3 Lump detection and lumpiness index

A residual image highlighting bright star-forming complexes - comprising H II regions and young clusters - was constructed by subtracting a smoothed version from the original B-band image for each galaxy. To obtain the former image a convenient method is to median filter the original image with a sliding square window. Relying instead on adaptive filtering techniques (i.e., on the IRAF task ADAPTIVE) did not improve on the results, thus we kept applying the simple median filtering method. For the window w some characteristic metric size should be chosen: we adopted $w = 0.2 R_{\rm eff}$, with $R_{\rm eff}$ being the effective radius of the galaxy. An example of images processed this way can be seen in Fig. 1. The galaxy shown is ESO 473-G024, with the left frame containing the original image, and the right frame presenting the residual image. From these latter, high-spatial frequency images we extract the following information:

(i) we detect and tabulate the locations of the bright lumps, thus constructing a data base for the distribution analysis below. Detection of bright lumps was done automatically and thus consistently for all galaxies. First, the sky-subtracted residual image is cleaned around and, concerning obvious foreground stars, within the galaxy. The few foreground stars that probably went undetected should have no potential to fake the statistical outcomes of this paper. Second, an appropriate point spread function (PSF) was looked for: a routine checks for the maximum pixel value corresponding to the brightest lump and determines its PSF. It may happen that the brightest lump takes part in a compact cluster of lumps; thus if the PSF's full-width-at-half-maximum was more than 10 pixels the routine assumed blending and searched for a smaller lump with a narrower PSF. Similarly, if the PSF was very peaky, an overseen foreground star was assumed and a broader PSF was applied for the lump search. Third, this PSF is then used by the IRAF task DAOFIND to search for all other lumps above a detection threshold of 3 sky sigmas. In ESO 473-G024, for example, 22 bright lumps were thus counted. Some galaxies are too fuzzy-looking to have any lumps detected. Finally, lump coordinates are stored in physical units with the center and the major axes of the 25th-mag/arcsec² isophotal ellipse providing the origin and the axes of the coordinate system; assuming axisymmetry, the lump coordinates will be deprojected to zero ellipticity for all applications. Note that we do not estimate lump luminosities in order to compare lump brightnesses or to provide luminosity functions; for blue luminosity functions of star-forming complexes in spiral and irregular galaxies see Elmegreen & Salzer (1999).

(ii) We determine the galaxy's lumpiness index $\chi$. Lumpiness (or flocculency) of a galaxy may be quantified by the high spatial frequency power $\chi$, pioneered by Isserstedt & Schindler (1986) and recently applied by Elmegreen & Salzer (1999) to spiral and irregular galaxies and by Takamiya (1999) to HDF-N galaxies with the aim of having a galaxy structural parameter at hand that is related to the current star formation rate. Following the notation of Takamiya (1999) it is defined as the ratio of the flux from the bright lumps, $f_{\rm l}$, and the total flux $f_{\rm g}$ of the galaxy, thus

$$\chi = \frac{f_{\rm l}}{f_{\rm g}}\cdot$$

By measuring the total fluxes of the residual and the original images for each galaxy, we obtained the $\chi$ values listed in Table 2. The lumpiness index will be applied below in Sect. 6.