The distribution of stars perpendicular to galactic disk

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Abstract
The combined Boltzmann and Poisson equations for the isothermal distribution of stars perpendicular to a galactic disk are solved in the presence of a spheroidal halo. The solutions depend in a simple way upon the ratio, epsilon, of effecive halo mass density to disk mass density in the fundamental plane of the disk. These results suggest a new way of measuring the ratio of halo to disk mass densities either by observing the number of stars of a given type as a function of height above the plane in the Galaxy or by observing the distribution of starlight perpendicular to the disks of other galaxies. Exact numerical - and approximate analytic solutions are derived for disks that are composed of one or several separate stellar components. Non-isothermal solutions are also discussed. The advantages of using the self-consistent models described here for the determination of the total amount of matter near the sun are enumerated.

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