CIRCUMSTELLAR DUST SHELLS AROUND LONG-PERIOD VARIABLES .6. AN APPROXIMATIVE FORMULA FOR THE MASS-LOSS RATE OF C-RICH STARS

We present an equation which relates the six parameters of dynamical w ind models to the resulting mass loss rate. These six parameters are t he stellar temperature, the stellar luminosity, the stellar mass, the abundance ratio of carbon to oxygen, the pulsational period and the ve locity amplitude of the pulsation. The equation is constructed by appl ying the maximum-likelihood method to a grid of 48 dynamical models. T hese models of circumstellar dust shells around carbon-rich long-perio d variables comprise the calculation of time-dependent hydrodynamics a s well as a detailed treatment of dust formation, growth and evaporati on. The main influence on the mass loss rate is given by the stellar t emperature, the stellar mass and luminosity. The influence of the carb on abundance, the pulsational period and the amplitude of the piston a re almost negligible. As this mass loss equation is based on physical models it is free of additional arbitrary parameters and could therefo re serve as a more reliable description of the mass loss rate e.g. in stellar evolution calculations. By applying the same method we also co nstructed two equations which relate the six parameters of dynamical w ind models to the averaged outflow velocity and to the averaged dust-t o-gas ratio respectively.