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Astron. Astrophys. 358, 812-818 (2000)

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4. The velocity field and the rotation curve

The observed velocity field is shown in Fig. 3. The velocity field is well mapped out to 1.5 arcmin from the centre. Outside this radius only a few H II regions are visible and therefore the extracted kinematic information for this region is less reliable. In order to calculate a rotation model for the galaxy, we used the standard procedure of fitting a tilted rings model (see Begeman 1989) to the observed velocity field. In order to minimize the number of free parameters and to simplify the fitting process we used known information from previous observations. Therefore we fixed the position of the kinematic centre at the same position than the optical centre. We fixed the inclination and position angles at [FORMULA] and [FORMULA] respectively, according to the values reported by S96, which allow us to make a better comparison with their results. These authors have shown that both angles remain constant in the inner 2 arcmin, which is the region for which we have data, and we therefore know that our results are not affected by this assumption. The systemic velocity for the galaxy was also taken from S96 to be 1582 km/s. We have checked that small variations of these parameters do not substantially change the model velocity field. The only free parameter left per ring, namely the rotational velocity, is fitted to the observed velocity field. Finally, to take into account that we have fewer data points in the outer part of the galaxy, we make the rings wider in this region to ensure that a minimum number of data points is included in a ring. This results in the outer rings being 4 times wider than the inner ones. The resulting rotation curve is shown in Fig. 4. It rises continuously out to about 100 arcsec from the centre, where it seems to become flat at a velocity of about 150 km/s. This value is somewhat higher than the rotational velocity reported by S96 of 130 km/s. In fact, the rotation velocities determined at every radius are always higher than those previously reported by S96 by around 20 km/s. It is worth noting than the last two data points in this curve are not fully reliable, as we remarked above that we only have a few H II regions lying outside 1.5 arcmin from the centre (most of them in the receding part of the galaxy) from which kinematical information can be obtained. If a value of 130 km/s is adopted for the rotational velocity in the outer part of the galaxy to match the observations in HI, then all the outermost regions, which trace one of the spiral arms, would have quite high residual velocities. Although this is not unlikely, we have no way to confirm that this is what is happening, and we therefore prefer to use the best fit to our data to calculate the residual velocity field and thus we use the rotation curve shown in Fig. 4. In the inner 1.5 arcmin, where our determination of the rotation curve is reliable, this is the best determination of the rotation curve (in both spatial and spectral resolution) for NGC 5668 up to date.

[FIGURE] Fig. 3. Observed velocity field for NGC 5668. Contour levels are shown each 10 km/s with the thick line corresponding to 0 km/s

[FIGURE] Fig. 4. Calculated rotation curve for NGC 5668. Error bars represent least-squares fit errors.

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© European Southern Observatory (ESO) 2000

Online publication: June 20, 2000