| Summary: | After reviewing several aspects about the thermodynamics of self-gravitating systems that undergo the evaporation (escape) of their constituents, some recent results obtained in the framework of fermionic King model are applied here to the analysis of galactic halos considering warm dark matter (WDM) particles. According to the present approach, the reported structural parameters of dwarf galaxies are consistent with the existence of a WDM particle with mass in the keV scale. Assuming that the dwarf galaxy Willman 1 belongs to the region III of fermionic King model (whose gravothermal collapse is a continuous phase transition), one obtains the interval 1.2 keV ≤ m ≤ 2.6 keV for the mass of WDM particle. This analysis improves previous estimates by de Vega and co-workers [Astropart. Phys. 46 (2013) 14–22] considering both the quantum degeneration and the incidence of the constituents evaporation. This same analysis evidences that most of galaxies are massive enough to undergo a violent gravothermal collapse (a discontinuous microcanonical phase transition) that leads to the formation of a degenerate core of WDM particles. It is also suggested that quantum-relativistic processes governing the cores of large galaxies (e.g., the formation of supermassive black holes) are somehow related to the gravothermal collapse of the WDM degenerate cores when the total mass of these systems are comparable to the quantum-relativistic characteristic mass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>c</mi></msub><mo>=</mo><msup><mfenced separators="" open="(" close=")"><mo>ℏ</mo><mi>c</mi><mo>/</mo><mi>G</mi></mfenced><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mi>m</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>≃</mo><msup><mn>10</mn><mn>12</mn></msup><msub><mi>M</mi><mo>⊙</mo></msub></mrow></semantics></math></inline-formula> obtained for WDM particles with mass <i>m</i> in the keV scale. The fact that a WDM particle with mass in the keV scale seems to be consistent with the observed properties of dwarf and large galaxies provides a strong support to this dark matter candidate.
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