标题： 双星潮汐相互作用的潜在宜居行星轨道演化 显示英文标题

标题： Orbital evolution of potentially habitable planets of tidally interacting binary stars

摘要： 我们模拟了短周期双星（轨道周期为$P_{orb} \lsim$8天）的恒星演化与潮汐演化耦合，以研究围绕双星的行星（CBPs）的轨道振荡、照度循环和轨道稳定性。 我们考虑了两种潮汐模型，并表明两者都预测了双星半长轴$a_{bin}$和偏心率$e_{bin}$的先向外再向内演化。 这种轨道演化驱动了CBP轨道稳定性最小半长轴的类似演化。 通过扩展之前的模型以包括质量集中度的演化，我们显示围绕双星的行星轨道稳定性极限的最大值通常发生在行星形成后100百万年，比之前的研究长一个数量级。 这一结果进一步支持了早期双星的恒星潮汐演化已将CBPs从短周期双星中移除的假设。 然后我们将模型应用于开普勒-47b，一颗围绕其宿主恒星稳定性极限附近运行的CBP，以表明如果该双星的初始$e_{bin} \gsim$为0.24，则该行星在过去会位于不稳定区域之内，可能无法幸存。 对于稳定性限制未达到行星轨道的稳定假设情况，我们发现 $a_{bin}$和$e_{bin}$振荡的幅度分别可以衰减高达10%和50%。 最后，我们考虑了$P_{orb} =$为7.5天的等质量恒星，并比较了宜居带与稳定性极限。 我们发现，对于恒星质量为$\lsim0.12M_{\odot}$的情况，宜居带完全不稳定，即使双星轨道是圆形的。对于 $e_{bin} \lsim$ 大于 0.5 时，这个限制增加到$0.17M_{\odot}$，并且对于高达$0.45M_{\odot}$ 的恒星质量，宜居带部分失去稳定性。这些结果可能有助于指导对潜在宜居的CBP（恒星伴行星）的搜索，以及在它们被发现后对其演化和支持生命的可能性进行表征。 显示英文摘要

摘要： We simulate the coupled stellar and tidal evolution of short-period binary stars (orbital period $P_{orb} \lsim$8 days) to investigate the orbital oscillations, instellation cycles, and orbital stability of circumbinary planets (CBPs). We consider two tidal models and show that both predict an outward-then-inward evolution of the binary's semi-major axis $a_{bin}$ and eccentricity $e_{bin}$. This orbital evolution drives a similar evolution of the minimum CBP semi-major axis for orbital stability. By expanding on previous models to include the evolution of the mass concentration, we show that the maximum in the CBP orbital stability limit tends to occur 100 Myr after the planets form, a factor of 100 longer than previous investigations. This result provides further support for the hypothesis that the early stellar-tidal evolution of binary stars has removed CBPs from short-period binaries. We then apply the models to Kepler-47 b, a CBP orbiting close to its host stars' stability limit, to show that if the binary's initial $e_{bin} \gsim$0.24, the planet would have been orbiting within the instability zone in the past and probably wouldn't have survived. For stable, hypothetical cases in which the stability limit does not reach a planet's orbit, we find that the amplitudes of $a_{bin}$ and $e_{bin}$ oscillations can damp by up to 10\% and 50\%, respectively. Finally, we consider equal-mass stars with $P_{orb} =$ 7.5 days and compare the HZ to the stability limit. We find that for stellar masses $\lsim0.12M_{\odot}$, the HZ is completely unstable, even if the binary orbit is circular. For $e_{bin} \lsim$0.5, that limit increases to $0.17M_{\odot}$, and the HZ is partially destabilized for stellar masses up to $0.45M_{\odot}$. These results may help guide searches for potentially habitable CBPs, as well as characterize their evolution and likelihood to support life after they are found.