The radial space distribution of KLUN-galaxies up to 200 Mpc: incompleteness or evidence for the behaviour predicted by fractal dimension ~ 2?
We have studied using the KLUN sample of 5171 spiral galaxies having Tully-Fisher distance moduli, the average radial space distribution of galaxies out to a distance of about 200 Mpc (for H_0=50 km/s/Mpc). One motivation came from the current debate on the fractal dimension D and maximum scale of fractality. To study this question, we used a new method based on photometric TF distances, independent of redshift, to construct the number density distribution. Our main results are: (1) While scattered below about 20 Mpc, at larger distances the radial distribution starts to follow, in terms of distance modulus mu_TF, the law log N = 0.46 mu + const., using diameter TF relation, and log N = 0.40 mu + const. for magnitudes. These are the predictions based on fractal dimensions 2.3 and 2.0, respectively. These radial density gradients are valid up to the limits of KLUN, or about 200 Mpc. (2) We have tried to understand the derived radial density behaviour as a result of some bias in KLUN or our analysis, however, without success. Numerical simulations have shown that the method itself works. If the density law is caused by incompleteness in the diameter limited KLUN sample, then the incompleteness should start at widely different angular diameters d_25 for different values of rotation parameter log V_M, which would be quite unexpected. (3) If correlation studies favoring long scale fractality (200 Mpc or more) and D ~ 2 are correct, the position of our Galaxy would be close to average in the Universe, with the galaxy density decreasing around us according to the expected law.