Planetary nebulae in the Andromeda galaxy and its companions

The identification and observation of planetary nebulae in the Andromeda galaxy (M31) and its companions provide a powerful means of studying their old stellar populations. The direct determination of chemical abundances and radial velocities for even the brightest individual old stars is impossible at the distance of M31. The strongest emission lines of planetary nebulae are as bright as the entire visual continuum of the most luminous giants. Consequently, spectrophotometry of planetary nebulae presently provides the only direct measure of chemical abundances, and, with the exception of globular clusters, the only radial velocity determinations for the old populations. Chemical compositions give data on nucleosynthesis in sequential generations of stars and the dependences of nucleosynthesis on the mass of the parent galaxy. Kinematical studies in galaxies such as M32 and NGC 205 allow the determination of halo velocity and consequently virial masses which are largely model independent. The number of planetary nebulae found in a galaxy provides an observational basis for estimating the death rate of old stars and the rate at which they produce an interstellar medium. The identification of planetary nebulae in M31 leads to a better understanding of the spatial distribution and luminosity function of planetary nebulae in our galaxy. Observations of the above are discussed and analysed. (Auth.)