(I) Bulge-dominated objects, i.e. the disks are fully embedded in the bulge and close to edge-on. In this case, the a4/a profile has a well defined peak (where the local disk-to-bulge ratio reaches a maximum) and falls to zero at large radii because the disk fades more quickly than the bulge. The rise and fall of the a4/a profile is accompanied by a similar behaviour of the ellipticity, because at both small and large radii, we see the ellipticity of the bulge. We distinguish here another subtype (Ib) which consists in a disk fully embedded in a boxy bulge. In this case, at large radii, the a4/a coefficient becomes negative and the ellipticity continues increasing.
(II) Disk-dominated objects, i.e. the disk dominates in the outer parts, with intermediate to high inclinations. Here, the a4/a profile also falls to zero at large radii because now the disk dominates (instead of the bulge) and the projected disk has pure elliptical isophotes. There are two indicators which allow to separate this case from case (I): (a) the ellipticity profile and (b) the surface brightness profile. If the disk becomes dominant at large radii, then the ellipticity remains constant in radius and directly reflects the inclination angle of the disk. Furthermore the surface brightness profile is generally closer to an exponential than to an r1/4 profile.
(III) Objects with barred disks being modestly inclined down to face-on. These objects are characterized by correlated and rather abrupt changes in diskiness (a4/a), position angle and ellipticity. Such behaviour is also observed in barred S0s (Magrelli et al. 1992; Shaw et al. 1993), which suggests that the isophotal twists in ellipticals could be caused by embedded bars (Nieto et al. 1992). Barred objects close to edge-on can generally not be distinguished from cases (I) or (II).
These three cases require different treatments. Case (I) and (II) will be decomposed by variants of the disk-bulge decomposition method developed by Scorza & Bender (1995). Case (III) cannot be decomposed reliably but the bar hypothesis can be tested via subtraction of a bulge model.
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