A Model of the Distribution of Mass in the Galactic System

Abstract

The paper deals with the distribution of mass in the Galactic System. Formulae for the potential and forces due to non-homogeneous oblate spheroids are derived (section 2). It is shown that, between the galactic centre and the sun, the central force in the galactic plane decreases almost linearly with the distance from the centre (section 3). A simple analytical expression for the densit in a non-homogeneous spheroid is found which gives such a linear decrease of the central force inside the spheroid (section 4). Section 5 summarizes the observational material which forms the basis for the construction of the mass model. A discussion of the values of the constants of differential rotation, A and B, and the distance to the galactic centre is given. Three models of the distribution of mass are described. Only the third model (section 9) reproduces all we know at present of the system at large. It is shown in section 10 that the second model (section 8) probably does not satisy conditions of continuity and equilibriu. The third model does not seem to present any difficulties in this respect. A set of nine additional homogeneous spheroids is introduced in section 11 to account for the deviations from a perfectly linear decrease of the central force in the inner part of the system. Together with the third model these form the final model. This final model of the mass distribution is described in section 12. Diagrams and tables of densities, potentials and forces are given for distances up to 17 kpc from the galactic centre. The total mass of the model is 0.70 x 10^(11)⊙; the velocity of escape near the sun exceeds the circular velocity by 70 km/sec. Sections 13 and 14 contain a new discussion of the space and velocity distributions of globular clusters. The system of globular clusters is found to be of ellipsoidal form. The axial ration of the inner part is about 0.25; it increases to a value near unity in the outer regions. It does not seem possible to draw any reliable conclusions about the differential rotation of the cluster system from the available radial velocities. The average rotational velocity is probably about 80 km/sec. In the final section the force exerted by a spiral arm, such as that found in the vicinity of the sun, has been estimated.

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