Figure 9 (click here) presents the observed velocity field of NGC 6181. It looks quite regular, with prominent signs of rotation. However in the center of the galaxy a twist of the zero-velocity line is seen which gives evidence for non-circular gas motions in this area in a good agreement with the photometrical data (see below).
Figure 9: Isovelocity map of NGC 6181. Velocities are in . Cross marks the nucleus location
A fit of the circular rotation model was made for the full velocity map, with dimensions of pixels (), or within a radius of about 75\ (12.2 kpc) from the center. Special codes were written for data processing. The galactic disk was supposed to be thin and flat, that is it does not have any tilt of warp within the optical radius; so, we looked for inclination i and position angle of the line of nodes MA for the full radius range. As a first step, we determined the position of the dynamical center and a systemic velocity suggesting a central symmetry of the velocity field. The dynamical center appears to coincide with the center of broadband isophotes with an accuracy of one pixel. The systemic velocity is found to be 2375 which agrees with earlier determinations (Tab. 1 (click here)). The dispersion of systemic velocity values determined over all pairs of symmetrically taken points of the galaxy is 16 which is close to our accuracy of individual velocity determinations. Then we verified if the whole line-of-sight velocity field can be fitted by a pure circular rotation. The mean line-of-sight velocity residuals (rms) were calculated for ranges of i and MA; the minimum of the velocity residual calculated over the total velocity field reveals the true values of these parameters. This approach assumes that any velocity field distortions, if they exist, are of local nature.
The agreement is found the best for the following orientation parameters: , , the MA being more strictly limited and having less accuracy. If one compares these values with the photometric parameters of NGC 6181 - for example, (Bottinelli et al. 1984) and (Nilson 1973) or with the data from the Table 1 (click here) - it becomes clear that the bulk of the gas in the galaxy rotates circularly.
Figure 10: Azimuthally averaged rotation curve of NGC 6181 obtained under the assumption of pure circular rotation. The inner region () is excluded because of the presence of non circular motions in the center
Figure 10 (click here) presents the azimuthally averaged rotation curve. For it is nicely flat at the level of with an rms error of individual points not worse than . The maximal rotation velocity estimated from the width of the HI line at 21 cm, W50, is (LEDA Consultation), so our rotation curve for NGC 6181 is in accordance with previously known data.
Despite the generally good accordance between the observed velocity field and the circular rotation model, there are three ranges of radial distances where essential systemic deviations from a pure circular rotation are detected with the regions of maximal deviations at , and . The first area is located near to the dynamical major axis and coincides neither with spiral arms nor with bright HII regions. However, the color profiles discussed in the previous section demonstrate a turnover of color radial trends at this radius. In the southern half of the galaxy this region is distinguished by the excess of azimuthal velocity of order of , and in the northern half of the galaxy there is a similar velocity depression of about the same value. As these two areas are located symmetrically with respect to the galactic center, this anomaly may be considered rather as a kind of regular wave distortion of the velocity field than as a local velocity anomaly.
Figure 11: Residual velocities from pure circular rotation for the inner part of the galaxy. Blank areas correspond to residual velocities between -20 and ; medium blackness to -40 to ; darkest regions represent positive residuals up to . The inner pair of shaded areas is related to the central mini-bar. The most remarkable extended shaded areas present the ring-like zone of radial gas motions at radius of about
The model velocity field calculated in the frame of pure circular rotation with the parameters mentioned above has been subtracted from the observed velocity field. The central part of the residual velocity field is presented in Fig. 11 (click here). Here we see two halves of the ring-like region where deviations from circular rotation model locally exceed . Being deprojected onto the plane of the galaxy, this region looks like three quarters of a perfect circular ring with a mean radius of 11 (about 1.8 kpc); the eastern half of the ring has positive residual velocities up to , the western part has negative ones, from -30 to . The width of the ring is at least 5 pixels, which corresponds to 0.8 kpc. The fact that the switching of residual velocity sign takes place near the line of nodes implies that the residual velocities here are mostly radial ones (here and below, we admit that the gas motion is in the plane of the disk). Together with a circular deprojected shape of the ring, it also gives evidences that the line of nodes of this structure is close to the MA of the global galactic disk and that the ring lies exactly in the galactic plane being purely an internal feature of the galactic gaseous subsystem. Stemming from the slightly asymmetric minor-axis surface brightness profile of the bulge one may conclude that the western half of the galactic disk is the nearest one to us. In this case we may conclude that NGC 6181 possesses a trailing spiral pattern and radially expanding gas motions in the ring.
It is worth noting that the ring of radially moving gas lies closer to the center than the beginning of the well-defined spiral arms and does not reveal itself in a brightness distribution. Nevertheless ionized gas in the ring shows systemic velocity residuals of much higher amplitude than in the bright spiral arms.
Figure 12: Azimuthal dependence of the line-of-sight velocity central gradients within the radius range . The solid curve represents a cosine law fitted by a least-square algorithm
In the very center of NGC 6181, within the region where the major axis
of continuum isophotes is twisted (), a clear sign of
elliptical gas rotation is seen in the two-dimensional velocity
field. Analysing an azimuthal dependence of central velocity
gradient, we find that the maximum of the cosine curve
computed by the least square approximation
is shifted by about relative to the line of nodes (Fig. 12 (click here)). Hence, circumnuclear gas rotation in NGC 6181 parallel with the isophote major axis twist gives strong evidence for the presence of a small bar in the very center of the galaxy. So NGC 6181 may be applied to a small number of known galaxies where nuclear bar reveals itself both from photometric and kinematic data.
A physical connection between the central mini-bar and the ring-like zone of gas expansion may be suspected. It follows from radial velocities of gas in the ring deprojected onto the plane of the galaxy, assuming that these motions are purely radial. Parameters of the galactic plane orientation used for deprojection were taken from the best fit model of circular rotation: , . It appeared that the radial velocity of the ring expansion varies along the eastern half of the ring from 50 to (Fig. 13 (click here)), and the position angle of the maximum expansion velocity roughly coincides with the position angle of the minimum of cosine curve describing the azimuthal dependence of the central velocity gradient. It gives some evidence that the position angle of the largest radial velocities is related to the orientation of nuclear bar.
Figure 13: Azimuthal dependence of the gas radial velocities in the ring-like zone with the radius of 12: residual velocities presented in Fig. 11 (click here) are deprojected onto the galactic plane under the assumption of pure radial motions with the galactic plane orientation parameters and
Kinematically distinct, ring-like inner regions of systemic radial motions of gas, similar to what we observe in NGC 6181, were not known yet. The only analogy, which can be mentioned, is the famous ``3 kpc arm" in our Galaxy: it possesses radial velocities of about and is probably connected with a triaxial structure of the Galactic center. The other radially expanding gaseous ring, found in NGC 4725 (Buta 1988), has a radius of being a structure of a quite different scale.
Note, that morphologically distinguished nuclear rings, which reveal themselves as zones of brightness, not of velocity, excess, often accompany nuclear bars (Buta & Crocker 1993). Numerical simulations confirm that gaseous subsystems may give ring-like response to a triaxial potential form (Combes & Gerin 1985). So what we found may be considered as a kinematical counterpart of such structures as nuclear rings, related to general disk structure. In this case, as in the case of our Galaxy, it is not necessary to interpret radial gas velocities in the ring-like zone as an evidence of its real expansion due to some explosion event: there is no hint of the presence of a shock front or enhanced star formation in front of the ring or in the ring itself. A more realistic explanation is that we observe here an unusually large amplitude of hydrodynamical oscillations of gas velocities associated with the density waves which penetrate deep into the inner part of the disk (Fridman et al., in preparation).
The other feature of the velocity field of NGC 6181 is a multicomponent structure of emission line profiles in some HII regions of the disk. We performed Gauss analysis of two-component emission line profiles for the central part of the galaxy pixels, or . The primary - more strong and everywhere narrow - component reveals a velocity field which excellently agrees with the field obtained in the previous analysis: a general circular rotation, elliptical gas motions in the center and ring-like zone of radial gas motions. The secondary, more weak and broad component (with gas velocity dispersion up to ) appears only in the four brightest HII regions; it is absolutely absent in the ring-like zone of the radial gas motions. The difference between the ``first" and the ``second" velocity component averaged over the total region of the galaxy is zero, but for the bright HII region, nearest to the dynamical center, there exists a switch of velocity difference sign between the northern and the southern halves. It allows to suspect that we deal with a proper rotation of a giant star formation site.