Planetary-sized pure quantum states

Picture a planet wandering intergalactic space. Such a planet would only couple to vacuum flucuations and the cosmic microwave background. (Ignore stray Hydrogen atoms.)

If this planet started as a pure quantum state, how fast would that state lose its coherence?

In such a system, clearly there are many more degrees of freedom that are isolated from the environment compared with those coupled to the outside. So I want to know if those isolated DOF somehow protect the purity of the quantum state.

Answer

I am just going to quote Schlosshauer as being pertinent to this question and discussion in comments.

Reference: Decoherence and the Quantum-to-Classical transition (page 84):

To summarize, we have distinguished three different cases for the type of preferred pointer states emerging from interactions with the environment:

1. The quantum-measurement limit. When the evolution of the system is dominated by $H_{int}$, i.e. by the interaction with the environment, the preferred states will be eigenstates of $H_{int}$ (and thus often eigenstates of position).


2. The quantum limit of decoherence. When the environment is slow and the self-Hamiltonian $H_S$ dominates the evolution of the system, a case frequently encountered in the microscopic domain, the preferred states will be energy eigenstates, i.e., eigenstates of $H_S$


3. The intermediary regime. When the evolution of the system is governed by $H_{int}$ and $H_S$ in roughly equal strengths, the resulting preferred states will represent a compromise between the first two cases. For instance in quantum Brownian motion the interaction Hamiltonian $H_{int}$ describes monitoring of the position of the system. However, through the intrinsic dynamics induced by $H_S$ this monitoring also leads to indirect decoherence in momentum. This combined influence of $H_{int}$ and $H_S$ results in the emergence of preferred states localized in phase space, i.e. in both position and momentum.