Advertisement

Astrophysics and Space Science

, Volume 2, Issue 1, pp 37–47 | Cite as

Hydrodynamic equations of differentially rotating stellar systems and the velocity ellipsoid

  • Shoji Kato
Article

Abstract

Anisotropic hydrodynamic equations for differentially rotating collisionless stellar systems are derived. These equations can describe the evolution of the systems in a time span longer than their rotation periods.

As a by-product of derivation of hydrodynamic equations, the well-known relation that the ratio of the principal axes of the velocity ellipse in a differentially rotating stellar disk is [B/(B-A)]1/2 is re-found if the system is in a purely circular rotation, whereA andB are the Oort's constants. In addition, we find a systematic mean motion superposed on a purely circular differential rotation makes the directions of axes of the velocity ellipse deviate from the radial and the transverse direction. The observed deviation of directions of axes in our neighbourhood in the Galaxy can be explained if in the mean motion superposed on a purely circular differential rotatin the ‘gas’ of stars near us is compressed in the radial direction or rarefied in the transverse directions, with irregularities of the order of 5 km/sec in amplitude of velocity and 1 kpc in size. These magnitudes of irregularities agree with those actually observed or with those anticipated from other theoretical considerations.

Keywords

Time Span Radial Direction Principal Axis Transverse Direction Theoretical Consideration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chandrasekhar, S.: 1942,Principles of Stellar Dynamics. University of Chicago Press, Chicago.Google Scholar
  2. Chew, G.F., Goldberger, M.L., andLow, F.E.: 1956,Proc. Roy. Soc. London A236, 112.Google Scholar
  3. Fujimoto, M.: 1968,Astrophys. J. in press.Google Scholar
  4. Lynds, B.T.: 1967,Sky & Tel. 34, 18.Google Scholar
  5. Marochnik, L.S.: 1964,Soviet Astron. AJ 8, 202.Google Scholar
  6. Marochnik, L.S.: 1967,Soviet Astron. AJ 10, 738.Google Scholar
  7. Schmidt, M.: 1965, inGalactic Structure (ed. by A. Blaauw and M. Schmidt). University of Chicago Press, Chicago, Chapter 22.Google Scholar

Copyright information

© D. Reidel Publishing Company 1968

Authors and Affiliations

  • Shoji Kato
    • 1
  1. 1.Department of AstronomyUniversity of TokyoJapan

Personalised recommendations