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.