2020/05/31 by Arindam Mazumdar, Somnath Bharadwaj, Debanjan Sarkar · 23 citations
Physics and Astronomy · #Bar (unit) #Bispectrum #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Mathematical physics #Multipole expansion #Order (exchange) #Physics #Quadrupole #Quantum mechanics #Radio Astronomy Observations and Technology #Redshift #Spectral density #Statistics #astro-ph.CO
paper · pdf · doi:10.1093/mnras/staa2548
published in Monthly Notices of the Royal Astronomical Society 498(3), 3975-3984 (Oxford University Press) · 20 pages, 10 figures, Matches accepted version to MNRAS
openalex publication_date 2020/08/20 · arxiv created 2020/09/30 · arxiv updated 2020/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
ABSTRACT The anisotrpy of the redshift space bispectrum Bs(\boldsymbol k1,\boldsymbol k2,\boldsymbol k3), which contains a wealth of cosmological information, is completely quantified using multipole moments Bmℓ (k1,μ ,t), where k1, the length of the largest side, and (μ, t), respectively, quantify the size and the shape of the triangle (\boldsymbol k1,\boldsymbol k2,\boldsymbol k3). We present analytical expressions for all the multipoles that are predicted to be non-zero (ℓ ≤ 8, m ≤ 6) at second-order perturbation theory. The multipoles also depend on β1, b1, and γ2, which quantify the linear redshift distortion parameter, linear bias and quadratic bias, respectively. Considering triangles of all possible shapes, we analyse the shape dependence of all of the multipoles holding k1=0.2 \rm Mpc-1, β 1=1, b1=1, and γ2 = 0 fixed. The monopole B00, which is positive everywhere, is minimum for equilateral triangles. B00 increases towards linear triangles, and is maximum for linear triangles close to the squeezed limit. Both B02 and B04 are similar to B00, however, the quadrupole B02 exceeds B00 over a significant range of shapes. The other multipoles, many of which become negative, have magnitudes smaller than B00. In most cases, the maxima or minima, or both, occur very close to the squeezed limit. | Bmℓ | is found to decrease rapidly if ℓ or m are increased. The shape dependence shown here is characteristic of non-linear gravitational clustering. Non-linear bias, if present, will lead to a different shape dependence.