We study the formation of non-linear structures in warm dark matter (WDM) modelsand in a long-lived charged massive particle (CHAMP) model.CHAMPs with a decay lifetime of about 1 yr induce characteristic suppression in the matter power spectrum at subgalactic scales through acoustic oscillations in the thermal background. We explore structure formation in such a model.We also study three WDM models, where the dark matter particles are producedthrough the following mechanisms:i) WDM particles are produced in the thermal background and then kinematically decoupled; ii) WDM particles are fermions produced by the decay of thermal heavy bosons; and iii) WDM particles are produced by the decay of non-relativistic heavy particles.We show that the linear matter power spectra for the three models are all characterised by the comoving Jeans scale at the matter-radiation equality.Furthermore, we can also describe the linear matter power spectrum for the long-lived CHAMP model in terms of a suitably defined characteristic cut-off scale kCh,similarly to the WDM models.We perform large cosmological N-body simulations to study the non-lineargrowth of structures in these four models.We compare the halo mass functions, the subhalo mass functions, and the radial distributions of subhalos in simulated Milky Way-size halos.For the characteristic cut-off scale kcut = 51 h Mpc−1, the subhalo abundance ( ∼ 109Msun) is suppressed by a factor of ∼ 10 compared with the standard ΛCDM model. We then study the models with kcut ≃ 51, 410, 820 h Mpc−1,and confirm that the halo and the subhalo abundances and the radial distributionsof subhalos are indeed similar between the different WDM models and the long-lived CHAMP model.The result suggests that the cut-off scale kcut not only characterises the linearpower spectra but also can be used to predict the non-linear clustering properties.The radial distribution of subhalos in Milky Way-size halos isconsistent with the observed distribution for kcut ∼ 50−800 h Mpc−1; such models resolve the so-called ``missing satellite problem".
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