Up: Dynamics of blue compact fields
In investigating the dynamics of the BCGs we prefer presenting a rotation curve (rather than just a position velocity cut) in order to indicate the real amplitude of the deprojected velocity field and to take into account data from a large fraction of the whole velocity field (and not only along a cut). However, we will see that the RCs are not always good tracers of the mass distribution in the galaxies.
The RC for each galaxy has been drawn by taking into account all velocity
points within degrees (in the sky plane) from the kinematical major
axis (i.e. the PA). This parameter was chosen to be as big as possible, still allowing
a regular RC. The half sector, S, used for each galaxy is indicated in the caption
of the figure showing its RC and in Table 3. The RCs are given in Figs. 1
to 14 at the bottom of the pages. Table 6 gives the RCs in tabular form (this table is
only published electronically). The "cloud'' of small
points seen in each RC, are all the velocity points within of the
major axis in the sky plane. Although these points represent only a portion of the
data (usually more data points are included in constructing the RC since normally
), they give a fair idea of the amount, dispersion and quality of the data
and the difference between the velocity on the major axis and the mean velocity. If the
discrepancy is large, it means that circular motion is not likely. The error bars
represent the dispersion in the velocity at each radius in the RC, and
is a combination of the intrinsic dispersion and observational and reduction errors. In
general the intrinsic dispersion is larger than the observational errors. Thus the
dispersion in the RC is in general caused by real irregularities in the velocity
fields. The rotation velocity scale has not been adjusted by the cosmological
correction (1+z).
The RCs assume axisymmetric objects with circular rotation and are sensitive to the
choice of inclination (Incl), position angle (PA) and dynamical centre.
The PA is defined as the angle (measured from north towards east) of the
receding side of the kinematical major axis, and in general lies along
velocity gradient, orthogonal to the isovelocity contours. The PA
was determined from the orientation of the velocity field with a typical accuracy of 5
to 10 degrees. The inclination was determined as to minimise the residuals and the
dispersion in the RC. The centre coordinates and systemic velocity were chosen to give
a RC with good agreement between the receding and approaching sides and to minimise the
dispersion. The centre coordinates could be determined with a typical accuracy of half
a pixel and in general the displacement between the dynamical centre and the broad band
photometric centre (determined from the 1st statistical moment) is within one pixel.
The inclination is in general the most uncertain parameter. Since many velocity fields
look perturbed, a wide range in Incl may give comparably good fits overall. A
typical accuracy for Incl is . Secondary components have in general less
well determined Incl. The uncertainties in Incl will enter in all mass estimates
based on the RCs.
Table 3:
Parameters for the rotation curves (RCs). For those galaxies where we have
more than one dynamical component, or have drawn more than one RC, "Component"
indicates which component the values refer to (see Sect. 6) and "RC" indicates the name
of the corresponding RC. The inclination (Incl) and position angle (PA) are the
ones used in constructing (and iteratively determined from) the RCs. S is the half
sector (measured from the major axis) of the velocity field included in calculating the
RCs. PA and Incl is the photometrically determined position
angle and inclination respectively; the uncertainties are of the same order as for the
kinematically determined properties. The absolute magnitudes and R_{25,B} are
based on the quoted radial velocities in Table 2 and a Hubble parameter
H_{0} = 75 km s^{1}/Mpc. is the determined systemic velocity in the
heliocentric restframe which has a typical accuracy of 1 km s^{1}. However may be systematically offset with one FSR (117 km s^{1}). The
R_{25,B} values are corrected for inclination (using the photometric value) and given
in arcseconds and kpc. A colon after the value indicates that it is
uncertain

The RC gives V(R), the rotational velocity as a function of radius, and in essence
the rotational velocity is the velocity in the sky plane divided by sin(Incl). Thus
the lower Incl, the more sensitive will the derived velocities will be to
uncertainties in Incl. The possible occurrence of warps or oval distortions and
irregularities limit the validity of the RC, since its derivation is based on the
assumption of a circular motions.
A rough estimate of the dynamical mass can be made using the simple model by
Lequeux (1983)
in which the mass within a radius R is:
 
(1) 
where V(R) is the rotational velocity at R, G the gravitational constant and
f is a constant which has a value between 0.5 and 1.0. This formula is valid for any
galaxy (in equilibrium) supported by rotation. For a disc with flat RC f=0.6 while
for a spherical distribution (e.g. a galaxy dominated by a dark halo) f=1.0. For a
disc with Keplerian decreasing RC outside R, f=0.5. Thus, according to this
model, for any rotating galaxy f should lie in the range: f=0.5 to 1.0,
independent of the presence of a massive halo. Mass estimates based on this equation
are given in Table 4, where we assumed f=0.8. The assumption f=0.8 is
not based on any physical reason, but was chosen simply to lie in the middle of the
allowed interval. In addition to the intrinsic uncertainty in this model, all the
uncertainties above affects the accurateness of this estimate. In Paper II we will
discuss these, and more refined, mass estimates of the observed galaxies. Of course,
the mass estimate provided by Eq. (1), will only be a good approximation of the true
dynamical mass if the galaxy is supported by rotation. If on the other hand the galaxy
is mainly supported by random motions, the presented mass will be a severe
underestimate.
The RC is based on the assumption of circular rotation. If this is not true, the RC will not give a good description of the dynamics and mass of a galaxy. Nevertheless, even when the velocity field is perturbed and the derived RC looks weird (as for ESO 338IG04, Fig. 5), the RC gives some insights to the dynamics of a galaxy. Even the failure of constructing a symmetric and tight RC is interesting, since it indicates that the system is complex or perturbed.
In Table 3 we give some parameters for the RCs. In some cases where we have
extracted more than one component, we provide information for both. We also provide
some photometric information, like Incl and PA, the
photometric inclination and position angle, respectively; and R_{25,B}, the radius
at which the B surface brightness drops to 25 magnitudes per square arcsecond,
corrected for inclination (cf. e.g.
Bergvall et al. 1999)
and Galactic reddening. This information is not used in itself in the present
investigation but provide complementary information. The R_{25,B} is given in the
RCs to give an idea of the size of the galaxy and the extent of the RC. When we did not
have Bband data, we scaled V or Rband data assuming crudely BV=0.5 and
VR=0.35. The position angle and inclination derived from kinematics and photometry
do not always agree which could be due to dynamical disturbances and instabilities in
the systems or internal absorption. Anyway, the only thing we used PA and
Incl for in this investigation was to calculate R_{25,B}. Detailed
surface photometry of some galaxies in this sample will be presented separately
(Bergvall & Östlin 1999).
Table 4:
Order of magnitude mass estimates. The first column gives the target name. In
those cases where the target seems to be composed of more than one dynamical component,
Col. 2 indicates which component is considered: "Total" means that it is the total
nondecomposed velocity field, "Main" means that it is the main component of the
galaxy, "2:nd" that it is the secondary (normally weaker), and "Comp" means that it
is a companion galaxy. Column 3 gives the rotational velocity at the radius R, at
which the mass is calculated. Column 5 contains the mass estimate, , where
we have assumed f = 0.8 in Eq. (1). See Sect. 5 for a discussion on the accuracy of
these mass estimates. Sometimes there are more than one mass estimate for each galaxy
(component); this is when the mass have been calculated at several radii, e.g. at the
radius of maximum rotational velocity (indicated by ) and at the last point
in the RC (indicated by ), if these do not coincide. In the other cases, the
maximum rotational velocity () occurs at the last point () in the
RC and these are also the values of V(R) and R given in the Table below. The note
"Both" indicates that the mass has been evaluated at the last point in the RC where
there is data both from the receding and approaching sides

Table 5:
Estimated H fluxes (), luminosities () and ionised gas masses(). The H luminosity was
calculated using the quoted radial velocities in Table 2. The mass was
calculated assuming an electron density of cm^{3}, an electron
temperature K, and a mean molecular weight of . The
H recombination coefficient was taken from
Osterbrock, Case B (1989)

Up: Dynamics of blue compact fields
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