11.5.3. Interpretation of the Data
a) Rotation Curves
For a solid-body rotation curve the iso-velocity contours are everywhere parallel to the minor axis, and the position profile along the major axis reproduces the shape of the beam-smoothed rotation curve. For any other rotation curve, interpretation is more difficult and we must resort to model fitting. If the rotation velocity falls to small values at a large radius, as in Figure 11.1, then the isovelocity contours form small closed areas at the high velocities, as in Figure 11.2. Provided that these closed regions occur well within the HI distribution, then the amplitude decreases at the velocity corresponding to the appearance of small closed regions in the isovelocity contours. The position indicated by the interferometer phase at this velocity gives an estimate of the "turnover radius," where rotation velocity is a maximum. This was the original interpretation given to the position profiles by Rogstad et al. (1967). Through a model-fitting procedure they deduced the turnover radius of the rotation curve and hence together with the rotation velocity the masses of the galaxies.
b) Hydrogen Distribution
The turnover radius deduced by Rogstad et al. (1967) is, on the average, a factor of two larger than rotation maxima measured by Burbidge, Burbidge, and Prendergast (1963), and others, by means of optical long-slit spectroscopy of HII regions.
This leads us to consider an alternative interpretation of the position profile in terms of the extent of the hydrogen distribution (Wright, 1971a). If the rotation velocity does not decrease beyond the maximum, as in Figure 11.1, but instead remains at a high value, then the small closed regions do not appear in the isovelocity contours. The amplitude response then decreases at a velocity where there is not much hydrogen. The position profile at this velocity then tells us the extent of the hydrogen distribution.
c) Shape of HI Distribution and Rotation Curve
In either of the above interpretations the position profile always gives us a lower limit to the extent of the hydrogen distribution, and comparison of this radius with that of the total mass and HII region distribution shows that the HI distribution is much wider than either (see Figure 11.3).
We can use the disagreement between the optically derived rotation maximum and that deduced from the first interpretation to invert the argument as follows: If the first explanation is not correct, then the rotation velocity cannot fall to a low value as in Figure 11.1, but must remain at a high velocity within the extent of the hydrogen distribution. This is quite consistent with observed rotation curves (see Section 11.7), which are indeed rather flat-topped.