wl_spectra¶
Compute various weak lensing C_ell from P(k,z) with the Limber integral
File |
shear/spectra/interface.so |
Attribution |
CosmoSIS team |
Matt Becker |
|
URL |
DEPRECATED: You should use the module cosmosis-standard-library/structure/projection/project_2d.py instead. The Limber approximation integrates a 3D power spectrum over the radial direction to get a 2D angular power spectrum. It is an approximation which is only valid on smaller scales.
\(C_\ell = A \int_0^{\chi_1} W_1(\chi) W_2(\chi) P(k=l/\chi, z(\chi)) / \chi^2 d\chi\)
The full integral must integrate over k(ell) also. For weak lensing, the power spectrum is the matter power spectrum and the two kernel functions W depend on the redshift bins being used and the geometry. Parts of this code and the underlying implementation of limber are based on cosmocalc: https://bitbucket.org/beckermr/cosmocalc-public
Assumptions¶
The Limber integral is valid on the scales in question
Setup Parameters¶
Name |
Type |
Default |
Description |
|---|---|---|---|
n_ell |
int |
Number of log-spaced ell values to compute |
|
ell_min |
real |
Minimum ell value to compute |
|
ell_max |
real |
Maximum ell value to compute |
|
shear_shear |
bool |
True |
Compute shear auto-spectra? |
intrinsic_alignments |
bool |
False |
Compute intrinsic alignments spectra? |
matter_spectra |
bool |
False |
Compute matter power spectra? |
ggl_spectra |
bool |
False |
Compute galaxy-galaxy lensing spectra? |
gal_IA_cross_spectra |
bool |
False |
Compute cross-power between galaxy positions and alignments? |
mag_gal_cross_spectra |
bool |
False |
Compute lensing magnification cross-spectra? |
mag_mag |
bool |
False |
Compute lensing magnification auto-spectra? |
Input values¶
Section |
Name |
Type |
Default |
Description |
|---|---|---|---|---|
cosmological_parameters |
omega_m |
real |
Density fraction of all matter; used in the prefactor |
|
h0 |
real |
Hubble factor H0 / 100 km/s/Mpc. |
||
distances |
z |
real 1d |
Redshift values of distance samples |
|
d_m |
real 1d |
Comoving distnace to redshift values in units of Mpc (no factor h) |
||
matter_power_nl |
z |
real 1d |
Redshift values of P(k,z) samples |
|
k_h |
real 1d |
Wavenumber k values of P(k,z) samples in units of Mpc/h |
||
P_k |
real 2d |
Non-linear matter power spectrum at samples in (Mpc/h)^{-3} |
||
wl_number_density |
nbin |
int |
Number of redshift bins |
|
z |
real 1d |
Redshift values of n(z) samples |
||
bin_ |
real 1d |
Bin n(z) values. Need not be normalized. bin_1, bin_2, bin_3, …. |
||
matter_power_gal |
z |
real 1d |
Redshift values of P(k,z) samples |
|
k_h |
real 1d |
Wavenumber k values of P(k,z) samples in units of Mpc/h |
||
P_k |
real 2d |
Non-linear galaxy power spectrum at samples in (Mpc/h)^{-3} |
||
matter_power_gal_mass |
z |
real 1d |
Redshift values of P(k,z) samples |
|
k_h |
real 1d |
Wavenumber k values of P_{gm}(k,z) samples in units of Mpc/h |
||
P_k |
real 2d |
Non-linear galaxy-mass cross-power spectrum at samples in (Mpc/h)^{-3} |
Output values¶
Section |
Name |
Type |
Description |
|---|---|---|---|
shear_cl |
ell |
real 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
shear_cl_ii |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
shear_cl_gi |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
matter_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
ggl_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
gal_IA_cross_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
magnification_galaxy_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
magnification_magnification_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
magnification_intrinsic_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |
|
magnification_shear_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |