Velocity structure in long period variable star atmospheres

A regression analysis of the dependence of absorption line velocities on wavelength, line strength, excitation potential, and ionization potential is presented. The method determines the region of formation of the absorption lines for a given data and wavelength region. It is concluded that the scatter which is frequently found in velocity measurements of absorption lines in long period variables is probably the result of a shock of moderate amplitude located in or near the reversing layer and that the frequently observed correlation of velocity with excitation and ionization are a result of the velocity gradients produced by this shock in the atmosphere. A simple interpretation of the signs of the coefficients of the regression analysis is presented in terms of preshock, post shock, or across the shock, together with criteria for evaluating the validity of the fit. The amplitude of the reversing layer shock is estimated from an analysis of a series of plates for four long period variable stars along with the most probable stellar velocity for these stars.