The stabilizing effects of haloes and spiral structure

Extract

The equilibrium and the stability of homogeneous gaseous and uniformly rotating MacLaurin spheroids imbedded in a rigid, homogeneous and spherical stellar halo are considered. Such systems may be useful as crude models of disk-halo galaxies. Explicitly, we have determined the modes of oscillations stemming from the fundamental radial mode of the homogeneous compressible sphere and its non radial “f” (or Kelvin) modes belonging to the second (ℓ=2) and third (ℓ=3) spherical harmonics, together with the first “pressure” and gravity modes p₁ and g₁ belonging to the first spherical harmonics (ℓ=1). It has been assumed that the oscillations are adiabatic with a ratio of specific heats γ=5/3, and several sequences of spheroids corresponding to various values of the halo mass have been examined.