In this section, I consider what we can tell about the general population of double-barred galaxies and the bars within them: how common they are, what type of galaxies they are, how large (or small) the bars are, etc. This is based primarily on two datasets. The first is an expanded version of the Erwin & Sparke (2003) sample, which now encompasses barred and unbarred galaxies of Hubble types S0-Sb with redshifts < 2000 km s-1 and major-axis diameters > 2.0. The other source is an updated version of the database published in Erwin (2004), which attempts to keep track of all well-defined double-barred galaxies in the literature. The latter dataset now includes 61 galaxies; it has the disadvantage of being drawn mostly from an extremely heterogeneous set of observations, and so is subject to a variety of poorly known selection effects.
In Figure 2 I show the double-bar fraction as a function of Hubble types, based on the aforementioned local sample (Erwin & Sparke 2003; Erwin et al., in prep). The double-bar frequency is roughly constant at ~ 30% of barred galaxies, or ~ 20% of all galaxies, from S0 down through Sab. There is some evidence that the fraction is smaller for Sb galaxies.
Figure 2. Fraction of barred galaxies (left) and all galaxies (right) which are double-barred, as a function of Hubble type.
Are double bars basically a phenomenon of early-type disks? Unfortunately, we lack systematic surveys of later Hubble types; such surveys would need to be in the near-IR to avoid dust extinction, and would need to have high spatial resolutions, since bars in late-type spirals are systematically smaller than early-type bars Erwin (2005). The current version of the Erwin (2004) catalog does have several double-barred Sbc galaxies, but only one confirmed double bar with a late Hubble type (NGC 6946, Sc). While this suggests a lower frequency of double bars in late Hubble types, the imaging surveys which provided most of the double-bar detections to date have historically been heavily biased towards Hubble types earlier than Sc, in part because many of these surveys have been aimed at Seyfert galaxies (and matched non-active galaxies), which are primarily early types.
Figure 3 shows the absolute and relative sizes of inner bars from the current catalog of double-barred galaxies. In absolute size, inner bars span about an order of magnitude, with semi-major axes ranging from ~ 100 pc all the way up to 1.2 kpc; the median size is ~ 500 pc (relative to R25, the range is 0.01-0.10, with a median of 0.04). The sizes of inner bars, while almost always smaller than outer or single bars in early-type disks, thus actually overlap with the low end of single-bar sizes in late-type spirals (Sc and later; see Erwin 2005).
Figure 3. Left: Absolute semi-major axis sizes of inner bars. Right: Relative semi-major axis sizes (inner bar size as a fraction of outer bar size). All sizes are deprojected.
Inner bar size does correlate with outer bar size, though not very strongly (Spearman r = 0.57). The median size ratio is 0.12; the true median may be slightly smaller, since resolution limits mean that small inner bars are less likely to be identified. There is a fairly clear upper limit of ~ 0.25, which is at least roughly consistent with theoretical arguments that inner bars cannot be too large without disrupting the orbits which support the outer bars.
The local S0-Sb sample mentioned above contains 55 single-barred and 21 double-barred galaxies. Are there systematic differences between the two types, which might help use understand why some galaxies have two bars and other have just one? The answer, for the most part, is no: single- and double-barred galaxies appear to be very similar in their global properties (e.g., absolute magnitude, rotation velocity, central velocity dispersion). The only genuinely significant difference appears to be in the sizes of the large-scale bars: the outer bars of double-barred systems are longer (typically ~ 4 kpc in radius) than the bars of single-barred galaxies (typically ~ 2.5 kpc).