An Interpretation of Flat Density Cores of Clusters of Galaxies by Degeneracy Pressure of Fermionic Dark Matter : A Case Study of Abell 1689

Flat density cores have been obtained for a limited number of clusters of galaxies by strong gravitational lensing. Using a phenomenological equation of state (EOS) describing the full-to-partial degeneracy, we integrate the equation of hydrostatic equilibrium. The EOS is based on an assumption that the local kinetic energy of a classical particle induced by the gravity dissolves the quantum statistical degeneracy. The density profile is uniquely determined by four parameters, the central density, ρ(0), the properties of a fermion, namely, the mass, m, and statistical weight, g, and the ratio of the total matter density and fermion density, δ. As a case study, we model the column density and 2D encircled mass profiles of A1689, whose column density profile has been observationally obtained by Broadhurst et al., using gravitational lensing. The column density and 2D encircled profiles at the core, are reasonably reproduced for models with a limited range of particle properties. In the case that previously unknown fermions with spin 1/2 dominate the dark matter, the acceptable particle mass range is between 2 and 4 eV. In the case that the dark matter consists of the mixture of degenerate relic neutrinos and classical collisionless cold dark matter particles, the mass range of neutrinos is between 1 and 2 eV, if the ratio of the two kinds of dark matter particles is fixed to its cosmic value. Both the pure fermionic dark matter models and neutrino-CDM-mixture models reproduce the observations equally well. Subject headings: neutrinos – equation of state – dense matter – dark matter – galaxies: clusters: individual (A1689)