Comparison of a new type of Dark Matter with the Milky Way and M31 grand rotation curves

In the electron Born self-energy (eBse) model, free electrons are of finite-size and possess both a rest mass, m_e, as well as, a Born mass, m_e^B = 74,000 m_e. The Born mass, which originates from the energy contained within the electric field that surrounds a finite-sized electron, serves as a Dark Matter (DM) particle in this theory (designated eBDM, electron Born Dark Matter). The equation of state for m_e^B is w = -1, which implies that two Born masses experience a repulsive gravitational interaction. This repulsive gravitational interaction stabilizes the formation of a DM halo of m_e^B particles, of typical halo size ~ 100 kpc, around a central mass M (e.g. a galaxy), where this gravitational stability arises from the competing attractive M - m_e^B and repulsive m_e^B - m_e^B interactions. A solution of the linearized Poisson-Boltzmann equation, for this system, allows one to derive an expression for the rotational velocity V_eBDM(R), as a function of radius R from the galactic center. A composite model composed of rotational velocity contributions from the galactic bulge, galactic disk, as well as, V_eBDM(R) is found to provide a good description of the Grand Rotation Curves for the Milky Way and M31 galaxies.