Amplitude of velocity perturbations at last scattering

[smallphi]

I need to know the magnitude of the velocity perturbations (peculiar velocities) dv at time of last scattering as function of the multipole moment.

The temperature power spectrum of CMB shows temperature fluctuations dT/T ~ 10^-5. That naively suggests the peculiar velocities were dv/c ~ 10^-5. I need more precise estimate than that since the Dopler effect is a small contribution to the dT/T in CMB.

Any reference where dv are derived and shown numerically for different multipole moments?
I need numbers like dv/c = 10^-5 or 10^-4 etc.

 

[Chalnoth]

I need to know the magnitude of the velocity perturbations (peculiar velocities) dv at time of last scattering as function of the multipole moment.

The temperature power spectrum of CMB shows temperature fluctuations dT/T ~ 10^-5. That naively suggests the peculiar velocities were dv/c ~ 10^-5. I need more precise estimate than that since the Dopler effect is a small contribution to the dT/T in CMB.

Any reference where dv are derived and shown numerically for different multipole moments?
I need numbers like dv/c = 10^-5 or 10^-4 etc.

Well, I can't give you an answer straight away, but it seems to me that a good way to go about this would be to first determine the gravitational potentials that result from having dT/T ~ 10^-5, and then compute the average velocities using the virial theorem. Going this route would requite some knowledge of linear perturbation theory.