4 General discussion

For the following discussion, we consider the sample of 116 galaxies listed in Table 1. The inhomogeneity is evident, since the data were extracted from observations with different radio telescopes. We ought to be careful particularly with the interferometric observations, because the extended component of the gas may have diminished values. Unless it has been added, the missing short spacing causes a zero-level depression, and large-scale structures may be lost. We can see this effect by comparing the values of the relative HI extension for the galaxies NGC 55, NGC 691, NGC 2366 and DDO 154 (see Table 1): the gas extension for interferometric observations is smaller than for single-dish observations, and the reduction is not larger than about 30%. Nevertheless, the interferometric observations of NGC 4236 seem to have detected the largest extension of gas.

Furthermore, if we compare the values of the gas extension among different single-dish observations of the same galaxy, we also find uncertainties. The errors, at most, reach values of $10\%-15\%$ (see NGC 4278, NGC 5194 and IC 10 in Table 1).

  

Table 1: Optical and HI parameters for the sample of galaxies used in this analysis

 

Table 1: continued

 

Table 1: continued

 

Table 1: continued

 

Table 1: continued

  

Figure 1: Maximum difference in the calculated HI extension derived from different observations for a given galaxy, $\Delta D_{\rm HI}$, in arcmin, versus the mean value of the HI extension, $D_{\rm HI}$, in arcmin. Hollow diamond symbols are for differences between single dish and interferometrical data. Filled dots are for differences between single-dish data. The slopes of the lines represent errors of 10% and 30%

We plot in Fig. 1 the differences of values for the HI isophotal diameter between single dish-single dish and single dish-interferometric observations, as discussed previously. The lines whose slopes represent errors of 10% and 30% have also been drawn in the figure. These differences come from errors produced as much in the observations and the HI maps as in the determinations of the isophotal HI diameters. These errors include the disagreements produced by the observations with different radio telescopes.

Figures 2, 4 and 5, show two lines that represent errors of 10% and 30% in the relative gas extension. It turns out that, due to the natural spread of values, the meaning of the graphics is not severely affected by the uncertainty in gas extension. In other words, it seems quite possible that these errors do not essentially modify the results obtained in the present paper by using the whole sample, including interferometrical data. Then, we decided to consider all the data for relying on a large sample of galaxies and a wide range of HI extensions to analyse the behaviour of the gas extension in galaxies. Of course, we must keep in mind that the values of the relative gas extension might be diminished for those galaxies in Table 1 having only interferometric observations, such as DDO 13, NGC 247, Izw 18, etc.

  

Figure 2: Ratio between the isophotal HI and optical extensions, $D_{\rm HI}/D_{0}$, versus the linear optical diameter, A(0), in Kpc. Diamond symbols joined by a line represent the extreme values of A(0) for galaxies with uncertain distance (see Table 1)

Figure 2 plots the HI extent relative to the optical ratio, $D_{\rm HI}/D_{0}$, as a function of the lineal optical diameter A(0) in kpc. Due to the fact that this plot is strongly distance-dependent, the galaxies with uncertain distance have been drawn with diamond symbols, and the two extreme values of A(0) have been joined by a dashed line. The two positions of LeoA may indicate that the more appropriate distance is the largest one, i.e. 1.5 Mpc.

  

Figure 3: Same as Fig. 2, where the data were separated according to the telescopes and their spatial resolutions. Hollow diamonds are for interferometrical observations with resolutions between 20'' and 4', filled triangles are for single-dish (Arecibo) observations with values of HPBW between 3' and $4\hbox{$.\mkern-4mu^\prime$} 5$ and filled dots are for those observations with resolutions lower than 8'. The lines represent the limits of telescopes for the three arrangement of data, calculated with characteristic values of the half power beam resolutions of 1' (full line), $3\hbox{$.\mkern-4mu^\prime$}5$ (dashed line) and 10' (dotted line)

Figure 2 shows a clear trend for the smallest galaxies to have higher values of the relative extension of neutral hydrogen. One might think that the lower envelope of this trend is produced by spatial resolution effects. For examining these effects, we have separated the data according to different telescopes. From Table 1, the sample contains 47 interferometric observations with spatial resolutions within $20''\, -\, 2'$ (VLA and Westerbork telescopes), 3 interferometric observations with lower spatial resolution (Cambridge Half Mile radio telescope), 18 single dish observations (Arecibo) within $3'-4\hbox{$.\mkern-4mu^\prime$}5$, 64 observations within 8'-11' (Effelsberg and 300-ft telescopes), and 12 observations with spatial resolution lower than 11' (MkI and MkIA telescopes, Parkes, Nançay and DRAO). Then, we group the data according to different telescopes and spatial resolutions, as shown in Fig. 3. There are no significant differences in the distribution of the data, with exception of the interferometrical observations. Diamond symbols seem to be spread below those that symbolize single-dish observations. We have also placed in this figure the lines that represent the natural limits of the telescopes calculated with the typical spatial resolution of the data set. The minimum distance taken for calculating these limit lines is 3.25 Mpc (assumed for the M 81 Group), although there are in the sample some nearer galaxies (in the Local Group). As can be seen, the telescope limit for the lowest spatial-resolution data could influence the presence of the lower envelope of the graphic. The rest of the data do not seem to be affected by the spatial resolution. Then we have no doubt about the certainty of the trend in the graphic: the smaller a galaxy, the bigger the gas extension will be found in it. This relation may come from the relation between the gas extension and the angular momentum of a galaxy. We found a similar trend when, instead of A(0), we plotted the angular momentum calculated in first approximation by the product of A(0) and the width of the profile.

On the other hand, it is interesting to note that the apparent lower and upper envelopes that are seen in Figs. 2 and 3 might be produced by a natural range in the sizes of the gas component. In Fig. 2, we traced two lines by hypothesis, that represent gas extensions of 10 and 100 kpc. Most of the galaxies seem to be located between these lines. A few galaxies lie outside the lines, having HI extensions smaller or greater than the values quoted previously. But we are dealing with tentative lines, with a parameter (the linear diameter) that depends strongly on the distance and its errors. The best example for the last remark is Leo A, which is the galaxy most detached from the lower established limit, but also has the most uncertain distance.

  

Figure 4: Ratio $D_{\rm HI}/D_{0}$ against morphological type

Figure 4 shows the distribution of the ratio $D_{\rm HI}/D_{0}$among the different morphological types. Despite the fact that the sample comprises a variety of morphologies, the present data show no dependence of the relative gas extension on the type. This result is similar to those obtained by Krumm & Salpeter (1979), Bosma (1981) and Hewitt et al. (1983). As many early as late-type galaxies have a wide range of extensions of gas. Nevertheless, the values of $D_{\rm HI}/D_{0}$ for a few galaxies support the usual belief that Irregulars have very large HI envelopes, while the gas in late-type galaxies lies, at most, up to the edge of the optical extension. As can be seen in Fig. 4, three galaxies have HI extensions quite lower than the optical. These are early-type galaxies. Also, the largest relative HI extension belongs to an Irregular galaxy.

  

Figure 5: Variation of $D_{\rm HI}/D_{0}$ against $\sigma _{\rm HI}$, the apparent density of HI mass

Figure 5 displays the apparent density of HI, independent of distance, versus the relative gas extension, also distance-independent. The HI density is apparent, because we are supposing that the gas is kept in the optical extension. If the real HI density is approximately the same for all the galaxies, then an increase of the gas extension beyond the optical size means an increase of the gaseous mass, and thus the apparent density. This built-in relationship is displayed in Fig. 5. Despite this dependence being known, we consider it interesting to derive the expression that relates the parameters. So, we can approach the value of the gas extension by means of the apparent HI density, which can be calculated only by an integral profile. A mean least squares fit yields:
$\log (D_{\rm HI}/D_{0}) = 0.58\ \log (\rho_{\rm HI}) - 11.81$
with a correlation coefficient of 0.85.
The slope is about 0.5, which means that there is a correlation of about one to one between the linear size of gas (in kpc) and the HI mass of the galaxy, as found by Hewit et al. (1983). This implies a nearly constant real HI surface density.

It is necessary to mention that we tried to get the truest value of the HI mass. We compared the values of the HI magnitude (m₂₁) as given by the LEDA catalogue with those obtained by integration of the HI maps as quoted in the catalogue of Paper I. For single-dish telescopes maps, the masses estimated by integration of the HI maps are, in general, greater than those calculated by m₂₁ (basically obtained from integral profiles). This is not the case for some galaxies observed by interferometrically. For these galaxies, we adopt the HI masses obtained from m₂₁, because of missing of the total HI gas detection in interferometric observations, such as NGC 3073, UGC 6940, NGC 4618, etc. We found that with this combination of masses, the graphic in Fig. 5 has the least dispersion. Without any doubt, A0355+66 gives an effective weight to this relation, because of its high apparent surface density.

  

Figure 6: Real density of HI mass ($\Sigma_{\rm HI}$) versus the morphological type

Figure 6 shows the distribution of the real HI surface density among the morphological types. It appears that Elliptical and S0 galaxies have low surface density of gas, except for NGC 694 as marked in the figure. The NGC 694/IC 167 complex belongs to the NGC 697 group of gravitationally interacting galaxies, with an outstanding HI intergalactic cloud. On this figure, the richest galaxies in HI gas density are the spirals, which have a broad dispersion of values without any remarkable trend. Within the spiral galaxies, the exception is UGC 6917, which is a companion of NGC 4026 and is probably interacting with other galaxies in the vicinity of UGC 6956 and NGC 6922.

In all previous graphics, we found no preferential sector either for isolated (like NGC 628, NGC 2712, NGC 3109, etc.) or interacting galaxies (like NGC 3627, NGC 4631 and NGC 4656, II Zw 70 and II Zw 71), except for those remarked in Fig. 6. Furthermore, we could not find any relationship between the gas extension and other properties of the galaxies, such as surface brightness, colours, infrared and blue magnitudes or profile width.