Properties of von Zeipel-Lidov-Kozai oscillations in triple systems at the quadrupole order: relaxing the test particle approximation

摘要: Von Zeipel-Lidov-Kozai (ZLK) oscillations in hierarchical triple systems have important astrophysical implications such as triggering strong interactions and producing, e.g., Type Ia supernovae gravitational wave sources. When considering analytic properties of ZLK at the lowest (quadrupole) expansion order, well complications due to higher-order terms, one usually assumes test particle limit, which bodies inner binary is massless. Although this approximation holds for, planetary systems, it less accurate for with more comparable masses stellar triples. Whereas non-test-particle effects are taken into account numerical simulations, a approach focusing on differences between general case (at quadrupole order) has, our knowledge, not been presented. Here, we derive several secular triples quadruple order. The latter applies even relatively compact triples, long similar mass that octupole-order suppressed. We consider conditions character (circular versus librating), minimum maximum eccentricities, timescales, all function $\gamma \equiv (1/2) L_1/G_2$, ratio inner-to-outer orbital angular momenta variables ($\gamma=0$ limit). In particular, eccentricity effective retrograde orientations non-zero $\gamma$; assuming zero initial eccentricity, peaks $\cos(i_\mathrm{rel,0}) = -\gamma$, where $i_\mathrm{rel,0}$ relative inclination. provide Python script can be used quickly compute these properties.