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First tomographic measurements of the angular clustering and bias of photometric quasars from S-PLUS

This paper presents the first tomographic measurements of the angular clustering and linear bias of 23,402 photometric quasars from the S-PLUS QuCatS catalog, finding results consistent with previous studies and the Laurent et al. (2017) bias evolution model while validating the photometric redshift calibration of the dataset.

Original authors: Maria Lopes, Felipe Avila, Armando Bernui, Lilianne Nakazono

Published 2026-09-02✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Maria Lopes, Felipe Avila, Armando Bernui, Lilianne Nakazono

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is not a random scattering of stars and galaxies; it is a vast, intricate web where matter clumps together in predictable patterns. To understand how this cosmic structure formed and evolved, astronomers study the "clustering" of objects—essentially measuring how often they appear near one another compared to a purely random distribution. One of the most powerful tools for this is the quasar, a brilliant beacon powered by a supermassive black hole at the center of a distant galaxy. Because quasars are so bright, they can be seen across immense distances, acting as signposts that map the invisible scaffolding of the universe. However, quasars do not trace the universe perfectly; they tend to live in the most massive, dense regions of dark matter, making them "biased" tracers. By measuring exactly how much they are biased, and how this bias changes as we look back in time, scientists can test our fundamental theories about how the universe grows and how dark matter behaves.

A team of researchers has now taken a significant step in this direction by analyzing a massive collection of quasars from the Southern Photometric Local Universe Survey, known as S-PLUS. Using a catalog called QuCatS, which contains hundreds of thousands of potential quasars, the team isolated a specific group of 23,402 high-confidence quasars. These objects are located at distances corresponding to a time when the universe was roughly one-third to one-half of its current age. The researchers divided these quasars into four distinct groups based on their distance, or redshift, allowing them to look at the universe at four different moments in its history. For each group, they measured how strongly the quasars clustered together on the sky, comparing these observations against the predictions of the standard model of cosmology, which assumes a universe dominated by dark energy and cold dark matter.

The study focused on a technique called tomography, which slices the universe into layers to see how things change over time. Because the distances to these quasars were estimated using light filters rather than detailed spectroscopic analysis, the researchers had to account for a degree of uncertainty in exactly where each object lies. To handle this, they used a sophisticated statistical method that treated the distance of each quasar as a range of probabilities rather than a single fixed point. They generated a thousand simulated versions of the universe, known as mock catalogs, which mimicked the survey's geometry and the expected distribution of matter. By comparing their real measurements against these simulations, they could calculate the statistical uncertainty of their results with high precision.

The results revealed a clear and consistent pattern: the bias of quasars increases as we look further back in time. In the closest group of quasars, those at a redshift of about 1.26, the bias was measured at approximately 2.17. As the team looked at progressively more distant groups, the bias grew steadily, reaching 2.67 at a redshift of 1.63, 3.29 at 2.04, and finally 4.05 for the most distant group at a redshift of 2.38. This progression confirms that quasars in the early universe were even more strongly associated with the densest regions of dark matter than their closer counterparts. The measurements align remarkably well with previous studies and with theoretical models that predict how these objects should evolve.

This work represents the first cosmological study of its kind using the S-PLUS dataset, providing a new, independent check on our understanding of the universe's large-scale structure. By demonstrating that photometric surveys can accurately measure the evolution of quasar bias, the study validates the methods used to calibrate the distances of these objects. It also paves the way for future research using even larger datasets from upcoming survey releases. The findings offer a robust confirmation that the standard model of cosmology correctly describes the growth of structure over billions of years, showing that the most energetic objects in the universe have always been the most faithful markers of the invisible dark matter that holds the cosmos together.

Technical Summary: First Tomographic Measurements of Angular Clustering and Bias of Photometric Quasars from S-PLUS

Problem and Objective
This study addresses the need to characterize the large-scale structure (LSS) of the universe using photometric quasar samples, specifically investigating the evolution of quasar bias across cosmic epochs. While spectroscopic surveys have established that quasar bias increases monotonically with redshift, photometric samples offer the potential for larger volumes but require rigorous handling of redshift uncertainties. The primary objective of this work is to perform the first cosmological study of the tomographic angular clustering of photometric quasars using data from the Southern Photometric Local Universe Survey (S-PLUS). The authors aim to measure the two-point angular correlation function (2PACF) and estimate the effective linear bias ( $b_Q$ ) in four distinct redshift bins within the range $1.1 \leq z_{phot} \leq 2.6$ , thereby testing the consistency of the QuCatS catalog's photometric redshift calibration and contributing to the mapping of bias evolution.

Methodology
The analysis utilizes the Quasar Catalog for S-PLUS (QuCatS), derived from the fourth data release (DR4) of the S-PLUS survey. The methodology proceeds through several critical stages:

Sample Selection: From the initial QuCatS catalog, a high-confidence sample was selected by restricting the analysis to two rectangular regions in the southern sky to avoid fragmented coverage and stellar contamination (e.g., Magellanic Clouds). A strict classification probability threshold of $PROB\_QSO \geq 0.95$ was applied to minimize contamination from stars and galaxies, which can dilute the clustering signal. This resulted in a final sample of 23,402 quasars.
Tomographic Binning and Redshift Handling: To account for photometric redshift uncertainties, the authors employed an inverse transform sampling method on the FlexCoDE probability density functions (PDFs) for each quasar. Instead of using single-point estimators, 1,000 Monte Carlo realizations of the redshifts were generated. The sample was divided into four tomographic bins ( $1.1 \leq z < 1.4$ , $1.4 \leq z < 1.9$ , $1.9 \leq z < 2.2$ , and $2.2 \leq z \leq 2.6$ ) based on these realizations.
Correlation Function Estimation: The two-point angular correlation function, $\omega(\theta)$ , was measured using the Landy–Szalay estimator. The analysis covered angular separations from $0.05^\circ$ to $1.0^\circ$ .
Covariance and Mocks: To estimate statistical uncertainties and the covariance matrix, 1,000 log-normal mock catalogs were generated using the GLASS package. These mocks incorporated the survey geometry, the observed redshift distribution (derived from the FlexCoDE PDFs), and a redshift-dependent bias function $b(z)$ based on the parameterization by [1].
Bias Estimation: The effective linear bias for each bin was determined by fitting the observed $\omega(\theta)$ to the theoretical matter correlation function $\omega_m(\theta)$ (calculated assuming a flat- $\Lambda$ CDM cosmology with $b_m=1$ ) via $\chi^2$ minimization. The effective redshift ( $z_{eff}$ ) for each bin was calculated as the mean of the normalized redshift distribution.

Key Results
The study successfully detected a positive clustering signal across all four tomographic bins. The measured effective linear biases ( $b_Q$ ) and their corresponding effective redshifts ( $z_{eff}$ ) are:

$b_Q(z_{eff} = 1.26) = 2.17^{+0.30}_{-0.35}$
$b_Q(z_{eff} = 1.63) = 2.67^{+0.36}_{-0.42}$
$b_Q(z_{eff} = 2.04) = 3.29^{+0.52}_{-0.62}$
$b_Q(z_{eff} = 2.38) = 4.05^{+0.71}_{-0.86}$

The results demonstrate a clear trend of increasing bias with increasing redshift. The reduced chi-squared values ( $\chi^2_{red}$ ) for the fits range from 0.34 to 0.81, indicating good agreement between the data and the theoretical models.

Significance and Claims
The authors claim that these measurements constitute the first cosmological study of the tomographic clustering of photometric quasars provided by the S-PLUS dataset. The significance of the work is threefold:

Validation of Calibration: The consistency of the results with previous spectroscopic and photometric analyses serves as a robust consistency test for the photometric redshift probability distribution calibration of the QuCatS catalog.
Bias Evolution: The measured evolution of the bias aligns well with the $b(z)$ parameterization proposed by [1] and is consistent with other literature results (e.g., [33], [82]), confirming the monotonic increase of quasar bias with redshift even in photometric samples.
Foundation for Future Surveys: While the current sample size limits the ability to tightly constrain complex bias parameterizations with multiple free parameters, the study paves the way for future analyses using larger S-PLUS data releases and other wide-field photometric surveys. The work demonstrates the viability of using inverse sampling of PDFs to mitigate photometric redshift errors in clustering analyses.

The paper concludes that despite higher uncertainties in high-redshift bins, these measurements provide valuable constraints on the evolution of linear bias and extend the observational mapping of large-scale structure to regimes where few photometric measurements currently exist.

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