Mass limits for dark clusters of degenerate fermions

¹ Departamento de Física TeóricaUniversidad de Zaragoza, 50009 Zaragoza, Spain
e-mail: membrado@unizar.es
² BIFI, Instituto de Biofísica y Física de Sistemas Complejos, Universidad de Zaragoza, 50009 Zaragoza, Spain
e-mail: amalio@unizar.es

Received: 11 July 2012
Accepted: 29 December 2012

Abstract

We calculate the range of possible masses for dark spheres of bound fully degenerate fermions as a function of the fermion mass. The cosmological constant is included in our calculations. We deduce that the minimum fermion mass that is able to give rise to degenerate fermion clusters is ~0.02   g^−1/4   eV, where g is the spin degeneracy parameter. We show that degenerate fermions of mc² ≈ (15−30)   g^−1/4   eV can build bound degenerate dark haloes that could reproduce the values of the rotation velocities of galaxies. The masses and radii derived for these degenerate dark haloes of typical galaxies, without considering any cosmological information, agree with the Jeans masses and radii of a cosmological background of ~(20−30)   g^−1/4   eV degenerate fermions at redshift z ≈ 50. However, degenerate fermion objects of 10¹⁵   M_⊙ composed of these particles are too small to constitute the dark halo of galaxy clusters. We also derive degeneracy conditions for hot and cold dark matter fermions.