Low X-Ray Luminosity Galaxy Clusters. IV. SDSS galaxy clusters at z < 0.2

This is the fourth of a series of papers on low X-ray luminosity galaxy clusters. The sample comprises 45 galaxy clusters with X-ray luminosities fainter than 0.7 10${}^{44}$ erg s${}^{-1}$ at redshifts lower than 0.2 in the regions of the Sloan Digital Sky Survey. The sample of spectroscopic members of the galaxy clusters was obtained with the criteria: r${}_p$ $\le$ 1 Mpc and $\mathrm{\Delta }V\le \sigma$ using our $\sigma$ estimates containing 21 galaxy clusters with more than 6 spectroscopic members. We have also defined a sample of photometric members with galaxies that satisfy r${}_p\le$ 1 Mpc, and $\Delta V \leq $ 6000 \kms including 45 galaxy clusters with more than 6 cluster members. We have divided the redshift range in three bins: $z\le 0.065$; 0.065 $<$ z $<$ 0.10; and z $\ge$ 0.10. We have stacked the galaxy clusters using the spectroscopic sub-sample and we have computed the best RS linear fit within 1$\sigma$ dispersion. With the photometric sub-sample, we have added more data to the RS obtaining the photometric 1$\sigma$ dispersion relative to the spectroscopic RS fit. We have computed the luminosity function using the $1\mathrm{/}{V}_{max}$ method fitting it with a Schechter function. The obtained parameters for these galaxy clusters with low X-ray luminosities are remarkably similar to those for groups and poor galaxy clusters at these lower redshifts.