The homogeneity scale in the Local Universe: model-independent estimate from S-PLUS DR4 blue galaxies

Abstract

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 $\theta_H = 9.01_{-3.61}^{+8.43}\;{\rm deg}$; and (ii) a non-parametric fractal correlation dimension method, computing $\mathcal{D}_2(\theta)$ directly from the correlation function, which results in $\theta_H = 6.28_{-4.43}^{+8.72}\;{\rm deg}$. From the mock catalogues generated with the GLASS algorithm, we find that the estimates from both methods are within $1 \sigma$ of the median values obtained by applying both methodologies to the mocks. The transition scale to homogeneity, according to the $\Lambda$CDM model, is defined for matter, i.e. $b = 1$. Measurements of this scale with observational data clearly depends on the cosmic tracer analysed, 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 $\Lambda$CDM model, obtaining a good concordance.