Analytic computation of the secular effects of encounters on a binary: features arising from second-order perturbation theory. (arXiv:1904.09624v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Hamers_A/0/1/0/all/0/1">Adrian S. Hamers</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Samsing_J/0/1/0/all/0/1">Johan Samsing</a>
Binary-single interactions play a crucial role in the evolution of dense
stellar systems such as globular clusters. In addition, they are believed to
drive black hole (BH) binary mergers in these systems. A subset of
binary-single interactions are secular encounters, for which the third body
approaches the binary on a relatively wide orbit, and such that it is justified
to average the equations of motion over the binary’s orbital phase. Previous
works used first-order perturbation theory to compute the effects of such
secular encounters on the binary. However, this approach can break down for
highly eccentric binaries, which are important for BH binary mergers and
gravitational wave sources. Here, we present an analytic computation using
second-order perturbation techniques, valid to the quadrupole-order
approximation. In our calculation, we take into account the instantaneous
back-reaction of the binary to the third body, and compute corrections to
previous first-order results. Using singly-averaged and direct 3-body
integrations, we demonstrate the validity of our expressions. In particular, we
show that the eccentricity change for highly eccentric binaries can reach a
plateau, associated with a large inclination change, and can even reverse sign.
These effects are not captured by previous first-order results. We provide a
simple script to conveniently evaluate our analytic expressions, including
routines for numerical integration and verification.
Binary-single interactions play a crucial role in the evolution of dense
stellar systems such as globular clusters. In addition, they are believed to
drive black hole (BH) binary mergers in these systems. A subset of
binary-single interactions are secular encounters, for which the third body
approaches the binary on a relatively wide orbit, and such that it is justified
to average the equations of motion over the binary’s orbital phase. Previous
works used first-order perturbation theory to compute the effects of such
secular encounters on the binary. However, this approach can break down for
highly eccentric binaries, which are important for BH binary mergers and
gravitational wave sources. Here, we present an analytic computation using
second-order perturbation techniques, valid to the quadrupole-order
approximation. In our calculation, we take into account the instantaneous
back-reaction of the binary to the third body, and compute corrections to
previous first-order results. Using singly-averaged and direct 3-body
integrations, we demonstrate the validity of our expressions. In particular, we
show that the eccentricity change for highly eccentric binaries can reach a
plateau, associated with a large inclination change, and can even reverse sign.
These effects are not captured by previous first-order results. We provide a
simple script to conveniently evaluate our analytic expressions, including
routines for numerical integration and verification.
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