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

TL;DR

The paper addresses the problem of determining the angular homogeneity scale in the Local Universe using a model-independent angular framework. It applies two independent estimators—the parametric Landy-Szalay TPACF fit and a non-parametric angular fractal-dimension (AFCD) approach—to a blue-galaxy sample from S-PLUS DR4, validated by 1000 GLASS log-normal mocks. The results yield $\theta_H$ values around $6.28$–$9.01$ degrees, which are consistent with ΛCDM predictions ($\theta_H^{\Lambda{\rm CDM}} \approx 8.1$ degrees) within uncertainty, and robust to redshift-uncertainty resampling. The study demonstrates a model-independent, tracer-aware method for testing cosmic homogeneity in the Local Universe and highlights the potential for applying this approach to larger sky areas in forthcoming data releases.

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

Figures (9)

• Figure 1: Distribution of the S-PLUS blue galaxies corresponding to the public data release 4 (DR4). Upper panel: Sky coverage of the S-PLUS (green) and the selected sample (purple) in equatorial coordinates. Middle panel: Footprint of the selected sample. The colour scale represents the redshift range. Bottom panel: Redshift distribution of the selected sample.
• Figure 2: The TPACF, $\omega(\theta)$, calculated from the blue galaxies sample following the Landy-Szalay methodology (see Section \ref{['sec:ls']} for details). The blue dots represent the binned TPACF data with $1\sigma$ uncertainties, and the gray curves are the TPACF computed for each one of the mocks. The solid red line corresponds to the best-fit model (see equation (\ref{['eq:2pacf-power']})).
• Figure 3: The correlation dimension, $\mathcal{D}_2(\theta)$, for the LS methodology. The solid blue curve was obtained from equation \ref{['eq:d2_2d']}, with the shaded region representing the $1\sigma$ interval. The solid gray line marks the theoretical expectation for a perfectly homogeneous angular distribution, while the dashed gray line corresponds to the $1\%$ criterion. The red mark indicated the angular homogeneity scale, $\theta_H = 9.01_{-3.61}^{+8.43}\;{\rm deg}$, defined as the transition where the measured $\mathcal{D}_2(\theta)$ meets the criterion.
• Figure 4: Distribution of angular homogeneity scales measured from $1,000$ mock catalogues using the LS methodology. The green vertical line indicates the median $\tilde{\theta}_H = 8.52\,{\rm deg}$, obtained from the mocks, while the green shaded region corresponds to the $1\sigma$ confidence interval. The blue dashed line corresponds to the value obtained analysing the S-PLUS blue galaxies sample, that is, $\theta_H = 9.01\,{\rm deg}$ (see Table \ref{['tab:theta_h']}).
• Figure 5: Same as Figure \ref{['fig:tpacf_ls']}, but for the Angular Fraction Correlation Dimension methodology (see Section \ref{['sec:d2_2d']} for details). Note that we did not fit the data because this approach does not use the best-fit parameters of the TPACF.