3 The H I distribution

Figure 3: Mosaic of a number of uncorrelated cleaned channel maps of NGC 3992 at a resolution of $30\arcsec \times 30\arcsec$. The velocities of the channels are given at the top right and the cross indicates the position of the dynamic centre. Contours are at levels of $-4{\sigma }, -2{\sigma },$ (dashed) $2{\sigma }, 4{\sigma }, 8{\sigma }, 16{\sigma },$ and $32{\sigma },$where $\sigma$ is the rms noise level of the channels at 0.55 K implying a level of $0.166\times 10^{20}$ H-atoms cm-2.

A collection of uncorrelated channel maps smoothed to a resolution of 30 $\arcsec \times 30\arcsec$ is displayed in Fig. 3. The smoothed channels are displayed because only then the gas in the outer regions becomes visible. When inspecting Fig. 3 one can note the regularity of the system. At first glance it looks like the rotation in the outer regions is lower than in the luminous disc region. This is because emission in the disc region already shows up at velocities further away from the systemic velocity than the emission of the outer regions.

A total H  I map has been constructed at full resolution and at 30 $\arcsec \times 30\arcsec$ resolution, both by means of the conditional transfer method. Details of this method will now be described for both resolutions. First the full resolution map. At positions in the 30 $\arcsec \times 30\arcsec$ map where the intensity level was higher than three times the $1\sigma$ noise level in that map, the data in the full resolution map were retained. Data not meeting this criterion were set to zero. In addition, all remaining positive noise patches in the full resolution maps were inspected, whether above the five sigma level or whether extended. Unresolved patches below this five sigma level were deleted. The remaining signal in each channel was summed to give the flux density as a function of velocity, or the full resolution line profile in Fig. 4. This is the typical double horned profile as observed for normal spiral galaxies. Summing the emission in the data cube along the velocity direction gives the total H  I map, shown in Fig. 5, top panel and as a greyscale already given in Fig. 2.

The H  I emission at 30 $\arcsec \times 30\arcsec$ resolution was determined as follows: The data cube was smoothed to a resolution of 90 $\arcsec \times 90\arcsec$. Data in the 30$\arcsec$ resolution map were retained there where in the 90$\arcsec$ resolution map data were above the three sigma level (=0.045 ${M}_{\odot}$ pc^-2). As above, unresolved patches below the five sigma level in the 30$\arcsec$ maps were deleted. The line profile is displayed in Fig. 4, and as can be seen the smoothed maps all contain slightly more emission than the full resolution maps. This is caused by some additional low level emission that has surpassed the $3\sigma$ level at 90$\arcsec$ resolution. Adding up all the emission gives a total H  I flux of 72.2 Jy km s^-1 resulting in a total H  I mass of $5.9 \times 10^9$  ${M}_{\odot}$. For the full resolution these numbers are slightly lower at respectively an H  I flux of 62.9 Jy km s^-1 and total H  I mass of $5.1\times 10^9$  ${M}_{\odot}$. Integration of the data cube along the velocity direction gives the total H  I map at 30$\arcsec$ resolution displayed in Fig. 5, bottom panel.

As can be seen in Fig. 5, at the lower resolution additional low level emission shows up in the outer regions. The gas distribution is symmetric with respect to the luminous structure. Large spiral arm density enhancements can not been seen, nor density features which can be associated with the bar. At the rim the distribution might be more patchy, especially at the North West side where the H  I is more concentrated in clouds. One very obvious feature which can be recognized immediately, both in Fig. 2 and in Fig. 5 is the central hole at exactly the region of the bar. But how empty is this hole?

Two qualitative tests have been done to determine this emptyness. First, of the full resolution data cube a position velocity (or x,v) slice has been made through the data cube, along the major axis and with a width of the size of the hole. Any emission would then show up as a narrow filament at the position of the galaxy rotation curve. The x,v diagram was inspected visually and nothing could be detected. As a second test the fact was used that near the centre one expects the rotation curve to be steeply rising. Therefore any emission in the hole should be at nearly the same positions in the relevant channel maps and to increase the signal-to-noise these channels can simply be added. After the rotation curve was determined, 21 channels were selected for this test, 10 on either side of the channel with a velocity of 1050 km s^-1. These channels were added and the result inspected. At the central position the level and noise characteristics were equal to regions outside the galaxy, meaning that no emission was detected.

Figure 4: The H  I profiles of the four galaxies. The two large profiles are for NGC 3992; at full resolution (dashed) and at $30\arcsec \times 30\arcsec$ resolution (full drawn). The smaller profiles are for the companions UGC 6923, 6940 (dashed), and UGC 6969. When placed at a distance of 18.6 Mpc the corresponding total H  I masses for NGC 3992 (smooth), UGC 6923, 6940, and 6969 are 5.9, 0.64, 0.16, and $0.44 \times 10^9~M_{\odot}$ respectively.

Figure 5: Total H  I map of NGC 3992 superposed on the optical image. Top: at full resolution. Contour levels successively increase by a factor two from $1.39 \times 10^{20}$ to $22.16 \times 10^{20}$ H-atoms cm-2. Bottom: at a resolution of 30 $\arcsec \times 30\arcsec$. Contour levels increase by a factor of two from $0.39 \times 10^{20}$to $12.4 \times 10^{20}$ H-atoms cm-2. The resolution is indicated in the lower left corner.

It is not straightforward to give a quantitative value for the upper limit of the surface density in the region of the hole. Let's give it a try. One channel at full resolution has a 1$\sigma$ noise level of 0.473 2. Adding N channels which have been Hanning smoothed, each having a noise of ${\sigma}_{\rm h}$ gives a total noise of ${{4}\over{\sqrt{6}}}\sqrt{N-{{3}\over{4}}} \ast {\sigma}_{\rm h}$. So adding ten channels all with the same noise gives a total noise level of 2.35 2, which is for one position on the sky. One expects approximately that, if added, those ten channels would fill half the hole, which can be covered by $\sim$16 beams. Then a $1\sigma$ upper limit for the surface density in the hole is found of approximately $2.35/\sqrt{16} = 0.6$ 2. There are other ways of reasoning to estimate the upper limit, but all arrive at the same or at a larger number.

To obtain the surface density as a function of radius, the observed total H  I map has been averaged on elliptic annuli. These annuli were given the same orientation as for the fit of a collection in tilted rings to the velocity field in order to derive the rotation curve (see Sect. 6). For radii less than 200$\arcsec$ the full resolution map was used with widths at the major axis of 10$\arcsec$ and for larger radii the smoothed map with widths of 20$\arcsec$. The average value of each ellipse was deprojected to face-on. The result for the two sides separately and averaged is shown in Fig. 6. It can be seen that the H  I emission for this galaxy is concentrated is a torus with a low level extension to large radii. Note that the Holmberg radius is at 250$\arcsec$ and at that radius the transition occurs from a high H  I density to the low level extension.

Figure 6: The deprojected H  I surface density as a function of radius. The surface densities were obtained by averaging the total H  I map over elliptic annuli with the same orientations as used for the rotation curve determination. For radii less than 200$\arcsec$ full resolution data were used, elsewhere the smoothed data. The H  I is distributed in a torus like structure with a shallow extension at large radii. The deprojected bar radius is 72$\farcs$5 so that the galaxy is devoid of H  I gas at the region of the bar.