As pointed out in §3.1, the intensity-weighted mean HI velocity map (Fig. 3.3) exhibits an S-shaped asymmetry characteristic of periodic orbits predicted theoretically for barred galaxies (e.g., Athanassoulas 1992, and reference therein). In general, such orbits are elliptical (and centered on the dynami-cal center of the galaxy), and in case of stellar system, the orbits have their major axes either parallel (x1 orbits) or orthogonal (x2 orbits) to the ma-jor axis of the bar, changing from one to the other between the locations of dynamical resonances. Specifically, beyond the inner Lindblad resonance (ILR) out to corotation (CR), orbits are x1. Within the ILR, orbits are x2. If there are 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 x2. 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. In moment maps, the predominant orbits detected are x1 orbits and hence the major kinematic axis is closely aligned with the galactic bar. In case of gas system, the change from x1 to x2 orbits and back between dynamical resonances is gradual, and therefore causes the S-shaped twist in the major kinematic axis on scales up to that comparable with the length of the galactic bar. In the outskirts of the HI disk (i.e., close to and beyond the stellar disk), changes in the position angle of the major kinematic axis may be produced by a warp in the galactic disk. Such a warp in the disk of NGC 7552 may be caused by tidal interactions with neighboring galaxies as described in §1.4.1.
To accurately derive the rotation curve of NGC 7552 from our measure-ments of the projected galaxy kinematics, we require a priori knowledge of the axial ratios (which change with galactic radius) of the x1 and x2 or-bits, 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 assume (as is common practice) circular orbits as a rough first approximation; i.e., that is, at our angular resolution, the orbital motion around a given radius is close to cir-cular.
We also assumed a constant inclination of 25◦ for NGC 7552 based on the axial ratio of its stellar disk as described in §1.4. For the major kinematic axis of the disk, we used a position angle 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 HI line.
The HCN (J = 1 - 0) to HCO+ (J = 1 - 0) emissions originate primarily if not entirely from the circumnuclear starburst ring, and are therefore use-ful 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+ (J = 1 - 0) line samples a larger radial range from 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 HI line provides a relatively robust estimate of the rotation curve beginning at or just beyond the outer regions probed in 12CO+ (J = 1 - 0) to far beyond the stellar optical disk. Using the task GAL in the AIPS package, we therefore computed rotation curves from the 12CO+ (J = 1 - 0) and HI first moment maps weighted by their corresponding zeroth moment maps. The derived deprojected rotational ve-locity (assuming circular orbits) as a function of galactic radius is plotted in Figure 5.2, where the moment maps in12CO (J = 1 - 0) have been sampled every 0.##3 and those in HI every 5.##0 in galactic radius. We also plot in this figure the rotational velocity inferred from HCN (J = 1 - 0) and HCO+ (J = 1 - 0) at the radius of the circumnuclear starburst ring. The values inferred from these lines are somewhat higher than that inferred from the 12CO (J = 1 - 0) line presumably because the latter also traces lower-velocity gas further out that is convolved into the ring by the relatively poor angular resolution of our observation.
In Figure 3.11 (lower right panel), we plot the rotation curve inferred from the 12CO+ (J = 1 - 0) line projected for an inclination of 25◦ onto the
Figure 5.2 Rotation curve derived for NGC 7552 from our 12CO (J = 2 -1) maps, plotted as black circles, and HI maps, plotted as black triangles.
The rotational velocity of the circumnuclear starburst ring as inferred from HCN (J = 1 - 0) is plotted as the red circle, and from HCO+ (J = 1 - 0) as the blue circle. We assumed a constant inclination of 25◦ and position angle for the kinematic major axis of 110◦. The formal uncertainties in the deprojected rotational velocities based on the fitting function used in our maps (see text) are smaller than the size of the individual symbols.
PV-diagram of this line cut along a position angle of 110◦. In Figure 5.3, we make the same plot but for the HI line. Because the major kinematic axis deviates significantly from 110◦ in the outer regions of the HI disk, the inferred rotation curve is in good agreement with the PV-diagram out to roughly only the radius of the stellar optical disk of 11 kpc.
Figure 5.3 Rotation curve of Figure 5.2 projected for an inclination of 25◦ shown in red circles overlaid on a PV-diagram derived from our HI maps at a position angle of 110◦ shown in contours. Contour levels are plotted at 1.5, 4, 7, 10, and 15 × 1.1 mJy beam−1.