Dark-Matter-only simulations of the 2cDM model with $\sigma(v)$ as a solution to the CDM small-scale problems

The standard CDM model is believed to have problems on small -- galactic and sub-galactic -- scales, namely the substructure problem (SSP), too-big-to-fail (TBTF) problem and core-cusp problem (CCP). Recently, we've shown that a two-component (e.g., flavor-mixed) dark matter (2cDM) model can resolve all these problems altogether via particle elastic collisions ({\it a l\'a} SIDM) and particle mass conversions. 2cDM does not have the early-universe problem faced by some alternative multicomponent models, yet it resolves the SSP and TBTF that SIDM cannot do. In the new suite of simulations reported here, we explored the velocity dependence of cross-sections of scattering and conversion, $\sigma(v)=\sigma_0 v^a$, where $\sigma_0$ and $a$ are constants. We found that (i) 2cDM predictions are robust; (ii) many specific 2cDM models are consistent with available observed velocity functions in a wide range of $\sigma_0$, i.e., between 1-0.1 cm$^2$/g, and even down to 0.01 cm$^2$/g for some; (iii) core sizes in dwarfs and clusters further constrain viable models. These models are to be explored in simulations with baryons, star formation and baryonic feedback.