Homogeneity scale in the local Universe: Model-independent estimate from S-PLUS iDR6 blue galaxies
We present a model-independent estimate of the angular homogeneity scale in the local Universe by analysing data from the Southern Photometric Local Universe Survey (S-PLUS). Two complementary estimators are employed: (i) a parametric approach fitting the power-law of the two-point angular correlation function, which yields the homogeneity scale $θ_H = 8.94_{-3.38}^{+1.20}\;{\rm deg}$; and (ii) a nonparametric fractal correlation dimension method, computing $\mathcal{D}_2(θ)$ directly from the correlation function, which results in $θ_H = 7.91_{-2.94}^{+5.50}\;{\rm deg}$. We apply both methodologies to a set of mock catalogs, generated with the Generator for Large Scale Structure algorithm, and find that both estimates are well within $1 σ$ of their respective median values. The transition scale to homogeneity, according to the $Λ$ cold dark matter (CDM) model, is defined for matter, i.e., $b = 1$. Measurements of this scale with observational data clearly depend on the cosmic tracer analyzed, and a calibration is necessary. Our study with blue galaxies, with bias $b \simeq 1$, provides a suitable estimate for comparison. Indeed, the results obtained in both approaches are compared with the value expected in the $Λ$CDM model, obtaining a good concordance.