pespace: A new tool of GPU-accelerated and auto-differentiable response generation and likelihood evaluation for space-borne gravitational wave detectors

TL;DR

pespace is a GPU-accelerated, auto-differentiable software tool for Bayesian parameter estimation of space-borne gravitational wave signals, enabling efficient analysis of massive black hole binaries with various detectors.

Contribution

It introduces pespace, integrating waveform models with automatic differentiation and hardware acceleration, enhancing gravitational wave data analysis capabilities.

Findings

Higher modes are crucial for breaking parameter degeneracies.

Detector networks improve source property measurements.

Fisher matrix approximations align well with Bayesian posteriors.

Abstract

Space-borne gravitational wave detectors will expand the scope of gravitational wave astronomy to the milli-Hertz band in the near future. The development of data analysis software infrastructure at the current stage is crucial. In this paper, we introduce \texttt{pespace} which can be used for the full Bayesian parameter estimation of massive black hole binaries with detectors including LISA, Taiji, and Tianqin. The core computations are implemented using the high-performance parallel programming framework \texttt{taichi-lang} which enables automatic differentiation and hardware acceleration across different architectures. We also reimplement the waveform models \texttt{PhenomXAS} and \texttt{PhenomXHM} in the separate package \texttt{tiwave} to integrate waveform generation within the \texttt{taichi-lang} scope, making the entire computation accelerated and differentiable. To demonstrate the functionality of the tool, we use a typical signal from a massive black hole binary to perform the full Bayesian parameter estimation with the complete likelihood function for three scenarios: including a single detector using the waveform with only the dominant mode; a single detector using the waveform including higher modes; and a detector network with higher modes included. The results demonstrate that higher modes are essential in breaking degeneracies, and coincident observations by the detector network can significantly improve the measurement of source properties. Additionally, automatic differentiation provides an accurate way to obtain the Fisher matrix without manual fine-tuning of the finite difference step size. Using a subset of extrinsic parameters, we show that the approximated posteriors obtained by the Fisher matrix agree well with those derived from Bayesian parameter estimation.