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Orbits of low-velocity stars in the gravitational field of a galaxy with spiral structure are studied on the basis of both first-order epicyclic theory and exact numerical integration of the equations of motion. An estimate is made of the matter density in the spiral arms in our Galaxy. Our results show that the slow secular increase of the velocity dispersion of the low-velocity stars in our Galaxy can be interpreted as being due to the gravitational effects of large-scale spiral structure, provided either (a) the density in the spiral structure a few billion years ago was three times as large as at present, or (b) the spiral structures had always about the present density, but dissolved and randomly reformed every few hundred million years. These results provide upper limits on the past spiral pattern in our Galaxy because other effects may contribute to the observed velocity dispersions.
Barbanis et al. (Wed,) studied this question.