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D. Brooks

Publications and source records attributed to D. Brooks.

At least 55 records · Page 3Linked to original sources
arXiv2026

CoLoRe-2LPT: Lyman-$α$ mock catalogues for the validation of DESI cosmological analyses

The Lyman-$α$ (Ly$α$) forest has become a crucial probe for studying the large-scale structure of the universe at high redshift ($z > 2$), providing powerful constraints on Baryon Acoustic Oscillations (BAO) and the full-shape (FS) clustering of matter. As a key ingredient for upcoming BAO and FS analyses, we present a new generation of fast cosmological Ly$α$ mocks based on second-order Lagrangian perturbation theory (2LPT). These new mocks significantly improve upon previous log-normal approaches, both at accurately capturing small scale clustering and at recovering the non-linear broadening of the BAO peak. They are able to reproduce Ly$α$ statistics within $10\%$ of the latest DESI measurement; including the Ly$α$ bias and the redshift-space distortion $β$ parameter, mean transmitted flux, and 1D power spectrum. The corresponding quasar (QSO) clustering is also improved with respect to previous approaches, calibrated against high-resolution Abacus simulations, recovering the observational QSO linear bias to less than $5\%$ and improving redshift-space distortions via 2LPT velocities and the addition of Fingers-of-God effects. Furthermore, these mocks incorporate high column density systems and metal lines, allowing us to explore the effects and systematics induced by these astrophysical contaminants. This new set of mocks has been key for enhancing the modeling and validation of the DESI DR2 Ly$α$ full shape cosmological analysis. This work provides a physically motivated and computationally efficient tool for simulating current and next-generation Ly$α$ surveys and validating FS and BAO analysis.

astro-ph.CO↗
arXiv2026

The Linear Point Standard Ruler with DESI DR1 and DR2 Data

The linear point, a purely geometric feature in the monopole of the two-point correlation function, has been proposed as an alternative standard ruler. Compared to the peak in the correlation function, it is more robust to late-time nonlinear effects at the percent level. In light of improved simulations and high quality data, we revisit the robustness of the linear point and use it as an alternative to template-based fitting approaches typically used in BAO analyses. We present the linear point measurements on galaxy samples from the first and second data releases (DR1 and DR2) of the DESI survey. We convert the linear point into a dimensionless parameter $α_{iso,LP}$, defined as the ratio of the linear point in the fiducial cosmology and the observed value, analogous to the isotropic BAO scaling parameter $α_{iso}$ used in previous BAO measurements. Using the 2nd generation of AbacusSummit mock catalogs, we find that linear point measurements are more precise when calculated in the post-reconstruction regime with 15-60% smaller uncertainties than those pre-reconstruction. We find a systematic shift in the linear point measurements compared against the isotropic BAO measurements in mocks; we attribute this to the isotropic damping parameter responsible for smearing the linear point in the nonlinear regime. We propose a sample-dependent correction that mitigates the impact of late-time nonlinear effects. While this introduces a cosmology dependence in an otherwise model-independent measurement, this is necessary given the sub-percent precision dictated by current cosmological surveys. Comparing $α_{iso,LP}$ with isotropic BAO measurements made on the DESI DR1 and DR2 galaxy samples, we find excellent agreement after applying this correction, particularly post-reconstruction. We discuss future scope regarding cosmological inference with linear point measurements.

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arXiv2026

Lyman-$α$ forest holography: 3D predictions from 1D measurements

Cosmological analyses of Lyman-$α$ forest clustering rely on either one-dimensional correlations along individual sightlines or three-dimensional correlations between different sightlines. Because these observables probe the matter distribution on very different scales, they have traditionally been analyzed independently. In this work, we bridge this gap using ForestFlow, an emulator trained on a suite of cosmological hydrodynamical simulations that provides a unified description of Lyman-$α$ forest clustering from linear to nonlinear scales. This framework enables us to determine the range of three-dimensional clustering models compatible with the DESI one-dimensional flux power spectrum ($P_{\rm 1D}$). The resulting predictions successfully reproduce the large-scale clustering measured by the DESI BAO analysis and provide physically motivated priors on nonlinear clustering that are used in a companion paper presenting the full-shape analysis of the DESI DR2 Lyman-$α$ forest. We validate our methodology using the large-volume, high-resolution hydrodynamical simulation ACCEL-2, demonstrating excellent agreement across the full range of scales considered. Finally, we combine constraints from the $P_{\rm 1D}$ and BAO analyses on the parameter combinations $b_δσ_8$ and $b_ηf σ_8$, finding that the two probes provide comparable constraining power while exhibiting complementary parameter degeneracies. Our results establish a direct connection between one- and three-dimensional Lyman-$α$ forest measurements through ForestFlow, an approach we term Lyman-$α$ holography by analogy with the reconstruction of higher-dimensional structure from lower-dimensional information.

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arXiv2026

Enhancing weak lensing redshift distribution characterization by optimizing the Dark Energy Survey Self-Organizing Map Photo-z method

Characterization of the redshift distribution of ensembles of galaxies is pivotal for large scale structure cosmological studies. In this work, we focus on improving the Self-Organizing Map (SOM) methodology for photometric redshift estimation (SOMPZ), specifically in anticipation of the Dark Energy Survey Year 6 (DES Y6) data. This data set, featuring deeper and fainter galaxies than DES Year 3 (DES Y3), demands adapted techniques to ensure accurate recovery of the underlying redshift distribution. We investigate three strategies for enhancing the existing SOM-based approach used in DES Y3: 1) Replacing the Y3 SOM algorithm with one tailored for redshift estimation challenges; 2) Incorporating $\textit{g}$-band flux information to refine redshift estimates (i.e. using $\textit{griz}$ fluxes as opposed to only $\textit{riz}$); 3) Augmenting redshift data for galaxies where available. These methods are applied to DES Y3 data, and results are compared to the Y3 fiducial ones. Our analysis indicates significant improvements with the first two strategies, notably reducing the overlap between redshift bins. By combining strategies 1 and 2, we have successfully managed to reduce redshift bin overlap in DES Y3 by up to 66$\%$. Conversely, the third strategy, involving the addition of redshift data for selected galaxies as an additional feature in the method, yields inferior results and is abandoned. Our findings contribute to the advancement of weak lensing redshift characterization and lay the groundwork for better redshift characterization in DES Year 6 and future stage IV surveys, like the Rubin Observatory.

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arXiv2026

1000 cataclysmic variables identified from DESI spectroscopy

Most cataclysmic variables (CVs) are discovered when they have an outburst generating an inherent selection bias against CVs that rarely, or never, outburst. CVs discovered by virtue of their spectroscopic characteristics are particularly valuable to offset this bias and we have used an established machine-learning technique to assist in searching 98 966 000 spectra obtained by the Dark Energy Spectroscopic Survey (DESI) to find such CVs. DESI observations are much deeper than previous spectroscopic surveys and we have identified 1029 CVs, 221 of which are new including ten of the AM CVn subtype. We have spectroscopically confirmed 441 CV candidates and obtained 84 new or improved orbital periods. We present revised space density estimates based upon this new data. We have also added ten more to the eight known examples of an intriguing class of CVs which exhibit peculiar changes in accretion.

astro-ph.SR↗
arXiv2026

Probing the matter-dominated expansion with multi-redshift Lyman-$α$ BAO from DESI DR2

We present a multi-redshift Baryon Acoustic Oscillations (BAO) analysis of the DESI Data Release 2 (DR2) Lyman-$α$ (Ly$α$) forest, splitting the forest auto-correlation and its cross-correlation with quasars into three redshift bins. We obtain BAO measurements at effective redshifts $z_{\rm eff} = 2.13$, $2.40$, and $2.81$ with $\sim2.0$--$2.5\%$ precision per bin in the radial and transverse directions, corresponding to $\sim1.1$--$1.2\%$ precision for the isotropic BAO measurement. Using the same data products and modeling framework as the DESI DR2 Ly$α$ BAO analysis, we validate the pipeline on $400$ synthetic datasets and find unbiased BAO recovery with well-calibrated uncertainties. The measurements show an increase in the isotropic dilation parameter $D_V/r_d$ from $30.26\pm0.39$ to $32.22\pm0.47$ and in the Alcock-Paczyński parameter $D_M/D_H$ from $3.96\pm0.15$ to $5.63^{+0.22}_{-0.24}$. The Hubble distance $D_H/r_d$ decreases from $9.40\pm0.20$ to $7.22\pm0.17$, providing a direct measurement of the expansion history consistent with $Λ$CDM and the expected matter-dominated scaling, with $H(z)\propto(1+z)^n$ giving $n=1.34\pm0.16$. The redshift split also provides a self-consistent measurement of clustering evolution: the Ly$α$ forest bias evolves as $(1+z)^γ$ with $γ_α=3.05\pm0.16$, the RSD parameter has a redshift evolution described by $γ_β=-0.97\pm0.26$, and the quasar bias evolves with $γ_Q=1.56\pm0.23$, consistent with independent quasar clustering measurements. Combining these three-bin BAO measurements with DESI DR2 galaxy and quasar BAO measurements yields cosmological constraints consistent with the single-bin Ly$α$ BAO analysis in flat $Λ$CDM and $w_0w_a$CDM and improves curvature constraints by $\sim12\%$ in $Λ$CDM$+Ω_\mathrm{K}$.

astro-ph.CO↗
arXiv2026

Electron temperature relations and the direct N, O, Ne, S and Ar abundances of 49959 star-forming galaxies in DESI Data Release 2

We present the largest direct-method abundance catalogue of galaxies to date, containing measurements of 49959 star-forming galaxies at z < 0.96 from DESI Data Release 2. By directly measuring electron temperatures across multiple ionisation zones, we provide constraints on a number of electron temperature relations. Using the temperature measurements, we derive reliable abundances for N, O, Ne, S and Ar and measure the evolution of abundances and abundance ratios of as a function of metallicity and other galaxy properties. Our measurements include direct oxygen abundances for 49507 galaxies, leading to the discovery of the two most metal-poor galaxies in the nearby Universe, with oxygen abundances of 12+log(O/H) = $\rm 12+\log(O/H) = 6.77_{-0.03}^{+0.03}~\rm dex $ (1.2\% $\rm Z_{\odot}$) and $\rm 12+\log(O/H) = 6.81_{-0.04}^{+0.04}~\rm dex$ (1.3\% $\rm Z_{\odot}$). We identify a rare outlier population of 24 galaxies with high N/O ratios at low metallicity, reminiscent of galaxy abundances observed in the early Universe. We find the Ne/O ratio is constant at low metallicity but increases gradually at $\rm 12+log(O/H) > 8.105\pm0.004$ dex. We show that the S/O and Ar/O abundance ratios are strongly correlated, consistent with the expected additional Type Ia enrichment channel for S and Ar. In this work we present an initial survey of the key properties of the sample, with this dataset serving as a foundation for extensive future work on galaxy abundances at low redshift.

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arXiv2026

OzDES Reverberation Mapping Program: CIV lags from six years of data

We present 29 successfully recovered CIV time lags in Active Galactic Nuclei from the complete Dark Energy Survey Reverberation Mapping campaign. The AGN in this sample span a redshift range of 1.9<z<3.5. We successfully measure the velocity dispersion from the CIV spectral linewidth for 25 of these 29 sources, and use these to calculate new high-redshift black hole mass estimates, finding masses between 0.8 and 1.3 billion solar masses. We also identify a selection effect due to the duration of the survey that can impact the radius-luminosity relation derived from this and other (high-redshift) data. This paper represents the culmination of the OzDES CIV campaign.

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arXiv2026

Beyond traditional emission-line diagnostics: using autoencoders to uncover active galactic nuclei in DESI spectra

The growing volume of spectroscopic data in modern surveys motivates data-driven approaches that complement traditional emission-line diagnostics for active galactic nuclei (AGN) identification. We present a machine learning framework that exploits the full optical spectrum using unsupervised representation learning within a semi-supervised classification scheme. We use the SPENDER autoencoder to compress DESI galaxy spectra into a low-dimensional latent space and classify sources through a k-d tree nearest-neighbor search. The model is trained on 50,222 DESI Main Survey spectra from the Guadalupe dataset and released as part of Data Release 1 (DR1), restricted to z <= 0.5. We validate the performance using labels derived from FastSpecFit's emission line measurements defining seven galaxy classes: AGN, broad-line (BL), composite, star-forming, passive, retired, and Other. The method achieves high accuracies for AGN (0.952) and broad-line AGN (0.965), reliably identifying these sources even in low signal-to-noise spectra and recovering AGN missed by standard single-diagnostic methods. Our classification metrics are benchmarked against traditional diagnostics, and we show they represent lower limits of the model's true performance. We also find that the learned latent space correlates with key galaxy properties such as stellar mass and star-formation rate, demonstrating that it captures physically meaningful information. These results show that unsupervised spectral representation learning, implemented within a semi-supervised classification framework, provides a scalable and effective approach for constructing more complete AGN catalogues for current and future spectroscopic surveys.

astro-ph.GA↗
arXiv2026

Alcock-Paczynski Blinding Scheme for the Ly-$α$ Forest Analysis

We present and validate a blinding method for the Lyman-$α$ (Ly$α$) forest analysis based on a modification of the Alcock-Paczynski test. In order to hide the background expansion history, the method employs a geometrical shift of each quasar (QSO) forest in wavelength space, once the quasar continuum has been fitted and the fluctuation field is extracted. The redshift positions for the QSO sample are also changed in a consistent manner. We show that the method remains effective when applied to real data, where contamination from metals and Lyman-$β$ is intrinsically mixed with the Lyman-$α$ forest. This limitation is primarily visible in the 1D correlation function, where other blinding strategies can mitigate the effect. To assess its effectiveness, the prescription is tested against a series of datasets of increasing complexity: from idealized low-noise mocks, to realistic DESI year one synthetic datasets, and finally to data from DESI first data release (DR1), using both the auto (Ly$α\times$Ly$α$) and cross (Ly$α\times$ QSO) correlations. We find that the method robustly shifts the BAO peak position from the 3D correlation functions to the expected value for cosmology changes of around 5\% in the matter content, without altering the shape of the posteriors in the model parameters. In conclusion, this catalog-level blinding strategy is a viable method for cosmological inference with the Lyman-$α$ forest, particularly if a cross-analysis with other tracers using the same blinding strategy is pursued.

astro-ph.CO↗
arXiv2026

Weak Evolution of Cosmic Atomic Hydrogen over the Past 4.5 Billion Years

The cosmic star formation rate density (CSFRD) has declined sharply toward the present day, but the roles of the atomic and molecular gas reservoirs remain uncertain. We measure the cosmic HI density, $Ω_{\mathrm{HI}}$, over $0<z<0.41$ by combining HI spectra from the Five-hundred-meter Aperture Spherical Telescope with optical spectroscopy from the Dark Energy Spectroscopic Instrument for $\sim2.5$ million galaxies across $\sim12,000\,{\rm deg}^2$. We measure a raw decrease in $Ω_{\mathrm{HI}}$ by a factor of $1.35\pm0.10$ over the past 4.5 Gyr. Even after applying the conservative systematic corrections from our forward model, the inferred decline is only $1.12\pm0.10$ -- still far weaker than the CSFRD decline (a factor of 2.46). The molecular gas density, in contrast, is known to evolve more closely with star formation. At fixed stellar mass, the average HI gas fraction evolves by less than 0.2 dex, showing that the weak evolution is present across the galaxy population. These quantitative differences rule out rapid depletion of galaxy HI as the primary driver of the late-time CSFRD decline, and provide a stringent benchmark for models of gas accretion, phase conversion and star-formation regulation.

astro-ph.GA↗
arXiv2026

The DESI DR1 Peculiar Velocity Survey: growth rate measurements from galaxy and momentum correlation functions

Joint analysis of the local peculiar velocity and galaxy density fields offers a promising route to testing cosmological models of gravity. We present a measurement of the normalised growth rate of structure, $fσ_8$, from the two-point correlations of velocity and density tracers from the DESI DR1 Peculiar Velocity and Bright Galaxy Surveys, the largest catalogues of their kind assembled to date. We fit the two-point correlation measurements with non-linear correlation function models, constructed from density and momentum power spectra generated using 1-loop Eulerian perturbation theory, and validate our methodology using representative mock catalogues. We find $fσ_8 = 0.391^{+0.080}_{-0.081}$, consistent to within $1σ$ with accompanying analyses of the same datasets using power spectrum and maximum-likelihood fields methods. Combining these growth rate results from different methods including appropriate correlations, we find a consensus determination $fσ_8(z = 0.07) = 0.4497 \pm 0.0548$, consistent with predictions from \textit{Planck}$+Λ$CDM cosmology. Jointly fitting to this consensus low-redshift growth rate and the DESI DR1 full-shape clustering dataset, we measure gravitational growth index $γ_{\rm L} = 0.580^{+0.110}_{-0.110}$, consistent with the prediction of general relativity.

astro-ph.CO↗
arXiv2026

The largest sample of AGN outflows in dwarf galaxies using DESI DR1

In the last decade, the presence of active galactic nuclei (AGN) outflows and feedback in dwarf galaxies ($\mathrm{M_\ast}$<$10^{10}\mathrm{M}_\odot$) has gained ground over supernova (SN) feedback as the main mechanism regulating star formation. In this work, we perform the first systematic search for AGN outflows in dwarf galaxies using the Dark Energy Spectroscopic Instrument Data Release 1 (DESI DR1). From $\sim$ 7 million galaxies at z$<$0.45, we identify ionized outflows through the detection of broad components in the [OIII]$\lambda5007$Åemission line. Galaxies are divided into dwarf and massive systems. Then, using emission-line diagnostic diagrams, we classify as star forming or AGN. We identify 1,502 AGN dwarf galaxies with outflow signatures. Comparing the distributions of star forming and AGN galaxies with outflows, we find that, among the 1,502 AGN dwarf galaxies with outflow signatures, AGN are the most likely drivers of the observed outflows in $\sim$83$\%$ of those with W$_{80}$ velocity $>250$ km s$^{-1}$. This constitutes the largest statistical sample of AGN outflows in dwarf galaxies to date. In massive galaxies, AGN dominance occurs above W$_{80}>350$ km s$^{-1}$. Therefore, two new velocity thresholds are proposed for identifying AGN-driven outflows in dwarf and massive galaxies. Besides, we find that outflows in dwarf galaxies are more likely to escape the dark matter halo than those in massive galaxies, allowing gas to be redistributed from the inner to the outer regions. This suggests that AGN outflows may have a major impact on dwarf galaxies.

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arXiv2026

Galaxy Clusters Selected via the Sunyaev-Zel'dovich Effect in 5 year data from the SPT-3G Main Survey

We report a new galaxy cluster catalog, selected using the thermal Sunyaev-Zel'dovich (SZ) effect, from 5 years of observations of the SPT-3G Main field. Drawn from arcminute-resolution data with white noise levels of 3.2, 2.5, and 8.9 $μ$K-arcmin at 95, 150, and 220 GHz, respectively, the sample consists of 8,892 cluster candidates detected above significance $ξ=4$, with an expected purity of $>82\%$ (4,480 at $ξ\ge5$ with purity $>99\%$). Using optical and infrared data we have confirmed 7,190 candidates as clusters. The sample spans a mass range $7.9 \times 10^{13}$ $M_\odot/h_{70}$ \ $< M_\textrm{500c} < $ $1.6 \times 10^{15}$ $M_\odot/h_{70}$ with a median mass of $1.65 \times 10^{14}$ $M_\odot/h_{70}$, and a redshift range of $0.037 1$ and 271 at $z>1.5$. Compared to previous SZ cluster samples from South Pole Telescope and Atacama Cosmology Telescope data, the SPT-3G sample is highly consistent in mass and redshift but is significantly deeper, with per-cluster detection signal-to-noise 2-4 times higher and a cluster density of 4.5 confirmed clusters/deg$^2$. We cross match with eRASS1 cluster and point source catalogs, finding 1,279 and 1,319 matches, respectively. The SPT and eROSITA cluster mass estimates are in relatively good agreement. We perform a series of validation checks using both internal data splits and comparisons to external samples. These tests show increasing correlated (dusty) emission with redshift, with a $\sim17\times$ larger 220 GHz temperature increment for clusters at $z\sim1.5$ than $z\sim0.25$, but only weak evidence for correlated synchrotron emission. Finally, a number of clusters are flagged as candidate strong gravitational lenses.

astro-ph.CO↗
arXiv2026

DESI DR2 Baryon Acoustic Oscillations from the Lyman Alpha Forest Multipoles

We present an alternative measurement of the Baryon Acoustic Oscillation (BAO) using the Legendre multipole representation of the Ly$α$ forest correlation functions from the second data release (DR2) of the Dark Energy Spectroscopic Instrument survey. Compressing the auto- and cross-correlation functions into Legendre multipoles yields a positive-definite covariance matrix without any smoothing -- unlike the baseline DR2 analysis -- thanks to a significantly reduced data vector size. We introduce the statistical corrections required to debias the finite-sample covariance matrix estimate and demonstrate that monopole and quadrupole terms for both auto- and cross-correlations can be used even when the correlation functions are distorted by continuum errors and contaminated by metals. This formalism has slightly diminished the constraining power of the BAO scale, while considerably weakening constraints on nuisance parameters. We measure the isotropic BAO scale with $0.93\%$ precision at $z_\mathrm{eff}=2.35$, the Hubble parameter $H(z_\mathrm{eff})=(239.5\pm3.4)~(147.09~\mathrm{Mpc}/r_d) ~\mathrm{km~s}^{-1}~\text{Mpc}^{-1}$, and the transverse comoving distance $D_M(z_\mathrm{eff})=(5.80 \pm 0.10)~(r_d/147.09~\mathrm{Mpc})$~Gpc for a given value of the sound horizon ($r_d$). Our BAO results are entirely consistent with the baseline DR2 analysis.

astro-ph.CO↗
arXiv2026

DESI DR2 Reference Mocks: Clustering results from UCHUU ELGs and QSOs

High-redshift galaxy clustering provides a powerful probe of the growth of structure, testing models of dark matter, dark energy, and galaxy formation during the epoch when the Universe was rapidly evolving. Emission line galaxies (ELGs) and quasars (QSOs) are used as tracers of dark matter by the Dark Energy Spectroscopic Instrument (DESI) to probe this redshift regime. We present results from ELG and QSO mock catalogs created from the Uchuu N-body simulation and tuned to DESI Data Release 2 (DR2) clustering. Employing a modified subhalo abundance matching (SHAM) technique, we populate Uchuu halos and subhalos with QSOs between 0.8 < z < 2.1. For ELGs, we modify this method to select satellite galaxies with low velocities relative to their associated central halos, and populate a separate set of Uchuu halos and subhalos with ELGs between 0.8 < z < 1.6. In this paper, we reproduce the redshift evolution of number density and clustering statistics across the fitted range of scales. We also measure the large-scale clustering bias of both the data and mock samples. These results improve simulated lightcone construction from cosmological models and enhance our understanding of the galaxy-halo connection.

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arXiv2026

Dark Energy Survey Year 6 Results: Redshift Calibration of the Weak Lensing Source Galaxies

Determining the distribution of redshifts for galaxies in wide-field photometric surveys is essential for robust cosmological studies of weak gravitational lensing. We present the methodology, calibrated redshift distributions, and uncertainties of the final Dark Energy Survey Year 6 (Y6) weak lensing galaxy data, divided into four redshift bins centered at $\langle z \rangle = [0.414, 0.538, 0.846, 1.157]$. We combine independent information from two methods on the full shape of redshift distributions: optical and near-infrared photometry within an improved Self-Organizing Map $p(z)$ (SOMPZ) framework, and cross-correlations with spectroscopic galaxy clustering measurements (WZ), which we demonstrate to be consistent both in terms of the redshift calibration itself and in terms of resulting cosmological constraints within 0.1$σ$. We describe the process used to produce an ensemble of redshift distributions that account for several known sources of uncertainty. Among these, imperfection in the calibration sample due to the lack of faint, representative spectra is the dominant factor. The final uncertainty on mean redshift in each bin is $σ_{\langle z\rangle} = [0.012, 0.008,0.009, 0.024]$. We ensure the robustness of the redshift distributions by leveraging new image simulations and a cross-check with galaxy shape information via the shear ratio (SR) method.

astro-ph.CO↗
arXiv2026

Clustering of high-redshift quasars with DESI DR2

We present clustering measurements for high-redshift quasars using data from the Dark Energy Spectroscopic Instrument Data Release 2. Our sample consists of quasars with $2.0 < z < 3.5$ in the luminosity range $M_{1450} \leq -19.94$\,mag. We measure the mean quasar bias $b_Q(\bar{z} = 2.48) = 3.61 \pm 0.01$ for the full sample of $\sim 715,000$ quasars and quantify the redshift evolution of quasar bias by dividing the sample into four equal redshift bins. There is strong evolution of the quasar bias with redshift that is well fit by the function $b_Q(z) = a [(1 + z)^2 - 6.565] + b$ with $a=0.230 \pm 0.007$ and $b=2.394 \pm 0.035$, and this fit is also a good match to lower redshift measurements in the literature. This bias evolution is consistent with a characteristic halo mass of $\bar{M}_{\mathrm{h}} \sim 10^{12}\,\mathrm{M_\odot}$ that does not vary significantly with redshift. The inferred duty cycles for quasars in our sample are $f_{\mathrm{duty}} \sim 10^{-2}$, staying mostly constant over redshifts. We investigate the luminosity dependence of quasar clustering by dividing each of our four redshift bins into three luminosity bins. The size of our quasar sample permits the first statistically significant measurement of the luminosity dependence of quasar bias at these redshifts. We measure weak dependence of quasar bias on luminosity at fixed redshift, inconsistent with no dependence, but weaker than predicted by a model in which quasar luminosity is tightly correlated with halo mass. These clustering measurements provide a stringent test for models of active black hole light curves and the black hole-halo connection at high redshift.

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