Madau-Dickinson Redshift
Sampler for the Madau-Dickinson rate-weighted source redshift distribution.
Functions:¶
madau_dickinson_redshift(key: Array, n_samples: int, z_max: float, *, z_min: float = 0.0, gamma: float = MADAU_DICKINSON_GAMMA, kappa: float = MADAU_DICKINSON_KAPPA, z_peak: float = MADAU_DICKINSON_Z_PEAK, hubble_constant: float = PLANCK18_H0_KM_S_MPC, omega_m: float = PLANCK18_OMEGA_M, n_grid: int = DEFAULT_LOOKUP_GRID_SIZE) -> Array
Draw source redshifts from the Madau-Dickinson rate-weighted distribution.
Samples p(z) proportional to psi(z) / (1 + z) * dVc/dz on [z_min, z_max]
by inverse-transform sampling on a redshift grid, where psi(z) is the
Madau-like rate shape and the single 1 / (1 + z) factor converts the
source-frame rate to the detector frame.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
key
|
Array
|
JAX PRNG key. |
required |
n_samples
|
int
|
Number of redshifts to sample. |
required |
z_max
|
float
|
Maximum redshift. |
required |
z_min
|
float
|
Minimum redshift (default 0). |
0.0
|
gamma
|
float
|
Low-redshift power-law slope. |
MADAU_DICKINSON_GAMMA
|
kappa
|
float
|
High-redshift fall-off exponent offset. |
MADAU_DICKINSON_KAPPA
|
z_peak
|
float
|
Redshift of the rate peak. |
MADAU_DICKINSON_Z_PEAK
|
hubble_constant
|
float
|
Hubble constant in km / s / Mpc. |
PLANCK18_H0_KM_S_MPC
|
omega_m
|
float
|
Matter density. |
PLANCK18_OMEGA_M
|
n_grid
|
int
|
Number of grid points for the inverse-CDF lookup. |
DEFAULT_LOOKUP_GRID_SIZE
|
Returns:
| Type | Description |
|---|---|
Array
|
Sampled redshifts of shape |