发表机构
Yale University; KTH Royal Institute of Technology and Stockholm University（耶鲁大学; 皇家理工学院和斯德哥尔摩大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将轨道偏心率随机性引入能量平衡模型，发现高平均偏心率下，行星雪球与非雪球状态的随机转变发生在恒星通量范围内，且系统达到稳态的概率降低，提示高偏心率行星或多处于永久瞬态。
AI 中文摘要
受Ji和Abbot（2025）最新研究发现的启发：在中等偏心率（0.2--0.3）下，行星的雪球双稳态会消失，我们将轨道偏心率的随机性引入Eisenman和Wettlaufer（2009）能量平衡模型的简化版本中，以研究类地行星。随机偏心率由年周期和日周期两个主导时间尺度近似，并通过开普勒方程分析引入。我们发现，除平均偏心率小于0.1的情况外，随机动力学在定量和定性上均与确定性动力学不同。对于固定的平均偏心率，偏心率波动会放大辐射通量强迫的不对称性和间歇性，从而延长达到稳定季节周期所需的时间。当平均偏心率超过0.1时，从雪球状态到非雪球状态的随机转变发生在平均恒星通量ΔS*的范围内，而非确定性情况下的特定恒星通量S*。此外，当平均偏心率从0.1增加，且年偏心率波动的方差增大时，ΔS*会增加，系统达到稳态并经历雪球到非雪球分岔的概率会降低。这意味着可能存在许多高偏心率行星系统处于永久瞬态状态。
英文摘要
Motivated by the recent finding of Ji and Abbot (2025) that at moderate eccentricity (0.2--0.3) the planetary Snowball bistability vanishes, we have introduced stochasticity of the orbital eccentricity into a simplified version of the energy balance model of Eisenman and Wettlaufer (2009) to study a general Earth-like planet. The stochastic eccentricity is approximated by two dominant time scales, annual and daily, and is introduced through an analysis of the Kepler equation. We find that, apart from mean eccentricities less than 0.1, the stochastic dynamics are quantitatively and qualitatively different than the deterministic dynamics. For a fixed mean eccentricity, fluctuations in eccentricity amplify the asymmetry and intermittency in radiative flux forcing, thereby increasing the time it takes to reach a stable seasonal cycle. As the mean eccentricity increases above 0.1, the stochastic transition from the Snowball to non-Snowball state occurs over a range of mean stellar flux $ΔS^*$ rather that at a particular stellar flux $S^*$ for the deterministic case. Moreover, as the mean eccentricity increases from 0.1 and the variance of the annual eccentricity fluctuations increases, $ΔS^*$ increases and the probability of the system reaching a steady state and experiencing a Snowball to non-Snowball bifurcation decreases. This implies that there may be many high eccentricity planetary systems in a perpetually transient state.
Comments30 pages, 19 figures
