CAMB: transfer function output
Posted: 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
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