Relativistic Effects on Triple Black Holes: Burrau’s Problem Revisited. (arXiv:2011.03046v2 [astro-ph.GA] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Chitan_A/0/1/0/all/0/1">Ariel Chitan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Myllari_A/0/1/0/all/0/1">Aleksandr Mylläri</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Haque_S/0/1/0/all/0/1">Shirin Haque</a>
The influence of relativistic corrections on the evolution of triple black
hole systems was studied. Numerical integration of orbits was conducted using
relativistic corrections (post-Newtonian) up to the 2.5$^{th}$ order. Initial
positions of black holes were at the vertices of a Pythagorean triangle(s) with
their mass being proportional to the length of the opposite side of the
triangle. All black holes began with zero initial velocity and zero angular
momentum. The 3,4,5 triangular configuration was studied in detail with mass
unit increasing from 10$^0$ M$_{odot}$ $-$ 10$^{12}$M$_{odot}$ in increasing
factors of 10$^{0.1}$M$_{odot}$ and distance units increasing from 10$^{-1}$pc
$-$ 10$^{4}$pc in increasing factors of 10$^{0.5}$pc. Subsequently, all other
Pythagorean triangles with hypotenuse $<$ 100 were used as initial
configurations. For each configuration, masses ranged from 10$^0$M$_{odot}$
$-$ 10$^{12}$M$_{odot}$ and the distance unit was kept fixed at 1pc. The
effect of distance was also investigated by conducting simulations for all of
the triangles and fixing the mass unit at 10$^{6}$M$_{odot}$. The distance
units were varied from 10$^{-2}$ pc to 10$^{4}$ pc. As a descriptor of the
evolution of the systems, the lifetimes, the number of binary encounters and
the number of mergers were all analysed. There was strong positive correlation
between the fraction of mergers and increasing mass unit (0.9868). There was
strong negative correlation between the average number of binary encounters and
increasing mass unit (-0.9016). The average lifetimes of the systems decayed
exponentially (determination coefficient of 0.9986) as mass unit increased.
The influence of relativistic corrections on the evolution of triple black
hole systems was studied. Numerical integration of orbits was conducted using
relativistic corrections (post-Newtonian) up to the 2.5$^{th}$ order. Initial
positions of black holes were at the vertices of a Pythagorean triangle(s) with
their mass being proportional to the length of the opposite side of the
triangle. All black holes began with zero initial velocity and zero angular
momentum. The 3,4,5 triangular configuration was studied in detail with mass
unit increasing from 10$^0$ M$_{odot}$ $-$ 10$^{12}$M$_{odot}$ in increasing
factors of 10$^{0.1}$M$_{odot}$ and distance units increasing from 10$^{-1}$pc
$-$ 10$^{4}$pc in increasing factors of 10$^{0.5}$pc. Subsequently, all other
Pythagorean triangles with hypotenuse $<$ 100 were used as initial
configurations. For each configuration, masses ranged from 10$^0$M$_{odot}$
$-$ 10$^{12}$M$_{odot}$ and the distance unit was kept fixed at 1pc. The
effect of distance was also investigated by conducting simulations for all of
the triangles and fixing the mass unit at 10$^{6}$M$_{odot}$. The distance
units were varied from 10$^{-2}$ pc to 10$^{4}$ pc. As a descriptor of the
evolution of the systems, the lifetimes, the number of binary encounters and
the number of mergers were all analysed. There was strong positive correlation
between the fraction of mergers and increasing mass unit (0.9868). There was
strong negative correlation between the average number of binary encounters and
increasing mass unit (-0.9016). The average lifetimes of the systems decayed
exponentially (determination coefficient of 0.9986) as mass unit increased.
http://arxiv.org/icons/sfx.gif
