Envelope tomography of long-period variable stars - II. Method

A tomographic method is described that makes it possible to follow the prop agation of shock waves across the photosphere of long-period variable stars . The method relies on the correlation of the observed spectrum with numeri cal masks probing layers of different atmospheric depths. The formation dep th of spectral lines is derived from synthetic spectra of non-variable red giant stars. When applied to Mira stars around maximum light, the tomograph ic masks reveal that the deepest photospheric layers are generally characte rized by blueshifted absorption lines (attesting to their upward motion), w hereas the uppermost layers generally exhibit redshifted absorption lines ( indicating their infalling motion). Double absorption lines are found in in termediate layers, where the shock front is located. At later phases, the s hock front is seen moving towards upper layers, until it leaves the photosp here.