Secondary CMB Anisotropy I: Reionization - Wayne Hu's Tutorials
Secondary CMB Anisotropy I: Reionization - Wayne Hu's Tutorials
Secondary CMB Anisotropy I: Reionization - Wayne Hu's Tutorials
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Integral Solution<br />
• Projection kernels (monopole, temperature; dipole, doppler):<br />
ℓs = 0, m = 0 α (0)<br />
0ℓ ≡ jℓ<br />
ℓs = 1, m = 0 α (0)<br />
1ℓ ≡ j′ ℓ<br />
• Integral solution: for Θ = ∆T/T<br />
Θ (m)<br />
ℓ (k, 0)<br />
2ℓ + 1 =<br />
• Power spectrum:<br />
Cℓ = 2<br />
π<br />
∞<br />
0<br />
dk<br />
k<br />
<br />
−τ<br />
dDe<br />
<br />
m<br />
ℓs<br />
k3 〈Θ (m)∗<br />
ℓ<br />
Θ(m)<br />
ℓ 〉<br />
(2ℓ + 1) 2<br />
S (m)<br />
ℓs α(m)<br />
ℓsℓ (kD)<br />
• Solving for Cℓ reduces to solving for the behavior of a handful of<br />
sources. Straightforward generalization to polarization.
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