Quantum model of galactic halos with an Navarro-Frenk-White dark matter profile

Abstract

A quantum model of a cold dark matter galactic halo is developed. The model requires specifying the mass and radius of the halo as well as its density profile. The structure of the halo resulting from the theory is predicted and its physical properties are determined. Verification of these theoretical predictions by observations is proposed and discussed. The model is constructed by analytically solving the governing equation and using its time-independent solutions to determine the internal structure of a galactic halo with an Navarro-Frenk-White cold dark matter density profile. The governing equation that is the basis of the developed theory is derived from the irreducible representations of the extended Galilean group. The method of finding the solutions is analytical, even though an Navarro-Frenk-White density profile is used in the calculations. The theory predicts a halo with a core composed of free dark matter particles that move randomly with frequent collisions. It also predicts an envelope in which the particles are confined to their orbits, which are quantized. Except in the close vicinity of the core, the population of the orbits remains fixed, and physical reasons for the nonexistence of quantum jumps between these orbits are presented. A quantum model of a galactic cold dark matter halo with a given Navarro-Frenk-White density profile is constructed. It predicts a quantum structure of the halo that is significantly different than any previously known dark matter model. The quantum model naturally accounts for dark matter being collisionless, and it predicts that dark matter can only emit radiation of one fixed frequency. The values of this frequency are computed for dark matter particles of different masses. A potential observational verification of the theory is also discussed.