  The presence of a liquid solvent is widely regarded as an essential
prerequisite for habitability. We investigate the conditions under which worlds
outside the habitable zones of stars are capable of supporting liquid solvents
on their surface over geologically significant timescales via combined
radiogenic and primordial heat. Our analysis suggests that super-Earths with
radionuclide abundances that are $\gtrsim 10^3$ times higher than Earth can
host long-lived water oceans. In contrast, the requirements for long-lived
ethane oceans, which have been explored in the context of alternative
biochemistries, are less restrictive: relative radionuclide abundances of
$\gtrsim 10^2$ could be sufficient. We find that this class of worlds might be
detectable ($10\sigma$ detection over $\sim 10$ days integration time at $12.8$
$\mu$m) in principle by the James Webb Space Telescope at distances of $\sim
10$ pc if their ages are $\lesssim 1$ Gyr.

Earth and Planetary Astrophysics;Solar and Stellar Astrophysics