We carefully develop the framework required to model the dynamical tidal
response of a spinning neutron star in an inspiralling binary system, in the
context of Newtonian gravity, making sure to include all relevant details and
connections to the existing literature. The tidal perturbation is decomposed in
terms of the normal oscillation modes, used to derive an expression for the
effective Love number which is valid for any rotation rate. In contrast to
previous work on the problem, our analysis highlights subtle issues relating to
the orthogonality condition required for the mode-sum representation of the
dynamical tide and shows how the prograde and retrograde modes combine to
provide the overall tidal response. Utilising a slow-rotation expansion, we
show that the dynamical tide (the effective Love number) is corrected at first
order in rotation, whereas in the case of the static tide (the static Love
number) the rotational corrections do not enter until second order.
This article presents a development in the study of dynamical tidal response in spinning neutron stars in inspiralling binary systems, focusing on the context of Newtonian gravity. The authors ensure that all necessary details and connections to existing literature are included in the framework they develop.
Conclusions
- The authors successfully decompose the tidal perturbation in terms of normal oscillation modes.
- An expression for the effective Love number, which is valid for any rotation rate, is derived using the normal oscillation modes.
- The analysis unveils important considerations related to the orthogonality condition required for the mode-sum representation of the dynamical tide.
- The combination of prograde and retrograde modes plays a crucial role in determining the overall tidal response.
- By utilizing a slow-rotation expansion, the authors demonstrate that the dynamical tide (effective Love number) is corrected at first order in rotation, while rotational corrections for the static tide (static Love number) begin at second order.
Roadmap for Readers
For readers interested in further exploring this topic, several potential challenges and opportunities lie on the horizon:
Challenges
- Understanding the subtleties of the orthogonality condition for the mode-sum representation of the dynamical tide.
- Investigating the specific mechanisms through which prograde and retrograde modes combine to produce the overall tidal response.
- Addressing possible limitations or assumptions introduced by the Newtonian gravity framework.
Opportunities
- Exploring applications of the derived expression for the effective Love number in various astrophysical scenarios.
- Extending the slow-rotation expansion method to higher orders and investigating the magnitude of rotational corrections to the effective Love number.
- Comparing the results obtained in the Newtonian gravity framework with those obtained using general relativity to understand the impact of relativistic effects on the tidal response.
Future Directions
The future research in this field could involve refining the understanding of the orthogonality condition and investigating its implications on the dynamical tide. Additionally, further studies could focus on the prograde and retrograde mode combination and its role in different astrophysical contexts. It would also be valuable to explore the limitations of the Newtonian gravity framework and potentially incorporate relativistic effects using general relativity. Finally, expanding the slow-rotation expansion technique to higher orders and examining its impact on the effective Love number would provide a deeper understanding of the rotational corrections.
Overall, this work paves the way for advancements in our understanding of tidal responses in spinning neutron stars and opens up avenues for future research in both theoretical and observational astrophysics.