Authors: Guillermo A Rios
It is clear that by measuring the density profile ρ(r) of a dark matter galactic halo we are also indirectly measuring the mass of the dark matter particles (or WIMPs.) So in this paper we will derive such mass value mwimp from an actual measured ρ(r) function. It is also undeniable that gravitational fields affect the form and shape of the wave functions Ψ(r,t) of quantum particles, since such wave functions must live in the space-time defined by the metric gμν consequence of the distribution of mass. In addition, in the case of dark matter, where no other interaction is assumed acting, such gravitational fields are the only potential energy present in the Hamiltonian to determine the shape of the quantum wave function Ψwimp(r,t). Therefore to determine such wave function of dark matter particles inside galactic halos we will consider a quantum equation containing in the Hamiltonian the gravitational potential energy due to the totality of the galactic matter, both baryonic and dark. At some point we will propose this, our derived quantum equation, as the sought after universal law for dark matter halos. Along this process we will pay some special attention to the fact that we will be solving a quantum equation, including boundary conditions, etc, under very unusual circumstances in terms of lengths of galactic proportions, extremely large information travel time across the whole halo quantum system, etc. Finally, taking the Milky Way as our case of study, we will solve our quantum equation to determine the mass mwimp of this elusive dark matter particle.
Comments: 40 Pages. Original research work
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