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Galactic Bars as Aligned Excentric Orbits

Published online by Cambridge University Press:  03 August 2017

V.L. Polyachenko*
Affiliation:
Astronomical Council of the USSR Academy of Sciences Moscow USSR

Extract

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The simplest analytical theory of bars made of stars in excentric orbits is suggested below (such a possibility was mentioned in [1]). Approximately, the subsystem of particles with elongated orbits may be described as consisting of hard “needles” elongated along radii, slowly (compared with radial oscillations of particles) rotating due to orbit precession. As a first approximation, we shall consider the needles mentioned to be infinitesimally thin ones. Besides, let us assume for simplicity that the radial energy of stars is fixed: E=Eo. Then we may introduce the distribution function of such needles, f=f(ϕ, Ω), so that dn = f(ϕ, Ω)dϕdΩ is the number of needles within the angles (ϕ, (ϕ+dϕ), rotating with the angular velocities Ω = ϕ, in the range (Ω, Ω+dΩ). Let us write now the collisionless kinetic equation in the form ∂f/∂t + Ω. ∂f/∂ϕ+P∂f/∂Ω = 0, where P=dΩ/dt=d2ϕ/dt2=Mtot/I; Mtot is the total torque acting on the needle, I is the needle's inertia momentum relative to the disk center.

Type
IV- Models of Spiral Structure
Copyright
Copyright © Kluwer 1991 

References

1. Lynden-Bell, D., Kalnajs, A.J. (1972) M.N.R.A.S. 157, 1 Google Scholar
2. Polyachenko, V.L. (1989) Pis'ma Astron. Zh. (USSR) 15, 890 Google Scholar