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Astron. Astrophys. 323, 349-356 (1997)

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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 [FORMULA] km/s/Mpc throughout this paper. The sample objects are listed in Table 1.


[TABLE]

Table 1. The objects. Columns 2-5 are taken from RC3.


4.1. NGC 1453

NGC 1453 is an E2 galaxy with [FORMULA], [FORMULA] (RC3) and a distance of 77 Mpc . The [FORMULA] image (Paper I) reveals the presence of an ionized gas disk misaligned with respect to the stellar isophotes by [FORMULA]. This misalignment together with the [FORMULA] twisting of the isophotes suggests that the intrinsic shape of NGC 1453 is triaxial. We have considered the geometrical constraints deduced in paper I [FORMULA]. Using this set of values we determined all the possible intrinsic shapes varying [FORMULA], [FORMULA], [FORMULA] and [FORMULA], 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 [FORMULA] 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 [FORMULA]. 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]

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) [FORMULA] ; (4) scale length [FORMULA] (arcsec); (5) total mass [FORMULA] (in units of [FORMULA] for the velocity field fit) or total blue luminosity [FORMULA] (in units of [FORMULA] for the surface brightness fit); (6) (7) viewing angles [FORMULA], [FORMULA] and [FORMULA] (degrees); (8)-(11) axial ratios; (12) r.m.s of the fit in units of [FORMULA] and [FORMULA] for the velocity field and surface brightness fits respectively. For NGC 1453 and NGC 2974 also the 68% confidence region is reported.


[FIGURE] Fig. 1. Observed (open dots) and model (full line) radial velocities curves for NGC 1453.
[FIGURE] 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 [FORMULA].
[FIGURE] 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 [FORMULA] 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 [FORMULA] 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 [FORMULA] profile is valid. The inner limit is due to the seeing while the outer limit represents the outermost last available kinematical measurement.

The model is able to reproduce the observed velocity field in a satisfactory way. Even along the minor axis (PA [FORMULA]), 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 [FORMULA] the major axis; the galaxy is oriented with viewing angles [FORMULA], [FORMULA] and [FORMULA] ; the intrinsic axial ratios are [FORMULA], [FORMULA], [FORMULA], [FORMULA]. The mass-to-light ratio radial profile slightly decreases from the value of [FORMULA] [FORMULA] at the innermost point to [FORMULA] [FORMULA] at the outermost point.

4.2. NGC 2974

NGC 2974 is an E4 of [FORMULA] and [FORMULA] (RC3) and 38.8 Mpc distant. The [FORMULA] image (Paper I) shows the presence of an ionized gas disk misaligned with respect to the stellar isophotes by about [FORMULA]. 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 [FORMULA] which add a new position angle to the 7 observed with higher resolution. NGC 2974 also possesses an HI disk which extends out to [FORMULA] (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: [FORMULA], [FORMULA] 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 [FORMULA]. Since this profile is in the R band we transformed it to the B band by adding the [FORMULA] 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] Fig. 4. Observed (open dots) and model (full line) radial velocities curves for NGC 2974.

The corresponding mass, luminosity and [FORMULA] profiles are plotted in fig. 5. The value of the inclination angle [FORMULA] is well constrained by the model to be [FORMULA] while [FORMULA] and [FORMULA]. The intrinsic shape of the galaxy is triaxial with axial ratios [FORMULA], [FORMULA], [FORMULA], [FORMULA] with the gas moving on the principal plane [FORMULA] the short axis. The [FORMULA] radial profile decreases from [FORMULA] [FORMULA] at the innermost point to [FORMULA] at the outermost point. This value is smaller than the value of 5 [FORMULA] obtained by Cinzano & van der Marel (1994) studying the stellar dynamics.

[FIGURE] Fig. 5. As Fig. 3 for NGC 2974. The 68% confidence region is bounded by the highest [FORMULA] model (dotted line) and by the best model (full line) that, in this case, represents also the lowest [FORMULA] model.

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 [FORMULA] (from B91) finding that the gaseous disk lies in the plane [FORMULA] 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 [FORMULA] 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 [FORMULA] is well determined by the fit and lies close to PA [FORMULA], The viewing angle [FORMULA] 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 [FORMULA] 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 [FORMULA] ratio profile are plotted in Fig. 7.

[FIGURE] Fig. 6. Observed (open dots) and model (full line) radial velocities curves for NGC 5077.
[FIGURE] Fig. 7. As Fig. 3 for NGC 5077. Only the best fit model is plotted.

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 ([FORMULA]) fall in the range indicated by B91. The axial ratios ([FORMULA], [FORMULA], [FORMULA], [FORMULA] also are in the region indicated by B91. The [FORMULA] profile increases slowly from the value of 4 [FORMULA] in the center to 8 [FORMULA] at the last measured point. This result is also consistent with B91, the higher value of [FORMULA] being due to the lower value of [FORMULA] here considered.

4.4. NGC 7097

NGC 7097 is an E5 of [FORMULA], [FORMULA] (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 [FORMULA] with respect to the line of sight finding an [FORMULA] ratio varying from less than 1 [FORMULA] in the center to 3.5 [FORMULA] at the last measured point, at [FORMULA].

For this galaxy we have 5 spectra at different position angles. The [FORMULA] image (Paper I) shows the presence of an ionized gas disk misaligned by about [FORMULA] with respect to the stellar isophotes and with an inclination of [FORMULA]. The geometrical constraints considered are [FORMULA] as indicated by the [FORMULA] and PA profiles in Paper I. When we apply the triaxial modeling we find a low value of the inclination, less than [FORMULA]. This result is in contradiction with the indication of the [FORMULA] image. Moreover the projected rotation velocity is about [FORMULA] (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 [FORMULA] 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 [FORMULA] indicated by the [FORMULA] image ([FORMULA]) 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 [FORMULA] profile. The geometrical constraints indicate that the gas is moving in the plane perpendicular to the short axis. [FORMULA] is constant with radius and is 8 [FORMULA].

[FIGURE] Fig. 8. Observed (open dots) and model (full line) radial velocities curves for NGC 7097.
[FIGURE] 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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