Searches for dark matter decaying into photons constrain its lifetime to be many orders of magnitude larger than the age of the Universe. A corollary statement is that the abundance of any particle that can decay into photons over cosmological timescales is constrained to be much smaller than the cold dark-matter density. We show that an irreducible freeze-in contribution to the relic density of axions is in violation of that statement in a large portion of the parameter space. This allows us to set stringent constraints on axions in the mass range 100 eV-100 MeV. At 10 keV our constraint on a photophilic axion is g_{aγγ}≲8.1×10^{-14}  GeV^{-1}, almost 3 orders of magnitude stronger than the bounds established using horizontal branch stars; at 100 keV our constraint on a photophobic axion coupled to electrons is g_{aee}≲8.0×10^{-15}, almost 4 orders of magnitude stronger than the present results. Although we focus on axions, our argument is more general and can be extended to, for instance, sterile neutrinos.

We study the evolution of isolated self-interacting dark matter halos using spherically symmetric gravothermal equations allowing for the scattering cross-section to be velocity dependent. We focus our attention on the large class of models where the core is in the long mean free path regime for a substantial time. We find that the temporal evolution exhibits an approximate universality that allows velocity-dependent models to be mapped onto velocity-independent models in a well-defined way using the scattering time-scale computed when the halo achieves its minimum central density. We show how this time-scale depends on the halo parameters and an average cross-section computed at the central velocity dispersion when the central density is minimum. The predicted collapse time is fully defined by the scattering time-scale, with negligible variation due to the velocity dependence of the cross-section. We derive new self-similar solutions that provide an analytic understanding of the numerical results.