Dissipative Evolution of Unequal-mass Binary–single Interactions and Its Relevance to Gravitational-wave Detections

Abstract

We present a study on binary-single interactions with energy loss terms such as tidal dissipation and gravitational wave emission added to the equation-of-motion. The inclusion of such terms leads to the formation of compact binaries that form during the three-body interaction through two-body captures. These binaries predominantly merge relative promptly at high eccentricity, with several observable and dynamical consequences to follow. Despite their possibility for being observed in both present and upcoming transient surveys, their outcomes are not firmly constrained. In this paper we present an analytical framework that allows to estimate the cross section of such two-body captures, which permits us to study how the corresponding rates depends on the initial orbital parameters, the mass hierarchy, the type of interacting objects, and the energy dissipation mechanism. This formalism is applied here to study the formation of two-body gravitational wave captures, for which we estimate absolute and relative rates relevant to Advanced LIGO detections. It is shown that two-body gravitational wave captures should have compelling observational implications if a sizable fraction of detected compact binaries are formed via dynamical interactions.

Highly spinning and aligned binary black hole merger in the Advanced LIGO first observing run

“…This is atypical of dynamical formation scenarios, in which binaries harden through successive binary-single interactions. Mergers with large mass-ratios are rare, and can occur if the heavier primary itself is the outcome of a previous BBH coalescence that was retained by the stellar cluster [81,82]. If the seed black holes are non-spinning, the merger product (our putative primary) typically has a spin of χ 1z 0.7; the likelihood of GW151216 nearly rules out the case in which the primary has χ 1z 0.7 and the secondary has a low spin (right panel in Figure 5).…”

Post-Newtonian dynamics in dense star clusters: Binary black holes in the LISA band

“…For this discussion, we use the analytical framework presented in [28,37,80]. For simplicity, the equal mass limit is assumed and we only include strong encounters up to binary-single.…”

Probing the black hole merger history in clusters using stellar tidal disruptions

“…the BBH at state i has a GW inspiral life time, t m,i , less than its binary-single encounter time, t bs,i . Using that the GW inspiral life time can be written as t m,i ≈ t cm,i × (1 − e 2 ) 7/2 , where t cm,i denotes the circular GW inspiral life time for which the BBH eccentricity e = 0 [85], and assuming that the BBH eccentricity distribution follows that of a so-called thermal distribution P (e) = 2e [80], the probabilityP i can then be written as [e.g., 49,51],…”