{"paper":{"title":"Wide Angle Redshift Distortions Revisited","arxiv_id":"astro-ph/0404477","primary_cat":"astro-ph","submitted_at":"2004-04-23T20:12:22+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.92,"id":"s0","own":true,"role":"contribution","text":"We explore linear redshift distortions in wide angle surveys from the point of view of symmetries.","hedge":{"p":0.81,"label":"asserted"},"own_p":0.87,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.07,"limitation":0.0,"future_work":0.0,"contribution":0.92,"interpretation":0.0}},{"i":1,"p":0.64,"id":"s1","own":true,"role":"result","text":"We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular momentum $S_{l_1 l_2 l_3}(\\hat x_1, \\hat x_2, \\hat x)$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.26,"quantitative":false,"quantitative_p":0.2,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.64,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.34,"interpretation":0.0}},{"i":2,"p":0.51,"id":"s2","own":true,"role":"interpretation","text":"The coefficients of the expansion $B_{l_1 l_2 l_3}$ are analogous to the $C_l$'s of the angular power spectrum, and express the anisotropy of the redshift space correlation function.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.14,"quantitative":true,"quantitative_p":0.51,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.35,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.11,"interpretation":0.51}},{"i":3,"p":0.7,"id":"s3","own":true,"role":"result","text":"Moreover, only a handful of $B_{l_1 l_2 l_3}$ are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.93,"main_claim_p":0.37,"quantitative":true,"quantitative_p":0.72,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.7,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.3}},{"i":4,"p":0.87,"id":"s4","own":true,"role":"result","text":"The $B_{l_1 l_2 l_3}$ depend on spherical Bessel moments of the power spectrum and $f = \\Omega^{0.6}/b$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.81,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.29,"role_probabilities":{"gap":0.0,"method":0.08,"result":0.87,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.0}},{"i":5,"p":0.88,"id":"s5","own":true,"role":"result","text":"In the plane parallel limit, the results of \\cite{Kaiser1987} and \\cite{Hamilton1993} are recovered.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.55,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.36,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.88,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.1}},{"i":6,"p":0.86,"id":"s6","own":true,"role":"contribution","text":"The general formalism is used to derive useful new expressions.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.88,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.12,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.86,"interpretation":0.0}},{"i":7,"p":0.75,"id":"s7","own":true,"role":"contribution","text":"We present a particularly simple trigonometric polynomial expansion, which is arguably the most compact expression of wide angle redshift distortions.","hedge":{"p":0.58,"label":"asserted"},"own_p":0.95,"main_claim_p":0.35,"quantitative":true,"quantitative_p":0.5,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.23,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.75,"interpretation":0.0}},{"i":8,"p":0.79,"id":"s8","own":true,"role":"interpretation","text":"These formulae are suitable to inversion due to the orthogonality of the basis functions.","hedge":{"p":0.9,"label":"asserted"},"own_p":0.79,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.11,"background":0.0,"limitation":0.0,"future_work":0.01,"contribution":0.07,"interpretation":0.79}},{"i":9,"p":0.64,"id":"s9","own":true,"role":"contribution","text":"An alternative Legendre polynomial expansion was obtained as well.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.9,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.31,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.64,"interpretation":0.0}},{"i":10,"p":0.72,"id":"s10","own":true,"role":"result","text":"This can be shown to be equivalent to the results of \\cite{SzalayEtal1998}.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.69,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.36,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.72,"background":0.04,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.18}},{"i":11,"p":0.52,"id":"s11","own":false,"role":"interpretation","text":"The simplicity of the underlying theory will admit similar calculations for higher order statistics as 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