Matter power spectrum and matter transfer function variables

The various matter power spectrum functions, e.g. get_matter_power_interpolator(), can calculate power spectra for various quantities. Each variable used to form the power spectrum has a name as follows:

name	number	description
k/h	1	\(k/h\)
delta_cdm	2	\(\Delta_c\), CDM density
delta_baryon	3	\(\Delta_b\), baryon density
delta_photon	4	\(\Delta_\gamma\), photon density
delta_neutrino	5	\(\Delta_r\), for massless neutrinos
delta_nu	6	\(\Delta_\nu\) for massive neutrinos
delta_tot	7	\(\frac{\rho_c\Delta_c+\rho_b\Delta_b+\rho_\nu\Delta_\nu}{\rho_c+\rho_b+\rho_\nu}\), CDM+baryons+massive neutrino density
delta_nonu	8	\(\frac{\rho_c\Delta_c+\rho_b\Delta_b}{\rho_b+\rho_c}\), CDM+baryon density
delta_tot_de	9	\(\frac{\rho_c\Delta_c+\rho_b\Delta_b+\rho_\nu\Delta_\nu +\rho_{ de}\Delta_{de}}{\rho_c+\rho_b+\rho_\nu}\), CDM+baryons+massive neutrinos+ dark energy (numerator only) density
Weyl	10	\(k^2\Psi\equiv k^2(\phi+\psi)/2\), the Weyl potential scaled by \(k^2\) to scale in \(k\) like a density.
v_newtonian_cdm	11	\(-v_{N,c}\, k/{\cal H}\) (where \(v_{N,c}\) is the Newtonian-gauge CDM velocity)
v_newtonian_baryon	12	\(-v_{N,b}\,k/{\cal H}\) (Newtonian-gauge baryon velocity \(v_{N,b}\))
v_baryon_cdm	13	\(v_b-v_c\), relative baryon-CDM velocity

The number here corresponds to a corresponding numerical index, in Fortran these are the same as model.name, where name are the Transfer_xxx variable names: Transfer_kh=1,Transfer_cdm=2, Transfer_b=3, Transfer_g=4, Transfer_r=5, Transfer_nu=6, Transfer_tot=7, Transfer_nonu=8, Transfer_tot_de=9, Transfer_Weyl=10, Transfer_Newt_vel_cdm=11, Transfer_Newt_vel_baryon=12, Transfer_vel_baryon_cdm = 13.

So for example, requesting var1=’delta_b’, var2=’Weyl’ or alternatively var1=model.Transfer_b, var2=model.Transfer_Weyl would get the power spectrum for the cross-correlation of the baryon density with the Weyl potential. All density variables \(\Delta_i\) here are synchronous gauge.

For transfer function variables (rather than matter power spectra), the variables are normalized corresponding to unit primordial curvature perturbation on super-horizon scales. The get_matter_transfer_data() function returns the above quantities divided by \(k^2\) (so they are roughly constant at low \(k\) on super-horizon scales).

The example notebook has various examples of getting the matter power spectrum, relating the Weyl-potential spectrum to lensing, and calculating the baryon-dark matter relative velocity spectra. There is also an explicit example of how to calculate the matter power spectrum manually from the matter transfer functions.

When generating dark-age 21cm power spectra (do21cm is set) the transfer functions are instead the model.name variables (see equations 20 and 25 of astro-ph/0702600)

name	number	description
Transfer_kh	1	\(k/h\)
Transfer_cdm	2	\(\Delta_c\), CDM density
Transfer_b	3	\(\Delta_b\), baryon density
Transfer_monopole	4	\(\Delta_s+(r_\tau-1)(\Delta_{b}-\Delta_{T_s})\), 21cm monopole source
Transfer_vnewt	5	\(r_\tau kv_{N,b}/\mathcal{H}\), 21cm Newtonian-gauge velocity source
Transfer_Tmat	6	\(\Delta_{T_m}\), matter temperature perturbation
Transfer_tot	7	\(\frac{\rho_c\Delta_c+\rho_b\Delta_b+\rho_\nu\Delta_\nu}{\rho_c+\rho_b+\rho_\nu}\), CDM+baryons+massive neutrino density
Transfer_nonu	8	\(\frac{\rho_c\Delta_c+\rho_b\Delta_b}{\rho_b+\rho_c}\), CDM+baryon density
Transfer_tot_de	9	\(\frac{\rho_c\Delta_c+\rho_b\Delta_b+\rho_\nu\Delta_\nu +\rho_{ de}\Delta_{de}}{\rho_c+\rho_b+\rho_\nu}\), CDM+baryons+massive neutrinos+ dark energy (numerator only) density
Transfer_Weyl	10	\(k^2\Psi\equiv k^2(\phi+\psi)/2\), the Weyl potential scaled by \(k^2\) to scale in \(k\) like a density.
Transfer_Newt_vel_cdm	11	\(-v_{N,c}\, k/{\cal H}\) (where \(v_{N,c}\) is the Newtonian-gauge CDM velocity)
Transfer_Newt_vel_baryon	12	\(-v_{N,b}\,k/{\cal H}\) (Newtonian-gauge baryon velocity \(v_{N,b}\))
Transfer_vel_baryon_cdm	13	\(v_b-v_c\), relative baryon-CDM velocity

If use_21cm_mK is set the 21cm results are multiplied by \(T_b\) to give results in mK units.