6 The nebulae

About 60% of emission objects in the survey possess the characteristics of nebulae. We may compare the new nebulae with already known ones in M33. The fullest list was compiled by Courtes et al. (1987) that contained 748 ${\rm H}\alpha$ nebulae classified according to morphological properties. We used the same images taken with the 6 m telescope. Courtes et al. (1987) picked out the nebulae by visual inspection of the images, whereas our nebulae were found in computer photometry. In the former case the sample must contain the largest nebulae with dimensions of more than at least a few arcseconds. In our case we have nebulae of no more than a few arcseconds in size so far as the basis of the list is provided by objects (IFM) having nearly star-like images in B and V bands.

Figure 7: Size distributions of 748 ${\rm H}\alpha$ nebulae from Courtes et al. (1987) (shaded) and our 334 nebulae are shown separately a) and as a sum distribution b)

Figure 7a presents distributions of sizes for 334 nebulae of types b and d from Table 1 and 748 nebulae from the sample of Courtes et al. (1987). We restrict ourselves to sizes $\le 40{}^{\prime\prime}$, which is sufficient for our study. Both distributions are normalized to the total number of objects in each sample. Maxima of these distributions are markedly different. The nebulae found with the visual inspection of the images has a wide maximum in region of $5{}^{\prime\prime}-12{}^{\prime\prime}$. It is evident that its location is determined by the selection of incomplete inclusion of nebulae smaller than $\approx 10''$ in size. Our nebulae maximum falls at sizes $3{}^{\prime\prime}-4{}^{\prime\prime}$, which corresponds to 10-14 pc. Estimates of the most likely size of HII regions in M33 are known from $4\hbox{$.\!\!^{\prime\prime}$ }5$ (Sabbadin et al. 1980) to $13{}^{\prime\prime}$(Boulestex et al. 1974). The most likely size derived depends on a number of factors, mainly on image scale (see review and discussion in Sharov 1988). It is improbable that distribution of real nebulae sizes in M33 should terminate at 10 pc. For instance, in the Galaxy, compact HII regions of smaller size occur fairly often (Wink et al. 1982). Therefore the position of the maximum in our sample is also explained by the selection effect in isolating nebulae. The losses of our nebulae caused by the selection originate at sizes smaller than $3{}^{\prime\prime}-4{}^{\prime\prime}$.

In Fig. 7b a total distribution of sizes of nebulae from the two lists is shown. It appears quite smooth and continuous. From comparison of Figs. 7a and 7b it can be concluded that in the region of sizes $5{}^{\prime\prime}-7{}^{\prime\prime}$ many nebulae are missing in our sample; the incompleteness of the list here is . For nebulae with sizes greater than $7{}^{\prime\prime}$ (25 pc) the incompleteness of our list sharply increases. This is probably due to the fact that a single early star is incapable of ionizing larger HII regions. Such regions are ionized by groups of stars or OB associations, which were, naturally, disregarded when compiling the catalogue by IFM. As it was shown (Ivanov 1991), the size distribution of OB associations in M33 fits well the distribution of HII regions from the list of Courtes et al. (1987).

Figure 8: Sizes (FWHM) of the bubble a) and diffuse nebulae b) from Table 1

In Fig. 8 the nebulae b and d from Table 1 are shown separately. The distribution peaks correspond to $3\hbox{$.\!\!^{\prime\prime}$ }2$ for bubbles and $3\hbox{$.\!\!^{\prime\prime}$ }7$ for diffuses, their mean sizes (Table 2) are $4\hbox{$.\!\!^{\prime\prime}$ }1$and $4\hbox{$.\!\!^{\prime\prime}$ }9$ correspondingly. Our nebulae d are, on the average, greater, their distribution is asymmetric. The distribution of bubbles is much more symmetric, their sizes are basically in the range $2{}^{\prime\prime}-6{}^{\prime\prime}$ (7-20 pc) with the mean value 14 pc, the distribution extends to 40 pc. It is noteworthy that the known galactic ring structures around WR and Of stars are about of the same size (Lozinskaya 1992) they are in range 3 $\div$ 30 pc. The sizes of galactic SN remnants have a somewhat greater dispersion -- from 7 to 50 pc.

In the list of Courtes et al. (1987) 23 bubbles are presented whose sizes range from 70 to 250 pc. Based on the character of distributions of b nebulae from these two samples it was suggested (see for more details Fabrika & Sholukhova 1997), that our bubbles of small sizes and the bubbles of Courtes et al. (1987) are of different physical nature, whereas the bubbles with sizes > 6'' may belong to the same population as these of Courtes et al. (1987).

Up to the sizes , the sample of Courtes et al. (1987) chiefly contains diffuse and compact objects, and the shaded histogram in Fig. 7a actually represents the distribution of objects only of these types. The distribution of objects from both lists looks compatible and supplement each other in Fig. 7. We can suggest that, as different from bubbles, diffuse nebulae of the two lists are likely to belong to the same population.

Figure 9: Colour indices as a function of nebulae sizes. The designations are the same as in Fig. 5

It can be seen from Fig. 9 that with growing size of the diffuse nebulae their U-B index decreases ( ${C(U\!-\!B, \, d)=-0.097\pm0.015}$). The figure supports the assumption that size of such a nebula, i.e. HII region, is determined by the star temperature. However the mean colours of the diffuses (Table 2) are in agreement with those calculated for an optically thick slab of hydrogen gas with temperature ${T \approx 10^4}$ K (Kolesov 1996). Comparing the data in Fig. 9 with the calculations one may conclude that with growing size of the diffuse nebulae their gas excitation temperature (or optical thickness) drops. It may also follow from the figure that with the growing size the Balmer line emission becomes brighter (or the contribution of the nebula spectrum to a total flux grows). The relations for bubble nebulae in Fig. 9 are insignificant. It is not improbable, however, that the bubbles get cooler and their gas temperature drops as the size increases (or the F( ${\rm H}\alpha$) flux increases, Fig. 5) since U-B decreases, while B-V grows. The significance of the relationships for the nebulae of type b allows this effect just to be suspected.

We present in Fig. 10 relationships between ${\rm H}\alpha$ surface brightness (SB) of b and d nebulae and their galactocentric distance. Besides the apparent separation of the nebulae into two groups in SB(it was discussed above), the brightness of bubbles is clearly seen to decrease with the distance from centre, C $({ SB, R_{\rm gc})=-0.024\pm0.004}$. The increasing brightness of the diffuses is also noticeable, but this is not so significant. The nebulae of d type in this figure show a considerable scatter. One can see that the diffuse nebulae whose surface brightness is not high ( ), do not show SB to depend on the distance, while in brighter objects SB is likely to grow with distance. In other words, the bright diffuse objects exhibit the dependence of SB on ${ R_{\rm gc}}$.

Figure 10: ${\rm H}\alpha$ surface brightness versus galactocentric distance of the nebulae. For bubbles (squares) the average values and their rms deviations in 100 $\hbox {$^{\prime \prime }$ }$ bins are shown also. The upper axis is graduated in kpc

It is evident from geometrical considerations that with increasing size of diffuse nebula its surface brightness rises, whereas it diminishes (or remains approximately constant) in a case of a bubble. The increase in SB of the bright diffuse nebulae with the galactic distance in Fig. 10 is quite consistent with results of Searle (1971), Smith (1975), Shields & Searle (1978), where the strengthening of ionizing radiation along the radius of M33 was discussed. This was derived in analysis of line intensity ratios [OIII]/ ${\rm H\beta}$and ${\rm H}\alpha$/[SII] with radius. The relationship for the nebulae of type d in Fig. 10 agrees with the assumption that the average temperature of hot stars grows with distance from the galactic nucleus. These relationships could be also explained by a chemical composition gradient, the more so that such a gradient has been determined in M33 (Kwitter & Aller 1981).

A value ${W'_{\rm H\alpha}}$ we obtained above assumes ${\rm H}\alpha$ line flux originating in nebula, while the underlying continuum flux is of stellar origin. This value is a direct function of the ratio of the star's luminosity beyond Lyman limit to the luminosity in V band, i.e. the star's temperature. In the diffuse nebulae $<{ W'_{\rm H\alpha}}>\ =\ 560\pm80$Å. From calculations of Churchwell & Walmsley (1973) this corresponds to effective spectral class of ionizing stars O9.5. The nebula size (Stromgren radius) is defined, in turn, by the luminosity and temperature of the star, as well as by a surrounding gas density. Taking the mean electron density ${ N_{\rm e}=1\,{\rm cm}^{-3}}$ and using data of Prentice & Haar (1969) for B0 stars, find the HII region sizes have to be from a few pc to tens of pc depending on luminosity class of the star. These values agree with typical sizes of the d type nebulae in our list.

The bubbles show inverse relationship between SB and ${ R_{\rm gc}}$. Such behaviour is due to the drop of interstellar gas pressure caused by the decrease of gravitational potential with increasing distance from the centre. The size of a bubble is defined by its internal energy and by the pressure of surrounding gas. In the case of envelopes around WR stars, the total energy of a bubble is the energy of gas ejected during the time of WR stage. Accordingly, in the case of SN remnant this is the kinetic energy of ejecta. With a possible considerable dispersion of those values the decrease in pressure with distance throughout the galaxy accounts for the relationship in Fig. 10. This effect was noticed earlier by Boulestex et al. (1974). They found that sizes of large, $30{}^{\prime\prime}- 60{}^{\prime\prime}$, bubbles grow with radial distance.

One can readily see (Fig. 10) together with the average fall of SBof bubbles with the galactic radius, this relation itself is not monotonic. There are two pronounced peaks near $400{}^{\prime\prime}-600{}^{\prime\prime}$ and $1000{}^{\prime\prime}-1200{}^{\prime\prime}$. In these distance intervals the bubbles surface brightness rises as if the interstellar medium pressure is maximum there. In order to emphasize this, we present the mean values of SB in 100'' bins denoted by the filled symbols. The deviations from the linear trend are considerable and amount to no less than 3-4 $\sigma$ in separate bins. These features are consistent with those discussed above when analyzing Fig. 6, namely: there are more emission stars and diffuse nebulae in about the same distance regions (spiral arms?), but the number of bubbles is smaller there. It can be seen in Fig. 10 that the latter have an enhanced surface brightness in these particular distances, which may be connected with the increase in interstellar gas pressure. Humphreys & Sandage (1980) isolated up to 10 arms in the M33 disk. This is quite possible because of non-uniform location of the arms as well as their different curvature that the spiral arms density turns out to be higher in some intervals. On the other hand the existence of ring structures in M33 may well be assumed. There is a lot of evidence (e.g. Mezger 1970) that such structures do exist in the Galaxy.

We may conclude that the diffuse nebulae are HII regions with an exciting star. These are chiefly situated in the central part of the galaxy, in the regions of enhanced gas density. The sizes of these nebulae in ${\rm H}\alpha$ are very sensitive to their central stars temperature. We believe that the brightness and colours of these objects are mainly defined by their stars. On the two-colour diagram (Fig. 4) they follow to the sequence of stars. Hydrogen emission is likely to predominate in their spectra, while nebular lines are weak. The bubbles are probably composed of a high excitation gas, nebula lines must predominate in their spectra. Their central stars contribution to the total flux of these objects may be insignificant. By their properties we identify these objects with envelopes round WR stars and with supernova remnants.