Stochastic and dynamic temperature changes in the interplanetary gas

Exact solutions have been found to the Fokker-Planck equations, incorporating stochastic velocity changes and modelling particles moving in an inverse square central force field under an inverse square collision frequency. The solutions for the velocity distribution contain a combination of collisional and dynamical (reversible) heating. At a general position, there are two populations each with three distinct temperatures, one normal to the orbital plane and the others closely parallel and perpendicular to the mean orbit. Collisional heating is strong and most readily detected in the secondary component of gas which reaches upstream directions along indirect orbits (attractive central force). For interplanetary helium gas reaching 1 a.u., the collisional heating ranges from effective transverse increase of 200 K and radial increase of 1500 K in the downstream wake, to several thousand K increase in radial temperature of the secondary component transverse to the initial gas stream. In interpreting 584 Å sky background radiation observations, the dynamical changes in the velocity spread have to be taken into account for helium gas that is initially hot, when Doppler shifts relative to the solar emission line are significant; the present solutions being the thermal approximations to the distribution function reveal the appropriate radial temperature as a function of space.