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Angular clustering and bias of photometric quasars in the Kilo-Degree Survey Data Release 4

This study presents the first cosmological application of photometric quasars from the Kilo-Degree Survey Data Release 4, utilizing a deep learning-based redshift calibration to measure their angular clustering and derive a redshift-dependent bias that indicates they reside in dark matter halos with masses between $10^{12.7}$ and $10^{12.9} h^{-1} M_\odot$ .

Original authors: Anjitha John William, Maciej Bilicki, Wojciech A. Hellwing, Szymon J. Nakoneczny, Priyanka Jalan

Published 2026-08-24

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CC BY 4.0

Original authors: Anjitha John William, Maciej Bilicki, Wojciech A. Hellwing, Szymon J. Nakoneczny, Priyanka Jalan

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 or endorsed 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, structured web where matter clumps together in predictable ways. At the heart of this cosmic architecture lies dark matter, an invisible substance that makes up most of the universe's mass. While we cannot see dark matter directly, we can see how it pulls on the visible things we can observe, such as quasars. Quasars are the brilliant, active cores of distant galaxies, powered by supermassive black holes that are greedily consuming surrounding gas. Because they are so bright, they can be seen across billions of light-years, acting as cosmic lighthouses that trace the distribution of matter throughout history. By studying how these quasars are grouped together in space, astronomers can map the invisible scaffolding of the universe and learn how the structures we see today grew from the early cosmos.

A team of astronomers has now taken a fresh look at a specific collection of these cosmic beacons, using data from the Kilo-Degree Survey, a massive project that maps a large portion of the southern sky. Their goal was to understand how the "clumping" of quasars changes as we look further back in time. To do this, they needed to know exactly how far away each quasar is. In astronomy, distance is often determined by measuring how much the light from an object has been stretched by the expansion of the universe, a value known as redshift. While the most precise way to measure this is by splitting the light into a detailed spectrum, a process that takes a great deal of telescope time, this team used a faster, photographic method. They applied a sophisticated computer program, a type of artificial intelligence, to estimate the distances of over 157,000 quasars based on the colors of their light captured in images.

The researchers first refined their distance estimates by training their computer model on a new, larger set of confirmed quasars from recent spectroscopic surveys. This allowed them to update the distances for the entire catalog of quasars found in the survey's fourth data release. Once they had these improved distance estimates, they divided the quasars into four groups based on how far away they appeared to be. For each group, they measured how often pairs of quasars were found close to one another compared to how often they would appear if they were scattered randomly. This measurement, known as the angular correlation, reveals how strongly the quasars are clustered together.

The results showed a clear and steady pattern: as the quasars get farther away, and thus as we look back to earlier times in the universe, they become more strongly clustered. At a distance corresponding to a time when the universe was roughly half its current age, the quasars were moderately grouped. However, at the greatest distances measured, corresponding to when the universe was much younger, the quasars were packed together much more tightly. This increase in clustering strength suggests that the most distant quasars live inside the most massive "halos" of dark matter. The team calculated that these halos have a mass roughly equivalent to a trillion times the mass of our Sun, and that the most distant quasars reside in halos that are even more massive than those hosting closer quasars.

The study also carefully checked for potential errors that could skew these results. One concern was that some of the objects identified as quasars might actually be ordinary stars in our own galaxy, which do not cluster in the same way. The team tested this by analyzing how the results changed when they adjusted for the likelihood of stellar contamination, finding that their conclusions about the clustering remained robust. They also investigated how the assumed distribution of distances affected their calculations. They found that using the raw photographic distance estimates gave slightly different results than using a method that relied on cross-referencing with spectroscopic data, highlighting that the precise way distances are modeled is critical for accurate cosmological measurements.

Ultimately, this work provides the first detailed map of how these bright cosmic beacons are arranged in the Kilo-Degree Survey. It confirms that the relationship between quasars and the invisible dark matter that surrounds them evolves predictably over time. The findings align with previous studies from other surveys, reinforcing the idea that the universe's structure grows in a consistent manner. By refining the tools used to measure these distances and understanding the limitations of photographic methods, this research paves the way for even more precise studies in the future, as larger surveys come online to map the entire sky with greater depth and clarity.

Technical Summary: Angular Clustering and Bias of Photometric Quasars in KiDS DR4

Problem Statement
Quasars serve as critical probes for understanding galaxy formation, black hole accretion physics, and the large-scale structure (LSS) of the Universe. While spectroscopic surveys provide precise redshifts, they are observationally expensive and limited in sky coverage. Photometric selection allows for larger, more complete catalogs but introduces significant challenges: (1) accurate photometric redshift ( $z_{phot}$ ) estimation is difficult due to the non-thermal emission and broad emission lines of quasars, which can cause degeneracies in color-redshift space; and (2) the presence of stellar contamination and uncertainties in the redshift distribution ($dN/dz$) can systematically bias clustering measurements and the derived effective bias ( $b$ ). This paper addresses these issues by updating the photometric redshifts for the Kilo-Degree Survey (KiDS) Data Release 4 (DR4) quasar sample and performing the first angular clustering analysis on this dataset to constrain quasar bias evolution.

Methodology
The study utilizes the KiDS DR4 quasar catalog, originally selected via an Artificial Neural Network (ANN) by Nakoneczny et al. (2021, N21). The authors focus on the "safe" subset of $\sim157,000$ quasars ( $r < 22$ mag) to ensure high purity.

Photometric Redshift Derivation (Hybrid-z):
- The authors replace the previous ANN-based $z_{phot}$ with a deep learning framework called Hybrid-z.
- Architecture: The model integrates two parallel branches: a Convolutional Neural Network (CNN) branch processing four-band ($ugri$) KiDS images (5" $\times$ 5" cutouts) and an Ordinary Neural Network (ONN) branch processing nine-band ( $ugriZYJHK_s$ ) KiDS+VIKING magnitudes.
- Training Data: Unlike N21, which used SDSS DR14, this model is trained on a joint sample of DESI DR1 and SDSS DR17 spectroscopic quasars cross-matched with KiDS. This provides $\sim104,000$ training objects with spectroscopic redshifts ( $z_{spec}$ ), extending the training coverage in color-redshift space.
- Training Strategy: The model uses $\zeta = \ln(1+z_{spec})$ as labels to stabilize gradients. Data augmentation (rotation, flipping, translation) is applied. The output layer uses a linear activation function to accommodate the high-redshift tail of quasars ( $z > 1$ ).
Clustering Analysis:
- The updated catalog is divided into four tomographic bins spanning $0.1 \le z_{phot} \le 2.7$ .
- The angular two-point correlation function (2PCF), $\omega(\theta)$ , is measured using the Landy & Szalay estimator over angular scales $0.05^\circ < \theta < 1^\circ$ .
- Covariance matrices are estimated via the Bootstrap method (200 spatial patches, 15,000 realizations) with Anderson-Hartlap-Kaufman (AHK) debiasing.
- Theoretical predictions for the matter 2PCF are computed using the Limber approximation and the Planck 2020 $\Lambda$ CDM cosmology.
- The effective bias $b(z)$ is inferred by fitting the relation $\omega_q(\theta) = b^2(z)\omega_m(\theta)$ via $\chi^2$ minimization.
Systematics Checks:
- Stellar Contamination: The authors model the observed 2PCF as a mixture of true quasar clustering and stellar clustering, correcting for purity using a threshold of $p_{star} \ge 0.99$ .
- Redshift Distribution: Two approaches for $dN/dz$ are compared: using the direct photometric distribution ( $dN/dz_{phot}$ ) versus a distribution derived from cross-matching the bins with spectroscopic samples ( $dN/dz_{spec}$ ).

Key Results

Photometric Redshift Performance: The Hybrid-z model achieves a mean bias $\langle \delta z \rangle < 0.01$ and a scatter $\sigma_{\Delta z} \approx 0.133$ (or SMAD $\approx 0.039$ ) on the test sample. This represents a significant improvement over the N21 derivations, reducing scatter by approximately 20% and correcting mean biases. However, characteristic "step-like" artifacts remain in the $z_{spec}$ vs. $z_{phot}$ distribution, attributed to emission line transitions across filter bands.
Bias Evolution: The effective quasar bias increases with redshift, rising from $b \approx 1.6$ at $z \approx 0.6$ to $b \approx 4.0$ at $z \approx 2.2$ . This evolution is well-described by a quadratic relation: $b(z) = 1.51 - 0.36z + 0.67z^2$ .
Halo Masses: The derived bias values correspond to effective host halo masses in the range $\log_{10}(M_{eff}/h^{-1}M_\odot) \approx 12.7 - 12.9$ , with effective peak heights $\nu_{eff}$ rising from $\sim1.5$ to $\sim2.9$ . These values are consistent with previous observational studies and halo bias models.
Systematics Impact:
- Stellar Contamination: Correcting for stellar contamination using high-purity stellar samples ( $p_{star} \ge 0.99$ ) has a negligible effect on the derived bias values.
- Redshift Distribution: The choice of $dN/dz$ significantly impacts the results. Using the spectroscopic cross-match distribution ( $dN/dz_{spec}$ ) yields systematically higher bias values compared to using the full photometric distribution ( $dN/dz_{phot}$ ). The authors adopt $dN/dz_{phot}$ as the fiducial result, arguing it better represents the full sample used in the clustering measurement.

Significance and Claims
The authors claim this work represents the first cosmological application of quasars selected from KiDS. By updating the photometric redshifts with a deep learning model trained on the latest DESI and SDSS spectroscopic data, they provide a robust framework for analyzing photometric quasar samples.

The paper emphasizes that while stellar contamination is manageable, the accuracy of the redshift distribution ($dN/dz$) is the dominant systematic affecting bias inference in photometric samples. The study establishes that KiDS quasars reside in dark matter halos consistent with theoretical expectations and that their bias evolution follows a quadratic trend, aligning with findings from other major surveys (e.g., SDSS, eBOSS, 2QZ).

The authors conclude that their results pave the way for future extensions using the final KiDS DR5, the Legacy Survey of Space and Time (LSST), and 4MOST, noting that precise redshift calibration remains the critical prerequisite for robust cosmological constraints from photometric quasars.

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