Astron. Astrophys. 323, 349-356 (1997)
4. The objects
Out of the six galaxies observed in Paper II, only 3 are suitable
for a detailed model study of the velocity field, namely
NGC 1453, NGC 2974, NGC 7097. In the other 3 galaxies
the presence of more than one kinematical component (NGC 3962,
NGC 6868) or the non regularity of the gas velocity field
(NGC 4636) invalidate the analysis that we are considering in the
present paper. We apply the triaxial model also to NGC 5077
previously studied by B91. For the first three galaxies we adopted the
same distances as Paper I while for NGC 5077 we considered the
same distance adopted by B91. We assumed
km/s/Mpc throughout this paper. The sample objects are listed in
Table 1.
![[TABLE]](img61.gif)
Table 1. The objects. Columns 2-5 are taken from RC3.
4.1. NGC 1453
NGC 1453 is an E2 galaxy with ,
(RC3) and a distance of 77 Mpc . The
image (Paper I) reveals the presence of an
ionized gas disk misaligned with respect to the stellar isophotes by
. This misalignment together with the
twisting of the isophotes suggests that the
intrinsic shape of NGC 1453 is triaxial. We have considered the
geometrical constraints deduced in paper I
. Using this set of values we determined all the
possible intrinsic shapes varying ,
, and
, and then we fitted the velocity field as
described in Sect. 3. The best fit model is listed in Table 2. In
fig. 1 we plot the observed and the best fit velocity field. The
mass, luminosity and profiles of the models are
shown in fig. 3. For the modeling of the surface brightness we
used the blue profile of Sparks et al. (1991) with a FWHM of
the seeing of . The result of the photometric
fit is plotted in fig. 2, is listed in Table 2 and the
corresponding density profile is plotted in fig. 3.
![[TABLE]](img72.gif)
Table 2. Triaxial models: best fit parameters. Parameter sets for different fits of the velocity field and of the surface brightness profile. (1) object; (2) FWHM (arcsec) of the seeing; (3) ; (4) scale length (arcsec); (5) total mass (in units of for the velocity field fit) or total blue luminosity (in units of for the surface brightness fit); (6) (7) viewing angles , and (degrees); (8)-(11) axial ratios; (12) r.m.s of the fit in units of and for the velocity field and surface brightness fits respectively. For NGC 1453 and NGC 2974 also the 68% confidence region is reported.
![[FIGURE]](img29.gif) |
Fig. 1. Observed (open dots) and model (full line) radial velocities curves for NGC 1453.
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![[FIGURE]](img76.gif) |
Fig. 2. Modeling the surface brightness profile of the four galaxies studied. In the upper panels the observed (open dots) and model surface brightness profile along the major axis of the objects are plotted. The dashed and dotted lines represents the model profile before and after the seeing convolution respectively. In the lower panels the full line represents the residuals .
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![[FIGURE]](img73.gif) |
Fig. 3. NGC 1453. Lower panel: mass and light (long dashed line) density profiles for the triaxial model listed in Table 2; the different lines represents the best fit kinematical model (full line) and the two models with the highest and lowest values at large r at the edge of the 68% confidence region (dotted and dashed lines). The radial distance is measured along the intermediate axis. Upper panel: local ratio given by the ratio of the profiles of the lower panel. The vertical lines in both the lower and upper panels define the spatial region within which the profile is valid. The inner limit is due to the seeing while the outer limit represents the outermost last available kinematical measurement.
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The model is able to reproduce the observed velocity field in a
satisfactory way. Even along the minor axis (PA
), where a spherical model will give zero
velocity, the triaxial model shows good agreement with the
observational data. The result of our analysis is the following: the
gaseous disk is the major axis; the galaxy is
oriented with viewing angles ,
and ; the intrinsic
axial ratios are , ,
, . The mass-to-light
ratio radial profile slightly decreases from the value of
at the innermost point to
at the outermost
point.
4.2. NGC 2974
NGC 2974 is an E4 of and
(RC3) and 38.8 Mpc distant. The
image (Paper I) shows the presence of an ionized
gas disk misaligned with respect to the stellar isophotes by about
. The velocity field of the gas has been
observed with 10 spectra taken at 8 different position angles. Three
of these spectra have low spatial and wavelength resolution with
respect to the others. For this reason we only considered, for our
kinematical modeling, the spectra at PA which
add a new position angle to the 7 observed with higher resolution.
NGC 2974 also possesses an HI disk which extends out to
(Kim et al. 1988). The HI disk has the same
rotation axis and velocity as the inner ionized one. It is likely that
the two disks are actually the same structure.
In the application of the triaxial model we assumed the following
geometrical constraints: ,
taking into account that a faint stellar disk
is present in this galaxy (Cinzano & van der Marel 1994). The
results of our kinematical fit are listed in Table 2 and plotted
in fig. 4. For the luminous density model we used the surface
brightness profile by Djorgovski (1985) assuming a FWHM of the seeing
of . Since this profile is in the R band we
transformed it to the B band by adding the
color of the galaxy, which equals 1.66 (Poulain & Nieto 1994). The
result of the luminosity fit is plotted in Fig. 2 and listed in
Table 2.
![[FIGURE]](img96.gif) |
Fig. 4. Observed (open dots) and model (full line) radial velocities curves for NGC 2974.
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The corresponding mass, luminosity and
profiles are plotted in fig. 5. The value of the inclination
angle is well constrained by the model to be
while and
. The intrinsic shape of the galaxy is triaxial
with axial ratios , ,
, with the gas moving on
the principal plane the short axis. The
radial profile decreases from
at the innermost point
to at the outermost point. This value is
smaller than the value of 5 obtained by Cinzano
& van der Marel (1994) studying the stellar dynamics.
![[FIGURE]](img107.gif) |
Fig. 5. As Fig. 3 for NGC 2974. The 68% confidence region is bounded by the highest model (dotted line) and by the best model (full line) that, in this case, represents also the lowest model.
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4.3. NGC 5077
NGC 5077, an E3 galaxy with a prominent minor axis dust lane,
has been the subject of a detailed study by B91 who modelled its
ionized gas velocity field by means of a triaxial potential without a
cusp. We assumed (from B91) finding that the
gaseous disk lies in the plane to the long
axis. This is as expected, because the ionized gas lies almost
perpendicular to the apparent major axis. No solutions are found for a
gaseous disk laying in the plane to the short
axis.
The best fitting values for NGC 5077 are shown in Table 2
and the model velocity curves are plotted in fig. 6. The angle
is well determined by the fit and lies close to
PA , The viewing angle
is poorly determined by the fit and, as a consequence, it gives an
uncertainty in the determination of the total mass of the galaxy but
it does not influence the trend of the density profile. The value of
found in this paper is close to the lower
limit stated by B91. The result of the luminosity fit is plotted in
fig. 2 and listed in Table 2. The light and mass density
profiles as well as the local ratio profile are
plotted in Fig. 7.
![[FIGURE]](img112.gif) |
Fig. 6. Observed (open dots) and model (full line) radial velocities curves for NGC 5077.
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![[FIGURE]](img114.gif) |
Fig. 7. As Fig. 3 for NGC 5077. Only the best fit model is plotted.
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The results obtained in the present work are in reasonable
agreement with B91. Due to the more restrictive geometrical
constraints here considered, i.e., not only the twisting between the
stellar body and the gaseous disk but also the twisting between the
inner and outer stellar isophotes, we do not find solutions for the
gas occupying the plane perpendicular to the short axis. The viewing
angles that we find ( ) fall in the range
indicated by B91. The axial ratios ( ,
, ,
also are in the region indicated by B91. The
profile increases slowly from the value of 4
in the center to 8 at the
last measured point. This result is also consistent with B91, the
higher value of being due to the lower value of
here considered.
4.4. NGC 7097
NGC 7097 is an E5 of ,
(RC3) at a distance of 45 Mpc. The stellar
kinematics reveal a counterrotating core (Caldwell et al. 1986,
Pizzella et al. 1996). The ionized gas velocity field of NGC 7097
has been studied by Caldwell et al. (1986). They considered a gaseous
disk inclined at with respect to the line of
sight finding an ratio varying from less than 1
in the center to 3.5 at
the last measured point, at .
For this galaxy we have 5 spectra at different position angles. The
image (Paper I) shows the presence of an ionized
gas disk misaligned by about with respect to
the stellar isophotes and with an inclination of
. The geometrical constraints considered are
as indicated by the
and PA profiles in Paper I. When we apply the triaxial modeling we
find a low value of the inclination, less than .
This result is in contradiction with the indication of the
image. Moreover the projected rotation velocity
is about (fig. 8) and a face-on disk will
produce huge and unusual deprojected rotation velocities. The problem
is mainly due to the rotation curve of PA as
is clearly visible in fig. 8 which represents the best fit
kinematical model. The poor fitting of this curve is not an artifact
of the triaxial modeling. Neither an error of the position angle of
the slit during the exposure can justify the discrepancy between the
observation and the model velocity curves. After these considerations,
we decided to use the value of indicated by the
image ( ) and proceeded
with the modeling. For the luminous density model we used the surface
brightness profile by Sparks et al. (1991) plotted in fig. 2
together with the best fit luminous model. In Table 2 we report
the results of the kinematical and luminosity models while in
fig. 9 we show the mass and luminous density profile with the
profile. The geometrical constraints indicate
that the gas is moving in the plane perpendicular to the short axis.
is constant with radius and is 8
.
![[FIGURE]](img133.gif) |
Fig. 8. Observed (open dots) and model (full line) radial velocities curves for NGC 7097.
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![[FIGURE]](img135.gif) |
Fig. 9. As Fig. 3 for NGC 7097. Only the best fit model is plotted.
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© European Southern Observatory (ESO) 1997
Online publication: June 5, 1998
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