The main properties of the whole sample galaxies are presented in
Table 2. The sample includes systems in a wide range of apparent
inclinations, from nearly face-on objects (NGC 2217, 
) to
galaxies seen almost edge-on (NGC 4442, 
). These galaxies
have been selected from RC3 among the SB0 with 
13 and 
.
As said in the introduction, our main purpose is to collect and make available a wide set of data on stellar kinematics of barred S0 galaxies. This data archive could be very useful to produce in the future more realistic models of stellar bars. We can, however, discuss here the main properties and problems encountered in analyzing our data.
In the sample of 14 galaxies considered in this paper only 4 show the
presence of [OIII] or H
emission lines: NGC 2217, NGC 4546, NGC
4684 and NGC 7079. This low percentage is in agreement with the fact
that early-type galaxies does not show the presence of ionized gas
with high frequency (Bregman et al. 1992). It is interesting to note
yet that in all the cases where emission lines were detectable, the
gas kinematics appears decoupled from that of the stars. In two cases
(NGC 4546 and NGC 7079) the gas is rotating in a direction opposite to
that of the stars (gas counter-rotation). This feature, revealed in
dozen of galaxies (see Galletta 1996 for a review), is generally
attributed to the accretion of gas from outside. An anomalous gas
structure has been also detected in NGC 2217; there, the ionized gas
seems to rotate in a warped disk whose inner part is perpendicular to
the bar, while the outer part lies on the main galaxy disk. Finally,
in NGC 4684 strong non-circular motions are observed, with ionized gas
in a thick central disk from where two opposite filaments arose, with
radial motions.
This peculiarity of gas motions is quite singular; due to the small number of objects involved, one cannot say if there is a connection between these peculiarities and the presence of a bar. The highly warped gas disk of NGC 2217 may have an internal origin. Friedly & Benz (1993) suggested that this gas disk may be modeled by vertical resonances driven by the bar.
Table 3: Deduced properties of sample galaxies
In five of the galaxies the rotation curve along the bar, when folded
about the center of symmetry, show a "waving pattern" (see Bettoni
1989 for a discussion of the feature). The galaxies are: NGC 2983
(
), NGC 6684 (
), NGC 7079 (
), NGC
4596 (
), and NGC 4643 (
). For NGC 4596, this
deviation appears also in the data of Kent (1990). Other SB0s not
included in our sample but where waving shape is present are IC 456
(Bettoni 1989), NGC 936 (Kormendy 1983), NGC 1543 and NGC 4477
(Jarvis
et al. 1988). This deviation appears superimposed to the general galaxy
rotation, and it is confined to the region dominated by the bar.
The waving pattern in the rotation curve has been always detected in
galaxies seen at intermediate inclination (between 
and
). The spiral NGC 6744 is close to this empirical upper limit
but has no waving pattern, while the SB0 NGC 7079, with apparently the
same inclination, have it. The lack of the waving pattern effect in
galaxies with low inclination suggests that the motions responsible of
this peculiarity predominate on the galaxy plane and have no vertical
components. On the other hand, inside edge-on galaxies this effect may
be submerged by the predominance of the disk dynamics.
The observed amplitude of the waving pattern is quite low, 
30
km s
and projected on the galaxy plane corresponds to non-circular
deviation of 30-50 km s
in radial direction. A theoretical
interpretation of this feature has been recently presented by Wozniak
& Pfenniger (1996) using self-consistent models. They conclude that
the waving pattern is due to the presence of retrograde orbits whose
amount in the galaxy can vary from 14 to 30%.
Table 4: Velocity dispersion trends with the radius measured along the
galaxy major axis and along the bars
The central value of the velocity dispersion is indicated in Table
2 (click here), mediated in the innermost 
. One goes from "warm'' systems,
with 
250 km s
, to quite "cold'' bulges, with values
lower than 100 km s
. Inside the galaxy, the shape of the velocity
dispersion profiles vary from almost flat (e.g. NGC 4596) to sharply
falling with increasing radius (e.g. NGC 3271). Table 4 (click here)
indicates the observed trend of 
measured along the bar and
outside the bar (typically along the galaxy major axis). From these
value we note that there is an agreement between the trend measured
along the bar and the global trend in the galaxy. When a plateau of
velocity dispersion is present, it is detected also outside the
bar. The only exception seems to be NGC 4371, with a quite constant
bar velocity dispersion, compared with a 
decreasing with
radius in the rest of the galaxy. There is, however, a tendency of
profiles to be more slowly decreasing inside the bar than
outside.
We can suspect that a non-asymmetric structure such as the bar should modify the global galaxy rotation, introducing non-circular motions. These deviations are observed in gas kinematics, both from HI- and optical emission- data, generating an S-shape of the zero-velocity line in the velocity fields (see Peterson et al. 1978; Peterson & Huntley 1980; Huntley 1978). In our galaxies, we are interested to test the amplitude of the deviations from circularity present in the stellar velocity fields. To this purpose, we adopted a simple model, as described in the following.
Every point on the plane of the galaxy is seen at a projected distance
from the center equal to:
being 
the position angle on the
sky formed by a line crossing the point and starting from the
center. R is the true distance on the galaxy plane and 
the
PA of the line-of-nodes. The angular distance of the bar from the
line-of-nodes on the galaxy plane is then
with 
the bar position angle.
We can describe the observed rotation curve along the line-of-nodes
with the equation: 
where i is the galaxy inclination with respect to the
sky plane and A, B parameters of the curve. The above formula was
adopted by Brandt (1960) to describe the rotation law of a galaxy
represented by a sequence of flattened spheroid. If the mean motions
are symmetric with respect to the galaxy rotation axis, every rotation
curve observed at a position angle 
will be described by
Here, 
is
the projection factor, equal to: 
Actually, the observed stellar rotation curves should differ from the intrinsic rotation law, because of the asymmetric drift and the integration of the stellar light along the line of sight. However, if the velocity field and the light distributions are symmetric with respect to the galaxy's axis, these effects also must be axially symmetric. In our case, we expect that the bar will generate an asymmetry of the potential that should reflect itself on the orbits as much as the bar is strong. On the other side, differently from gas, stellar orbits tend to fill all the energy levels in the space phase, and this may minimize the deviations.
We assumed then for every galaxy a mean rotation curve along the
line-of-sight, as described above and we projected it at all the PAs
corresponding to our spectra. The disagreement between this
circular rotation and the observed curves give us an indication
of the non-circular motions present in the galaxy. For practical use,
the Brandt formula was rewritten in function of two observable
quantities: the maximum rotational velocity 
and the radius 
at which this velocity is reached. The parametric expression of the
observed rotation curves is then: 
The model curves were then fitted to the observed ones, deducing
, 
, 
and i. They are represented in figures
from 2 to 7 as full lines, while the observed data are
represented by full squares. The galaxy inclination was deduced also
in different way, from the observed axial ratio of the disk, measured
at 25 mag/
, reported in RC3 (de Vaucouleurs et al. 1991) and
assuming an intrinsic axial ratio 0.25 (see Table 2 (click here)). Also
the line-of-nodes was, as a first guess, assumed to be coincident with
the PA of the galaxy's major axis, according to the idea that the
intrinsic structure of the disk is oblate. The derived properties
under the assumption of circular motions are reported in Table
3 (click here). The angle 
between the bar axis and the
line-of-nodes is reported in Table 3 (click here), while the intrinsic
bar diameter 
is reported in Table 2 (click here).
Looking at the two tables, we can see that the differences between the
inclination deduced in photometric way (Table 2 (click here)) and that
obtained by fitting the mean rotation (Table 3 (click here)) do not differ
more than 
, a probable random deviation taking into
account the uncertainties on the observed and intrinsic axial ratios of
the galaxy. Also the angle 
do not differs more than 
from the PA of the apparent galaxy major axis, giving support to
the hypothesis of oblateness (axial symmetry) of the sample
galaxies. The only exception is NGC 6684, where a deviation of 
must be attributed to the presence of a triaxial bulge (Bettoni & Galletta
1988).
The existence of non-circular motions can be checked by means of the
circular velocity represented by the model fit and the true velocities
observed at different position angles. According to the tests made by
Kormendy (1982b) in the case of NGC 936, we considered the following
parameters: 1) the presence of deviations with respect to the systemic
velocity along the disk minor axis; 2) the ratio 
.
The parameter 
represents the velocity difference
between the major axis rotation curve, projected on the bar position
angle, and the bar velocity curve. 
is the projected circular
velocity expected along the bar. Positive values of both tests
indicate the presence of elongated orbits.
In the first test, we found velocity deviations, in some case quite
irregular, along the minor axes of seven galaxies (see figures). Among
the remaining cases, NGC 2217, NGC 4267, NGC 4371, NGC 4643 and NGC
6684 exhibit bars close to the apparent major axis (as indicated by
the angle 
in Table 3 (click here)) and the observed motions reflect
the stellar motions inside the bars. Only NGC 4754 does not show
appreciable deviations from systemic velocity along its minor
axis.
The result of the second test is indicated in Table 3 (click here). Most part of deviations are due to the waving pattern presents along the bar, indicated in the last column of the table and described in the previous Sect. 3.2 (click here). The amount of the remaining deviation from circular motions is from 10% to 20%. Only NGC 4371, with a bar coincident with the galaxy minor axis, does not show deviations. Finally, in the almost edge-on galaxy NGC 4442 the predominant deviation is caused by a cylindric rotation, with equal velocities at different heights from the equatorial plane.
In conclusion, the stellar velocity field shows, in the bar region, deviations from circular velocities lower than 20%. In the outer regions and outside of the bar, the motions seems to be circular.
Acknowledgements
This work has been partially supported by the grant "Astrofisica e Fisica Cosmica" Fondi 40% of the Italian Ministry of University and Scientific and Technologic Research (MURST).