Kinetic theory of rarefied atmospheres— What a realistic kinetic theory of ionized gases prescribes about the heating of the solar corona

Abstract

Abstract The observed inversions of kinetic temperature in all known planetary thermospheres and the solar corona have similarities which appear to be a natural and unavoidable consequence of the manner in which a real gas stratifies its properties in a gravitational field. The classical kinetic theory of a gas bound by a gravitational field has severe limitations when the gas becomes too rarefied, and it incorrectly predicts that the field should induce no vertical gradients of kinetic temperature in an atmosphere. Correcting the classical theory to apply to rarefied gases implies a contrary conclusion, a kinetic temperature which increases with altitude at the average rate mg/3k in the transition region of a neutral atmosphere. The correction rests upon the experimentally supported postulate that in a sufficiently rarefied atmosphere, in which the mean free path exceeds about one-tenth percent of its scale height, the distribution of speed of the particles varies with altitude according to a modified Boltzmann probability distribution in which the kinetic energy of the individual particles replaces their average kinetic energy or temperature in the latter distribution. In an ionized atmosphere the temperature increases at a much greater rate which is determined by the relative scattering cross sections of its particles compared to those of a neutral atmosphere under the same conditions. Furthermore, the strong electrical forces between particles cause any departures from Maxwellian conditions throughout the region of transition to be very small, which is in contrast to the greater departures which may occur in neutral planetary atmospheres. The present theory appears correctly to predict simultaneously and without any arbitrary parameters the observed profiles as a function of altitude of both the solar coronal density of hydrogen and of the temperature. From near the base of the region of transition of the solar corona to just below the altitude at which the temperature profile saturates, the present theory prescribes that the temperature increases as the one-third power of the normalized distance from that base, 6amgx/kT in which a is a known parameter from plasma theory, m is the mass of the hydrogen atom, g is the solar gravitational acceleration, k is Boltzmann's constant, T is the temperature at the base, and x is the geometric distance. The coronal density of hydrogen decreases as the inverse one-half power of that same normalized distance.