Orbital dynamics of circumbinary planets. (arXiv:1908.06331v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Chen_C/0/1/0/all/0/1">Cheng Chen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Franchini_A/0/1/0/all/0/1">Alessia Franchini</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lubow_S/0/1/0/all/0/1">Stephen H. Lubow</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Martin_R/0/1/0/all/0/1">Rebecca G. Martin</a>
We investigate the dynamics of a nonzero mass, circular orbit planet around
an eccentric orbit binary for various values of the binary eccentricity, binary
mass fraction, planet mass, and planet semi–major axis by means of numerical
simulations. Previous studies investigated the secular dynamics mainly by
approximate analytic methods. In the stationary inclination state, the planet
and binary precess together with no change in relative tilt. For both prograde
and retrograde planetary orbits, we explore the conditions for planetary
orbital libration versus circulation and the conditions for stationary
inclination. As was predicted by analytic models, for sufficiently high initial
inclination, a prograde planet’s orbit librates about the stationary tilted
state. For a fixed binary eccentricity, the stationary angle is a monotonically
decreasing function of the ratio of the planet–to–binary angular momentum
$j$. The larger $j$, the stronger the evolutionary changes in the binary
eccentricity and inclination. We also calculate the critical tilt angle that
separates the circulating from the librating orbits for both prograde and
retrograde planet orbits. The properties of the librating orbits and stationary
angles are quite different for prograde versus retrograde orbits. The results
of the numerical simulations are in very good quantitative agreement with the
analytic models. Our results have implications for circumbinary planet
formation and evolution.
We investigate the dynamics of a nonzero mass, circular orbit planet around
an eccentric orbit binary for various values of the binary eccentricity, binary
mass fraction, planet mass, and planet semi–major axis by means of numerical
simulations. Previous studies investigated the secular dynamics mainly by
approximate analytic methods. In the stationary inclination state, the planet
and binary precess together with no change in relative tilt. For both prograde
and retrograde planetary orbits, we explore the conditions for planetary
orbital libration versus circulation and the conditions for stationary
inclination. As was predicted by analytic models, for sufficiently high initial
inclination, a prograde planet’s orbit librates about the stationary tilted
state. For a fixed binary eccentricity, the stationary angle is a monotonically
decreasing function of the ratio of the planet–to–binary angular momentum
$j$. The larger $j$, the stronger the evolutionary changes in the binary
eccentricity and inclination. We also calculate the critical tilt angle that
separates the circulating from the librating orbits for both prograde and
retrograde planet orbits. The properties of the librating orbits and stationary
angles are quite different for prograde versus retrograde orbits. The results
of the numerical simulations are in very good quantitative agreement with the
analytic models. Our results have implications for circumbinary planet
formation and evolution.
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