The Formation and Growth of Carbon Particles in the Atmospheres of Cool Carbon Stars

A system of equations is developed which describes the formation and growth of solid particles in an adiabatic gas undergoing sinusoidal time variations of temperature. The system of equations is solved throughout a cycle of temperature variation for a gas having an initial temperature, pressure and composition representative of the atmosphere of a cool carbon star and having a period and amplitude of temperature variation typical of long period variables. The results show that the particles form and grow to nearly their maximum size during a relatively small fraction of the period of temperature variation. The particles attain a maximum mean particle size of about 0.2 microns. The extinction due to the particles is calculated and found to be several orders of magnitude greater than the expected atomic and molecular extinction.