CONSTANT SURFACE GRAVITY AND DENSITY PROFILE OF DARK MATTER

Cumulative observational evidence confirms that the surface gravity of dark matter (DM) halos mu(0D) = r(0)rho(0), where r(0) and rho(0) are the halo core radius and central density, respectively, is nearly constant and independent of galaxy luminosity for a high number of galactic systems (spirals, dwarf irregular and spheroidals, elliptics) spanning over 14 magnitudes in luminosity and of different Hubble types. Remarkably, its numerical value, mu(0D) similar or equal to 140M(circle dot)/pc(2) = (18.6 MeV)(3), is approximately the same (up to a factor of 2) in all these systems. First, we present the physical consequences of the independence of mu(0D) from r(0): the energy scales as the volume similar to r(0)(3), while the mass and the entropy scale as the surface similar to r(0)(2) and the surface times log r(0), respectively. Namely, the entropy scales similarly to the black hole entropy but with a much smaller coefficient. Second, we compute the surface gravity and the density profile for small scales from first principles and the evolution of primordial density fluctuations from the end of inflation till today using the linearized Boltzmann Vlasov equation. The density profile rho lin(r) obtained in this way decreases as r(-1-ns/2) for intermediate scales, where n(s) similar or equal to 0.964 is the primordial spectral index. This scaling is in remarkable agreement with the empirical behavior found observationally and in N-body simulations: r(-1.6+/-0.4). The observed value of POD indicates that the DM particle mass or is on the keV scale. The theoretically derived density profiles rho(lin)(r) turn to be cored for or on the keV scale and they are cusped for no on the GeV scale or beyond. We consider both fermions and bosons as DM particles decoupling either ultrarelativistically or nonrelativistically. Our results do not use any particle physics model and vary slightly with the statistics of the DM particle.