covariance, though some non-Gaussian shot-noise terms still remain. I make the link between this complete derivation and partial terms which have been used previously in the literature, including super-sample covariance (SSC). I uncover a wealth of additional terms which were not previously considered, including a whole new class which I dub braiding terms as it contains multipole-mixing kernels. The importance of all these new terms is discussed with analytical arguments. I find that they become comparable to, if not bigger than, SSC if the survey is large or deep enough to probe scales comparable with the matter-radiation equality k eq . A short self-contained summary of the equations is provided in Sect. 9 for the busy reader, ready to be implemented numerically for analysis of current and future galaxy surveys.