The elaboration of physically motivated definitions of stellar systems can be more difficult than one might naively expect. The very definition of a galaxy is still beyond our grasp (see Forbes & Kroupa 2011), even though we seem to recognize a galaxy when we see one; at least most times. One should not be led to think that searching for definitions is a futile exercise of semantics, since, for one thing, the process of devising such definitions in fact brings much insight on the physical nature of stellar systems.
The word `bulge' in the literature is used to address systems with different physical natures, which is potentially confusing and frustrating, making the task of working on a clear disambiguation a pressing one. Evidently, today's ideas on what a bulge is have their roots on previous studies. Perhaps the most important historical reference is that in Hubble (1926) describing his morphological sequence of disk galaxies. Along this sequence, the "relative size of the unresolved nuclear region" - later referred to as elliptical-like - changes monotonically. A physically motivated definition for a bulge should characterize a stellar system with fundamentally different physical properties than those of the surrounding disk, as well as other galactic components, indicating a different formation history.
Let us now look at three working definitions, based on different criteria, concerning galaxy structure and photometry:
Morphology. Different structural components can be unveiled by signatures in isophotal contour maps of galaxies. Figure 2 shows such signatures schematically and in a real galaxy. The bulge can thus be defined as a structural component described by a different set of isophotes, as compared to the surrounding disk. A positive aspect of this definition is that it reflects truly a different physical component. Disadvantages include: (i), it might depend on projection effects, (ii), how much different the isophotes have to be (e.g. in terms of position angle and ellipticity) to define an extra component has to be set arbitrarily, and (iii), the extra component can have varied physical natures, i.e., the `bulge' so defined can be a lot of different things (e.g. a bar).
Figure 2. Defining a bulge from its morphology. The top left corner shows schematically how differences in the morphology of a bulge, as compared to the surrounding disk, can show up in isophotal contours. Also shown is a real example concerning the barred galaxy IC 486 (taken from Gadotti 2008). The horizontal lines on the radial profiles of position angle and ellipticity (derived from ellipse fits) show the corresponding values for bulge and disk.
Geometry. If a disk galaxy is seen edge-on or highly inclined, physical structural components that extend vertically further from the disk can sometimes be easily identified (see Fig. 3). Defining bulge as that vertically prominent component has the advantage that it can be easy and objective. However, it only works for very inclined galaxies, and it is also somewhat arbitrary (how much further from the disk is not the disk anymore?). As in the morphological definition, the `bulge' here can also be a lot of different things, such as a box/peanut or a thick disk.
Figure 3. Defining a bulge from its geometry. In edge-on or highly inclined galaxies, any structure vertically more extended than the disk can sometimes be easily identified.
Photometry. The disk component in disk galaxies is thought to have a radial light profile with at least one exponential component going all the way to the galaxy center. A photometric bulge can be defined as the inner extra light apart from the disk (Fig. 4). The advantage of this definition is that it should be easily reproduced. The disadvantage, again, is that it can indicate components with different physical natures. For instance, - perhaps an extreme case - the nuclear cluster in NGC 300 is a photometric bulge (see Bland-Hawthorn et al. 2005).
Figure 4. Defining a bulge from photometry. The left corner shows schematically the radial surface brightness profile of a galaxy with an exponential outer disk, as well as an extra photometric inner component. A bulge can thus be defined as such photometric component: the photometric bulge is the extra light above the inner extrapolation of the disk profile. The right corner shows again the reality as for IC 486 (taken from Gadotti 2008).
Possibly, the best working definition is the photometric one, given its reproducibility and the fact that it is relatively independent of projection effects. In any case, further analysis (e.g. including kinematics) is necessary to properly address the nature of the photometric bulge. It is worth noting how overly simplistic it is to assume that disk galaxies have only two components, bulge and disk. A list of possible components include (and are not restricted to):
Each of these structural components has different (though in some cases similar) formation histories and physical properties. The photometric bulge can actually be several of these, even simultaneously.