The impact of massive neutrinos on the abundance of massive clusters
  We study the spherical, top-hat collapse model for a mixed dark matter model
including cold dark matter (CDM) and massive neutrinos of mass scales ranging
from m_nu= 0.05 to a few 0.1eV, the range of lower- and upper-bounds implied
from the neutrino oscillation experiments and the cosmological constraints. To
develop this model, we properly take into account relative differences between
the density perturbation amplitudes of different components (radiation, baryon,
CDM and neutrinos) around the top-hat CDM overdensity region assuming the
adiabatic initial conditions. Furthermore, we solve the linearized Boltzmann
hierarchy equations to obtain time evolution of the lineariezed neutrino
perturbations, yet including the effect of nonlinear gravitational potential
due to the nonlinear CDM and baryon overdensities in the late stage. We find
that the presence of massive neutrinos slows down the collapse of CDM (plus
baryon) overdensity, however, that the neutrinos cannot fully catch up with the
the nonlinear CDM perturbation due to its large free-streaming velocity for the
ranges of neutrino masses and halo masses we consider. We find that, just like
CDM models, the collapse time of CDM overdensity is well monitored by the
linear-theory extrapolated overdensity of CDM plus baryon perturbation,
smoothed with a given halo mass scale, if taking into account the suppression
effect of the massive neutrinos on the linear growth rate. Using these
findings, we argue that the presence of massive neutrinos of mass scales 0.05
or 0.1eV may cause a significant decrease in the abundance of massive halos
compared to the model without the massive neutrinos; e.g., by 25% or factor 2,
respectively, for halos with 10^15Ms and at z=1.
