Open AccessProjected bispectrum in spherical harmonics and its application to angular galaxy catalogues
Author(s) -
Verde Licia,
Heavens Alan F.,
Matarrese Sabino
Publication year - 2000
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2000.03774.x
Subject(s) - physics , bispectrum , galaxy , redshift , astrophysics , spherical harmonics , cosmic microwave background , sky , degeneracy (biology) , photometric redshift , gravitational lens , correlation function (quantum field theory) , projection (relational algebra) , astronomy , spectral density , algorithm , statistics , optics , quantum mechanics , computer science , bioinformatics , mathematics , optoelectronics , anisotropy , dielectric , biology
We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies. By expanding the 2D distribution of galaxies on the sky in spherical harmonics, we show how the three‐point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can be achieved, it would allow a lifting of the degeneracy between the bias and the matter density parameter of the Universe, which occurs in linear analysis of 3D galaxy catalogues. In previous papers, we have shown how a similar analysis can be done in three dimensions, and we show here through an error analysis and by implementing the method on a simulated projected catalogue that ongoing three‐dimensional galaxy redshift surveys (even with all the additional uncertainties introduced by partial sky coverage, redshift‐space distortions and smaller numbers) will do far better than all‐sky projected catalogues with similar selection function.