Measuring Mass-Loss Evolution at the Tip of the Asymptotic Giant Branch

In the final stages of stellar evolution low- to intermediate-mass stars lose their envelope in increasingly massive stellar winds. Such winds affect the interstellar medium and the galactic chemical evolution as well as the circumstellar envelope where planetary nebulae form subsequently. Characteristics of this mass loss depend on both stellar properties and properties of gas and dust in the wind formation region. In this paper we present an approach towards studies of mass loss using both observations and models, focussing on the stage where the stellar envelope is nearly empty of mass. In a recent study we measure the mass-loss evolution, and other properties, of four planetary nebulae in the Galactic disk. Specifically we use the method of integral field spectroscopy on faint halos, which are found outside the much brighter central parts of a planetary nebula. We begin with a brief comparison between our and other observational methods to determine mass-loss rates in order to illustrate how they differ and complement each other. An advantage of our method is that it measures the gas component directly requiring no assumptions of properties of dust in the wind. Thereafter we present our observational approach in more detail in terms of its validity and its assumptions. In the second part of this paper we discuss capabilities and assumptions of current models of stellar winds. We propose and discuss improvements to such models that will allow meaningful comparisons with our observations. Currently the physically most complete models include too little mass in the model domain to permit a formation of winds with as high mass-loss rates as our observations show.