Abstract
Given the potential, the equation of continuity and Poisson’s equation are solved for the variation perpendicular to the Galactic plane for a thin galaxy in a steady state. Simple expressions are obtained for the joint density function for the mass density and velocity, and for the distribution function for the velocity and its moments.
These results are applied using a potential suggested by Woolley and Stewart (1967) and Whitley (1977), which is Camm’s potential due to an isothermal gas stratified in parallel layers, plus the potential due to the Galactic centre. The resulting velocity distribution is quite close to the normal distribution usually assumed and cannot be distinguished from it by the data. The mass density distribution fits the log (relative density) curves better than the Camm solution, especially at large distances from the Galactic plane.
A formu1a, valid under conditions more genera1 than usual, is found for the total mass density in the neighbourhood of the Sun.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Breiman, L. 1973,Statistics with a View towards Applications, Houghton Mifflin, Boston, p. 213.
Burton, W. B. 1979, Ed.,IAU Symp. 84: The Large-Scale Characteristics of the Galaxy, D. Reidel Dordrecht.
Camm, G. L. 1950,Mon. Not. R. astr. Soc.,110, 305.
Einasto, J. 1979, inIAU Symp. 84: The Large-Scale Characteristics of the Galaxy, Ed. W. B. Burton, D. Reidel, Dordrecht, p. 451.
Freeman, K. 1975,Galaxies ana the Universe, Eds A. Sandage and J. Kristian, University of Chicago Press, p. 409.
Hill, G., Hilditch, R. W., Barnes, J. V. 1979,Mon. Not. R. astr. Soc.,186, 813.
Hochstadt, H. 1973,Integral Equations, Wiley, New York, p. 42.
Kendall, M., Stuart, A. 1977,The Advanced Theory of Statistics, Vol. 1, Hafner, New York.
Lin, C. C., Segel, L. A. 1974,Mathematics Applied to Deterministic Problems in the Natural Sciences, Macmillan, New York, p. 17.
Lindblad, B. 1959, inHandbuch der Physik, Vol. 53, Ed. S. Flugge, Springer-Verlag, Berlin, p. 2
Morse, P., Feshbach, H. 1953,Methods of Theoretical Physics, Vol. 1, McGraw-Hill, New York, p. 974.
Oort, J. 1965, inGalactic Structure, Eds A. Blaauw and M. Schmidt, University of Chicago Press, p. 455.
Perry, C. L. 1969,Astr. J.,74, 139.
Prendergast, K. H. 1954,Astr. J.,59, 260.
Whitley, R. 1977,Astr. Astrophys.,59, 329.
Woolley, R. 1957,Mon. Not. R. astr. Soc.,117, 198.
Woolley, R. 1965, inGalactic Structure, Eds A. Blaauw and M. Schmidt, University of Chicago Press, p. 85.
Woolley, R., Stewart, J. M. 1967,Mon. Not. R. astr. Soc.,136, 329.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Whitley, R. The jeans problem for a thin galaxy in steady state. J Astrophys Astron 3, 111–123 (1982). https://doi.org/10.1007/BF02714796
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02714796