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.