3 Luminosity functions

The full count of HII regions seen in Fig. 2 is presented in differential form, as a log-log plot in bins of 0.15 dex, in Fig. 3. The luminosity range in HH$\alpha$ is limited at the high end by the luminosity of the brightest detected region, and at the low end by our criteria for a detection, and covers log $L_{\rm H\alpha} = 37.0$ to log $L_{\rm H\alpha} = 41.0$. The limit of completeness, however, is log $L_{\rm H\alpha} = 38.0$, so that the apparent broad peak in the distribution just below this luminosity is an artefact due to observational selection. The best single linear fit of the data to the points above log $L_{\rm H\alpha} =38$, corresponding to a power law d$N(L)=AL{\alpha}$dL, has a gradient -0.83 $\pm$ 0.06 (i.e. $\alpha=-1.83$ $\pm$ 0.06). We have also carried out a bi-linear fit, based on the evidence that at log L $\sim$ 38.8 there is an apparent change in slope and the two slopes correspond to values of $\alpha=$$-1.33\pm0.04$ and $-1.99\pm0.07$. The correlation coefficients for the rms fits are, for the single linear case 0.969, and for the bi-linear case 0.979 and 0.978 respectively.

  

Figure 3: Luminosity function for the complete sample of HII regions from the catalogue. The straight line indicates the best linear fit for luminosities greater than the completeness limit log L = 38.0

  

Figure 4: Bi-linear fit for the luminosity function, based on previous experience with late-type spirals (Rozas et al. 1996a; Rand 1992; Knapen et al. 1993; Kennicutt et al. 1989). The plot has more scatter than those found for other spirals due to the irregularity of the LF of the HII regions in the bar (see Fig. 6)

  

Figure 5: Bi-linear fit for the luminosity function of the HII regions of the disc. The change in slope is seen at log L=38.65 (erg s-1) close to the values previously found for other spiral discs

  

Figure 6: Luminosity function of the HII regions of the bar. The function is clearly less well-behaved than that for the disc

The LF for NGC 7479 is broadly similar to LF's of other spirals. As noted above, the total number of regions catalogued is 1009. A total between 500 - 1000 is typical of the number of distinguishable regions in galaxies with masses in the range of that of the Galaxy, at distances between 10 - 35 Mpc (Rozas et al. 1996a).

The criteria limiting the detection of a region at low luminosity cause the observational cut-off and give rise to the artificial peak in the LF just below log $L_{\rm H\alpha} =38$. The true complete LF presumably rises with decreasing luminosity, but probably flattens off in the range below log $L_{\rm H\alpha} = 36.0$ as found by Walterbos et al. (1992) for M 31.

In previous work on other spiral galaxies (Rozas et al. 1996a) we found the change in slope in the LF and we explained it as a manifestation of a transition in the physical properties of the regions, but in these cases the luminosity of the transition was always log $L_{\rm Str}\sim$ 38.6 ($\sim$0.2 dex lower than in NGC 7479). As NGC 7479 is a barred galaxy with unusually strong star formation in the bar, we tested the hypothesis that the differences in the LF might be due to this intense star formation activity under somewhat different physical conditions from those in the disc. To perform this test we constructed separately the LF's for the HII regions of the bar and of the disc. The results are shown in Figs. 5 and 6. The extent and structure of the bar were obtained from a bulge-disc-bar decomposition of the surface brightness profiles along the major and minor semiaxes of the bar according to the decomposition method of Prieto et al. (1998). Using the fit obtained by this method, the length of the bar was $\sim$ 60 '' in the I band. The LF for the 629 HII regions detected in the disc is presented in Fig. 5. For this LF the change in slope is cleaner than for the total LF. The slopes for the bi-linear fit give $\alpha$ values of $-1.25~\pm ~0.04$ and $-2.10~\pm~0.07$ with correlation coefficients r=0.956 and 0.980 respectively, while in the best single linear fit $\alpha=-1.82~\pm~0.07$ and r=0.958. The change in slope for the HII regions in the LF of the disc occurs at log $L= 38.65 ~\pm ~0.15$ which is in the range found for the galaxies we cited above. The change of slope, accompanied by a slight bump in the LF, has been detected in the seven galaxies so far examined in this degree of detail (Rozas et al. 1996b; Knapen et al. 1993; Cepa & Beckman 1989, 1990). Adding the value for NGC 7479 to the set of values previously measured for other galaxies, we find that the rms scatter in $L_{\rm Str}$ in the full set of objects is 0.08 mag. This low scatter can be explained if the IMF at the high luminosity end of the mass function changes little from galaxy to galaxy, i.e. varies little with metallicity. For evidence on this point we can quote Massey et al. (1995), who show that the IMF slopes in the range of stellar masses above 10 $M_\odot$ are the same for the Galaxy and for the LMC, whose metallicity is 10 times lower. Another necessary condition is that the rate of emission of ionizing photons from a young stellar cluster rises more rapidly than the mass of its placental cloud, a condition which we have examined (Beckman et al. 1999), and shown to hold where the appropriate observations exist.

If we look at Fig. 6, where the LF for the 380 HII regions of the bar is presented, we can see clearly that the irregularity found in the total LF is due to the incorporation of the HII regions of the bar in the total LF. The LF of the bar regions shows far greater departures from linearity in the log-log plane. The number of very luminous regions is especially high. Clearly star formation conditions in the bar differ from those in the disc.