Relativistic three-body effects in hierarchical triples. (arXiv:2001.03654v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Lim_H/0/1/0/all/0/1">Halston Lim</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Rodriguez_C/0/1/0/all/0/1">Carl L. Rodriguez</a>

The hierarchical three-body problem has many applications in relativistic
astrophysics, and can potentially explain all of the binary black hole mergers
detected by LIGO/Virgo. However, the majority of studies have only included
relativistic corrections to the two-body equations of motion, and have ignored
the relativistic effects that arise in the presence of a third body. We revisit
this problem and develop a fully consistent derivation of the secular
three-body problem to first post-Newtonian order. We start with the
Einstein-Infeld-Hoffman equations for a three-body system and expand the
accelerations as a power series in the ratio of the semi-major axes of the
inner ($a_1$) and outer ($a_2$) binary. We then perform a post-Keplerian,
two-parameter expansion of the single orbit-averaged Lagrange planetary
equations in $delta = v^2/c^2$ and $epsilon = a_1/a_2$ using the method of
multiple scales. It is well established that eccentricity growth through the
Lidov-Kozai (LK) mechanism can be suppressed or amplified by two-body 1pN
(2BpN) precession. In this study, we derive and investigate three-body 1pN
(3BpN) effects. We find that these effects can lead to eccentricity growth in
triples, occurring over hundreds of LK cycles. The octupole terms can enhance
these effects and lead to even greater eccentricities. In such cases, inclusion
of these effects can substantially alter the evolution of three-body systems as
compared to an analysis in which they are neglected. Careful analysis of
post-Newtonian three-body effects will be important to understand the formation
and properties of coalescing binaries that form via three-body dynamical
processes.

The hierarchical three-body problem has many applications in relativistic
astrophysics, and can potentially explain all of the binary black hole mergers
detected by LIGO/Virgo. However, the majority of studies have only included
relativistic corrections to the two-body equations of motion, and have ignored
the relativistic effects that arise in the presence of a third body. We revisit
this problem and develop a fully consistent derivation of the secular
three-body problem to first post-Newtonian order. We start with the
Einstein-Infeld-Hoffman equations for a three-body system and expand the
accelerations as a power series in the ratio of the semi-major axes of the
inner ($a_1$) and outer ($a_2$) binary. We then perform a post-Keplerian,
two-parameter expansion of the single orbit-averaged Lagrange planetary
equations in $delta = v^2/c^2$ and $epsilon = a_1/a_2$ using the method of
multiple scales. It is well established that eccentricity growth through the
Lidov-Kozai (LK) mechanism can be suppressed or amplified by two-body 1pN
(2BpN) precession. In this study, we derive and investigate three-body 1pN
(3BpN) effects. We find that these effects can lead to eccentricity growth in
triples, occurring over hundreds of LK cycles. The octupole terms can enhance
these effects and lead to even greater eccentricities. In such cases, inclusion
of these effects can substantially alter the evolution of three-body systems as
compared to an analysis in which they are neglected. Careful analysis of
post-Newtonian three-body effects will be important to understand the formation
and properties of coalescing binaries that form via three-body dynamical
processes.

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