LISA (Laser Interferometer Space Antenna) is a low-frequency gravitational wave observatory (0.1 mHz - 1 Hz) that will be launched by the ESA in 2035. It aims to observe several populations of relativistic binary stars: white dwarf binaries in our Galaxy, supermassive black holes in coalescence, stellar-mass black holes captured by supermassive black holes in galactic nuclei, etc. In addition, we hope to observe stochastic gravitational wave signals from the early Universe. Due to the dominant seismic noise at these frequencies, these sources cannot be observed by ground-based detectors. The observation of these sources will provide unique information about the history of the early Universe, the formation of large structures, the verification of the theory of general relativity, and perhaps the nature of dark matter.
We expect to detect thousands to tens of thousands of sources during the lifetime of the mission, with signals overlapping in time and frequency. In addition, we expect gaps in the data and artefacts from the instrument and the environment (e.g., the impact of micrometeorites or asteroid flybys). We must detect all these sources and characterise them simultaneously: this problem is often referred to as ‘global fit’ and is the main subject of doctoral theses.
1. Mathematical concept (statistics).
Numerous gravitational wave signals dominate the data. The ‘noise’ is in fact made up of a large number of weak sources, which overlap, creating a stochastic foreground. This complicates the concept of source ‘detectability’ and requires it to be treated within a statistical framework. This mathematical framework is necessary even for detected sources in order to measure the quality of the solution found, or when several solutions are identified, to determine their statistical compatibility.
2. Perform an analysis on simulated (realistic) data.
The objective is to reliably detect and characterise all resolvable sources. These results will be used to create the catalogue of gravitational sources available to the scientific community. The main challenge is that some sources are correlated with each other and that all sources are correlated with the shape and level of noise. The simultaneous adjustment/detection of all sources is a difficult problem due to the enormous dimensionality. We will address this problem using Bayesian methods augmented by modern machine learning techniques.