size_function.h#

#include <sif/model/size_function.h>
SIF_MODEL_SIZE_FUNCTION_H#

Model void size functions, and the spherical-evolution mapping they are expressed in.

The models predict a number density per radius bin in the same container the measurement fills, so a prediction and a catalogue can be plotted and compared directly.

sif_real sif_spherical_map_nonlinear(sif_real delta_linear, sif_option opt)#

Non-linear density contrast a void of a given linear contrast evolves to.

Under SIF_SPHERICAL_B94, the Bernardeau (1994) fit quoted by Jennings, Li & Hu (2013) eq. (A4): delta_NL = (1 - delta_L/c)^-c - 1. Under SIF_SPHERICAL_EXACT, the Einstein-de Sitter expansion solution, by root-find. The two agree to better than 0.1% on the expansion factor.

Note

Only the expanding branch is implemented; a non-negative linear contrast collapses rather than expands.

Parameters:

  • delta_linear – Linear density contrast, strictly negative

  • opt – SIF_SPHERICAL_B94 (default) or SIF_SPHERICAL_EXACT

Returns:

The non-linear contrast, strictly between -1 and 0, or 0 for input outside that branch. A valid result is never 0, so the two are distinguishable.

sif_real sif_spherical_map_linear(sif_real delta_nonlinear, sif_option opt)#

Linear density contrast that evolves into a given non-linear one, the inverse of sif_spherical_map_nonlinear.

Wanted when a barrier is quoted as an observed underdensity rather than as a linear threshold.

Parameters:

  • delta_nonlinear – Non-linear density contrast, strictly between -1 and 0

  • opt – SIF_SPHERICAL_B94 (default) or SIF_SPHERICAL_EXACT

Returns:

The linear contrast, strictly negative, or 0 for input outside that range.

sif_size_function_t *sif_size_function_svdw(const sif_real *k, const sif_real *pk, uint32_t n_points, const sif_real *radii, uint32_t n_radii, sif_real delta_v, sif_real delta_c, sif_option opt)#

Sheth & van de Weygaert void size function.

Jennings, Li & Hu (2013) eqs. (9) and (10): the number-conserving mapping, in which the linear abundance is evaluated at r_L = r / F and reported against r without rescaling its amplitude.

Note

Number conservation makes this model exceed a void volume fraction of one at large radii, which is why Vdn exists. It is reproduced here as the reference, not as a recommendation.

Parameters:

  • k – Wavenumbers, strictly positive and strictly increasing

  • pk – Linear power spectrum sampled at k

  • n_points – Length of k and pk, at least 2

  • radii – Eulerian (observed) void radii, strictly positive

  • n_radii – Number of radii

  • delta_v – Linear void barrier, strictly negative

  • delta_c – Collapse barrier, strictly positive

  • opt – SIF_VSF_BIN_LN (default) or SIF_VSF_BIN_LINEAR for the units, combined with SIF_SPHERICAL_B94 (default) or SIF_SPHERICAL_EXACT for the mapping used to expand the radii. The window is always a top-hat, which is what the barriers are calibrated against.

Note

The Lagrangian-to-Eulerian expansion factor is not an argument: it is (1 + delta_NL)^(-1/3), which delta_v already determines.

Returns:

Newly allocated size function with n_bins = n_radii, released with sif_size_function_free, or NULL on invalid input.

sif_size_function_t *sif_size_function_vdn(const sif_real *k, const sif_real *pk, uint32_t n_points, const sif_real *radii, uint32_t n_radii, sif_real delta_v, sif_real delta_c, sif_option opt)#

Volume-conserving (Vdn) void size function.

Jennings, Li & Hu (2013) eq. (12). Identical to SvdW except that the abundance is divided by the Eulerian volume rather than the Lagrangian one, which conserves volume instead of number and keeps the void volume fraction below unity.

Parameters are as sif_size_function_svdw.

Returns:

Newly allocated size function with n_bins = n_radii, released with sif_size_function_free, or NULL on invalid input.