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 $\hat{I}{¸}_H=9.01_{-3.61}^{+8.43}\mathrm{deg}$; and (ii) a non-parametric fractal correlation dimension method, computing ${\mathcal{D}}_2(\hat{I}¸)$ directly from the correlation function, which results in $\hat{I}{¸}_H=6.28_{-4.43}^{+8.72}\mathrm{deg}$. From the mock catalogues generated with the GLASS algorithm, we find that the estimates from both methods are within $1\ddot{I}ƒ$ of the median values obtained by applying both methodologies to the mocks. The transition scale to homogeneity, according to the $\hat{I}›$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 $\hat{I}›$CDM model, obtaining a good concordance.

11 pages, 9 figures, 1 appendix