Basic Simulation of Short Gamma-Ray Burst Detection Rates

Overview

This is a toolkit which comprises python scripts designed for simulating the detections of sGRBs. The scripts are using methods described in "Revisiting Coincidence Rate Between Gravitational Wave Detection and Short Gamma-Ray Burst for the Advanced and Third Generation" by Regimbau et al.

This was written to addresses the following:

• Streamlines the process of simulating the detection rates of Short Gamma Ray Bursts.
• consolidates the sGRB simulation work carried out by the authors into a single toolkit.
• Simplifies the simulation of sGRB detections.
• Provides a basic statistical and visual analysis of simulated points and direct comparisons to real data from the SWIFT satellite, providing a benchmark for accuracy and relevance.

Features

• Detection Rate Visualization: Tools for generating detailed graphs that illustrate the detection rates of GW and sGRB under various parameters.

• Automated Redshift Analysis: Scripts to calculate and analyze the redshift probabilities for detected events, crucial for understanding the cosmological distance and origins of these phenomena.

• Rejection Sampling Simulation: Implementation of the rejection sampling method for realistic simulation of detection events, based on probabilistic models.

• Data Preparation: Scripts to prepare SWIFT data points for analysis and comparison to simulated data.

• Detection Rate Visualization: Tools for creating graphs that illustrate the detection abilities of the SWIFT observatory.

• Automated Redshift Distribution: The ability to draw Redshift probability distribution given a number of star formation rates as described in "Revisiting Coincidence Rate Between Gravitational Wave Detection and Short Gamma-Ray Burst for the Advanced and Third Generation"

• Rejection Sampling Simulation: A basic implementation of a rejection sampling method for the detection of sGRBs based on probabilistic models. -Work in Progress MCMC: A work in progress implementation of a Markov Chain Monte Carlo method for the detection of sGRBs based on probabilistic models using the EMCEE package.

File Descriptions

This is a breakdown of each of the scripts outlining the functionality and their purpose.

swift_data_clean.py

• Purpose: Cleans and prepares SWIFT data for analysis and comparison to simulated data.
• Key Functions:
  • Moves the entries with missing values to a separate such that it can be added at a later date.
  • Ensures consistent units for all data points.
  • Outputs a cleaned dataset that will be used for further analysis.
• Dependencies: requires grb_table of data collected by the Swift Observatory (https://swift.gsfc.nasa.gov/archive/grb_table), ensure the correct columns are selected.

Pz_Redshift.py and Pz_Auto.py

• Purpose: Calculates a redshift probability distribution for sGRBs based on a variety of different SFR. Pz_Redshift.py offeres a manual way allowing for finer control and Pz_Auto.py will automatically calculate the redshift probability distribution for all provided SFR at tmin values of $20 \times 10^{-3}, 100 \times 10^{-3}, 1000 \times 10^{-3}, 3000 \times 10^{-3}, 5000 \times 10^{-3}$
• Key Functions: -Constructs a probability distribution by normalising (in the interval 0–10) the coalescence rate as described by Regimbau et al.
• Dependencies: requires the txt file SFR_Rome.txt to generate the redshift probability distribution for the Rome model, this file was provided by K. Siellez

Rejection_Method.py

• Purpose: Implements a basic rejection sampling method to simulate sGRBs

• Key Functions:

  • Applies a rejection sampling technique to generate a set of simualted sGRBs which are then exported as a txt file for further analysis.
  • Allows the user to specify the number of sGRBs to be simulated, the Pz distribution to be used.

• Dependencies: This script requires the desired Pz distribution to be specified in the Pz file as outputted by either Pz_Redshift.py or Pz_Auto.py

Emcee_Method.py

• Purpose: a starting point for a MCMC simulation of sGRBs using the emcee package

Detection_rate_graph.py

• Purpose: Generates a graph that illustrates the detection rates of sGRBs and compares them to the SWIFT data points and sensitivity curves.
• Key Functions:
  • Creates a graph that compares the simulated population of sGRBs to the SWIFT data points.
  • Allows for detection rate analysis which includes the ability to specify the number of sGRBs above a certain detection threshold.
• Dependencies: This scripts requires the output of the Rejection_Method.py script and the output of swift_data_clean.py to plot the required points.

All of the scripts are designed and implemented to run independently of each other however they do depend on files generated by teh scripts before them.

Dependencies

• Python 3.x
• re
• NumPy
• Matplotlib
• SciPy
• AstroPy
• emcee (for MCMC)

Acknowledgments

This project draws upon the research and findings of T. Regimbau, K. Siellez, D. Meacher, B. Gendre, and M. Boer, whose work has significantly contributed to the field.

Disclaimer

These scripts are intended for research and educational purposes only.