Quasi-secular evolution of mildly hierarchical triple systems: analytics and applications for GW sources and hot Jupiters

Abstract

In hierarchical triple systems, the inner binary is perturbed by a distant\ncompanion. For large mutual inclinations, the Lidov-Kozai mechanism secularly\nexcites large eccentricity and inclination oscillations of the inner binary.\nThe maximal eccentricity attained, $e_{\\rm max}$ is simply derived and widely\nused. However, for mildly hierarchical systems (i.e. the companion is\nrelatively close and massive), non-secular perturbations affect the evolution.\nHere we account for fast non-secular variations and find new analytic formula\nfor $e_{{\\rm max}}$, in terms of the system's hierarchy level, correcting\nprevious work and reproducing the orbital flip criteria. We find that $e_{{\\rm\nmax}}$ is generally enhanced, allowing closer encounters between the inner\nbinary components, thus significantly changing their interaction and its final\noutcome. We then extend our approach to include additional relativistic and\ntidal forces. Using our results, we show that the merger time of\ngravitational-wave (GW) sources orbiting massive black-holes in galactic nuclei\nis enhanced compared with previous analysis accounting only for the secular\nregime. Consequently, this affects the distribution and rates of such GW\nsources in the relevant mild-hierarchy regime. We test and confirm our\npredictions with direct N-body and 2.5-level Post-Newtonian codes. Finally, we\ncalculate the formation and disruption rates of hot-Jupiters (HJ) in planetary\nsystems using a statistical approach, which incorporates our novel results for\n$e_{{\\rm max}}$. We find that more HJ migrate from further out, but they are\nalso tidally disrupted more frequently. Remarkably, the overall formation rate\nof HJs remains similar to that found in previous studies. Nevertheless, the\ndifferent rates could manifest in different underlying distribution of observed\nwarm-Jupiters.\n