Variable Eccentricity-Driven Snowball Bifurcation and Hysteresis of Planetary Climate

In binary star systems, planets orbiting one star can experience strong gravitational perturbation from the secondary star. The Zeipel-Kozai-Lidov mechanism can propel exoplanets into orbits of high eccentricity, resulting in changes in both seasonal variation and mean instellation flux. Such oscillations in the annual global mean instellation flux might lead to global climate transitions between perennial-ice (snowball), seasonal-ice states, and ice-free states. Owing to the nonlinearity caused by the albedo contrast between sea ice and open ocean, climate transitions are associated with the snowball bifurcation. On the other hand, the seasonal variation could stabilize the climate system and hinder such a bifurcation. Understanding the dynamics of planetary climate transitions, such as the snowball bifurcation and associated hysteresis, is pivotal for unraveling planetary climate forced by orbital variations in a binary star system. We investigate how the bifurcation behavior depends on parameters, map climate regimes, and unravel hysteresis phenomena during Kozai cycles for an idealized Earth-like planet. We examine how the snowball bifurcation is affected by the ice-ocean albedo contrast, the sharpness of the albedo transition and the ocean mixed layer depth. The albedo contrast primarily determines the range of eccentricity and semi-major axis where bistability occurs. During the Kozai cycle, besides the hysteresis associated with the bifurcation, there is also rate-dependent hysteresis. This leads to a phase lag in the surface temperature’s temporal evolution in response to variations in instellation. Notably, this phase lag becomes a dominant factor in shorter Kozai cycles when considering the role of the deep ocean. The deep ocean’s influence can prevent planets orbiting close to the mean-stellar-flux limit from entering a snowball state.