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        Critical Configurations for a System of Semidegenerate Fermions

        Carlos R. Arg¨uelles,Remo Ruffini,Bernardo M. O. Fraga 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.65 No.6

        We study an isothermal system of semidegenerate self-gravitating fermions in general relativity. Such systems present mass density solutions with a central degenerate core, a plateau and a tail, thislast following a power law behavior r−2. The different solutions are governed by the free parametersof the model: the degeneracy and the temperature parameters at the center and the particle mass m. We then analyze in detail the free parameter space for a fixed m in the keV region, by studying theone-parameter sequences of equilibrium configurations up to the critical point, which is representedby the maximum in a central density (0) vs. core mass (Mc) diagram. We show that for fullydegenerate cores, the known expression for the critical core mass Mcrc / m3pl/m2 is obtained, whilefor low degenerate cores, the critical core mass increases, showing temperature effects in a nonlinearway. The main result of this work is that when applying this theory to model the distribution ofdark matter in galaxies from the very center to the outer halos, we do not find any critical corehaloconfiguration of self-gravitating fermions that would be able to explain the super-massive darkobject in their centers and the outer halo simultaneously.

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