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Magnetic protection of potentially habitable planets plays a central role in determining their actual habitability and/or the chances of detecting atmospheric biosignatures. Here we develop a thermal evolution model of potentially habitable Earth-like planets and super-Earths (SEs). Using up-to-date dynamo-scaling laws, we predict the properties of core dynamo magnetic fields and study the influence of thermal evolution on their properties. The level of magnetic protection of tidally locked and unlocked planets is estimated by combining simplified models of the planetary magnetosphere and a phenomenological description of the stellar wind. Thermal evolution introduces a strong dependence of magnetic protection on planetary mass and rotation rate. Tidally locked terrestrial planets with an Earth-like composition would have early dayside magnetopause distances between 1.5 and 4.0 Rp , larger than previously estimated. Unlocked planets with periods of rotation ~1 day are protected by magnetospheres extending between 3 and 8 Rp . Our results are robust in comparison with variations in planetary bulk composition and uncertainties in other critical model parameters. For illustration purposes, the thermal evolution and magnetic protection of the potentially habitable SEs GL 581d, GJ 667Cc, and HD 40307g were also studied. Assuming an Earth-like composition, we found that the dynamos of these planets are already extinct or close to being shut down. While GL 581d is the best protected, the protection of HD 40307g cannot be reliably estimated. GJ 667Cc, even under optimistic conditions, seems to be severely exposed to the stellar wind, and, under the conditions of our model, has probably suffered massive atmospheric losses.
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