Abstract

The primary, obscure and normal particles with respective limiting velocities c1, c2 and c3,solutions from bicubic equation, offer comfortable venues to tackle the newly emergent dark matter particles. Particular emphasis is given to particles with velocities of O(10-3c) ( with c the velocity of light) and whose energies are from 1eV to over 100GeV for which the congruent parameter z = 3p3mv2/2E assumes values of 10-6 and 10-7. At z = 10-6 with mc2 = 100GeV one can have E = 260GeV or with E = 1eV one can have mc2 = 0:38eV; while at z = 10-7 with mc2 = 100GeV one can have E = 2:6TeV or with E = 1eV one can have mc2 = 0:038eV. The small values of the congruent parameter z allow the limiting velocities c1, c2 and c3 as well as the resulting energy expressions be written down perturbatevly in terms of the congruent parameter z.
It is shown that for mc2 = 100GeV particle in the MilkyWay Dark Matter Velocity Profile (Laha, 2016), the derived limiting velocities of primary, obscure and normal particles as dark matter particles are: c1 = 1; 7c (z = 10-7), 1:34c; 2:15c (z = 10-6); c2 = +-i1; 7c (z = 10-7), +-i1:34c; +-i2:15c (z = 10-6), and c3 = v (z = 10-7; 10-6). Perturbatively, for a very small common primary and obscure particle velocity v compared to the absolute values of their limiting velocities, one shows that the obscure particle acquires (-mv2) intrinsic negative energy with respect to the primary particle,with m being their common mass.

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