= Angular projection of density and Doppler acoustic sources
{title2=$\Theta_\ell\sim\frac{\delta_\gamma}{4}j_\ell(kD_*)-k\theta_bj_\ell'(kD_*)$}
For an outward sightline, Fourier velocity $v_b^i=ik^i\theta_b$, and sudden last scattering, intrinsic photon temperature projects with a <Spherical Bessel function>, while the Doppler term projects with its derivative. Density and velocity acoustic sources are approximately a quarter cycle out of phase. Their amplitude is suppressed by photon diffusion, giving a power damping envelope $e^{-2k^2/k_D^2}$. Projection maps the sound scale to peak spacing approximately $\pi D_*/r_s$ and the damping scale to angular multipoles of order $k_DD_*$.
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