= Solution
The <rotation-anisotropy diagram> below uses the <oblate-rotator flattening proxy> for $\beta=0,0.2,0.4$. Each curve starts at $e=\beta$ and rises as $e$ increases. The plotted domains cover typical spheroid values, roughly $0\le e\lesssim0.7$ and $0\le v/\sigma\lesssim1.5$, with the upper axis extended to show the reference curve's rise. The shaded regions are schematic overlapping populations, not measurements or sharp classification boundaries.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-72-rotation-support.png]
{title=Approximate rotation-anisotropy curves and schematic elliptical-galaxy and bulge populations}
Giant <elliptical galaxies> commonly have low ordered rotation for their observed flattening, lying below the <oblate isotropic rotator> reference. Anisotropic <velocity dispersions> and, in many cases, triaxial structure provide support. Lower-luminosity <elliptical galaxies> are more commonly rotating, disky systems near the isotropic reference. Classical <galactic bulges> of <spiral galaxies> often overlap this rotating-spheroid locus; disk-like bulges can be more strongly rotation supported. These are population trends with substantial overlap, not universal rules for individual <galaxies>.
Observations usually use projected ellipticity and a line-of-sight rotation measure such as peak speed divided by a central <velocity dispersion>. The intrinsic $e$ and global dispersions used in the derivation are different quantities. Inclination, apertures, and unresolved streaming can change both coordinates. Consequently \b[a point below the reference suggests extra random-motion support, but does not uniquely measure $\beta$.]
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