5 Construction of the velocity field

At first, several line profiles distributed over the galaxy have been inspected by eye. It appears that almost all profiles are symmetric. In addition there are no regions in the galaxy where there is a systematic skewness of the profiles in any velocity direction. Hence there is no need to make a fit by a model profile other than that of a Gaussian.

Two velocity fields were constructed, one at full resolution and one at $30\arcsec \times 30\arcsec$ resolution. For both fields the method of construction was equal and will be described presently. The Gaussian fitting procedure needs decent initial estimates for the profiles. To that aim, a Gaussian fit was made to the conditionally transferred channels. The resulting parameters were then fed to the fitting procedure for the whole data cube. In this way it is assured that only line profiles are found there where it was judged already before where the H  I gas was situated. If the initial estimate had a dispersion of less than 5 km s^-1 or a peak amplitude less than 1.5 the noise level, it was discarded.

With these estimates a fit to the complete data cube was made. Again, results with dispersions less than 5 km s^-1 and amplitudes less than 1.5 times the noise level were judged to be unphysical and were rejected. The velocity field was inspected by eye to check for continuity of the data. It appeared necessary to remove only a small number, between 10 and 20, deviating pixels for both velocity fields. These pixels either had a strongly aberrant velocity or a velocity dispersion larger than 65 km s^-1 and were nearly all situated at the low intensity edges.

Of the resulting dispersions of the profiles, 70% had a value between 5 and 25 km s^-1, 25% between 25 and 45 km s^-1, and 5% above 45 km s^-1. The instrumental FWHM velocity resolution of 33.3 km s^-1 equals an instrumental dispersion $(1\sigma)$ resolution of 14.1 km s^-1 and thus most of the profiles are not resolved in velocity by the telescope. This is a reflection of the inherently low gas velocity dispersion in galactic discs, between 6 and 12 km s^-1 (Kamphuis 1993; Dickey et al. 1990).

The velocity fields at both resolutions are displayed in Fig. 8, top half. In general the velocity field of NGC 3992 is astonishingly regular. Large warp or bar signatures are not present. Some streaming motions can be observed along spiral arms, especially on the North West side.

Figure 8: Optical image of NGC 3992 with superposed the velocity field at full resolution (top left), the velocity field at 30 $\arcsec \times 30\arcsec$ resolution (top right), the residual velocity field at full resolution (bottom left), and the residual velocity field at 30 $\arcsec \times 30\arcsec$ resolution (bottom right). For the velocity fields the systemic velocity of 1049 km s-1 is at the first black contour next to the white contours. Contours differ by 15 km s-1 and increase from left to right. For the residual maps contours differ by 5 km s-1, white is negative, black positive velocities. The residual velocity field is obtained by subtracting a model velocity field determined by a tilted ring fit (see Fig. 9) from the observed field. One may notice streaming motions along the spiral arms, especially on the North-West in the full resolution velocity field. Only near the rim of the central hole there are some systematic residuals that may be attributed to the bar potential.