FORMATION OF DENSE MOLECULAR GAS AND STARS AT THE CIRCUMNUCLEAR STARBURST RING IN THE BARRED GALAXY NGC 7552

The optical observations of NGC 7552 reported here are the product of a winning entry in the 2011 Australian Gemini School Astronomy Contest, for which one of us (S. Ryder) was a co-investigator on the contest proposal. Images of the galaxy in g', r', and i' filters were obtained with the Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) attached to the Gemini South Telescope as part of the program GS-2011A-Q-12 (PI: C. Onken). The filters are similar to the filters used by the Sloan Digital Sky Survey (SDSS). We also obtained an Hα image with a narrow-band Hα filter centered on 656 nm with a 7 nm wide bandpass. The observations were done in seeing between 06–08 under photometric conditions on 2011 July 23 UT. Four exposures per filter were obtained with integration time between 100 and 300 s, with each exposure offset by 10'' spatially to allow filling-in of the inter-CCD gaps in GMOS. On-chip binning yielded a pixel scale of 0146 pixel⁻¹.

The data were reduced and combined using the gemini package (V1.10) within iraf.⁸ A master bias frame (constructed by averaging with 3σ clipping a series of bias frames) was subtracted from all raw images. Images of the twilight sky were used to flat field the images, then the dithered galaxy images were registered and averaged together with the imcoadd task to eliminate the inter-CCD gaps, bad pixels, and cosmic rays.

2.2.1. H i

2.2.2. Radio Continuum

2.2.3. HCN and HCO⁺

We observed NGC 7552 in ¹²CO (2–1) and ¹³CO (2–1) in the compact configuration of the Submillimeter Array (SMA; Ho et al. 2004) on 2006 August 4. Observations were centered at $\rm \alpha _{2000}=23^{\rm h}16^{\rm m}10\buildrel{\mathrm{s}}\over{.}7$ and δ₂₀₀₀ = −42°35'0541, coinciding with the center of the circumnuclear starburst ring as defined by Forbes et al. (1994a). The primary beam of the antennas at the wavelengths of the observed molecular lines is 55''. Seven out of the eight antennas of the SMA were available during our observation. As summarized in Table 1, with baseline lengths ranging from 16 m to 69 m, the largest structure (of uniform brightness) that we expect to be sensitive to is about 16''. The receiver was tuned and the correlator configured to cover the frequency range 227.6–229.6 GHz in the upper sideband (USB) thus including the ¹²CO (2–1) line, and 217.6–219.6 GHz in the lower sideband (LSB) thus including the ¹³CO (2–1) line. The correlator provided a total of 24 spectral windows (chunks) in each sideband, with a total of 128 channels and a bandwidth of 104 MHz in each chunk. To make the channel maps in ¹²CO (2–1), we averaged 10 channels together, resulting in a velocity resolution of 10 km s⁻¹. Because the signal is weaker in ¹³CO (2–1), to make the channel maps in this line we averaged 18 channels together resulting in a velocity resolution of 18 km s⁻¹.

We calibrated the data separately for bandpass, amplitude, and phase using SMA-specific MIR tasks adopted from the MMA software package (written in IDL), which was originally developed for the Owens Valley Radio Observatory (OVRO; Scoville et al. 1993). The bandpass was calibrated using Uranus. For complex gain calibration, we observed the quasars J2235–485 and J2258–279 for a duration of 6 minutes every 30 minutes. We used J2235–485, which is located at an angular distance of 93 from our target source, for phase calibration. J2235–485, however, is too weak for amplitude calibration. We therefore used J2258–279, which is located at a larger angular distance of 15° from our target source, for amplitude calibration. Because the amplitude solutions derived from the individual scans did not differ significantly between adjacent scans, we applied time smoothing scale of three scans of J2258–279 to derive more precise amplitude solutions. We derived the absolute flux calibration scale from Uranus, which we assumed had a flux density of 36.836 Jy at the time of our observation.

We imaged the data using MIRIAD. To deconvolve the sidelobes, we first CLEANed the dirty maps without any preselection to judge which features are likely to be real and which are likely to be sidelobes. We then placed boxes around those features judged to be real on the basis that they do not appear to resemble the sidelobes of the dirty beam, and that their structure changed continuously between adjacent channels. As shown in Section 3.5, the features in each channel have a sufficiently simple structure that we are confident of having picked out only those that are real. The ¹²CO (2–1) channel maps have an angular resolution of 70 × 28 at P.A. = −119, and a rms noise level of 78 mJy beam⁻¹ at a velocity resolution of 10 km s⁻¹. The ¹³CO (2–1) channel maps were made with 18 km s⁻¹ velocity binning, resulting in an angular resolution of 69 × 28 at a P.A. = −89, and a rms noise level of 39 mJy beam⁻¹. Because the features detected span an angular extent from the pointing center that is significantly smaller than the primary beam, we did not apply a primary beam correction to the maps.

Figure 1 shows the optical images obtained with Gemini South. Distinct dust lanes are often seen in late-type barred galaxies along the leading edges of the bar, as is the case also for NGC 7552. In the g'-band image of Figure 1, we indicate the location of the dust lanes with a more direct tracer, dust emission as imaged by Spitzer at 5.8 μm. The overall extent of this dust emission is indicated by a contour, which perfectly matches the dust lanes seen in the optical.

The Hα image of Figure 1 highlights regions of recent activity involving massive stars. The circumnuclear starburst ring as traced in the 3 cm continuum is overlaid on the Hα image to show the overall extent of this ring. The physical size of the ring at 3 cm is comparable to the size of the central bright bulge of NGC 7552 in the optical images. A magnified view of the central region in Hα and 3 cm continuum is shown in Figure 3. In addition to the circumnuclear starburst ring, a bright H ii region, detected in both Hα and radio continuum, is apparent ∼3.5 kpc east of the nucleus along the bar. This H ii region was also detected in earlier Hα images by Forbes et al. (1994a).

A map of the integrated H i intensity (zeroth moment) is shown in Figure 2 (left panel). As pointed out by Dahlem (2005), the H i gas traces the large-scale disk of NGC 7552. For ease of comparison, the optical i'-band image of the galaxy shown earlier in Figure 1 is overlaid as contours. Along the major axis the H i disk can be detected out to a projected radius of about 2100'' (∼20 kpc), about twice as far out as the optical disk. Similarly, along the minor axis, the H i disk can be detected out to a projected radius of about 121'' (∼13 kpc), again about twice as far out as the optical disk. There is a prominent ring-like enhancement in H i that peaks at or close to the ends of the large-scale optical bar. Finally, a central depression can be seen in the integrated H i intensity map. This central depression has a size that closely coincides with the angular extent of the circumnuclear molecular gas detected in our observations as described below (Sections 3.4 and 3.5).

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Figure 2 (right panel) shows a map of the intensity-weighted mean H i velocity (first moment). Assuming a systemic velocity of 1586 km s⁻¹ as found in the optical and as derived below (Section 3.5) from our molecular line observations, emission can be seen spanning the velocity range from −100 km s⁻¹ to 100 km s⁻¹ about the systemic velocity. As can be seen, the kinematic major axis is aligned roughly east–west, coincident with the major axis of the optical bar. Blueshifted emission (negative velocities) originates primarily westward and redshifted emission (positive velocities) primarily eastward of the galactic center. On close scrutiny, the P.A. of the kinematic major axis can be seen to change with galactic radius, creating an S-shaped pattern in the gas kinematics. Such S-shaped kinematic patterns are commonly attributed to non-circular motions under the non-axisymmetric gravitational potential of a galactic bar (see Section 5.1 for detailed discussion). Far beyond the optical bar however, the P.A. of the kinematic major axis continues to change, suggesting that the outskirts of the galaxy may be warped (by gravitational interactions with one or more neighboring galaxies as described in Section 1).

Figure 3 shows the central part of our radio continuum images at 6 cm (left panel) and 3 cm (right panel), both of which were recreated from the data taken by Forbes et al. (1994a). Over the field shown, the radio continuum emission originates from a ring, which as mentioned by Forbes et al. (1994a) corresponds to the circumnuclear starburst ring, as can be seen in Figure 3 (right panel) where the 3 cm image (contours) is overlaid on our Hα image (color). This ring has an outer extent comparable to the central H i depression mentioned above.

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Five peaks are clearly visible in the 3 cm image (right panel), whereas only three peaks are visible in the 6 cm image (left panel) that has a lower angular resolution than the 3 cm image. To study the spectral index of each knot, we have convolved the 3 cm image to the same angular resolution as the 6 cm image. After degrading the angular resolution, we find that only three knots are discernible in the 3 cm image, which now resembles the 6 cm image. The spectral indices (α, where S∝ν^α with S the flux density and ν the observing frequency) of the three knots (see the left panel of Figure 3) are −1.11 ± 0.02 (upper right), −0.84 ± 0.03 (upper left), and −0.72 ± 0.05 (bottom left), with an average value of −0.89 ± 0.06 that is similar to that inferred by Forbes et al. (1994a). The negative spectral indices indicate that the emission of all the knots is dominated by, if not produced entirely by (non-thermal), synchrotron emission.

Figure 4 shows our channel maps of the HCN (black contours) and HCO⁺ (1–0) (cyan contours) lines. Both HCN (1–0) and HCO⁺ (1–0) emission are concentrated in two knots located to the north and south of the galactic nucleus. The northern knot is detectable over a velocity range from −133 km s⁻¹ to 32 km s⁻¹ with respect to the optically determined systemic velocity of the galaxy, and is therefore preferentially blueshifted. The southern knot is detectable over a velocity range from about −43 km s⁻¹ to 92 km s⁻¹ with respect to the systemic velocity, and is therefore preferentially redshifted. The centroids of both knots shift from west to east with increasing (i.e., from blueshifted to redshifted) velocities.

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Figure 5 (left panel) shows a map of the integrated HCN (1–0) intensity in black contours. The overall size of the emitting region is comparable with the central H i depression described above in Section 3.2, suggesting that the gas density is so high here that the atomic hydrogen gas has been largely converted to molecular hydrogen gas. The HCN (1–0) contours are overlaid on a gray-scale image of the 3 cm continuum emission shown earlier in Figure 3 (right panel) but now convolved to the same angular resolution as the HCN (1–0) map. At this angular resolution, the 3 cm continuum map shows two knots just like the HCN (1–0) map. The observed HCN (1–0) emission therefore originates from the circumnuclear starburst ring, and exhibits a central depression or possibly a hole. Notice the small displacement between the centroids of the HCN (1–0) gas and radio continuum knots, a point we shall return to in Section 6.2.

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Figure 5 (right panel) shows a map of the intensity-weighted mean HCN (1–0) velocity. A velocity gradient is discernible roughly along the east–west direction, with the kinematic major axis lying at a P.A. of 110°. The kinematic major axis in HCN (1–0), as well as in HCO⁺ (1–0) as described below, are both aligned with the kinematic major axis at the innermost region of the large-scale H i disk as described in Section 3.2. The good agreement suggests that there is a continuous velocity field between the outermost region in molecular gas and innermost region in neutral atomic gas.

Figure 6 shows our moment maps of the HCO⁺ (1–0) line. The emission in all these maps is virtually identical to that seen in HCN (1–0). Both HCN (1–0) and HCO⁺ (1–0) have comparable critical densities of ∼10⁶ cm⁻³, suggesting that both are tracing the same regions of dense gas.

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Figure 7 shows our channel maps of the ¹³CO (2–1) line, which by contrast with both the HCN (1–0) and HCO⁺ (1–0) has a much lower critical density of just ∼10³ cm⁻³. Only a single compact component is discernible that shifts from west to east across the center of the galaxy with increasing velocity, just like that seen in HCN (1–0) and HCO⁺ (1–0) as described above in Section 3.4. We have convolved both the HCN(1–0) and HCO⁺ (1–0) maps to the same angular resolution as the ¹³CO (2–1) map, and found that all show the same spatial-kinematic structure suggesting that they all trace the same global features. In the ¹³CO (2–1) map, emission is detectable over the velocity range from about −95 km s⁻¹ to 100 km s⁻¹ with respect to the systemic velocity, comparable to the detectable velocity range of the emission in both the HCN (1–0) and HCO⁺ (1–0) maps.

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Figure 8 (left panel) shows the integrated ¹³CO (2–1) intensity map in black contours overlaid on the integrated HCN (1–0) intensity map, taken from Figure 5 but convolved to the same angular resolution as the ¹³CO (2–1) map, in gray scale. Figure 8 (right panel) shows a map of the intensity-weighted mean ¹³CO (2–1) velocity. As can be seen, the compact central component detected in ¹³CO (2–1) has a similar size and kinematics as the circumnuclear HCN (1–0) (and HCO⁺ (1–0)) emission. In Figure 9, we show position–velocity (P–V) diagrams of the HCN (1–0), HCO⁺ (1–0), and ¹³CO (2–1) emission along a P.A. of 110°, which corresponds to the orientation of the kinematic major axis. As can be seen, the P–V diagram in ¹³CO (2–1) closely resembles that in the higher density tracers of molecular hydrogen gas. We therefore believe that the observed ¹³CO (2–1) emission originates from essentially the same regions of the circumnuclear starburst ring as the observed HCN (1–0) or HCO⁺ (1–0) emission. Of course, any central depression or hole of the same size as that seen in HCN (1–0) and HCO⁺ (1–0) would not be discernible at the angular resolution of our ¹³CO (2–1) observation.

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The P–V diagrams of Figure 9 reveal that the systemic velocity at the center of the circumnuclear starburst ring, which presumably coincides with the dynamical center of the galaxy, is about 1580 km s⁻¹. This is consistent with the optically determined value of 1586 ± 5 km s⁻¹ (RC3), but significantly smaller than that determined from the global H i profile of 1608 ± 5 km s⁻¹ (The H i Parkes All Sky Survey; Barnes et al. 2001).

Figure 10 shows our channel maps of the ¹²CO (2–1) line. By contrast with the simplicity of the ¹³CO (2–1) channel maps, three components are now discernible: a compact central component that is the counterpart of that seen in ¹³CO (2–1), and two extensions on opposite sides of the center with one arm extending east from north and the other arm west from south. The compact central component is detectable over the velocity range from about −125 km s⁻¹ to 135 km s⁻¹ with respect to the systemic velocity, somewhat larger than the detectable velocity range of its counterparts in ¹³CO (2–1), HCN (1–0), and HCO⁺ (1–0). By contrast, both the eastern and western arm-like components are detectable over a narrower velocity range than the compact central component in any of the observed molecular lines. The western arm is detectable over the velocity range from about −85 km s⁻¹ to 55 km s⁻¹ and is therefore preferentially blueshifted, whereas the eastern arm is detectable over the velocity range from about −55 km s⁻¹ to 75 km s⁻¹ and is therefore preferentially redshifted.

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Figure 11 (upper left panel) shows a map of the integrated ¹²CO (2–1) intensity in black/white contours overlaid on the optical i'-band image of the inner part of the galaxy. Dust lanes are visible as silhouettes in the optical image running east and west of the center, as well as in emission at 5.8 μm as shown by the cyan contour based on the observations by Kennicutt et al. (2003) in their Spitzer SINGS project. The eastern and western ¹²CO (2–1) arms coincide with the innermost regions of these dust lanes. These arms appear to connect with the circumnuclear starburst ring at or near the locations where we detected two knots of dense molecular gas as traced in HCN (1–0) and HCO⁺ (1–0) (see Section 3.4), as shown in the lower left panel of Figure 11 where the integrated ¹²CO (2–1) intensity is plotted in green contours and integrated HCN (1–0) intensity in black contours. We note that, for the same ratio in intensity between the arms and compact central component, the stronger western arm should be detectable (at 4.5σ) at the sensitivity of our HCN (1–0)/HCO⁺ (1–0) maps.

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Figure 11 (lower right panel) shows a map of the intensity-weighted mean ¹²CO (2–1) velocity. At our angular resolution, the kinematics of the compact central component cannot be completely separated from the individual kinematics of the eastern and western arms, and vice versa. Nevertheless, the S-shape velocity field (contours) indicates the existence of non-circular motion, which is similar to what is observed in other barred galaxies. In Figure 9, we show a P–V diagram made from the CO (2–1) channel maps at a P.A. of 110°. As can be seen, the kinematics of the compact central component are similar to its counterparts in the other observed molecular lines. The western arm is preferentially blueshifted whereas the eastern arm preferentially redshifted, and therefore both arms share the same overall kinematics as the large-scale galactic disk seen in H i.

We derive the mass of molecular hydrogen gas in all the three features detected in ¹²CO (2–1) in the standard manner using the Galactic conversion factor between CO intensity and mass of molecular hydrogen gas of X_CO = 3 × 10²⁰ cm ⁻² (K km s⁻¹)⁻¹ (Solomon et al. 1987). This conversion is based on the ¹²CO (1–0) line, and in the present situation requires knowledge of the ratio in ¹²CO (2–1) to ¹²CO (1–0) intensities. Aalto et al. (1995) find a ratio in brightness temperatures between these two lines of 1.2  ±  0.1 based on single-dish observations with the Swedish-ESO 15 m Submillimeter Telescope (SEST) toward the center of NGC 7552. For simplicity, we shall therefore assume a ratio in brightness temperature of unity for ¹²CO (2–1) to ¹²CO (1–0) throughout this work. Accordingly, the compact central component (corresponding to the circumnuclear starburst ring, and perhaps regions within), which has an integrated intensity in ¹²CO (2–1) of 1487.1 ± 20.3 Jy km s⁻¹, has a gas mass of (3.2 ± 0.1) × 10⁹ M_☉, including the mass of the heavy elements other than molecular hydrogen ($M_{\mathrm{gas}}=1.36M_{\mathrm{H_{2}}}$). The integrated ¹²CO (2–1) intensity detected over the entire region is 2330.5 ± 34.7 Jy km s⁻¹, and hence the mass of molecular gas in the eastern and western arms combined is (1.7 ± 0.2) × 10⁹ M_☉.

The dense gas fraction can be estimated by comparing the mass derived from ¹²CO (2–1) and HCN (1–0). Assuming that the gas traced by HCN (1–0) is gravitationally bound (Solomon et al. 1992), the HCN-to-H₂ conversion factor $X_{\mathrm{HCN}}\equiv N(\mathrm{H_{2}})/L^{\prime }_\mathrm{{HCN}}$ is ∼20 M_☉ (K km s⁻¹ pc⁻²)⁻¹, where N(H₂) is the column density of molecular hydrogen gas and $L^{\prime }_\mathrm{{HCN}}$ the HCN (1–0) luminosity. For the measured $L^{\prime }_\mathrm{{HCN}} \approx 7.5 \times 10^{7} \,\rm K \,km \,s^{-1} \,pc^{-2}$, the corresponding mass in dense gas, as traced in HCN (1–0), is ∼1.5 × 10⁹ M_☉. The dense gas fraction is therefore about 50% at the compact central component, much higher than is usually found in Galactic GMCs. We note, however, that the inferred dense gas fraction may contain considerable uncertainty because the conversion factors X_HCN and X_CO used may not be appropriate for the circumnuclear regions of galaxies (although the use of different conversion factors can either raise or lower the dense gas fraction). For example, based on virial arguments for the circumnuclear starburst ring of the nearby barred spiral galaxy IC 342, Meier & Turner (2001) argue that X_CO is only 1 × 10²⁰ cm ⁻² (K km s⁻¹)⁻¹ or even smaller, in which case the dense gas fraction at the compact central component becomes nearly 100%.

Line ratios inferred with an interferometer can be compromised if there exist uniformly bright features with sizes beyond that detectable even by the shortest baseline. Aalto et al. (1995) have observed the central region of NGC 7552 with the SEST in ¹²CO (1–0), ¹²CO (2–1), ¹³CO (1–0), ¹³CO (2–1), and HCN (1–0). They do not show line profiles for any of the transitions observed, but only quote the line intensities or ratio in brightness temperatures of the different lines. After convolving our channel maps to the same angular resolution as in the observation of the corresponding line with the SEST, we found that our SMA observation recovered 54% ± 9% of the ¹²CO (2–1) emission detected by the SEST. Given typical systematic uncertainties of about 20% in the absolute flux calibration at millimeter wavelengths, we may well have recovered the bulk of the circumnuclear emission in ¹²CO (2–1). Our ATCA observation recovered 76% ± 16% of the HCN (1–0) emission detected by the SEST, suggesting once again that the bulk, if not all, of the circumnuclear emission in this line has been recovered. Surprisingly, our SMA observation recovered only 26% ± 10% of the ¹³CO (2–1) emission detected by the SEST, despite the fact that ¹³CO (2–1) traces higher column densities and therefore more compact regions than ¹²CO (2–1) as evidenced by the maps presented in Figure 8. The ¹³CO (2–1) line however was detected at a confidence level of only 3σ–4σ in the SEST observation, and we therefore do not place a high degree of confidence on this particular comparison.

We computed the physical properties (density and temperature) of the molecular gas associated with the circumnuclear starburst ring from the ratio in brightness temperatures of the HCN (1–0) to ¹³CO (2–1) lines using the large velocity gradient (LVG) approximation (e.g., Goldreich & Kwan 1974; Scoville & Solomon 1974). We used the ¹³CO (2–1) line because it is more likely than the ¹²CO (2–1) line to trace the same region as the HCN (1–0) line, as the maps we presented earlier indicate (see Section 3.5 and Figure 8). HCN (1–0) is a tracer of high density molecular hydrogen gas; as the ¹³CO (2–1) emission is much more optically thin than the ¹²CO (2–1) emission, the former is more strongly weighted toward regions of high column density and therefore also density. Indeed, as we shall show, the ¹³CO (2–1) emission is optically thin and therefore a good tracer of column density.

To derive the ratio between the HCN (1–0) and ¹³CO (2–1) intensities, we first convolved our HCN (1–0) map to the same angular resolution as our ¹³CO (2–1) map (see Figure 8). The circumnuclear starburst ring is spatially unresolved at this angular resolution, and so the line ratio we derive for HCN (1–0) to ¹³CO (2–1) of 2.0 ± 0.2 is an average over the entire ring. We assumed Galactic abundances for the ¹³CO and HCN molecules of [¹³CO]/[H₂] ≈ 10⁻⁶ (Solomon et al. 1979) and [HCN]/[H₂] ≈ 2 × 10⁻⁸ (Irvine et al. 1987). Finally, we estimated a velocity gradient of 0.24 km s⁻¹ pc⁻¹ from the P–V diagram along the kinematic major axis of the HCN (1–0) emission as shown earlier in Figure 9.

Figure 12 shows a plot of the density of molecular hydrogen gas, n(H₂), as a function of the product Z(¹³CO)/(dv/dr), where Z(¹³CO) is the ¹³CO abundance and dv/dr the velocity gradient along the radial direction. For the adopted or inferred values above, Z(¹³CO)/(dv/dr) ≈ 4 × 10⁻⁶, which is displayed with the blue vertical line in each panel. The different panels in this figure correspond to different kinetic temperatures (from 10 K to 1000 K). The red contours in each panel indicate acceptable solutions in the n(H₂) and Z(¹³CO)/(dv/dr) phase space for different HCN (1–0) to ¹³CO (2–1) line ratios based on our LVG calculations. The black lines indicate the ¹³CO (2–1) opacity. As can be seen, for a HCN (1–0) to ¹³CO (2–1) line ratio of 2.0 ± 0.2, and Z(¹³CO)/(dv/dr) ≈ 4 × 10⁻⁶, solutions can only be found for kinetic temperatures well above 100 K, for which the ¹³CO (2–1) emission is optically thin. At such temperatures, the density of the molecular gas (averaged over the line-emitting regions) is around 10^{5 ± 1} cm⁻³. A similar result has been seen in the circumnuclear starburst ring of the barred spiral galaxy NGC 1097 (Hsieh et al. 2008).

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On the other hand, the adopted Galactic abundance for ¹³CO of [¹³CO]/[H₂] ≈ 10⁻⁶ may be too high for starburst regions (Taniguchi & Ohyama 1998). The ¹³CO abundance is controlled primarily by fractionation reactions and photodissociation. Fractionation reactions enhance the ¹³CO abundance, but such reactions are only effective in regions where the temperature is less than ∼35 K (Watson et al. 1976) and hence not exposed to vigorous star formation. Photodissociation, naturally, is even more effective in regions where the SFR is higher. If the combination of these factors reduces [¹³CO]/[H₂] by, say, an order of magnitude to ∼10⁻⁷, then acceptable solutions to the observed HCN (1–0) to ¹³CO (2–1) line ratios can be found for temperatures ∼50–100 K and densities ∼10⁵ cm⁻³. Thus, unless the ¹³CO abundance is even lower than the range of values considered above, the molecular gas that we detected in the starburst ring is relatively warm and dense, as would be expected for gas associated with regions that have recently undergone vigorous star formation (see also Matsushita et al. 1998, 2010).

In many galaxies exhibiting nuclear activity, it is often difficult tell whether this activity is produced by active galactic nuclei (AGN) or starburst. Kohno et al. (2001) suggest that such galaxies can be distinguished by plotting the line ratio of HCN (1–0) to HCO⁺ (1–0) against that of HCN (1–0) to ¹²CO (1–0) (Figure 13). They show that galaxies dominated by or exhibiting only AGN activity lie in the upper right corner of such a diagram, having high values in both line ratios. By comparison, galaxies exhibiting only starburst activity or a mix of starburst and AGN activity lie in the lower left corner, having low values in both line ratios. In the case of NGC 7552, we can clearly see that the nuclear activity is dominated by a starburst (i.e., circumnuclear starburst ring), and our observations are able to confidently separate the molecular gas associated with the starburst from any associated with the nucleus in HCN (1–0) and HCO⁺ (1–0), and also to some degree of confidence in ¹²CO (2–1) and ¹³CO (2–1) (based on the similarity of the gas kinematics in all four lines). Such is not the case for the galaxies used to make the abovementioned plot in Kohno et al. (2001). For NGC 7552, the HCN (1–0) to HCO⁺ (1–0) line ratio, averaged over the circumnuclear starburst ring, is 1.13 ± 0.04. The HCN (1–0) to ¹²CO (1–0) ratio, assuming that the ¹²CO (1–0) is equal to the ¹²CO (2–1) intensity for the reason mentioned earlier (see Section 4.1), is 0.181 ± 0.005. This places NGC 7552 firmly in the region occupied by galaxies with nuclear activity dominated by a starburst, enhancing the validity of the plot made by Kohno et al. (2001).

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We examine whether the molecular gas in the circumnuclear starburst ring is dynamically stable according to the Toomre criterion (Toomre 1964). For a disk to be stable against collapse due to its own gravity, the Toomre Q parameter, which is defined as the ratio of the critical surface gas density to the actual surface gas density, Σ_crit/Σ_gas, is required to have a value equal to or exceeding unity.

We compute the average surface gas density in a circular region of radius of 10'' (∼1 kpc), just encompassing the circumnuclear starburst ring, using the molecular gas mass derived in Section 3.5 to find Σ_gas ≈ 900 M_☉ pc⁻². Because the ¹²CO (2–1) emission likely exhibits a central depression or hole within the circumnuclear starburst ring, the value we computed is likely to be a lower limit. We estimated the critical surface gas density using the relationship from Kohno et al. (1999)

$$\begin{equation} \Sigma _{\rm crit}=630\left(\frac{\sigma }{15\,{\rm km \,s^{-1}}} \right)\left(\frac{\kappa }{0.57\,{\rm km \,s^{-1}\,pc^{-1}}} \right)\,{M_{\odot } \,\rm pc^{-2}} \end{equation} \tag{ 1 }$$

where σ is the one-dimensional velocity dispersion, for which we estimated a value of 12 km s⁻¹ based on a second moment map of the ¹²CO (2–1) emission (not shown), and κ the epicyclic frequency. As shown below in Section 5.2, we derived an epicyclic frequency of 0.4 km s⁻¹ pc⁻¹ at the radius of the circumnuclear starburst, and therefore Σ_crit ≈ 354 M_☉ pc⁻². The Toomre Q parameter is therefore no larger than 0.4 in the circumnuclear starburst ring, indicating that the molecular gas there is (highly) unstable to gravitational collapse.

As pointed out in Section 3.2, the intensity-weighted mean H i velocity map (Figure 2) exhibits an S-shaped asymmetry characteristic of periodic orbits predicted theoretically for barred galaxies (e.g., Athanassoula 1992 and references therein). In general, such orbits are elliptical (and centered on the dynamical center of the galaxy), and have their major axes either parallel (x₁ orbits) or orthogonal (x₂ orbits) to the major axis of the bar, changing from one to the other between the locations of dynamical resonances. Specifically, beyond the ILR out to corotation (CR), orbits are x₁. Within the ILR, orbits are x₂. If there is both an outer ILR (oILR) as well as an inner ILR (iILR), orbits are x₁ inside the iILR and x₂ between the iILR and oILR. Between CR and the outer Lindblad resonance (OLR), orbits are x₁. Close to and beyond the major axis of the bar (predicted theoretically to terminate at or before CR), both x₁ and x₂ orbits become progressively more (and are predicted to be usually close to) circular. Close to a bar potential, x₁ is the predominant orbit, hence the major kinematic axis is closely aligned with the galactic bar. The change from x₁ to x₂ orbits and back between dynamical resonances causes the S-shaped twist in the major kinematic axis on scales up to that comparable with the length of the galactic bar.

To accurately derive the rotation curve of NGC 7552 from our measurements of the projected galaxy kinematics, we require a priori knowledge of the axial ratios (which change with galactic radius) of the x₁ and x₂ orbits, and the inclination of the galaxy (including any variation in inclination with galactic radius if the disk is warped). As these parameters (apart from perhaps inclination) are not in general known, we assumed a constant inclination of 25° for NGC 7552 based on the axial ratio of its stellar disk as described in Section 1. For the major kinematic axis of the disk, we used a P.A. of 110° as indicated by the first moment map in all four molecular lines as well as the inner region of the first moment map in the H i line.

The HCN (1–0) to HCO⁺ (1–0) emissions originate primarily, if not entirely, from the circumnuclear starburst ring, and are therefore useful for inferring the rotational velocity of this ring. Sampling only a limited and furthermore spatially unresolved radial range, however, these lines do not provide a meaningful rotation curve at the center of the galaxy. The ¹²CO (2–1) line samples a larger radial range from (presumably) the ring to the innermost regions of the dust lanes, and is useful for making a crude estimate of the rotation curve over this range. The H i line provides a relatively robust estimate of the rotation curve beyond the outer regions probed in ¹²CO (2–1) to far beyond the stellar optical disk.

The rotation curve is directly derived from P–V diagrams of ¹²CO (2–1) and H i from cuts along 110°, as shown earlier in Figure 9, with the envelope-tracing method (see details and more examples in Sofue 1996, 1997). The method traces terminal velocity (or tangent-points) on P–V diagram and corrects for the ISM velocity dispersion. The deprojected rotational velocity is derived from the terminal velocity V_t:

$$\begin{equation} V_{\mathrm{rot}}=V_{\mathrm{t}} /\sin i\: -\: \left(\sigma _{\mathrm{obs}}^{2}\: +\:\sigma _{\mathrm{ISM}}^{2} \right), \end{equation} \tag{ 2 }$$

where i is the inclination, σ_obs the velocity resolution of the observation, and σ_ISM the velocity dispersion of interstellar gas. We adopt an ISM velocity of 7 km s⁻¹ (Stark & Brand 1989; Malhotra 1994). The terminal velocity is the velocity at which the intensity (I_t) is equal to

$$\begin{equation} I_{\mathrm{t}}=\left[ \left(\eta I_{\mathrm{max}} \right)^{2}\: +\: I_{\mathrm{lc}}^{2} \right]^{1/2} \end{equation} \tag{ 3 }$$

on the P–V diagram, where I_max and I_lc are, respectively, the maximum intensity and intensity of the lowest (typically the 3σ) contour level. If the intensity is high enough, I_t ∼ I_lc and is therefore approximately defined by the locus of the rotation curve. η is taken as 0.2 as suggested in Sofue (1996), corresponding to the 20% level of the intensity profile at a fixed position, i.e., I_t ≃ 0.2 × I_max. The accuracy of the obtained V_t along with the V_rot by the envelope-tracing method is ∼ ±15 km s⁻¹, corresponding to ∼ ±15 km s⁻¹/sin i in deprojected velocity (Sofue 1996, 1997).

In Figure 14, we plot the projected rotation curve derived from the ¹²CO (2–1) (from 0 to ∼0.8 kpc) and H i (beyond 1 kpc) lines onto the P–V diagram of both these lines cut along a P.A. of 110°. The projected uncertainties of ±15 km s⁻¹ are plotted on the approaching side of the rotation curve to indicate the size of the error bars. Due to the imperfect physical connection between the two tracers and asymmetry of P–V diagrams, the rotation curve between 0.5 to 1 kpc is poorly connected; we indicate these regions with gray shading in Figure 14.

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The deprojected inner and the entire derived rotation curves are shown respectively in Figures 15(a) and (b). The open and solid black circles denote the receding and approaching sides of the rotation curve respectively, and the red open circles indicate the average of the two sides at the radii where both receding and approaching velocities are seen. The deprojected uncertainties are plotted in the lower right of each panel.

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Because the intensity of the approaching side in the H i map is significantly weaker than that of the receding side, together with the asymmetry of the derived rotation curve on each side, we determine the dynamical resonances for each side of the galaxy separately. We compute where dynamical resonances are theoretically predicted to occur using the usual assumption that the angular velocity of the bar (its pattern speed, Ω_p) is equal to the angular velocity of the galaxy at the outermost ends of the bar (i.e., the CR). We determined the length of the bar in NGC 7552 from the Two Micron All Sky Survey (2MASS) image at 2.2 μm, assuming that the bar ends where the two prominent spiral arms first appear to emerge at a radius of about 5 kpc.

The average rotation curve shows that the angular velocity of the galaxy at the bar's end (5 kpc) is about 38 km s⁻¹ kpc⁻¹, which we therefore take to be the pattern speed of the bar. In Figure 16, we plot the angular velocity (velocity divided by radius, V/R) of the galaxy, Ω (filled circles), as derived from the rotation curve. The solid line is an interpolation between adjacent angular velocity data points, from which we derived the epicyclic frequency, κ, of the orbits, where κ² = 2((v²/R²)  +  (v/R)(dv/dR)). We then computed the Ω − κ/2 curve (triangles) to infer the location(s) of the ILRs, the Ω − κ/4 curve (diamonds) to infer the location of the Ultra Harmonic Resonance (UHR), and the Ω + κ/2 curve (squares) to infer the location of the OLR. The uncertainties in these curves are rather large so we do not show the error bars in Figure 16 for clarity, but show the possible radial ranges of the resonances taking these uncertainties into account.

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We therefore constrain the following possible locations of dynamical resonances in NGC 7552. The Ω + κ/2 curve (open squares) cross the value of Ω_p at >8 kpc, the predicted location of the OLR. Theory predicts that the OLR in spiral galaxies should occur just beyond the outermost reaches of their spiral arms, which in the case of NGC 7552 can be traced out to a (deprojected) radius of about 10 kpc. The computed Ω − κ/4 curve implies that the UHR occurs at roughly 2–4 kpc. Forbes et al. (1994b) suggest that an isolated bright H ii region located at a (deprojected) radius of 3.5 kpc coincides with the UHR. The Ω − κ/2 curve implies two ILRs. The oILR is located at a radius of about 1.7 kpc, which is beyond the circumnuclear starburst ring that has a radius of about 0.5 kpc. Further inward the angular velocity might eventually drop to a value of 0 km s⁻¹ (in principle) at the center of the galaxy, and so an iILR could exist somewhere within the circumnuclear starburst ring. On the other hand, we do not exclude the possibility that the rotation curve keeps rising due to a black hole in the galactic center, resulting in the absence of an iILR. Our finding that the circumnuclear starburst ring is located within the oILR and beyond, possibly, the iILR, is consistent with theoretical predictions (Buta & Combes 1996). The reasonable agreement between the computed and anticipated locations of dynamical resonances in NGC 7552 provides a measure of confidence in our understanding of the global kinematics of this galaxy.

The radio continuum observations of Forbes et al. (1994a), the data from which we reprocessed here, provides the cleanest (i.e., not subject to extinction, emission detected at high S/N) measure of the SFR in the circumnuclear ring. Like Forbes et al. (1994a), we used the standard prescription suggested by Condon (1992) to derive the supernova rate as ∼0.1 yr⁻¹ from the measured radio luminosity for the ring. We then estimated the SFR from the supernova rate in the manner also suggested by Condon (1992), but corrected for a Salpeter initial mass function (IMF) as suggested by Condon et al. (2002), as about 15 M_☉ yr⁻¹. An independent estimate of the SFR in the ring can be made from hydrogen recombination lines in the optical and near-infrared, although such estimates are affected by extinction. The luminosity of the Hα line of 1.5 × 10⁴² erg s⁻¹ derived from the Gemini image, using the relationship L_Hα–SFR suggested by Kennicutt (1998), implies an SFR of about 12 M_☉ yr⁻¹. Moorwood & Oliva (1988) find a luminosity in the Brγ line of 9.8 × 10³⁹ erg s⁻¹ for the circumnuclear ring. Using the relationship between the Brγ line luminosity and SFR suggested by Kennicutt (1998), the SFR is about 8 M_☉ yr⁻¹. The correlation between the global HCN (1–0) and far-infrared luminosities found by Gao & Solomon (2004) for normal to extreme star-forming galaxies can be used to provide an estimate of the SFR using the measured HCN (1–0) luminosity ($L{}^{\prime }_{\mathrm{HCN}}$) as a proxy for the infrared luminosity (L_IR). With an $L{}^{\prime }_{\mathrm{HCN}}\approx 7.5 \times 10^{7}$ K km s⁻¹ pc² and hence L_IR of (5.5 ± 0.1) × 10¹⁰ L_☉ in the circumnuclear starburst ring, the corresponding SFR (for a Salpeter IMF) is 11.0 ± 0.2 M_☉ yr⁻¹. Therefore, in summary, the SFR in the circumnuclear starburst ring of NGC 7552 is about 10–15 M_☉ yr⁻¹.

For comparison, the global SFR derived in the same manner from observations of the entire galaxy in the radio continuum at 20 cm by Schmitt et al. (2006) is about 18 M_☉ yr⁻¹. The global SFR derived from the Hα line, based on our Gemini observations, is about 47 M_☉ yr⁻¹. The global SFR can also be estimated from the far-IR measurements of NGC 7552 with IRAS by Sanders et al. (2003). They find an infrared luminosity for this galaxy of 1.1 × 10¹¹ L_☉, thus placing NGC 7552 right at the threshold for a luminous infrared galaxy. Using as above the conversion between infrared luminosity and SFR suggested by Gao & Solomon (2004) for a Salpeter IMF, the SFR is about 22 M_☉ yr⁻¹. Because the SFR estimated from Hα can be highly uncertain (e.g., up to 99% of UV photons can leak out of H ii regions; Kennicutt 1998), we give more weight to the other methods of estimating SFR as described above. Thus, the circumnuclear region of NGC 7552 contributes ∼50%–80% of the galaxy's entire star formation, and being strongly concentrated in the circumnuclear ring, results in an extremely high SFR surface density of ≳ 4 × 10⁻⁶ M_☉ yr⁻¹ pc⁻¹.

The SFR in the circumnuclear ring, divided by the mass of molecular gas present, is about (3–5) × 10⁻⁹ yr⁻¹. The inverse of this ratio represents the timescale for gas exhaustion and is ∼3 × 10⁸ yr. Such a short gas exhaustion timescale is comparable to that of interacting objects and ULIRGs (few × 10⁸ yr) and about 10 times shorter than that in normal galaxies (Bigiel et al. 2008). Note that even though the gas exhaustion timescale of a circumnuclear starburst ring is short, as the galaxies with circumnuclear rings are generally harboring stronger bars than the galaxies lacking rings, the gas is likely to be nearly continuously replenished at the circumnuclear region through, presumably, the bar-driven gas inflow.

The most prominent optical features—circumnuclear starburst ring, large-scale bar, and spiral arms—in NGC 7552 are remarkably similar to those of NGC 6951, including even the orientation of these features on the sky, thus providing a simple and direct comparison. Like NGC 7552, the bar in NGC 6951 is oriented east–west, with spiral arms emerging from the bar and curling north on the western side and south on the eastern side. Dust lanes that run along the bar intersect the circumnuclear starburst ring at its northern and southern sides, just like those seen in NGC 7552.

Kohno et al. (1999) reported observations of the circumnuclear starburst ring of NGC 6951 in both ¹²CO (1–0) and HCN (1–0) with resolution of ∼500 pc in both lines. They found twin CO knots at or close to the location where the dust lanes meet the ring, and twin HCN knots displaced downstream (assuming that the spiral arms are trailing) from the CO knots. On this basis, Kohno et al. (1999) suggested that the molecular gas at the locations where the dust lanes meet the ring—the twin CO knots, comprising gas channeled inward by the bar—is too turbulent to form dense molecular clouds. Instead, it is only when this gas moves from x₁ orbits (closely traced by the dust lanes) beyond the oILR to x₂ orbits within the oILR (the circumnuclear starburst ring) that dense molecular gas—seen as the twin HCN knots—are able to form; the velocity dispersion along x₂ orbits is predicted to be much smaller than that along x₁ orbits, and hence the molecular gas along x₂ orbits is much more susceptible to gravitational instabilities (see their Figure 17). This scenario is not supported in our observation at least in a global sense as we find that the molecular gas in the circumnuclear starburst ring is very unstable to collapse.

Krips et al. (2007) have observed the circumnuclear starburst ring of NGC 6951 at significantly higher angular resolution (∼240 pc) and sensitivity also in ¹²CO (2–1) and HCN (1–0). An examination of their results (see their Figure 1) reveals no discernible displacement between the centroids of the CO knot and dominant HCN knot in the northern part of the ring, and at best a small displacement between the centroids of the CO knot and dominant HCN knot in the southern part of the ring. (There is a weaker HCN knot located just downstream of each dominant HCN knot: together, these knots, when convolved to the lower angular resolution attained in the observation by Kohno et al. 1999, produce an apparent angular displacement between the HCN and CO knots.) The centroids of all these knots are located at or close to where the dust lanes meet the ring, just as we see for the two HCN knots in the circumnuclear starburst ring of NGC 7552. It is possible that collisions between gas clouds at the intersection of x₁ orbits (closely traced by the dust lanes) and the x₂ orbits (the circumnuclear starburst ring) give rise to relatively dense molecular gas (e.g., Combes & Gerin 1985), although the relative collision velocity must not be so high (≲ 50 km s⁻¹) as to dissociate or ionize the molecular gas. Alternatively, or in addition, turbulence generated by shocks help compress the molecular gas (Elmegreen 1994); turbulence can help support GMCs against collapse on large scales, and promote the formation of dense condensations—from which stars form—on small scales.

As sketched in Figure 17, both our observations of NGC 7552 and that by Krips et al. (2007) of NGC 6951 therefore suggest an important revision to the picture proposed by Kohno et al. (1999). In both these galaxies, we suggest that collisions between diffuse (CO) molecular gas being channeled inward along the dust lanes, turbulence generated by shocks, along with gravitational instabilities perhaps help promote the formation of dense molecular gas at or close to the intersection of the x₁ and x₂ orbits where the dust lanes meet the circumnuclear starburst ring. Indeed, for NGC 7552, the ratio in brightness temperature of the HCN (1–0) to ¹²CO (2–1) emission averaged over the ring is ∼0.18, whereas that at the stronger ¹²CO (2–1) western arm has a 3σ upper limit of ∼0.12. This indicates that the formation of dense molecular gas is promoted where the dust lanes meet the ring, relative to regions immediately beyond, along the same (at the very least for the western) dust lanes.

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Our revised picture also helps explain another observed property of the circumnuclear starburst ring in both NGC 7552 an NGC 6591, and that is the displacement between the centroids of their HCN and radio continuum knots. Such a displacement was pointed out above for NGC 7552 (see Section 3.4 and Figure 5), and is obvious even through a cursory visual comparison of the molecular line maps made by Krips et al. (2007) with the radio continuum maps made by Saikia et al. (2002) in NGC 6951. If we assume that the spiral arms in NGC 7552 are trailing as assumed by Kohno et al. (1999) for NGC 6951, then the radio continuum knots are located downstream of the HCN knots in both NGC 7552 and NGC 6951. The most straightforward explanation for this displacement is that it reflects the timescale between the formation of massive stars from dense molecular gas at or close to the intersection of the x₁ and x₂ orbits, and the eventual demise of these stars in supernova explosions. This argument can be checked by calculating the time it would take for the rotation of the circumnuclear starburst ring to have carried the radio continuum knots downstream away from the present location where the dust lanes meet the ring (specifically, the present location of the HCN knots), keeping in mind that during this time the pattern speed of the bar also carries the dust lane downstream with respect to the ring, albeit by a smaller angular distance.

Figure 18 shows the 3 cm radio continuum map of Figure 3 and HCN integrated intensity map of Figure 5 plotted in polar coordinates. The northern radio and HCN knots have a deprojected angular offset 047 ± 005 (∼50 pc), and the southern radio and HCN knots a deprojected angular offset of 067 ± 008 (∼70 pc). As shown in Section 5.1, the average rotational velocity of both sides of the circumnuclear starburst ring is about 218 km s⁻¹, and the pattern speed of the bar about 38 km s⁻¹ kpc⁻¹, corresponding to 19 km s⁻¹ at the ring (0.5 kpc); their net velocity is therefore about 199 km s⁻¹. The propagation time between the northern radio and HCN knots is therefore (2.4 ± 0.3) × 10⁵ year, and that between the southern radio and HCN knots (3.4 ± 0.4) × 10⁵ year. These timescales are about an order of magnitude shorter than the 5–10 Myr timescale for OB stars to explode as supernovae. It is possible that the true pattern speed is significantly higher and/or the rotational velocity of the ring significantly slower than what we inferred, although it seems unlikely that both these speeds have been underestimated by up to an order of magnitude.

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In the case of NGC 6951, the centroids of the twin radio continuum knots imaged by Saikia et al. (2002) coincide closely with the centroids of the twin HCN knots as imaged by Kohno et al. (1999), who estimated a propagation time between their observed twin CO and HCN knots of a few million years. This is in better agreement with, although as in NGC 7552 on the shorter side of, the timescale for the demise of massive stars with a Salpeter-like IMF. We point out that the model proposed above for the formation of dense gas and stars in the circumnuclear starburst ring can be more cleanly applied to NGC 6951 than NGC 7552. The latter exhibits not just two but five radio continuum knots in its circumnuclear starburst ring (see Figure 3, right panel), indicating that the actual pattern for star formation—and by extension formation of dense molecular gas—is more complicated than can be fully captured by the simple model proposed in Figure 17. In reality, dense molecular gas may form in the dust lanes, as they have been found in some bar galaxies with HCN (1–0) observations (e.g., Leon et al. 2008), before being channeled into the circumnuclear starburst ring (albeit, as shown in the case of NGC 7552, not as efficiently as at the intersection of these dust lanes with the ring), and continue to form in the circumnuclear starburst ring downstream from where the dust lanes meet the ring (e.g., through gravitational instabilities).

Even in the simpler case of NGC 6591, let alone NGC 7552, there are further complications that need to be taken into account. The formation of dense molecular gas at any given location may not proceed at a constant rate but is modulated in time. Some star formation may therefore occur even before gas is channeled into the ring and continue further downstream away from where the dust lanes meet the ring. In addition, we are not able to separate thermal and non-thermal contributions to the radio continuum at this stage, and thus cannot attribute all the emission to a post-supernova stage. Condon (1992) suggests a simple way to separate the thermal emission from the total observed radio flux at a given frequency based on the spectral index. For a spectral index of −0.89 derived in Section 3.3, the fraction of thermal emission is about 40% at 3 cm (∼10 GHz). If thermal (i.e., free–free emission from H ii regions) is enhanced at or just downstream of the HCN knots due to star formation, then the convolution (due to the limited angular resolution of our observation) of this emission with non-thermal emission produced further downstream by supernovae would tend to shift the centroid of the combined emission upstream toward the HCN knots. The result is a smaller apparent propagation time between the HCN and radio continuum knots than is actually the case. On the other hand, the bright millimeter lines seen at the contact points may reflect high velocity dispersions (Downes et al. 1993) and therefore large line widths, and the concentrations of dense molecular gas actually peak somewhat downstream of the HCN knots. In this case, the result is a larger apparent propagation time between the HCN and radio continuum knots than is actually the case. Finally, the IMF for star formation in the ring may be top-heavy, resulting in a shorter than usual timescale between the formation and death of the majority of massive stars (specifically, the time at which the radio intensity of all their supernovae combined peaks following the formation of these stars at the same epoch) compared with a Salpeter-like IMF. Papadopoulos (2010) and Papadopoulos et al. (2011) have pointed out that, in regions of high star formation densities, the resulting high cosmic-ray densities can heat molecular gas to much higher temperatures than is the case in Galactic GMCs, in agreement with the relatively high temperatures than we infer for the molecular gas in the starburst ring of NGC 7552. The higher temperature of the molecular gas requires a correspondingly higher characteristic Jeans mass for star formation in this gas, resulting in (1) stars with larger masses than are found in Galactic GMCs and (2) a top-heavy IMF as low-mass star formation is suppressed (Papadopoulos et al. 2011).

Our revised model of the sequence of star formation in this circumnuclear ring is consistent with the pearls on a string scenario of Böker et al. (2008, see their Figure 7), which is based on their near infrared (H- and K-band) observations along with the age identification using the intensity ratios of emission lines. The pearls on a string model proposes that the overdense region is close to where the gas enters the ring, and therefore where the starburst is triggered. The star clusters formed subsequently will continue their orbit along the circumnuclear ring. In this scenario, a bipolar age gradient is expected, as has been seen in some galaxies, based on infrared and optical studies, such as NGC 1068 (Davies et al. 1998), NGC 7771 (Smith et al. 1999), M100 (Ryder et al. 2001; Allard et al. 2005), IC 4933 (Ryder et al. 2010), and M83 (Knapen et al. 2010).

The infrared age dating method has been applied to NGC 7552 by Brandl et al. (2012), who identify nine unresolved mid-infrared peaks (star clusters) in the starburst ring. There are tentative signs of an age gradient, in that the relatively young clusters are located near the north contact point, while the older clusters are found more than a quarter of the way around the ring away from the contact points. This result is qualitatively consistent with the age gradient expected by the pearls on a string scenario and our revised model, although it must be noted that the age difference among the clusters is rather small at between only 5.5 and 6.3 Myr (see Figure 10 in Brandl et al. 2012).

Even though the aforementioned bipolar age gradients are found in the circumnuclear ring surveys of Böker et al. (2008) and Mazzuca et al. (2008), the detection rate of such age gradient patterns is only 60% and 43%, respectively, in these two surveys. We cannot therefore rule out the possibility of other scenarios for star formation, in addition to that described above, in the circumnuclear starburst ring of NGC 7552. For example, Böker et al. (2008) suggest a second Popcorn model in which the gas clouds become gravitationally unstable due to turbulence (Elmegreen 1994), and collapse at more random times and locations. Accordingly, there is no clear age gradient expected in the Popcorn model, as found by Hsieh et al. (2011) for the circumnuclear starburst ring of NGC 1097.

In NGC 7552, we detect five radio continuum knots, not just two. In NGC 6591, apart from the two dominant HCN(1–0) peaks, there are two other HCN(1–0) knots in the circumnuclear starburst ring. Thus, even for NGC 7552 and NGC 6591, the overall picture for the formation of dense molecular gas and stars in circumnuclear starburst rings cannot be as simple as that sketched in Figure 17. In reality, the formation of dense molecular gas may be promoted at the contact points, but also elsewhere in the circumnuclear starburst ring and star formation also occur there. Both the pearls on a string and Popcorn models may operate simultaneously in any given circumnuclear starburst ring, complicating any single interpretation. What we present here is a zeroth-order model; the true picture requires observations at higher angular resolutions to properly study all locations where dense molecular gas is forming.