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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., Comment: 21 pages, 14 figures

Understanding of the observed structure in the universe can be reached only in the theoretical framework of dark matter. N-body simulations are indispensable for the analysis of the formation and evolution of the dark matter web. Two primary fields - density and velocity fields - are used in most of studies. However dark matter provides two additional fields which are unique for collisionless media only. These are the multi- stream field in Eulerian space and flip-flop field in Lagrangian space. The flip-flop field represents the number of sign reversals of an elementary volume of each collisionless fluid element. This field can be estimated by counting the sign reversals of the Jacobian at each particle at every time step of the simulation. The Jacobian is evaluated by numerical differentiation of the Lagrangian submanifold, i.e., the three-dimensional dark matter sheet in the six-dimensional space formed by three Lagrangian and three Eulerian coordinates. We present the results of the statistical study of the evolution of the flip-flop field from z = 50 to the present time z = 0. A number of statistical characteristics show that the pattern of the flip-flop field remains remarkably stable from z = 30 to the present time. As a result the flip-flop field evaluated at z = 0 stores a wealth of information about the dynamical history of the dark matter web. In particular one of the most intriguing properties of the flip-flop is a unique capability to preserve the information about the merging history of dark matter haloes., Comment: 19 pages, 25 figures, submitted to MNRAS

We consider radiation emitted by the jitter mechanism in a Blandford-McKee self-similar blastwave. We assume the magnetic field configuration throughout the whole blastwave meets the condition for the emission of jitter radiation and we compute the ensuing images, light curves and spectra. The calculations are performed for both a uniform and a wind environment. We compare our jitter results to synchrotron results. We show that jitter radiation produces slightly different spectra than synchrotron, in particular between the self-absorption and the peak frequency, where the jitter spectrum is flat, while the synchrotron spectrum grows as \nu^{1/3}. The spectral difference is reflected in the early decay slope of the light curves. We conclude that jitter and synchrotron afterglows can be distinguished from each other with good quality observations. However, it is unlikely that the difference can explain the peculiar behavior of several recent observations, such as flat X-ray slopes and uncorrelated optical and X-ray behavior., Comment: 11 pages, 7 postscript figures. Accepted for publication in MNRAS

Medvedev & Narayan have described a hot accretion flow onto a spinning neutron star in which the gas viscously brakes the spin of the star. Their self-similar solution has the surprising property that the density, temperature and angular velocity of the gas at any radius are completely independent of the outer boundary conditions. Hence, the solution cannot be matched to a general external medium. We resolve this paradoxical situation by showing that there is a second self-similar solution which bridges the gap between the original solution and the external medium. This new solution has an extra degree of freedom which permits it to match general outer boundary conditions. We confirm the main features of the analytical results with a full numerical solution., 6 pages, 1 figure, MNRAS accepted