3. RINGS

Rings in galaxies are common, and are thought to trace resonances in the disk. This means that they can be used as easily observable tracers of the underlying dynamical structure of the galaxy. Of the three main categories of `resonance rings', outer, inner, and nuclear rings, the former two types can be recognised on standard optical imaging of galaxies, and have thus been classified as part of the main galaxy catalogues. In particular, the RC3 catalogue (de Vaucouleurs et al. 1991) assigns the categories `R' for outer ring, and `r' for inner ring (pseudorings were also classified but are outside the scope of this review). The classification scheme has been perfected in the De Vaucouleurs Atlas of Galaxies (Buta et al. 2007), and most recently by Buta et al. (2010b). In the latter paper, we used Spitzer mid-IR images from the S<sup>4</sup>G survey to classify 207 galaxies, and introduced also the third class of rings, nuclear rings, into the classification (`nr').

In contrast to inner and outer rings, it is much harder to recognize nuclear rings in the images typically used for galaxy classification. As a result, there has not been a complete inventory of nuclear rings. This we have remedied with AINUR (Comerón et al. 2010), where 113 bona fide nuclear rings in 107 galaxies were catalogued and studied. The main aims of AINUR were, first, to make an inventory as complete as possible of nuclear rings in the local Universe, and second, to study in a statistical sense their properties in relation to the properties of their host galaxies. The importance of nuclear rings lies primarily in the fact that they are assumed to be tracers of recent gas inflow to the circumnuclear region (Combes & Gerin 1985; Shlosman et al. 1990; Athanassoula 1994; Knapen et al. 1995; Heller & Shlosman 1996; Combes 2001; Regan & Teuben 2003). They form significant quantities of stars (Kennicutt et al. 2005) and may thus help the secular building of a bulge, and are close to the region where non-stellar activity occurs in many galaxies (Knapen 2005).

As seen in Fig. 5, the radii of nuclear rings vary from a few tens of pc (the limit allowed by space-based imaging) to over 3 kpc. We can reliably recognise nuclear rings in galaxies up to a distance of some 80 Mpc, although only the larger rings are seen in galaxies over some 20 Mpc away. In AINUR, we define a nuclear ring primarily as a star-forming ring-like feature in the proximity of the nucleus, employing a number of additional criteria relating to the ring width and radius. It is usually easy to decide whether rings are nuclear or inner, because inner rings occur near the end of a bar (Schwarz 1984), whereas nuclear rings occur well within the bar. In the absence of a bar, and if only one ring is present, distinguishing between nuclear and inner rings may be impossible. We do not include pseudo-rings (intermediate between nuclear spiral and nuclear ring) but the dividing line is somewhat fuzzy.

Figure 5. Distribution of nuclear ring radius as a function of distance to the host galaxy for the 113 nuclear rings in AINUR. Reproduced with permission from Comerón et al. (2010).

On the basis of a complete sample of galaxies within AINUR, the fraction of disk galaxies with morphological types in the range -3 < T < 7 that host a star-forming nuclear ring is confirmed to be 20% ± 2% (see also Knapen 2005). This is a high fraction, and considering that the star formation activity is mostly seen in emission from massive stars (UV, H) and thus quite possibly short-lived (Allard et al. 2006; Sarzi et al. 2007), one can conclude that nuclear rings are very frequent indeed.

Using basic nuclear ring parameters such as size determined from the AINUR imaging (mostly HST), and host galaxy and bar parameters (e.g., bar length, bar ellipticity, Q_g) determined from near-IR images from the 2 Micron All-Sky Survey (2MASS), Comerón et al. (2010) explored relations between the nuclear rings and their host galaxies and bars (where present).

Fig. 6 shows two examples. In the left panel, it is seen that for small values of Q_g (the non-axisymmetric torque of the galaxy, which in most cases is dominated by the bar - small Q_g values thus generally denote weak bars, and high values strong bars) a wide range of relative nuclear ring sizes is allowed, where galaxies with high Q_g can only have small rings. This had been found from a much smaller sample of nuclear rings by Knapen (2005), and seen in simulations by Salo et al. (1999). Large nuclear rings can only occur in weak bars. Analogous to what we found for the bar dust lanes (Sect. 2.2), the bar strength does not prescribe the nuclear ring size, but does set an upper limit. What determines the exact size of a nuclear ring within the range allowed by its bar is not clear, but must be related to the shape of the gravitational potential which conditions the location of the Inner Lindblad Resonances (ILRs).

Figure 6. Left panel: relative nuclear ring size, normalised by the host galaxy disk size, as a function of the bar strength parameter Qg, and separated by morphological type. Encircled symbols denote unbarred galaxies. Right panel: Absolute nuclear ring size versus the bar length. Dashed line indicates bar lengths four times the ring radii. Reproduced with permission from Comerón et al. (2010).

The right panel of Fig. 6 shows how the length of the bar limits the radius of the nuclear ring (to around r_ring = r_bar / 4), while rings smaller than the upper limit are apparently allowed. Both these relations confirm that the size of the nuclear ring is limited by basic parameters of the bar, and thus that the rings must be closely related dynamically to the bar.

Further evidence for the intricate links between host galaxy, bar, and nuclear ring is provided by Mazzuca et al. (2010) from a study of the inner rotation curves of 13 nuclear ring host galaxies. They obtained H velocity fields using the DensePak integral field unit on the 3.5 m Wisconsin, Indiana, Yale & NOAO (WIYN) telescope and the TAURUS Fabry-Perot instrument on the 4.2 m William Herschel Telescope. From these, they derived rotation curves after assuring that the non-circular motions were small enough to allow such a derivation. As the rotation curve is, theoretically, intricately linked to the gravitational potential and to the location of the ILRs which give rise to the nuclear rings (Knapen et al. 1995), Mazzuca et al. (2010) then parametrized the inner part of the rotation curve and compared the results with the location of the nuclear ring, as well as the properties of the bar.

The main rotation curve parameter considered by Mazzuca et al. (2010) is its rise rate, defined as the ratio between the velocity difference between that at the turnover point (where the rotation curve stops rising and flattens out) and that at the origin, and the difference in radius between those two points. As can be seen in Fig. 7, plotting the rise rate of the rotation curve as a function of the relative nuclear ring size or the nuclear ring width yields diagrams reminiscent of the ones we have presented earlier in this paper: they outline an upper limit, indicating that ring size and width limit the rotation curve rise rate or vice versa. Large nuclear rings, and wide nuclear rings, can only occur when the rotation curve rises slowly. In the case of a rapidly rising rotation curve, the nuclear ring can only be small, and narrow.

Figure 7. Rise rate of the inner part of the rotation curve as a function of the nuclear ring size relative to the disk size (left panel), and the nuclear ring width (right panel). The thirteen different galaxies in this sample are indicated with different symbols. Data from Mazzuca et al. (2010).

Mazzuca et al. (2010) thus present a neat observational confirmation that the rotation curve and the metric parameters of the nuclear ring are intricately linked. The physical background of this link must include the location of the resonances: linear theory ² predicts that ILRs, and nuclear rings, occur where the rate of change of the circular velocity is highest - this is where the rotation curve turns over. The rise rate of the rotation curve is thus a measure of where the ILRs are located: as rotation curves tend to flatten out at circular velocities of between 100 and 200 km s^-1, a high rise rate means that the ILRs are close to the nucleus, and thus that the nuclear ring must be small. It also implies that the ILRs are close together radially, which leads to narrower nuclear rings. All this is exactly as seen observationally. A slowly rising rotation curve implies that the ILRs can be located further out from the nucleus, but also that the distance between the inner and outer ILRs (which in linear theory limit the radial range where the nuclear ring can occur) can increase. Depending on the precise shape of the gravitational potential in the inner region, the inner ILR can still be relatively close to the nucleus, which might explain that in galaxies with slowly rising rotation curves large and wide nuclear rings can occur, but small and narrow ones are not excluded.

Fig. 8 shows that the rotation curve rise rate is also located to the bar strength, measured here through the non-axisymmetric torque parameter Q_g. The figure indicates a general trend of more steeply rising rotation curves as Q_g increases (the one notable exception is NGC 1530 which is a galaxy with a bar that is exceptional in many more ways). It is not clear whether the two parameters plotted here are directly or indirectly related - we have already seen that stronger bars tend to host smaller rings. But as a general conclusion, it is beyond doubt now that the underlying dynamics of a host galaxy influences its appearance and kinematics, as well as detailed aspects of some of the structural components such as bars and rings.

Figure 8. Non-axisymmetric torque parameter Qg, which can be interpreted as an indicator of the strength of the bar, plotted against the rotation curve rise rate. Data from Mazzuca et al. (2010).

² In the linear approximation the gravitational potential of the bar is considered to be axisymmetric. While this may be reasonable for weak bars, it is not correct in the case of a strong bar (Sellwood & Wilkinson 1993; Shlosman 2001). Nevertheless, as an intuitive tool it can provide a useful illustration. Back.