• Earth;
  • hydrodynamics;
  • methods: numerical;
  • planetary systems;
  • turbulence


In this paper we explore the potential multistability of the climate for a planet around the habitable zone. We focus on conditions reminiscent to those of the Earth system, but our investigation has more general relevance and aims at presenting a general methodology for dealing with exoplanets. We describe a formalism able to provide a thorough analysis of the non-equilibrium thermodynamical properties of the climate system and explore, using a flexible climate model, how such properties depend on the energy input of the parent star, on the infrared atmospheric opacity, and on the rotation rate of the planet. We first show that it is possible to reproduce the multi-stability properties reminiscent of the paleoclimatologically relevant snowball (SB)–warm (W) conditions. We then characterise the thermodynamics of the simulated Wand SB states, clarifying the central role of the hydrological cycle in shaping the irreversibility and the efficiency of the W states, and emphasizing the extreme diversity of the SB states, where dry conditions are realized. Thermodynamics provides the clue for studying the tipping points of the system and leads us to constructing empirical parametrizations allowing for expressing the main thermodynamic properties as functions of the emission temperature of the planet only. Such empirical functions are shown to be rather robust with respect to changing the rotation rate of the planet from the current terrestrial one to half of it. Furthermore, we explore the dynamical range where the length of the day and the length of the year are comparable. We clearly find that there is a critical rotation rate below which the multi-stability properties are lost, and the ice-albedo feedback responsible for the presence of SB and W conditions is damped. The bifurcation graph of the system suggests the presence of a phase transition in the planetary system. Such critical rotation rate corresponds roughly to the phase-lock 2:1 condition. Therefore, if an Earth-like planet is 1:1 phase-locked with respect to the parent star, only one climatic state would be compatible with a given set of astronomical and astro-physical parameters. These results have relevance for the general theory of planetary circulation and for the definition of necessary and sufficient conditions for habitability. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)