C. Destri, H. J. de Vega, N. G. Sanchez
The fermionic dark matter (DM) phase-space density Q(r) = rho(r)/sigma^3(r) must be smaller than K m^4/\hbar^3 where m is the DM particle mass, sigma(r) is the DM velocity dispersion and K is a pure number of order one which we estimate. This bound follows from the Pauli principle which restricts the phase-space distribution function of fermionic spin-1/2 dark matter (DM) particles to be f(r,p) < 2. Cusped profiles from N-body galaxy simulations produce a divergent Q(r) at r = 0 violating this quantum bound. Combining this quantum bound with the behavior of Q(r) from simulations and with galaxy observational data on Q, implies that classical galaxy dynamics breaks down for fermionic DM at a distance from the centre of at least r_q. For keV scale WDM r_q turns to be in the parsec scale. For cold dark matter (CDM), r_q is between dozens of kilometers and a few meters, astronomically compatible with zero. For fermionic hot dark matter (HDM) r_q is from kpc to Mpc. This quantum bound rules out the presence of galaxy cusps for fermionic WDM. This is in agreement with astronomical observations which show that the DM halos are cored. The formation of cusps would be allowed for bosonic DM for which the Pauli principle does not apply. Hence, bosonic DM is strongly disfavored by the observation of galaxy cores. Quantum dynamical calculations become necessary to compute galaxy structures at kpc scales and below. N-body simulations can be used at scales larger than a kpc and matched with the quantum evolution.The Thomas-Fermi quantum approximation to self-gravitating fermions with masses in the keV scale yields galaxy properties as halo radius, mass and velocity dispersion consistent with the observations. Namely, fermionic WDM treated quantum mechanically, as it must be, reproduces the observed DM cores of galaxies.
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http://arxiv.org/abs/1204.3090
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