ler.gw_source_population.sfr_with_time_delay

Module for computing star formation rates with time delays.

This module provides functions for computing the star formation rate at a given redshift, accounting for time delays between formation and observation. The time delay distribution follows a 1/t power-law form, and the formation redshift is computed using the cosmological age-redshift relation.

Key Features:

  • Time-delayed star formation rate computation

  • Integration with Madau & Fragos (2017) SFR model

  • Monte Carlo integration for time delay averaging

  • Cosmological calculations using Astropy

Copyright (C) 2026 Hemanta Ph. Distributed under MIT License.

Module Contents

Functions

sfr_with_time_delay_function(input_args)

Compute star formation rate at observed redshift with time delay.
ler.gw_source_population.sfr_with_time_delay.sfr_with_time_delay_function(input_args)[source]

Compute star formation rate at observed redshift with time delay.

The star formation rate is time-delayed relative to the observed redshift, with a time delay uniformly distributed between td_min and td_max. The formation redshift is computed using the cosmological age-redshift relation.

Parameters:
input_argslist

List containing the following elements in order:

  • z (float): Observed redshift

  • idx (int): Index identifier for the computation

  • td_min (float): Minimum time delay (Gyr)

  • td_max (float): Maximum time delay (Gyr)

  • H0 (float): Hubble constant (km/s/Mpc)

  • Omega_M (float): Matter density parameter

  • Omega_Lambda (float): Dark energy density parameter

  • a (float): Madau-Fragos SFR normalization parameter

  • b (float): Madau-Fragos low-z power-law slope

  • c (float): Madau-Fragos turnover parameter

  • d (float): Madau-Fragos high-z power-law slope

Returns:
idxint

Index identifier (same as input).

resultfloat

Time-averaged star formation rate at observed redshift z.

Examples

>>> from ler.gw_source_population.sfr_with_time_delay import sfr_with_time_delay
>>> args = [0.5, 0, 0.02, 13.0, 70.0, 0.3, 0.7, 0.01, 2.6, 3.2, 6.2]
>>> idx, sfr = sfr_with_time_delay(args)