A simple example of return mapping
This example illustrates return mapping for multipole number ℓ = 6, utilizing the WMAP ILC map data. The analysis focuses on the multipole expansion, specifically examining the phases of m=0, m=1, m=2, and m=3. Coordinate points such as (1.2783, 5.9600) and (3.1416, 1.2783) are crucial for demonstrating phase relationships in the context of angular power spectra. The resulting mappings provide insights on multipole behavior and their phase relationships in the cosmic microwave background field.
A simple example of return mapping
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Presentation Transcript
A simple example of return mapping Return mapping for Dm=1 The multipole number ℓ = 6 from the WMAP ILC map : m Fℓ,m (3.3140, 6.2222) 0 3.1416 (3.1416, 1.2783) Phase of m=1 and m=2 form a point (x,y)=(1.2783, 5.9600) 1 1.2783 (1.2783, 5.9600) (6.2222, 3.8744) 2 5.9600 (5.9600, 3.3140) 3 3.3140 Fℓ,m+1 (5.9600, 3.3140) (3.3140, 6.2222) 4 6.2222 (6.2222, 3.8744) 5 3.8744 Phases of m=0 and m=1 form a point with coordinate (x,y)=(3.1416, 1.2783) (3.8744, 1.1580) 6 1.1580 (3.8744, 1.1580) Fℓ,m
A simple example of return mapping Return mapping for Dm=2 m Fℓ,m (5.9600, 6.2222) 0 3.1416 Phases of m=0 and m=2 form a point (x,y)=(3.1416, 5.9600) (3.1416, 5.9600) 1 1.2783 (1.2783, 3.3140) 2 5.9600 3 3.3140 (5.9600, 6.2222) Fℓ,m+2 (3.3140, 3.8744) 4 6.2222 (3.3140, 3.8744) Phases of m=1 and m=3 form a point (x,y)=(1.2783, 3.3140) 5 3.8744 (6.2222, 1.1580) 6 1.1580 (6.2222, 1.1580) Fℓ,m
