Boltzmann–Poisson Theory of Nonthermal Self-gravitating Gases, Cold Dark Matter, and Solar Atmosphere

Abstract Space and astrophysical plasmas or gases can reach various states of thermal or nonthermal quasi-equilibrium, depending on the collisional age of the observed system. Widely observed in space plasmas, the Kappa (or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>κ</mml:mi> </mml:math> —power-law) velocity distribution (KVD) is eloquent evidence of nonthermal states. M. P. Leubner has developed KVD models for luminous gases and cold dark matter (DM) with empirical density profiles described by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>κ</mml:mi> </mml:math> &gt; 0 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>κ</mml:mi> </mml:math> &lt; 0, respectively. The predicted temperature profiles, however, are not in qualitative agreement with the nonmonotonic features expected in some gas and DM models. This study adopts the more consistent regularized Kappa distribution (RKD) to derive the equilibrium profiles of self-gravitating gas and DM halos within a Boltzmann–Poisson theoretical approach. The new RKD models can replicate better than the KVD models the Navarro–Frenk–White density profile of the DM near the basic halos and can also produce nonmonotonic temperature profiles. The same RKD formalism is also applied to non-self-gravitating astrophysical systems, which shows that for highly nonthermal cases ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>κ</mml:mi> <mml:mo>~</mml:mo> <mml:mn>1</mml:mn> </mml:math> &lt; 3/2), the temperature of the surrounding gases decreases initially in a narrow region. The temperature then increases sharply and reaches a high saturated value, resembling the overheated solar atmosphere, while the density profile near the surface may depart from the observations. Compared to the KVD models, the new RKD models can provide improved descriptions of gravitational equilibrium systems, especially for highly nonthermal cases and temperature profiles.