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Approach to the separatrix with eccentric orbits
by Guillaume Lhost, Geoffrey Compère
Submission summary
| Authors (as registered SciPost users): | Geoffrey Compère · Guillaume Lhost |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2412.04249v1 (pdf) |
| Code repository: | https://github.com/gcompere/Approach-to-the-separatrix-with-eccentric-orbits?tab=readme-ov-file |
| Data repository: | https://github.com/gcompere/Approach-to-the-separatrix-with-eccentric-orbits?tab=readme-ov-file |
| Date submitted: | Dec. 17, 2024, 2:03 p.m. |
| Submitted by: | Lhost, Guillaume |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Eccentric binary compact mergers are prime targets of current and future gravitational wave observatories. In the small mass ratio expansion, post-adiabatic inspirals have been modeled up to the separatrix, where first-principle modeling currently ends. In this paper, we derive the analytic late time solution to the adiabatic inspiral in terms of self-force coefficients at the separatrix. We identify the role of the Lambert W−1 function as a key mathematical ingredient in the approach to the separatrix.
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This paper studies how bound orbits of a Schwarzschild black hole evolve under gravitational radiation reaction near the separatrix between bound and plunging orbits. The paper analyses the adiabatic evolution of such inspirals and forms a foundation upon which to develop future transition (from inspiral to plunge) frameworks extending what as been done for quasi-circular inspirals. The results in this paper significantly extend previous analysis (e.g., Cutler, Kennefick and Poisson and Glampedakis and Kennefick) and as such it is a very welcome addition to the literature.
I have a few minor comments and corrections that I will list below. I also have one major question that I would like the authors to answer: In Figure 3 it looks like the separatrix is reached at apoastron. I assume this cannot be a generic feature of the approach to the separatrix so has it occured in this case because of the particular parameter choice? I note that in the work by Becker and Hughes (arXiv:2410.09160) this does not appear to occur in general -- see e.g., their Fig. 4. It is also slightly confusing for the orbit to be at apastron but ψr∗=2.4 (rather than π). Has this occurred due to the rapid evolution of p and e?
Requested changes
- An explanation for the behaviour mentioned above in Fig. 3 should be provided
- In the second paragraph there is a citation to Stein and Warburton -- Ref. [28]. This citation is about the separatrix but the sentence making the citation is referring to an evolving inspiral. I suggest a change of wording here to clarify, e.g., "for a thorough description of the separatrix, see [28])
- In Eq. (2.7) and (2.8) the * notation is used for the first time. I think it should be clarified that "hereafter a * subscript denotes a quantity evaluated at the separatrix"
- In Eq. (3.1) I am not sure e(0) has been defined. Although it is clear what is being referred to it looks to me like its definition should appear in Eq. (2.8)
- The authors may consider merging the two plots in Fig. 1 into one plot, with logδ plotted on the x-axis
- page 16 "as it his described" -> "as it is described"
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)