Dark matter halos in the multicomponent model. I. Substructure
  Multicomponent dark matter with self-interactions, which allows for
inter-conversions of species into one another, is a promising paradigm that is
known to successfully and simultaneously resolve major problems of the
conventional $\Lambda$CDM cosmology at galactic and sub-galactic scales. In
this paper, we present $N$-body simulations of the simplest two-component
(2cDM) model aimed at studying the distribution of dark matter halos with
masses $M\lesssim10^{12}M_\odot$. In particular, we investigate how the maximum
circular velocity function of the halos is affected by the velocity dependence
of the self-interaction cross-sections, $\sigma(v)\propto v^a$, and compare
them with available observational data. The results demonstrate that the 2cDM
paradigm with the range of self-interaction cross-section per particle mass
(evaluated at $v=100$ km s$^{-1}$) of $0.01\lesssim \sigma_0/m\lesssim 1 $
cm$^2$g$^{-1}$ and the mass degeneracy $\Delta m/m\sim 10^{-7}-10^{-8}$ is
robustly resolving the substructure and too-big-to-fail problems by suppressing
the substructure having small maximum circular velocities, $V_{\rm
max}\lesssim100$ km s$^{-1}$. We also discuss the disagreement between the
radial distribution of dwarfs in a host halo observed in the Local Group and
simulated with CDM. This can be considered as one more small-scale problem of
CDM. We demonstrate that such a disagreement is alleviated in 2cDM. Finally,
the computed matter power-spectra of the 2cDM structure indicate the model's
consistency with the existing Ly-$\alpha$ forest constraints.
