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Astron. Astrophys. 334, 395-403 (1998)

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4. Discussion and concluding remarks

As it appears from the preceding analysis, we have arrived at the conclusion that KLUN galaxies seem to indicate a "thinning" of the galaxy universe from [FORMULA] up to [FORMULA]. In order to see the actual range, the distance moduli must be corrected for the Malmquist bias of the first kind which in the case of [FORMULA] 2 becomes [FORMULA] 1.382 [FORMULA] for the magnitudes and [FORMULA]   [FORMULA] for the diameters (see e.g. Teerikorpi 1997). Using [FORMULA] mag and [FORMULA] for magnitudes and (log)diameters, respectively, these corrections make the maximal distance probed by both the diameter and magnitude relations about 200 Mpc, corresponding to the first point beyond the maximum of the highest [FORMULA] distribution.

This result, using photometric distances independently of redshifts, and an all-sky sample, offers a complementary piece of evidence for the debate on the dimension and maximum scale of fractality. The value [FORMULA] 2 which has appeared in several correlation studies (Klypin et al. 1989, Einasto 1991, 1992, Guzzo et al. 1991, Calzetti et al. 1992, Di Nella et al. 1996, Guzzo 1997, Sylos Labini et al. 1998a), is here seen as a density law up to 200 Mpc, the limit of the KLUN sample. Taken alone, the present study does not prove any large scale fractality, it only suggests the existence of such an average density law around us (which in a restricted distance range could be caused by filamentary structure and voids or a large flattened system; Einasto 1992, Einasto et al. 1994, Paturel et al. 1994). On the other hand, within the framework of a large scale fractal distribution, our position on a peak surrounded by a decreasing density is as expected (Mandelbrot 1982). In this sense, when considered together with large scale correlation studies leading to [FORMULA] 2, the present result is consistent with the view that the Milky Way occupies a typical position in the fractal structure. This agrees with recent studies by Karachentsev (1996) and Governato et al. (1997) who conclude that the Local Group is a typical representation of other small groups, both in structure and environmental dynamics.

The result of our work is also consistent with recent results on the supercluster-void network (M. Einasto et al. 1994, 1997) and arguments based on the correlation analysis of rich clusters of galaxies (Einasto & Gramann 1993, J. Einasto et al. 1997). These studies claim that the observed transition scale to homogeneity is about 200-300 Mpc.

In view of local structures, fractal or not, we would not expect any perfect [FORMULA] -law. Nevertheless, we have tried to understand if such a strong deviation from a homogeneous distribution could be due to some systematic error. However, numerical tests have shown that the method works, though it tends to somewhat underestimate the density gradient.

Naturally, the present study must be seen as a first step which uses distance moduli in the described manner and the method must be developed along with the increasing size of KLUN. A promising prospect is offered by the ongoing DENIS project (collecting 200000 galaxies by 1999) and the FORT project improving the efficiency of the Nançay radio telescope (see Theureau 1997). A deeper sample will allow us to better recognize systematic errors and the real space density trend.

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© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998