Waveform Modelling for the Laser Interferometer Space Antenna (2311.01300v2)

Abstract: LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

Insights from Waveform Modelling for LISA

The Laser Interferometer Space Antenna (LISA) represents a transformative step in gravitational-wave astronomy, poised to explore the millihertz sky and detect a diverse array of sources. This paper by the LISA Consortium Waveform Working Group provides an exhaustive review of the waveform modelling efforts tailored for LISA's unique detection environment. The focus is on establishing robust waveform models crucial for interpreting signals from ultra-compact binaries in our galaxy, mergers of massive black holes at cosmological distances, and other intriguing sources.

Core Components of LISA Waveform Modelling

1. Analytical and Numerical Waveforms: The paper outlines several approaches to waveform modelling, including the use of post-Newtonian (PN) and post-Minkowskian (PM) approximations, numerical relativity, and gravitational self-force techniques. Each approach targets different regions of the binary parameter space—numerical relativity is effective for comparable mass binaries, PN for wide orbit systems, and gravitational self-force for binaries with large mass ratios such as EMRIs.
2. Challenges across Methods: Numerical relativity requires extensive computational resources and poses significant challenges in simulating high mass ratios and eccentricities. The PN and PM frameworks strive to incorporate increasingly precise higher-order corrections, while gravitational self-force and perturbation theory unlock novel regimes in extreme mass ratios and compact-object envelope modelling.
3. Harmony and Calibration: Additionally, the integration of Effective-One-Body (EOB) models and Phenomenological Waveforms help synthesize inputs from all four primary techniques, facilitating the modelling of LISA's expected sources across vast swathes of parameter space. These models leverage analytical calculations and calibrate against numerical results to extend coverage robustly. Successful waveform modelling requires iterating across complementary methodologies, which is vital for ensuring accuracy and facilitating data analysis.

Numerical Results and Bold Claims

The paper systematically presents waveform modelling efforts, addressing the challenges of generating accurate predictions for detection with LISA. There are strong numerical results particularly emphasizing on modulation techniques and hybrid models, which combine various analytical and numerical inputs for more comprehensive waveform predictions. Such results are crucial for parameter estimation and ensuring the reliability of source detectability across cosmological distances.

Implications and Future Prospects

• Expansion of Sources: LISA's data promises to extend the gravitational-wave frontier, probing epochs of the Universe currently inaccessible. The versatility offered by finalized or hybrid waveform models paves the path for groundbreaking astrophysical discoveries, like understanding binary formation mechanisms, and probing beyond GR effects.
• Astrophysical Insights: The science gained from interpreting LISA's detections could unravel mysteries surrounding \MBH mergers, and enhance our understanding of galaxy formation processes through accurate spin and mass measurements.
• Cosmological Parameters: The capacity to distinguish electromagnetic counterparts offers potential pathways for \GW-based cosmography, marking potential advances in measuring the Hubble constant and dark energy density parameters.

Path Forward in AI Developments and System Enhancements

The incorporation of AI and machine learning in increasing analysis efficiency, waveform synthesis speed, and error mitigation could prove vital as LISA missions progress. Coupling AI advancements with sophisticated waveform models ensures LISA becomes not just a detection tool, but a pivotal scientific instrument for exploring the unexplored gravitational-wave universe.

In summary, the LISA waveform working group's paper presents a concerted effort to provide the space-based gravitational wave community with the necessary tools to unravel the mysteries of the Universe's compact-object binary systems with unprecedented accuracy.