dsf.covariance.ingredients.sigma_crit module

Critical-surface-density ingredients for Delta Sigma covariance calculations.

This module computes inverse comoving critical surface densities and effective source-noise conversion factors for lens-source tomographic bin pairs.

dsf.covariance.ingredients.sigma_crit.effective_sigma_crit_squared(cosmo, *, z_lens, nz_lens, z_source, nz_source)[source]

Return the inverse squared mean inverse critical surface density.

This quantity converts source shape noise into Delta Sigma covariance units for a lens-source tomographic bin pair.

Parameters:

  • cosmo (Cosmology) – CCL cosmology object.

  • z_lens (NDArray[float64]) – Lens redshift grid.

  • nz_lens (NDArray[float64]) – Normalized lens redshift distribution.

  • z_source (NDArray[float64]) – Source redshift grid.

  • nz_source (NDArray[float64]) – Normalized source redshift distribution.

Returns:

Effective \(\Sigma_c^2\) factor for the lens-source bin pair.

Return type:

float

dsf.covariance.ingredients.sigma_crit.effective_squared_sigma_crit(cosmo, *, z_lens, nz_lens, z_source, nz_source)[source]

Return the inverse of the averaged squared inverse critical surface density.

This computes the inverse of the lens- and source-averaged \(\Sigma_{\mathrm{crit}}^{-2}\).

This quantity converts source shape noise into DeltaSigma covariance units for a lens-source tomographic bin pair.

Parameters:

  • cosmo (Cosmology) – CCL cosmology object.

  • z_lens (NDArray[float64]) – Lens redshift grid.

  • nz_lens (NDArray[float64]) – Normalized lens redshift distribution.

  • z_source (NDArray[float64]) – Source redshift grid.

  • nz_source (NDArray[float64]) – Normalized source redshift distribution.

Returns:

Effective \(\Sigma_c^2\) factor for the lens-source bin pair.

Return type:

float

dsf.covariance.ingredients.sigma_crit.sigma_crit_inverse_comoving(cosmo, z_lens, z_source)[source]

Return the inverse comoving critical surface density for one lens redshift.

Sources behind the lens receive non-zero lensing efficiency. Sources at or in front of the lens are assigned zero contribution.

Parameters:

  • cosmo (Cosmology) – CCL cosmology object.

  • z_lens (float) – Lens redshift.

  • z_source (NDArray[float64]) – Source redshift grid.

Returns:

Inverse comoving critical surface density in pc^2 / (h Msun) evaluated on z_source.

Return type:

NDArray[float64]

dsf.covariance.ingredients.sigma_crit.sigma_crit_inverse_source_average(cosmo, *, z_lens, z_source, nz_source)[source]

Return the source-averaged inverse comoving critical surface density.

This averages the lensing efficiency for a fixed lens redshift over the source redshift distribution.

Parameters:

  • cosmo (Cosmology) – CCL cosmology object.

  • z_lens (float) – Lens redshift.

  • z_source (NDArray[float64]) – Source redshift grid.

  • nz_source (NDArray[float64]) – Normalized source redshift distribution.

Returns:

Source-averaged inverse comoving critical surface density.

Return type:

float

dsf.covariance.ingredients.sigma_crit.sigma_crit_squared_average(cosmo, *, z_lens, nz_lens, z_source, nz_source)[source]

Return the effective critical-surface-density squared factor.

This alias preserves the previous public function name.

Parameters:

  • cosmo (Cosmology)

  • z_lens (NDArray[float64])

  • nz_lens (NDArray[float64])

  • z_source (NDArray[float64])

  • nz_source (NDArray[float64])

Return type:

float

dsf.covariance.ingredients.sigma_crit.sigma_crit_squared_inverse_source_average(cosmo, *, z_lens, z_source, nz_source)[source]

Return the source-averaged squared inverse comoving critical surface density.

This averages the lensing efficiency squared for a fixed lens redshift over the source redshift distribution.

Parameters:

  • cosmo (Cosmology) – CCL cosmology object.

  • z_lens (float) – Lens redshift.

  • z_source (NDArray[float64]) – Source redshift grid.

  • nz_source (NDArray[float64]) – Normalized source redshift distribution.

Returns:

Source-averaged squared inverse comoving critical surface density.

Return type:

float