CAMB: transfer function output

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Kyungjin Ahn
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Joined: May 02 2008
Affiliation: Chosun University
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CAMB: transfer function output

Post by Kyungjin Ahn » August 12 2018

Hi,

First off, the version I'm using is Jan 2015 one. I'm cooking an initial condition generator and came up with the following normalization issue.

I have a quick question on the transfer function output, on columns 11-13. Following CAMB Readme the 11th, 12th and 13th columns of the transfer function output file are $-v_{\rm cdm}*k/H$, $-v_{\rm b}*k/H$ and $(v_{\rm b}-v_{\rm cdm})$, respectively, aside from the common $/k^2$ factor. So I've been trying to check whether (col11-col12)$/k*H$ is identical to col13 (col # being #th column), but with no success. So I must be using wrong units for either $k$ or $H$, or both.

So my questions are
1. Is $k$ in column 12 in Mpc$^{-1}$ unit?
2. Is $H$ in column 12 the Hubble parameter at the designated redshift $H(z)$?
3. What is the unit of $H$? I tried Myr$^{-1}$, yr$^{-1}$, s$^{-1}$, km/s/Mpc, but nothing gives me the expected match.

For now I am just using (Newtonian) continuity equation to generate velocity fields of $v_{\rm cdm}$ and $v_{\rm b}$: e.g. for $v_{\rm cdm}$ first getting -d(col2)/dt from two nearby redshifts and using it as the divergence of $v_{\rm cdm}$. This seems to pick up the $\sim d\Phi/dt$ term at $k\lesssim$0.01/Mpc at $z\sim 1000$ because I'm using Newtonian continuity equation but it's OK now because my interest is in subhorizon physics. But I may come to a point of using columns 11 and 12 in the end, so I'd really appreciate if anyone can help. There's also a tiny issue in finite-differencing two nearby data so understanding these units would be better. I fully understand column 13's units and whatnot.

Many thanks in advance!

Kyungjin

Antony Lewis
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Joined: September 23 2004
Affiliation: University of Sussex
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Re: CAMB: transfer function output

Post by Antony Lewis » August 13 2018

$k/\mathcal{H}$ is dimensionless, and everything internally uses Mpc units (H here is the $\mathcal{H}$, the comoving Hubble parameter in ${\rm Mpc}^{-1}$ units).

Kyungjin Ahn
Posts: 4
Joined: May 02 2008
Affiliation: Chosun University
Contact:

Re: CAMB: transfer function output

Post by Kyungjin Ahn » August 13 2018

Thanks a lot for the fast reply Antony! Now I can use these columns.

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