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Are inner bars simply miniature versions of large-scale bars, or are they a different type of beast altogether? Theoretical arguments and models suggest that inner bars should rotate relatively slowly, with corotation well outside the end of the bar. Thus, they should differ dynamically from typical large-scale bars in early-type disks (where most double bars are found); these large-scale bars tend to be "fast" in the relative sense, with corotation at or just beyond the end of the bar. So we might wonder if this hypothesized difference in relative speeds is reflected in a difference in structure. In addition, as more realistic models of inner bars emerge (e.g., from N-body simulations), there is some hope that we can test these models by comparing their stellar structure with that of real inner bars.

What is curious, then, about the gross photometric structure of inner bars is that it is often rather similar to that of large-scale bars. A crude comparison can be had via the use of unsharp masks (e.g. Erwin & Sparke 2003, Erwin 2004), which suggests that inner bars have distinct "ends" (i.e., regions where the surface brightness steepens abruptly), and that same inner bars may have rather high axis ratios.

This can be seem more directly by comparing surface-brightness profiles along the bar major axis. Figure 4 does this for NGC 2950, where the profile of the inner bar appears to be a scaled-down replica of the outer bar: a relatively shallow profile (extending out of the bulge-dominated region) which breaks at a certain radius and then falls off more steeply, gradually blending into the disk outside. These are classical examples of what Elmegreen & Elmegreen (1985) first identified (for large-scale bars!) as "flat" bar profiles, which are common in early-type disks but rare in late types, where the bar profile is usually a steep exponential.

Figure 4

Figure 4. Profiles along major axes of outer and inner bars of NGC 2950. Because the bars are (almost) perpendicular, it is easier to trace their profiles independently. Both bars have remarkably similar profiles - excellent examples of so-called "flat" profiles first identified for large-scale bars by Elmegreen & Elmegreen (1985)]. Vertical dashed lines mark the radius of maximum isophotal ellipticity for each bar.

3.1. Dissections

Just as Padova (the site of this workshop) was where Galileo undertook much of his pioneering research - which helped break the dogma of Classical (Aristotelean and Ptolemaic) physics - it was also the place where the anatomist Andreas Vesalius helped break the dogma of Classical medicine, by performing a ground-breaking series of dissections, culminating in De humani corporis fabrica Vesalius (1543). Taking this as inspiration, then, I present selections from an ongoing project aimed at "dissecting" several double-barred galaxies.

The main approach is modeled on that of Ohta, Hamabe, & Wakamatsu (1990), who extracted large-scale bars from several early-type spirals by modeling and subtracting the disk and bulge, with the residue being the bar proper. An elaboration of this process applied to NGC 1543 and NGC 2859 (Erwin 2009, in prep) produces two isolated inner bars (Figure 5). That of NGC 1543 is quite narrow (axis ratio approx 4:1), and strikingly similar to at least some large-scale bars (e.g., several of those in Ohta et al.); evidence for a very faint stellar nuclear ring can be seen. In NGC 2859, the bar is less elongated and is embedded in a region of twisted isophotes outside, possible forming a lens. As the profiles make clear, both bars are indeed "flat" in the sense of Elmegreen & Elmegreen (1985). Although one should not generalize too freely from a sample of two, it is curious that at least some inner bars do resemble scaled-down outer (or single) bars quite closely, given that the theoretical expectation is that they should differ dynamically.

Figure 5

Figure 5. Isolated inner bars of NGC 1543 (left, WFPC2 F814W) and NGC 2859 (right, ACS/WFC F814W). All other galaxy components except stellar nuclei have been subtracted. Upper panels show logarithmically scaled isophotes; red lines indicate outer-bar position angle for each galaxy. Lower panels show cuts along the major axis of each inner bar; both profiles are "flat" in the sense of Elmegreen & Elmegreen (1985).

As a bonus, we can use the extracted bars as direct estimates of how massive these inner bars are - i.e., what fraction of the total stellar light (and thus stellar mass) they make up. This turns out to be ~ 4% in the case of NGC 1543 and ~ 10% for NGC 2859; put another way, the inner bar is ~ 7% of the outer bar's mass in NGC 1543, but it is ~ 25% of the outer bar's mass in NGC 2859. These latter values can potentially test models of double-barred galaxies, since theoretical arguments suggest that an inner bar must be massive enough to to produce orbits which can support it, but cannot be too massive or it will disrupt the orbits making up the outer bar (e.g. Maciejewski & Sparke 2000, El-Zant & Shlosman 2003, Maciejewski & Athanassoula 2008).

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