MODERN COSMOLOGY

Interpretation of standard results 375

Figure 13.3. Correlation length s 0 versus sample luminosityMlim,forseveralVL
samples. VL samples, with the same luminosityMlim, have differentvolumesand very
differents 0. This is in contrast toluminosity segregationand in agreement with a fractal
distribution inside the sampleVo l u m e.

expected dependence of the clustering features on the internal properties of

galaxies, such morphology, colour, surface brightness and internal dynamics

[15, 19–23].

(2) In the fractal model, the increase inξ(s)is just a geometrical effect and it

is not related to any variation of the clustering of the corresponding data-

set, as shown in equation (13.7). The effect is simply a byproduct of the

inappropriate use of a statistical tool for the distribution under analysis [2,6].

The two interpretations seem to be equivalent; this is the reason why
the same data-set is considered to confirm both fractality (and no luminosity
segregation) and homogeneity (with luminosity segregation).
In our opinion there is a difference between the two interpretations: for the
fractal case we have a quantitative prediction of an increase ins 0 within the sample
size, while the theoretical expectation for luminosity segregation does not have a
general consensus [24].
In principle it is possible to disentangle the two effects. A possible test is
presented in figure 13.3. Here, we have reported the value ofs 0 for the collection
of VL samples versus the luminosityMlimof the corresponding samples. Samples
with the sameMlimhavedifferent volumes.
For each value of luminosityMlimthere is a range of values ofs 0 .These
appearin contradictionto theluminosity segregation effect, according to which
we should find only a single value fors 0 for samples with the same luminosity