6 Comparing clustering, spreading, and relative luminosity of the lumps

In the course of this paper we encountered three indices, namely the lumpiness index $\chi$ (Sect. 3), the concentration index CI(Sect. 4.3), and the cluster dimension D (Sect. 5). The first one has been introduced only, but has not been applied until now. To make up leeway and to draw some first conclusions, we plot in Fig. 8 the values resulting from applying the three indices against each other. Several distinctive features are present. First, and most notable, the lumpiness index $\chi$anticorrelates with cluster dimension (upper left panel): the higher the lumpiness index , i.e. the higher the fraction of total galaxy light in the lumps, the smaller the cluster dimension, i.e. the more clustered are the bright lumps. Without plotting the corresponding graphs, we note that the lumpiness index shows no dependence on galaxy luminosity; this is contrary to the behaviour of the cluster dimension. In terms of porosity, this behaviour means that lumpier galaxies are also more porous, and vice versa.

Figure 8: Comparison of three morphological indices, as applied to bright lumps within irregular dwarf galaxies: the lumpiness index $\chi$, the normalized concentration index CI(x) (where $x=R_{25}/R_{\rm d}$), and the reduced cluster dimension D (taking into account the effect of differing disk scale lengths).

Second, the degree of lumpiness and concentration behave such that the galaxies with the highest values for the lumpiness index all have low values for the concentration index (lower panel). In other words, high fractional lump luminosities come with star-forming complexes that are widely scattered within a galaxy disk. On the other hand, those galaxies with lumps very centrally concentrated, i.e. with ${\it CI} > 3$, come with low fractional lump luminosities, i.e. with low $\chi$values. This is somewhat surprising because there are BCD- and BCD-like galaxies with central starbursts (high CI) that are expected to be very lumpy (high $\chi$) at the same time. But indeed, no galaxy with high fractional lump luminosity is observed, not even a BCD galaxy, to be centrally concentrated. This means that even for actively star-forming galaxies the main body of light is still clearly dominated by the total galaxy light. We disclaim a selection bias to the disadvantage of dwarfs with central starbursts in the next section by providing two representative examples.

Finally, no relation seems to hold between concentration index and cluster dimension (right panel). In particular, galaxies with highest lump concentrations present any cluster dimensions. In other words, lump location and the degree of self-similar clustering are independent of each other; this argues, as done in Sect. 4, for the introduction of some mean galaxy porosity that may vary among galaxies.