“Closed-form Expressions for Ringdown Complex Amplitudes in Eccentric Binaries”

arXiv:2406.19442v1 Announce Type: new
Abstract: Closed-form expressions for the ringdown complex amplitudes of nonspinning unequal-mass binaries in arbitrarily eccentric orbits are presented. They are built upon 237 numerical simulations contained within the RIT catalog, through the parameterisation introduced in [Phys. Rev. Lett. 132, 101401]. Global fits for the complex amplitudes, associated to linear quasinormal mode frequencies of the dominant ringdown modes, are obtained in a factorised form immediately applicable to any existing quasi-circular model. Similarly to merger amplitudes, ringdown ones increase by more than 50% compared to the circular case for high impact parameters (medium eccentricities), while strongly suppressed in the low impact parameter (highly eccentric) limit. Such reduction can be explained by a transition between an “orbital-type” and an “infall-type” dynamics. The amplitudes (phases) fits accuracy lies around a few percent (deciradians) for the majority of the dataset, comparable to the accuracy of current state-of-the-art quasi-circular ringdown models, and well within current statistical errors of current LIGO-Virgo-Kagra ringdown observations. These expressions constitute another building block towards the construction of complete general-relativistic inspiral-merger-ringdown semi-analytical templates, and allow to extend numerically-informed spectroscopic analyses beyond the circular limit. Such generalisations are key to achieve accurate inference of compact binaries astrophysical properties, and tame astrophysical systematics within observational investigations of strong-field general relativistic dynamics.

Ringdown Complex Amplitudes of Nonspinning Unequal-Mass Binaries in Eccentric Orbits

In this article, closed-form expressions for the ringdown complex amplitudes of nonspinning unequal-mass binaries in arbitrarily eccentric orbits are presented. These expressions are based on 237 numerical simulations from the RIT catalog and are obtained using a parameterisation technique introduced in a previous study [Phys. Rev. Lett. 132, 101401]. The complex amplitudes are associated with linear quasinormal mode frequencies of the dominant ringdown modes, allowing for easy application to existing quasi-circular models.

Conclusions

• Ringdown amplitudes for nonspinning unequal-mass binaries increase by more than 50% compared to the circular case for high impact parameters (medium eccentricities).
• Ringdown amplitudes are strongly suppressed in the low impact parameter (highly eccentric) limit.
• The accuracy of the amplitude fits is within a few percent for the majority of the dataset, comparable to current state-of-the-art quasi-circular ringdown models.
• The phase fits accuracy is within a few deciradians for the majority of the dataset.
• These expressions are a building block for the construction of complete general-relativistic inspiral-merger-ringdown semi-analytical templates.
• The expressions allow for the extension of numerically-informed spectroscopic analyses beyond the circular limit.
• Accurate inference of compact binaries astrophysical properties can be achieved using these generalizations.
• Astrophysical systematics can be controlled within observational investigations of strong-field general relativistic dynamics using these expressions.

Future Roadmap

The findings of this study open up several opportunities and challenges for future research in the field of compact binary astrophysics and gravitational wave observations.

Opportunities:

1. The ringdown amplitudes for nonspinning unequal-mass binaries provide valuable insights into the dynamics of eccentric orbits. Further studies can investigate the physical mechanisms behind the increase in amplitudes for high impact parameters and the suppression for low impact parameters.
2. The accuracy of the amplitude and phase fits, comparable to current state-of-the-art models, allows for improved accuracy in the inference of astrophysical properties of compact binaries. This can lead to a better understanding of black hole mergers and their implications in cosmology.
3. The ability to extend numerically-informed spectroscopic analyses beyond the circular limit opens up new avenues for studying the behavior of compact binaries in eccentric orbits. This can provide valuable data for testing and refining theoretical predictions.

Challenges:

• One challenge is to validate the closed-form expressions presented in this study using independent numerical simulations or experimental data. This would ensure the reliability and accuracy of the derived expressions.
• Further investigations are needed to understand the physical significance of the transition between “orbital-type” and “infall-type” dynamics and its impact on the ringdown amplitudes. This could involve more detailed numerical simulations and analytical modeling.
• Efforts should be made to incorporate these findings into existing gravitational wave data analysis pipelines. This requires developing techniques to efficiently and accurately include the effects of eccentric orbits in the analysis frameworks.

In conclusion, the presented closed-form expressions for ringdown complex amplitudes of nonspinning unequal-mass binaries in eccentric orbits provide valuable insights and tools for future research in compact binary astrophysics and gravitational wave observations. Despite the challenges ahead, the opportunities for advancing our understanding of strong-field general relativistic dynamics and improving the accuracy of astrophysical parameter inference are substantial.

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