Welcome to ler’s documentation!

ler

ler (/ˈɛlɚ/): LVK (LIGO-Virgo-KAGRA collaboration) Event (compact-binary mergers) Rate calculator and simulator.

ler is a statistical based python package whose core function is to calculate detectable rates of gravitational waves events (both lensed and un-lensed events). Description available in the Summary section.

The code is available at github.ler.

For reaching out to the developer, please raise issue in github.ler.issue.

ler is closely integarted with a gravitational waves SNR calculator package gwsnr.

ler main developer: Hemanta Ph.

ler developer and analyst: Anupreeta More, Harsh Narola, Ng Chung Yin (Leo), Justin Janquart, Chris Van Den Broeck, Otto Akseli Hannuksela, Neha Singh, David Keitel

Glossary

Gravitational waves

Animation showing the propagation of gravitational waves from inspiraling binary black holes. Source : Jeffrey Bryant, Wolfram|Alpha, LLC.

Ripples in the fabric of space-time caused by some of the most violent and energetic processes in the Universe, such as merger of compact binaries (e.g., black holes and neutron stars) and supernovae explosions. Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity, but it took a century to detect them directly. The first detection was made in 2015 by the LIGO and Virgo collaborations, which won the 2017 Nobel Prize in Physics. Gravitational waves are invisible, yet incredibly fast; they travel at the speed of light, squeezing and stretching anything in their path.

Lensing of gravitational waves

Interactive animation showing the lensing of gravitational waves by a massive object.

A process similar to the gravitational lensing of light, where gravitational waves emitted from distant astrophysical events are bent and splitted (strong-lensing case) into multiple images by the gravity of intervening massive objects, such as galaxy and galaxy cluster. This can magnify and change the arrival time of the gravitational waves.

Animation showing the bending of light by a massive object. Source : NASA, ESA, and Goddard Space Flight Center/K. Jackson.

Rate calculation and statistics

Figure showing the merger rate density of binary black hole (BBH) mergers as a function of redshift. Source : generated by the LeR package.

In the context of astrophysics and gravitational wave science, rate calculation involves predicting the frequency of events such as compact-binary mergers based on observed data and theoretical models. Statistical methods are used to analyze and interpret the data, estimate parameters, and test hypotheses.

Contents:

• Installation
  • ler for development
  • Installation of numba with conda
• Summary
  • Sampling Gravitational Wave Source Properties:
  • Lensing Related:
  • Calculation of Detectable Merger Rates Per Year:
  • Distribution binary black hole (BBH) in terms of redshift.
• Code overview
• Gravitational wave event rates
  • Annual Rate of Detectable Gravitational Wave Events
  • Compact Binaries Merger Rate Density
  • Compact binaries mass distribution
  • Sampling Methods for Compact Binary Sources
  • Statistical Form of Detectable Merger Rate (Monte Carlo Integration)
• Gravitational wave events sampling (Analytical formulation)
  • Initial setup
  • Rate equation (statistical formulation)
  • The order of sampling and rate calculation steps in LeR are listed below.
• Lensed event rates
  • Annual Rate of Detectable Lensed Gravitational Wave Events
  • SNR Operator for Lensed Gravitational Wave Events
  • Redshift distribution of lensed GW compact binary coalescences (CBC)
  • Sampling Lens Properties
  • Sampling of Source Position
  • Calculation of Images properties
  • Statistical Form of Detectable Merger Rate of lensed events (Monte Carlo Integration)
• Lensed event sampling (Analytical formulation)
  • Initial setup
  • General formulation of rate equation.
  • Optical depth

Examples:

• LeR complete examples
  • TOC:
  • Short lensed or unlensed BBH example with three detectors.
  • Using custom functions and parameters.
  • Uning available model functions
  • Generating particular number of detectable events.
  • Using custom detection criteria.
• GWRATES complete exmaples
  • Short BBH (Binary Black Hole) example with three detectors
  • Simulation of the GW CBC population
  • Plot the generated parameters
  • Custom functions
  • Using internal model functions
  • Generating particular number of detectable events
  • Using custom detection criteria
  • BNS (Binary Neutron Star) example
• Calculation of detectable Gamma ray burst (GRB) event rate associated with Binary Neutron Star (BNS) mergers.
  • Equations (GRB)
  • Probability of detection of GRBs
  • Rate calculation of GRB with LeR
  • Rate calculation of GW with LeR
  • Final results
• LeR complete examples of BNS events (O4 design sensitivity)
  • Models Considered
  • Un-lensed events
  • Lensed events
  • Time delay distribution
  • Magnification distribution
• Event Rates with 3G detectors
  • With ANN snr (IMRphenomXPHM)
• Merger rate density evolution with redshift
  • Plotting differential comoving volume
  • Merger rate evolution with redshift (detector frame)
  • BBH
  • BNS
  • Redshift distribution (BBH)
• Merger rate density model comparision
  • Introduction
  • BBH/BNS merger rate at source redshift \(z_s\) (in small dz)
  • BBH/BNS pop I/II Oguri et al. 2018 model
  • Star formation rate
  • BBH pop III model, Ng et al. 2022
• Primordial BBH model, Ng et al. 2022
  • Plots and comparison
  • Merger rate density (detector frame)
  • Conclusion
  • Bonus plot
• Sampling parameters for a compact binary
  • Introduction
  • Sampling of parameters
  • Available priors and their comparisions
  • BBHs mass distribution with different origins (popI/II vs popIII vs primordial black holes)
• Statistical study of changing Mass model paramter(s)
  • Binary Black Hole (BBH) Mass Model
  • Binary Neutron Star (BNS) Mass Model
  • Calculation of rates (per year)
  • Un-lensed
• Statistical study of cosmological friction and its effect on the redshift vs inferred chirp-mass relation of gravitational waves
  • Function to convert from luminosity distance to redshift
  • Functional form of change in the luminosity distance due to cosmological friction
  • BBH events (O4 sensitivity)
  • Inferred source chirp-mass vs redshift
  • BBH (3G sensitivities)
  • Rates of detectable events per year
• Lens parameter distributions
  • Model 1
  • Model 2
• Optical depth SIE model validation
  • Let’s look at the available functions and priors
• Validation of SIS model (Numerical vs Analytical)
• Study of Time delays and magnification of lensed gravitational waves.
  • data generation
  • 2-image case
  • KDE
  • corner plots
  • magnification plot
  • Contour plot
  • 4-image case

Indices and tables

• Index

• Module Index

• Search Page