Shapes and Rotation of Elliptical Galaxies. Barnes, J., E. Volume 0. Shapes and Rotation of Elliptical Galaxies, pages 0-3. ![Shapes and Rotation of Elliptical Galaxies [pdf]](https://bibbase.org/img/filetypes/pdf.svg "pdf")
Paper Website abstract bibtex An elliptical galaxy's rotation does not always correlate with its flattening. A detailed analysis based on moments of the collisionless Boltzmann equation predicts that galaxies flattened by rotation obey a simple one-to-one relationship between rotation velocity and shape. Bright E galaxies do not obey this relationship; their non-spherical shapes may instead be maintained by anisotropic random velocities. Anisotropic velocities can support triaxial equilibria, as Schwarzschild explicitly showed by numerically constructing equilibrium models of triaxial galaxies. In such galaxies the rotation axis need not be parallel to the minor axis; such kinematic misalignments are indeed observed in some ellipticals. 12.1 Oblate Rotators and E Galaxies Consider an idealized model of an oblate galaxy with density contours which are similar, concentric spheroids. The short axis of the model is aligned with the z axis of the coordinate system. From Chapter 2.5 of BT08, we know that the potential energy tensor is diagonalized in this coordinate system and that W xx = W yy , W xx W zz = q(!) > 1 , (12.1) where ! = 1 − c/a is the ellipticity of the model and the function q(!) may be calculated from the expressions given in Table 2.2 of BT08; a reasonably accurate approximation is q(!) 1 + ! 2(1 − !) . (12.2) The motions of stars within the model may be split into a net streaming motion and a random dispersion with respect to the streaming motion at each point. The total kinetic energy tensor is just the sum of the tensors for these separate motions. Assuming that the only streaming motion is rotation about the z axis, the associated KE tensor is 2K (s) = 1 2 Mv 2 0 1 0 0 0 1 0 0 0 0 , (12.3) 83
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abstract = {An elliptical galaxy's rotation does not always correlate with its flattening. A detailed analysis based on moments of the collisionless Boltzmann equation predicts that galaxies flattened by rotation obey a simple one-to-one relationship between rotation velocity and shape. Bright E galaxies do not obey this relationship; their non-spherical shapes may instead be maintained by anisotropic random velocities. Anisotropic velocities can support triaxial equilibria, as Schwarzschild explicitly showed by numerically constructing equilibrium models of triaxial galaxies. In such galaxies the rotation axis need not be parallel to the minor axis; such kinematic misalignments are indeed observed in some ellipticals. 12.1 Oblate Rotators and E Galaxies Consider an idealized model of an oblate galaxy with density contours which are similar, concentric spheroids. The short axis of the model is aligned with the z axis of the coordinate system. From Chapter 2.5 of BT08, we know that the potential energy tensor is diagonalized in this coordinate system and that W xx = W yy , W xx W zz = q(!) > 1 , (12.1) where ! = 1 − c/a is the ellipticity of the model and the function q(!) may be calculated from the expressions given in Table 2.2 of BT08; a reasonably accurate approximation is q(!) 1 + ! 2(1 − !) . (12.2) The motions of stars within the model may be split into a net streaming motion and a random dispersion with respect to the streaming motion at each point. The total kinetic energy tensor is just the sum of the tensors for these separate motions. Assuming that the only streaming motion is rotation about the z axis, the associated KE tensor is 2K (s) = 1 2 Mv 2 0 1 0 0 0 1 0 0 0 0 , (12.3) 83},
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