I. Small Angle Scattering of Radiation. II. Molecular Emission Lines Around Evolved Stars

Abstract

This dissertation is in two Parts. Part I consists of a paper on the effect of small angle scattering on a pulse of radiation, and an analysis of the particular case of X-rays scattering off interstellar grains. Part II concerns the excitation of SiO emission lines around evolved stars. There are two papers, the first on 'thermal' emission lines and the second on maser emission lines. Each paper has its own abstract. Part I: We have analyzed in detail the general problem of the propagation of a pulse of radiation through a uniform medium containing small angle scatterers. Simple expressions for the first moment of the arrival time delay and for the second and fourth moments of the arrival angle of the pulse photons are given, valid for any optical depth. Using the first two of these we find a simple method of distance determination. Joint and individual distribution functions for arrival time and angle are derived in the small and large optical depth limits. An exponential tail in the arrival time distribution is characteristic in both limits. The analysis has been applied to a burst of x-rays from a source near the galactic center propagating through the dust of the interstellar medium. The grains responsible for interstellar reddening can have very little observable effect. However, the observed lengths, energy dependence, and variability of the burst tails can be readily accounted for by a population of large ~3μ grains. We derive useful constraints on the grain distribution from observations of the burst tails. Part II (i): We have investigated the excitation of the microwave lines in the ground vibrational state of the SiO molecule in the expanding envelope of cool Mira-type stars. The rotational levels are excited when an SiO molecule absorbs an 8μ photon and is left in the lowest excited vibrational state; the spontaneous decay of the excited vibrational state preferentially leaves the molecule with a higher rotational quantum number than it had before. In all of the cases investigated the majority of the microwave transitions were optically thick, and photon trapping causes the excitation temperature to increase with optical depth in such a way that the antenna temperature measured by a distant observer is proportional to the flux of SiO leaving the star, to the square root of the ambient 8μ flux and inversely to the square of the asymptotic velocity. We have analysed the reported detection of J = 1 → 2, v = 0 emission from three Miras and VY CMa, and find that the flux of SiO leaving the stars is very low. This indicates that either they are losing very little mass, or more probably that grain formation very effectively removes a large fraction of gaseous SiO molecules. Part II (ii): We have investigated the excitation of the microwave lines in the excited vibrational states of the SiO molecules in the expanding envelopes of cool Mira-type stars. The excited vibrational states are populated principally by the absorption of 8μ photons. The inversions occur when the gas temperature exceeds the excitation temperature of the vibrational levels, and upward vibrational collisions selectively populate higher rotational levels. The masers are all saturated. We discuss the line profiles, and show how the profile is determined by the velocity gradient and the ambient radiation field. The SiO abundance required for the masers is large. We discuss this in the light of our earlier calculation that the abundance is low in the outer envelope, and argue that grain formation is an efficient process.