Analytic Lyman-Alpha Wing Diagnostics and the Chromospheric Excitation Balance in Cool Dwarfs

I show that the Lyman alpha wings of cool dwarfs can be understood in terms of a very simple model, based on a simplified representation of the chromospheric hydrogen excitation balance and approximate analytic wing diagnostics in partial redistribution. Much of the complexity of the radiation transfer in the partially coherent and steeply temperature-sensitive Lyman alpha line is circumvented by this technique. The result is an expedient scheme for inverting the Lyman alpha wing profile to determine the characteristic free electron density and its gradient in the middle chromosphere. This represents an important new diagnostic for constraining chromospheric models and their radiative losses. I apply this diagnostic to the Lyman alpha wing profiles of the Sun and AU Mic and show that current instrumentation, most notably the Goddard High Resolution Spectrograph (GHRS) on the Hubble Space Telescope, is capable of providing the necessary data.