Generalized quasi-Keplerian solution for eccentric, nonspinning compact binaries at 4PN order and the associated inspiral-merger-ringdown waveform

Abstract

We derive fourth post-Newtonian (4PN) contributions to the Keplerian type parametric solution associated with the conservative dynamics of eccentric, nonspinning compact binaries. The solution has been computed while ignoring certain zero-average, oscillatory terms arising due to 4PN tail effects. We provide explicit expressions for the parametric solution and various orbital elements in terms of the conserved energy, angular momentum and symmetric mass ratio. Canonical perturbation theory (along with the technique of Padé approximant) is used to incorporate the 4PN nonlocal-in-time tail effects within the action-angles framework. We then employ the resulting solution to obtain an updated inspiral-merger-ringdown (IMR) waveform that models the coalescence of nonspinning, moderately eccentric black hole binaries, influenced by Hinder et al.[Phys. Rev. D 98, 044015 ( 2018)]. Our updated waveform is expected to be valid over a similar parameter range as the above reference. We also present a related waveform which makes use of only the post-Newtonian equations and thus is valid only for the inspiral stage. This waveform is expected to work for a much larger range of eccentricity (e t ≲ 0.85) than our full IMR waveform (which assumes circularization of the binaries close to merger). We finally pursue preliminary data analysis studies to probe the importance of including the 4PN contributions to the binary dynamics while constructing gravitational waveform templates for eccentric mergers.

Eccentric catastrophes & what to do with them

“…The values of the f-mode frequency and damping time for this choice of mass and radius are ω = 6.9 kHz and τ = 9.3 seconds. We allow p to vary between [4,30]M to vary the values of kR,I . Note that the above values of (ω, τ ) are not representative of results from more realistic NS EOSs.…”

“…Analytic models of the inspiral phase have been developed for binaries with eccentricity e ≲ 0.6 to third post-Newtonian (PN) order [23,24], and in the high eccentricity (e ∼ 1) limit at leading PN order (so-called Newtonian order in both conservative and dissipative dynamics) [25,26]. Significant progress has also been made to extend the effective one-body (EOB) waveforms to arbitrary eccentricity [27][28][29], as well as extend the PN inspiral-only waveforms to full inspiral-merger-ringdown (IMR) waveforms [30]. However, presently it is difficult to quantify exactly how accurate these waveform models are in the high eccentricity regime due to the lack of an 'exact' waveform, specifically those provided by numerical relativity (NR).…”

Inferring eccentricity evolution from observations of coalescing binary black holes

“…Early attempts at incorporating eccentricity within the EOB framework were presented in [20][21][22] but have seen numerous improvements over recent years [23][24][25][26][27][28][29][30][31]. In addition to EOB, there have also been numerous developments using alternative approaches towards modeling the complete IMR signal from eccentric binaries, including numerical relativity (NR) surrogates [32,33] and hybrid models that blend post-Newtonian (PN) evolutions with NR simulations [34][35][36][37]. A key limitation of these approaches, however, is that they are often constrained by the availability of accurate numerical relativity simulations that span the full parameter space and-in the case of surrogates-by the length of the simulations themselves, which often do not cover the early inspiral of the system.…”

Global dynamical analysis of an electronic spin–orbit coupling system

“…Besides these, there are many other advantages for the analysis of dynamical behaviors in the canonical formalism. Up to now, the doubt of chaos in the spinning compact binary system has been explored completely [18,[25][26][27][28][29]. These are attributed to some examples on the spin effects increasing the extension of chaos of objects.…”