The close-in planet orbiting GJ 436 presents a puzzling orbital eccentricity considering its very short orbital period. Given the age of the system, this planet should have been tidally circularized a long time ago. Many attempts to explain this were proposed in recent years, either involving abnormally weak tides, or the perturbing action of a distant companion. We address here the latter issue based on Kozai migration. We propose that GJ 436b was formerly located further away from the star and that it underwent a migration induced by a massive, inclined perturber via Kozai mechanism. In this context, the perturbations by the companion trigger high amplitude variations to GJ 436b that cause tides to act at periastron. Then the orbit tidally shrinks to reach its present day location. We numerically integrate the 3-body system including tides and General Relativity correction. We first show that starting from the present-day location of GJ 436b inevitably leads to damping the Kozai oscillations and to rapidly circularizing the planet. Conversely, starting from 5-10 times further away allows the onset of Kozai cycles. The tides act in peak eccentricity phases and reduce the semi-major axis of the planet. The net result is an evolution characterized by two phases: a first one with Kozai cycles and a slowly shrinking semi-major axis, and a second one once the planet gets out of the Kozai resonance characterized by a more rapid decrease. The timescale of this process appears in most cases much longer than the standard circularization time of the planet by a factor larger than 50. This model can provide a solution to the eccentricity paradox of GJ 436b. Depending on the various orbital configurations, it can take several Gyrs to GJ 436b to achieve a full orbital decrease and circularization. According to this scenario, we could be witnessing today the second phase of the scenario where the semi-major axis is already reduced while the eccentricity is still significant. We then explore the parameter space and derive in which conditions this model can be realistic given the age of the system. This yields constraints on the characteristics of the putative companion.
The Role of the Kozai-Lidov Mechanism in Black Hole Binary Mergers in Galactic Centers
为了了解恒星质量黑洞双星（BHB）通过引力波（GW）辐射的合并速率，确定合并的主要途径是很重要的。我们用数值模拟的方法研究了银心超大质量黑洞影响半径内BHB的演化。在这一地区的双星的演变是由中央SMBH的扰动为主。特别地，如Antonini和Perets首先指出的，Kozai-Lidov（KL）机制将BHB相对于SMBH的相对倾斜度交换为BHB的偏心率，并且对于某些取向，可以使BHB的偏心率接近1。在非常高的偏心率下，来自BHB的GW发射可以变得有效，导致BHB的成员聚结。我们使用一种新的组合的两个N体代码遵循这种演变。我们被迫模拟小系统来准确地遵循行为。我们已经完成了400个模拟，范围从$\sim$ 300恒星周围的$10^{3}$ M $_{\odot}$黑洞到$\sim$ 4500恒星周围的$10^{4}$ M $_{\odot}$黑洞。这些模拟是第一次遵循SMBH附近的双星的内部轨道，同时也遵循其外部轨道自洽的变化。我们发现，这种机制可以产生合并的最大速率每体积的$\sim 100$ $^{-3}$年$^{-1}$或相当少，如果倾斜振荡的二进制保持不变的BHB倾斜SMBH的变化，或者如果二进制黑洞分数是小的。
Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel-Lidov-Kozai Cycles: Implications in the HD 41004 System
