The overall radial velocity histogram of the 70 SMC carbon stars of Table 1a is shown in Fig. 2 (click here). The LMC stars of Table 1b are too few to warrant further analysis. They are only used as a control sample, for this paper. The following discussion refers to the 70 SMC stars alone, unless clearly stated otherwise. The histogram of Fig. 2 (click here) shows no evidence of the peak bifurcation (corresponding to a separation of 30 km/s between the two main peaks) observed in some samples of young stars (see e.g. Torres & Carranza 1987). Similarly, no bifurcation was observed in the sample of carbon stars in the central region of the SMC studied by Hardy et al. (1989). Interestingly, the new high resolution measurements of HI in the SMC (Staveley-Smith et al. 1995, 1996), which presumably trace a young stellar population, also do not show bifurcation.
Figure 2: The heliocentric radial velocity histogram of the sample
of Table 1a
The mean radial velocity
of the whole sample is 
km/s (LSR), with a dispersion
of 
km/s. This value for the velocity dispersion was
derived after having taken into account the contribution of the observational
errors,
as described in Da Costa et al. (1977).
The radial velocities confirm that all of the stars in the sample are
indeed members of the MCs, as expected from their locations and
apparent magnitudes. There is one exception of
a very high velocity star in the sample (star MH 928
with a velocity of 363 km/s). This star
was not included in the calculations of the characteristics of the
velocity distribution.
Table 3: A summary of recent studies of the kinematics of
relatively old stellar populations in the SMC, along with the results
from the current study.
Column 1 gives the source, Column 2 the type of stars studied
in each case, Column 3 the location of the sample, Column 4
the sample size, and finally Columns 5 & 6 the mean heliocentric
(LSR) radial velocity and radial velocity dispersion with the
associated errors, corresponding to each case
It is interesting to compare these values with the ones obtained for other
samples of intermediate-age and old stars, mentioned in Sect. 1.
Table 3 (click here) shows a summary of the previous results, along with the present ones.
There is generally good agreement between the radial velocity dispersions,
with the possible exception of the Hatzidimitriou et al. (1993)
sample,
which has an apparently higher dispersion. However, if the correlation
between velocity and distance along the line of sight -which is present in
that sample-
is taken into account, the velocity dispersion drops to 
km/s.
As far as the mean radial velocity of the SMC is concerned, there are
about 
discrepancies between the different samples, which can be partly attributed
to errors in the zero-point of the velocity calibrations, and -probably-
partly to the different locations of the samples.
Although there are no multi-epoch observations for the carbon stars of Table 1, with the exception of 5 stars that were observed in both observing runs, it is important to try to evaluate the effect that binaries could have on the estimated velocity dispersion of our sample. As mentioned earlier, it is possible that one of the five stars that were observed in both observing runs as well as one of the velocity standards, could be binaries. We have performed simulations of the effects of different proportions of binaries in the observed velocity dispersion.
This was done using a sample of 70 stars, and 1000
trials, with an initial normal distribution of velocities (with a standard
deviation of 25 km/s).
Onto this distribution, the effects of binaries were added, given a fraction
of stars in binary systems, and an upper and lower limit to the binary
orbital velocity of the carbon star. The orientation of the orbit was
randomly distributed, and the orbit assumed circular (an elliptical orbit
will result in the stars spending more time further apart, with lower
orbital speed).
Three cases were considered:
1) 20% of the stars in binaries with orbital velocities of 25 km/s.
2) 50% of the stars in binaries with orbital velocities uniformly
distributed between 0 and 25 km/s.
3) 20% of stars in binaries with orbital velocities of 32.5 km/s.
The choice of the possible fractions of binary stars are based
The choice of the maximum velocity limits is based on two basic assumptions:
First, that no mass transfer occurs, and second, that the companion star
would contribute less than 10% to the light of the carbon stars. This
second condition comes from the following argument:
most observed carbon stars have C
bands which have essentially zero
light in the band heads. This puts a limit on the light contribution from
any possible companion (unless it is an eclipsing binary, with the
companion behind the carbon star - in this case the orbital velocity at the
time of the observation will
be in the plane of the sky, and will not affect the observed radial
velocity significantly).
The velocity dispersion increases from 25 km/s to 25.7 km/s in the first two cases and to 26.3 km/s in the third case (with an rms of 1 km/s in all cases). Therefore, the effect of such distributions of binaries would be that the measured velocity dispersion would be 1km higher than the actual. Therefore, we conclude that the measured velocity dispersion of 25.2 could be revised to 24.2 km/s if such a binary distribution is assumed to exist.
The sample of outer LMC carbon stars observed -located in the SW
of the LMC, i.e. in the general direction of the SMC (Table 1b)-
have a mean velocity of
km/s and a velocity dispersion of 
km/s.
If we excude the two lowest velocity stars in the sample (12 and 16),
we get a mean velocity of
km/s and a velocity dispersion of 
km/s. The
velocity dispersion is remarkably low, however one should
keep in mind the small size of the sample and its spatial distribution
within a small area of the LMC halo.
The spatial distribution of stars of different velocities may offer some
insights into the dynamics of the SMC. We have already seen that at least
in some directions (e.g. in the NE sample of Hatzidimitriou et al.
1993, and in the Wing, from Hardy et al. 1989)
there are streaming
motions that affect the calculated overall mean velocities and velocity
dispersions.
In Fig. 1 (click here)
we have marked with different symbols the different velocity
groups (arbitrarily defined, for the sake of the presentation).
There are three points that can be made:
(i) The stars that could be postulated as belonging to the outer
Wing of the SMC and possibly to the intercloud region (although
the distinction between the two is not clear), seem to have
a systematically higher mean velocity.
There are eight such stars in the sample (MH 1171, MH 1173, MH 1175, MH 1176,
MH 1177, MH 1180, MH 1181, MH 1185). They have a mean heliocentric velocity
of 
km/s (or 
km/s, removing the highest velocity star).
The rest of the SMC stars then have a mean radial velocity of 
km/s
and a velocity dispersion of 
km/s, which are more
representative of the main body of the SMC.
There is no apparent correlation of the velocities
of the eight "Outer Wing'' stars
with projected distance from the SMC centre,
or with projected distance along
the Wing axis. However, the number of stars
in the "Outer Wing'' sample is too low for further statistical analysis.
It is important to note that with the exception of one star
(MH 1173, with a velocity of 253.3 km/s,
and radial projected distance from the
centre of the SMC of 5.2 deg), all of these remote stars,
some of which are very close to the
outer regions of the LMC (in projection), have velocities too low to be LMC
members.
Star MH 1173, which has the highest velocity of 253.3 km/s,
is close to the SMC centre and well within the SMC contours, therefore more
likely to be an SMC star.
It should be mentioned that at least two of the
LMC stars, 12 and 16 may also be outer Wing/intercloud members.
(ii) Morgan & Hatzidimitriou (1995) noticed the presence of an elongated feature in the spatial distribution of carbon stars in the SMC, at the southernmost extremity of the galaxy. Six of the stars of Table 1a seem to belong to this feature (stars MH 1033, MH 1106, MH 1111, MH 1112, MH 1155, MH 1165). If they are removed from the sample of SMC stars, no change is observed in the mean velocity and velocity dispersion. There is no obvious kinematical signature of this group of southern stars. It is probably worth noting, however, that the southernmost star of this feature has a rather high velocity (195.5 km/s).
(iii) No convincing rotation was found around either the major or the minor axes of the SMC, or any other axis examined (i.e. all projected axes, every 20 deg). This is in agreement with the result of Hardy et al. (1989).
Dopita et al. (1985) and
Hardy et al. (1989) have used their
estimates
of the velocity dispersion in the central regions of the SMC to calculate
the mass of the SMC (within the central parts), by applying the virial
theorem. Although the validity of this method is very questionable in the
case of the SMC with its possibly disturbed dynamics, we shall
attempt a similar calculation for the sake of comparison with the
previous results, especially since our sample has a much larger radial extent.
Using the result on the overall velocity dispersion (without the Wing region)
of
21 km/s out to a radius of 6 kpc and assuming a simple spherical
distribution of matter (which is certainly an over-simplification),
we derive a total mass of 
, which
lies in between the values estimated by Hindman (1967) from HI data,
and by Dopita et al. (1985) and
Hardy et al. (1989)
from the kinematics of planetary
nebulae and carbon stars respectively in the inner regions of the SMC.
Acknowledgements
We would like to thank the Mount Stromlo and Siding Spring Observatories of the Australian National University for the observing time allocated to this project. We would also like to thank Miss Clare Mollison, who was funded by the Nuffield Foundation, for scanning the plates and measuring the coordinates for the LMC stars using the HST Digitized Sky Survey version of the SERC J Southern Sky Survey.