Triangle-GB

This repository provides the fast time-delay interferometry (TDI) response model of Galactic binaries (GBs) for space-based detectors, together with tutorials for the corresponding data-analysis tasks. 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, and further extended to a space-detector network of arbitrary configuration (e.g. LISA-Taiji-TianQin). 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.

The tutorials cover time-domain vs frequency-domain waveform modeling and cross-validation, rapid search of GB signals with $\mathcal{F}$-statistics, posterior inference of individual GBs with nested sampling, GB reconstruction on LISA Data Challenge data, and joint parameter estimation with a LISA-Taiji-TianQin network.

The response model is shipped as the Python package Triangle_GB, whose source lives in the Triangle_GB/ folder of this repository:

Path	Content
Triangle_GB/	Source of the Triangle_GB package: the TDIFly / TDIFlyGB / TDIFlyGBNetwork classes
Examples/	Tutorial notebooks

Installation

Triangle_GB uses Triangle-Simulator for essential constants, utilities, orbit and TDI response functions, so Triangle-Simulator must be installed first.

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

   conda activate tri_env 

2. Download or Clone the Repository, then

   cd Triangle-GB

3. Install Triangle_GB
   Install the package contained in the Triangle_GB folder into the active tri_env environment by

   pip install -e . 

   After that the fast response model can be imported from anywhere, without being inside this repository:

   from Triangle_GB.TDIFly import *   # TDIFly, TDIFlyGB, TDIFlyGBNetwork

   The response model can also be run on GPU (use_gpu=True), which requires cupy.

4. Install Nested Sampling Tools to Run the Examples

   pip install bilby nessai-bilby

References

• The TDC II paper.
• The fast GB response model for arbitray detector orbit, TDI combinations, and space detector network