Browsing by Author "Barrera Retamal, Carlos Mariano"
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Item The Chaotic Four-Body Problem in Newtonian Gravity - II. An ansatz-based approach to analytic solutions.(Universidad de Concepción, 2023) Barrera Retamal, Carlos Mariano; Leigh, Nathan William CecilThe interaction between four bodies is of critical importance to understanding the evolution of star clusters. This is because these interactions have been shown to occur regularly in clusters with high binary fractions (above ∼ 10%), and are critical to deciding the time evolution of the system at high central densities. In this work we continue our analysis of the chaotic four-body problem by presenting a general ansatz-based analytic treatment using statistical mechanics, where each outcome of the four-body problem is regarded as some variation of the three-body problem (e.g., when two single stars are produced, each ejection event is modeled as its own three-body interaction by assuming that the ejections are well separated in time). This is a generalization of the statistical mechanics treatment of the three-body problem first developed by Monaghan (1976a). In our case, we focus on the interaction of two binary systems, after which we divide our results into three possible outcome scenarios (2+2, 2+1+1, and 3+1). For each outcome, we apply an ansatz-based approach to deriving analytic distribution functions that describe the properties of the products of chaotic four-body interactions involving point particles. To test our theoretical distributions, we perform a set of scattering simulations in the equal-mass point particle limit using FEWBODY. We compare our final theoretical distributions to the simulations for each particular scenario, finding consistently good agreement between the two whenever we are able to compare them.