The impact of massive neutrinos on the abundance of massive clusters

摘要

We study the spherical, top-hat collapse model for a mixed dark matter modelincluding cold dark matter (CDM) and massive neutrinos of mass scales rangingfrom m_nu= 0.05 to a few 0.1eV, the range of lower- and upper-bounds impliedfrom the neutrino oscillation experiments and the cosmological constraints. Todevelop this model, we properly take into account relative differences betweenthe density perturbation amplitudes of different components (radiation, baryon,CDM and neutrinos) around the top-hat CDM overdensity region assuming theadiabatic initial conditions. Furthermore, we solve the linearized Boltzmannhierarchy equations to obtain time evolution of the lineariezed neutrinoperturbations, yet including the effect of nonlinear gravitational potentialdue to the nonlinear CDM and baryon overdensities in the late stage. We findthat the presence of massive neutrinos slows down the collapse of CDM (plusbaryon) overdensity, however, that the neutrinos cannot fully catch up with thethe nonlinear CDM perturbation due to its large free-streaming velocity for theranges of neutrino masses and halo masses we consider. We find that, just likeCDM models, the collapse time of CDM overdensity is well monitored by thelinear-theory extrapolated overdensity of CDM plus baryon perturbation,smoothed with a given halo mass scale, if taking into account the suppressioneffect of the massive neutrinos on the linear growth rate. Using thesefindings, we argue that the presence of massive neutrinos of mass scales 0.05or 0.1eV may cause a significant decrease in the abundance of massive haloscompared to the model without the massive neutrinos; e.g., by 25% or factor 2,respectively, for halos with 10^15Ms and at z=1.