We propose a new method to constrain alternative models for dark matter with
observations. Specifically, we consider hybrid models in which cold dark matter
(CDM) phenomena on cosmological scales and Modified Newtonian Dynamics (MOND)
phenomena on galactic scales share a common origin. Various such models were
recently proposed. They typically contain a mode that is directly coupled to
matter (for MOND) and has a non-relativistic sound speed (for CDM). This allows
even non-relativistic objects like stars to lose energy through Cherenkov
radiation. This is unusual. Most modified gravity models have a relativistic
sound speed, so that only high-energy cosmic rays emit Cherenkov radiation. We
discuss the consequences of this Cherenkov radiation from stars.

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