Triangle-GB

This repository provides examples for the fast time-delay interferometry (TDI) response model of Galactic binaries (GBs), along with tutorials for some simple data analysis tasks based on Taiji Data Challenge II and LISA Data Challenge. The response model is inspired by the "TDI on the fly" approach proposed in N. J. Cornish et al, PRD (2025), and has been reformulated to support arbitrary detector orbit​ and arbitrary TDI combination. Our implementation of the fast response model has been validated against the more precise (but slower) time-domain simulation implemented in Triangle-Simulator, with residuals well below the instrumental noise level.

Installation

Please ensure Triangle-Simulator is available in your Python environment, which provides essential constants, utilities, and response functions, and you may also need to install bilby for some examples.

1. Install Triangle-Simulator
   install Triangle-Simulator and activate the tri_env environment by

   conda activate tri_env 

2. Install Nested Sampling Tools for some Examples

   pip install bilby nessai-bilby

What's in the examples

• Waveform modeling in both time and frequency domains;
• Rapid search of GB signals using $\mathcal{F}$-statistics and maximum likelihood estimation;
• Posterior inference of GB signals with nested sampling;
• Application on both Taiji Data Challenge II and LISA Data Challenge.

References

• The TDC II paper.
• The fast GB response model for arbitray orbit and TDI (in preparation)