Dark matter annihilations can generate significant amounts of internal heat inside planets if dark matter consists mainly of particles with nuclear cross sections in the microbarn range or larger (SIMPs). By considering a detailed model of Uranus's interior, we calculate upper limits on the S-wave annihilation cross section for these particles as a function of their mass. These upper limits, together with other experimental and theoretical constraints, rule out SIMPs with masses between 150 MeV and 10(4) GeV.
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