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Astron. Astrophys. 354, 823-835 (2000)

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4. Statistical properties

4.1. Luminosity function

All the HII regions in the catalogue, represented in Fig 2, are plotted in the luminosity function (LF) in Fig 3; the plot is logarithmic, with luminosity bins of 0.2 dex. At the high luminosity end the plot is limited by the luminosity of the brightest region, and at the low luminosity end by our detection criteria; the limits are [FORMULA] and [FORMULA] (in erg s-1) respectively. The completeness limit is, however, 37.0 so that the apparent peak in the distribution just below this luminosity is an artefact due to a combination of the logarithmic representation (equal logarithmic bins represent decreasing linear bins) and observational selection. The best straight line fit to the data points above [FORMULA] (erg s-1) corresponds to a power law [FORMULA] has a gradient -0.69[FORMULA]0.06 (i.e. to [FORMULA]). From our previous studies of ghe LF's of HII regions in spirals (Rozas et al. 1996b; Beckman et al. 2000; Rozas et al. 1999a) we expected to find a change in slope at [FORMULA] (erg s-1), and in fact this change is evident for NGC 3359. The corresponding double linear fit to the plotted data gave two values of [FORMULA]: [FORMULA] -1.44[FORMULA]0.02 for the luminosity range below [FORMULA]=38.60 (erg s-1), and -2.10[FORMULA]0.12 for the range above this dividing luminosity. The correlation coefficients for the rms fits are, for the single linear fit, -0.969, and for the double linear fit, -0.979 and -0.978, respectively. The LF for NGC 3359 is thus similar to the LF's of other spirals showing the change of gradient in the luminosity at [FORMULA]=38.60 (erg s-1) which we have attributed to the change in regime from ionization bounding at lower luminosities to density bounding at higher values (Rozas et al. 1996b; Beckman et al. 2000; Rozas et al. 1999a).

[FIGURE] Fig. 3. Luminosity function (LF) in H[FORMULA] for the complete sample of HII regions in the NGC 3359 catalogue. The double linear fit is based on our previous experience with late-type spirals (Kennicutt et al. 1989; Rand 1992; Knapen et al. 1993; Rozas et al. 1996a, 1999a). We also show the single linear fit for comparison. The error bars show the statistical uncertainty in a given luminosity bin.

4.2. Diameter distribution

In Fig 4 we present the integral diameter distribution: the number of HII regions with diameters greater than a given value as a function of diameter. Previous studies (van den Bergh 1981; Hodge 1987; Cepa & Beckman 1989; Ye 1992; Knapen et al. 1993; Rozas et al. 1996a; Knapen 1998; Rozas et al. 1999a) have shown that this distribution can be well fitted by an exponential: N([FORMULA]D)= [FORMULA] [FORMULA]) where [FORMULA] is a characteristic diameter and [FORMULA] is an extrapolated integral value for the full number of regions in the galaxy. The observations in Fig 4 yield values of [FORMULA]=1900[FORMULA]200, and [FORMULA]=121[FORMULA]3 pc, using for [FORMULA] a value of 75 km s-1 Mpc-1. These values are both within the ranges found previously for late type spirals, given in the references cited in the present paragraph.

[FIGURE] Fig. 4. Integral diameter distribution function of all the HII regions in NGC 3359. The straight line is the optimum linear fit.

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© European Southern Observatory (ESO) 2000

Online publication: February 25, 2000