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3.4 Intrinsic Shapes

3.4.1 MINOR AXIS ROTATION Davies and Birkinshaw found the first elliptical (NGC 4261) with strong minor axis rotation (150 km s-1), and almost no rotation along the major axis (66). Many more systems show significant rotation along the minor axis (67, 125, 182, 304, 360). This is impossible in an oblate axisymmetric system, and is a signature of triaxiality or prolateness (41, 63, 188).

Minor axis rotation can be caused by two effects: first, for nearly all viewing angles the projection of a triaxial galaxy has an apparent minor axis that is at a position angle which differs from that of the projected short axis of the galaxy. Hence, if the galaxy rotates intrinsically around its short axis, the observer will measure a gradient along the apparent minor axis (2) The geometric misalignment Thetamin between the apparent and intrinsic short axis is a function of the two axial ratios b / a and c / a, and the two viewing angles phi, theta. Here a, b, and c are the semi-axes, with a geq b geq c. The dependence of Thetamin on the axial ratios can be simplified to Thetamin(b / a, c / a, phi, theta)= Thetamin (T, phi, theta), where the triaxiality parameter T is defined by T = (1 - b2 / a2) / (1 - c2 / a2) (124). For oblate galaxies T = 0, and for prolate galaxies T = 1 (Figure 1).

Secondly, the total angular momentum of a triaxial galaxy can lie anywhere in the plane containing the long and the short axis (Section 2.2.2, 211). The observation that the minor axis rotation is small for many galaxies is surprising, since it shows that the angle psiint between the intrinsic short axis and the angular momentum is generally small. Apparently, the formation mechanism produced a good (but not perfect?) alignment of the angular momentum and the intrinsic short axis. There is good indication that at least 2 galaxies rotate around their intrinsic long axis. NGC 4365 and NGC 4406 show minor axis rotation in their outer parts, and major axis rotation in their inner parts. The 90° misalignment between the inner and the outer parts suggests that one system rotates around the short axis, and the other around the long axis. An analysis of the projection effects shows that the outer parts are rotating around the long axis (125). Hence psiint neq 0 for at least two galaxies.

Figure 3

Figure 3. Histogram of apparent kinematic misalignment angle psi. All galaxies with misalignments determined to 30° or better are included (FIZ).

Binney showed that a statistical analysis of minor axis rotation can constrain the intrinsic shapes of triaxial galaxies (41). Franx, Illingworth and de Zeeuw (124, FIZ) have extended his analysis, and have applied it to the now available data. The three intrinsic parameters b / a, c / a and psiint are constrained by two observables: the apparent ellipticity epsilon and the apparent misalignment psi, defined by tan psi = vmin / vmaj. A histogram of observed psi-values is shown in Figure 3. The distribution of psi follows from that of T and psiint, while the distribution of epsilon is determined mainly by the distribution of c / a; it depends only weakly on T. FIZ inverted the epsilon-distribution to derive the distribution of c / a for various assumptions about T. The resulting distribution shows a peak near c / a = 0.6-0.7, and is zero or near-zero for round galaxies. The distribution of psi can be reproduced by a wide variety of models, even when a relation is assumed between T and psiint. A model of psiint = 0 and a very smooth distribution of T fits the data just as well as a model with psiint = 0 and 60% of galaxies oblate and 40% of galaxies prolate. The mean triaxiality and mean intrinsic misalignment are better constrained: all solutions have < T > leq 0.4 and < psiint > leq 20°. The larger < psiint >, the smaller < T >. These numbers are still uncertain as the sample of galaxies is small and not complete in ellipticity.

2 The rotation can be non-zero along the projected intrinsic short axis when the streamlines are non-circular. Back.

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