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D. Kirkby

Publications and source records attributed to D. Kirkby.

At least 19 recordsLinked to original sources
arXiv2026

Improved constraints on the Milky Way potential using the M68 stream and DESI spectroscopic data

We present a selection of stars belonging to the stellar stream of the M68 (NGC 4590) globular cluster, also known as Fjörm. This star selection is an improvement on previous ones that used only Gaia data, as it incorporates spectroscopic measurements from the DESI survey and photometric data from the DESI Legacy Surveys. The selection contains 96 stars, each with five phase-space parameters from Gaia-DR3 and radial velocity from DESI, covering the entire observed section of the stream. This constitutes the largest selection of M68 stream stars with measured radial velocities to date. The observed stream is wider than expected from N-body simulations, and the stars farthest from the centre of the stream appear to be correlated in radial velocity space. This suggests that these stars cannot have been stripped from the cluster in a static axisymmetric potential. By modelling a mock sample of stream stars created using an N-body simulation, we found that we could reliably constrain the disc mass $M_{\rm d}$ and the dark matter halo axis ratio $q_{\rm h}$ of the Milky Way. This is because the stream flows close to and almost parallel to the disc. Using the 44 stars that are consistent with having been stripped from the cluster, combined with measurements of the Milky Way's rotation curve, we constrain the Galactic potential, obtaining $M_{\rm d} = 5.34 \pm 0.57 \times 10^{10}$ M$_{\rm sun}$ and an oblate halo of $q_{\rm h} = 0.83^{+0.06}_{-0.05}$. Additionally, by fitting the stream track, we estimate the Heliocentric distance of M68 to be $r=10.55\pm0.09$ kpc.

astro-ph.GA↗
arXiv2026

The scale of homogeneity in DESI Data Release 1

We present measurements of the scale of cosmic homogeneity using the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI), the largest publicly available spectroscopic extragalactic survey to date. Using a counts-in-spheres estimator applied to nearly 5 million galaxies and quasars across six independent redshift bins spanning $0.1 < z < 2.1$, we measure the correlation dimension $D_2(r)$ and define the homogeneity scale $R_H$ as the point at which the galaxy distribution reaches within 1\% of the homogeneous asymptotic value. We find that all tracers clearly transition to homogeneity, with the galaxy homogeneity scale ranging from $93.8^{+0.9}_{-0.7}$ to $142.6^{+1.4}_{-1.4}$ $h^{-1}$Mpc depending on the tracer redshift, galaxy bias, and modelling used to extract the scale. Using a cosmology-dependent model, we reconstruct the underlying matter homogeneity scale, finding it decreases monotonically with redshift in excellent agreement with $Λ$CDM predictions. We identify a systematic offset of up to $\sim 10\%$ between measurements in the North and South Galactic Caps, largely due to fiber assignment effects reproduced in our simulations. Accounting for this, and with a complementary demonstration using toy models that our methodology correctly identifies inhomogeneous universes in all but rather finely-tuned observer configurations, this hence provides strong evidence in favour of the cosmological principle across our full redshift range. Our matter homogeneity scale measurements are consistent with, and substantially more precise than, previous constraints from WiggleZ and SDSS, demonstrating the power of DESI data for precision tests of the cosmological principle.

astro-ph.CO↗
arXiv2026

Unveiling Hidden Lyman Alpha Emitters in the DESI DR1 Data

We present an automatic method based on machine-learning convolutional neural network (CNN) architecture to detect Lyman alpha emitters (LAE) hidden in the Data Release 1 spectroscopic dataset of the Dark Energy Spectroscopic Instrument (DESI). Those LAEs mostly have incorrect redshift estimations because the current DESI pipeline is not designed to detect and measure the redshifts of galaxies at $z>2$. To uncover those sources, we first visually inspect thousands of DESI spectra and construct a sample, consisting of both LAEs and non-LAEs, for training and testing the CNN-based model to (1) detect LAEs in DESI spectra and (2) determine their Ly$α$ redshifts. The final model yields $95.2\%$ purity and $95.9\%$ completeness for detecting LAEs. We apply this model to approximately $2\times10^{6}$ spectra of sources targeted as emission-line galaxies and detect 19,685 LAEs from $z\sim2$ to $3.5$ within 12 minutes with a single GPU, illustrating the high efficiency of this model for identifying LAEs. The detected LAEs are mostly at the bright end of the luminosity function with Ly$α$ luminosity $L_{\rm Lyα} \gtrsim 10^{43}$ erg/s. The high signal-to-noise composite spectrum of the detected LAEs further shows various spectral features, including P-Cygni profiles of metal lines and MgII emission lines, possible indicators of Lyman continuum escape fraction, revealing the rich astrophysical information in this LAE sample. Finally, this sample can be used to train and validate the pipelines for redshift determination of LAEs for the preparation of the DESI-II survey.

astro-ph.GA↗
arXiv2026

Cosmological constraints from the DESI DR1 Bispectrum Full-Shape and DR2 BAO

We present cosmological constraints from DESI DR1 full-shape measurements, including the LRG bispectrum, combined with DESI DR2 BAO data. The analysis accounts for cross-covariance using mocks, while ShapeFit compression mitigates prior volume effects in beyond-$Λ$CDM analyses. In $Λ$CDM, the DESI1.5 (P+B) analysis yields $σ_8=0.868\pm0.026$ and $S_8=0.880\pm0.028$, compared with $σ_8=0.822\pm0.034$ and $S_8=0.827\pm0.036$ in the previous power-spectrum-only analysis. The marginalized uncertainties are reduced by 24% and 22%, respectively. For $w_0w_a$CDM, DESI-only analyses with the bispectrum shift dark energy parameters toward $Λ$CDM, consistent with a cosmological constant within $1σ$ in the $w_0$--$w_a$ plane. Adding CMB creates a preference for evolving dark energy: DESI+CMB (P+B) shows a $2.8σ$ deviation from $Λ$CDM. Including DES-Dovekie supernovae alone reduces this to $1.6σ$, while the full combination gives $3.1σ$. The bispectrum weakens evidence for time-varying dark energy relative to power-spectrum-only analyses. It also enhances sensitivity to massive neutrinos: in DESI-only data, the power-spectrum-only posterior for $\sum m_ν$ is consistent with zero, whereas adding the bispectrum yields $0.26\pm0.18$ eV and a 95% upper limit of $0.59$ eV, shifting the peak into the positive region. For modified gravity, the bispectrum constrains $μ_0 = 0.12\pm0.51$ from DESI-only data, consistent with general relativity.

astro-ph.CO↗
arXiv2026

Probing Baryons with the Kinematic Sunyae Zel'dovich Effect and Machine Learning Derived Peculiar Velocities using DESI DR2 and ACT DR6

We present novel empirical constraints on average optical depths and gas density profiles from combining kinematic Sunyaev Zel'dovich effect (kSZ) measurements and nonlinear peculiar velocities, reconstructed using machine learning, for massive halos traced by DESI DR2 luminous red galaxies (LRG). The pairwise kSZ is measured using two ACT DR6 cosmic microwave background (CMB) temperature maps (ILC and 150 GHz maps) for seven luminosity-selected LRG samples. We find consistent results between the two maps and significant detections across the samples. We reconstruct LRG line-of-sight peculiar velocities in two cosmic epochs, centered on $z=$ 0.55 and 0.8, using a simulation-trained Transformer machine learning model to extend beyond the linear approximation. Average optical depths are inferred by comparing the kSZ pairwise correlation to the measured pairwise velocity correlation from the reconstructed velocity field and, separately, from a theoretical prediction using the best fit Planck cosmology, with the highest significance reaching SNR = 14.2 and 15.1 respectively. We also obtain velocity-weighted AP-filtered kSZ-stacked cluster density profiles, which show evidence of extended ionized gas around massive LRG groups and no strong redshift evolution within current measurement uncertainties. These results demonstrate the power of combining spectroscopic galaxy and CMB data, and employing machine learning methods, to probe diffuse baryons and coherent large-scale velocity fields. They open up new avenues to leverage upcoming galaxy survey data from Euclid, Roman and Rubin LSST, in tandem with multi-frequency CMB/sub-mm data from CCAT and Simons Observatory.

astro-ph.CO↗
arXiv2026

Radio Quasars in the Cosmic Dawn: A Spectroscopic Sample from the DESI Survey

We present the largest statistical spectroscopic sample of radio quasars at 4.7 10$). With radio luminosities of $\sim10^{25-28}$ W/Hz, the radio emission in all 83 quasars is expected to be jet-dominated rather than powered by star formation. Analysis of their rest-frame ultra-violet (UV) spectra reveals broadly similar composite spectral properties and CIV velocity shifts compared to radio non-detected quasars. The radio-detected and radio-loud quasars exhibit slightly smaller Ly$α$ and CIV equivalent widths on average, however, we find no significant evidence ($\sim1.3σ$) for a higher fraction of weak-line quasars (WLQs; ~10+/-4% versus ~4+/-1% for radio non-detected quasars). We further find that the broad absorption line (BAL) quasars are predominantly radio-quiet, and no correlation is observed between absorption index and radio-loudness, suggesting that radio emission is not produced by the BAL outflows themselves and are physically distinct phenomena. Our results demonstrate that powerful radio jets were already well-established by z~5.

astro-ph.GA↗
arXiv2026

Intrinsic Tidal Shear at the Largest Scales: Galaxy Multiplet Alignment in DESI DR2

We measure the intrinsic alignment (IA) of galaxy multiplets with the large-scale tidal field traced by galaxy positions in DESI Data Release 2. Using the BGS, LRG, and ELG samples spanning $0.01 < z < 1.6$, we optimize the scales which define multiplets in each sample to minimize measurement noise. We measure multiplet tidal alignment $\mathcal{E}_+$ on scales beyond 100 $h^{-1}$Mpc in all samples, and detect alignment over 200 $h^{-1}$Mpc, up to 4.5$σ$ in the highest LRG redshift bin. We additionally present the multiplet shape-shape autocorrelation, $\mathcal{E}_{++}$, which is independent of galaxy bias and provides a consistency check of our NLA (nonlinear alignment) model. We do not detect a baryon acoustic feature in the projected estimator. We also find the alignment strength of multiplets is correlated with redshift and galaxy morphology. Multiplet alignment offers direct access to the tidal shear field in all galaxy samples, even where individual galaxy alignment cannot, and extends IA detection to the largest scales yet probed.

astro-ph.CO↗
arXiv2026

Combined tracer analysis for DESI 2024 BAO

This paper demonstrates how the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) and future baryon acoustic oscillations (BAO) analyses can optimally combine overlapping tracers (galaxies of distinct types) in the same redshift range. We make a unified catalog of Luminous Red Galaxies (LRGs) and Emission Line Galaxies (ELGs) in the redshift range 0.8 < z < 1.1 and investigate the impact on the BAO constraints. DESI DR1 contains ~30% of the final DESI LRG sample and less than 25% of the final ELG sample, and the combination of LRGs and ELGs increases the number density and reduces the shot noise. We developed a pipeline to merge the overlapping tracers using galaxy bias as an approximately optimal weight and tested the pipeline on a suite of Abacus simulations, calibrated on the final version of the DESI Early Data Release. When applying our pipeline to the DESI DR1 catalog, we find an improvement in the BAO constraints of 11% for $α_\mathrm{iso}$ and ~7.0% for $α_\mathrm{AP}$ consistent with our findings in mock catalogs. Our analysis was integrated into the DESI DR1 BAO analysis to produce the LRG+ELG result in the 0.8 < z < 1.1 redshift bin, which provided the most precise BAO measurement from DESI DR1 with a 0.86% constraint on the BAO distance scale and a $9.1σ$ detection of the isotropic BAO feature.

astro-ph.CO↗
arXiv2026

Sizing the Universe with DESI Galaxy Sizes: Plain Fundamentals of Fundamental-Plane Lensing

Weak gravitational lensing provides a powerful way to map cosmic structure, but most current measurements rely on galaxy shape distortions from deep imaging surveys and are affected by systematics such as intrinsic alignments, photometric-redshift uncertainties and shape-measurement biases. Here we present a spectroscopic galaxy-galaxy lensing magnification measurement using Fundamental-Plane (FP) size residuals, $δ_r\equivΔ\log_{10}R_\mathrm{e}$, from 3.26 million DESI luminous red galaxy (LRG) sources behind DESI Bright Galaxy Survey lenses. The FP-like relation predicts the intrinsic sizes of LRGs from lensing-invariant quantities, including velocity dispersion $σ_0$ and surface brightness $I_\mathrm{e}$, with a scatter of about 0.06-0.07 dex. Lensing magnifies LRG sizes, giving the direct convergence response $δ_r(κ)=κ/\ln 10$, but we show that the full lensing response is modified by magnification bias, because fitting $R_\mathrm{e}$ with $I_\mathrm{e}$ inevitably induces a magnitude dependence in $\barδ_r(m)$. After calibrating this response, we recover surface-density profiles with uncertainties comparable to those from individual Stage-III shear surveys using 5-20 million higher-redshift sources. The corresponding excess surface-density profiles agree with shear-based measurements. We further show that the estimator is robust to size-measurement uncertainties, with a convergence multiplicative bias only $\simeq -0.2$ times the size bias. FP lensing therefore provides a clean, spectroscopic and complementary probe of cosmic structure.

astro-ph.CO↗
arXiv2026

A Finely-Binned Measurement of the Connected Even-Parity Galaxy 4-Point Correlation Function of DESI Year 1 Luminous Red Galaxies

We present the connected even-parity galaxy 4-Point Correlation Function (4PCF) of DESI Year 1 (Y1) Luminous Red Galaxies (LRGs). This is one of the first measurements of the connected 4PCF on data, and shows a clear detection at $\sim$12 to 17$σ$ in the full-sky analysis. We test the robustness of the signal by varying three factors: hemisphere (north vs. south), redshift range (either the full range $0.4 < z < 1.1$ or the higher-number-density interval $0.4 < z < 0.8$), and sample completeness (the full sample vs. only the most complete regions within the number density-motivated cut). Finally, we cross-correlate different patches that are spatially well-separated, and thus should have largely independent noise. This approach, at leading order, is able to remove mismatch between the covariance matrix of the data and that of the mocks; however, in certain cases at the cost of sensitivity. We find $\sim$15$σ$ evidence for an even-parity 4PCF in this approach. Overall, the studies of the 4PCF presented here probe sensitively any mismatch between mock catalogs and data, and also open up the prospect of fitting a model, constraining cosmological parameters and galaxy biases, and searching for Baryon Acoustic Oscillation (BAO) features.

astro-ph.CO↗
arXiv2026

A measurement of $H_0$ from DESI DR1 using energy densities

We present a new measurement of the Hubble constant, independent of standard rulers and robust to pre-recombination modifications such as Early Dark Energy (EDE), obtained by calibrating the total energy density of the Universe. We start using the present-day photon density as an anchor, and use the baryon-to-photon ratio from Big Bang Nucleosynthesis based measurements and the baryon-to-matter ratio from the baryons' imprint on galaxy clustering to translate to a physical matter density at present day. We then compare this to measurements of the ratio of the matter density to the critical density ($Ω_{\mathrm{m}}$), calculated using the relative positions of the baryon acoustic oscillations, to measure the critical density of the universe and hence $H_0$. The important measurements of the evolution of the energy density all happen at low redshift, so we consider this a low-redshift measurement. We validate our method both on a suite of $N$-body mocks and on noiseless theory vectors generated across a wide range of Hubble parameters in both $Λ$CDM and EDE cosmologies. Using DESI DR1 data combined with the angular CMB acoustic scale and the latest BBN constraints, we find $H_0 = 69.0 \pm 2.5$ km s$^{-1}$ Mpc$^{-1}$, consistent with existing early and late-time determinations of the Hubble constant. We consider the impact of non-standard dark energy evolution on our measurement. Future data, including that from further iterations of DESI and from Euclid, will add to these results providing a powerful test of the Hubble tension.

astro-ph.CO↗
arXiv2026

A Unified Tracer Analysis of DESI DR2 Baryon Acoustic Oscillations

We improve upon previous efforts to optimally combine overlapping galaxy samples in the DESI baryon acoustic oscillation analysis. By weighting each galaxy by its linear bias, overlapping galaxies are combined into a single, unified catalog, naturally avoiding double counting of cosmic volume and including all auto- and cross- information at the catalog level. Improvements over the previous effort include the addition of QSO out to $z=1.6$ to account for all overlapping DR2 tracers and redshift-dependent bias treatment to improve reconstruction. We report distance measurements using this unified tracer, and find them to be highly consistent with the baseline DR2 BAO analysis. We also test for tracer-dependent systematics within the DESI data, and find no evidence of tracer-dependent systematics within $0.8<z<1.6$. Finally, we take advantage of the unified tracer to rebin the analysis in redshift in order to more finely resolve the redshift-to-distance relation. Dynamical dark energy results on this finer redshift binning indicate that there is no missed feature in the expansion history in the redshifts $0.8<z<1.6$, and reproduces DESI's preference for an evolving dark energy equation of state.

astro-ph.CO↗
arXiv2026

Spatially-Resolved Spectra of Diffuse Galactic Light using 10.8 M DESI Sky Fibers

Using 10.8 million ``blank'' sky spectra from the DESI Year 3 dataset, we measure the diffuse galactic light (DGL) spectrum in the optical at spectral resolution $R \sim 4000$ by correlating with far-infrared emission from IRAS. Subdividing the sky into 54 deg$^2$ pixels (HEALPix, NSIDE = 8), we map the variation of the DGL correlation spectrum and nebular emission lines across the DESI footprint in the high-Galactic-latitude sky. The increased data volume over previous SDSS-based analyses enables several new detections in the DGL, including scattering both onto and out of the line of sight from neutral interstellar sodium and potassium. We further detect direct emission from ro-vibrational transitions of molecular hydrogen in the near-infrared with an absolute radiance of $0.65\substack{+0.13 \\ -0.12}\times10^{-9}~{\rm erg\, cm^{-2}\,s^{-1}\,sr^{-1}}$, roughly consistent with theoretical expectations, but with an apparent ortho-to-para line ratio that is lower by a factor of $0.60\substack{+0.28 \\ -0.27}$. We confirm previous detections of extended red emission (ERE) in the DGL and map its spatial variation. Our spatially resolved DGL maps provide important observational constraints for the radiative transfer efforts that are now possible with recent 3D models of the Milky Way.

astro-ph.GA↗
arXiv2026

DESI Data Release 1: Stellar Catalogue

In this paper we present the stellar Value-Added Catalogue (VAC) based on the DESI Data Release 1. This VAC contains stellar parameter, abundance and radial velocity measurements for more than 4 million stars. It also contains, for the first time, measurements from individual epochs for more than a million stars with at least two observations. The main contribution to the catalogue comes from the bright program of the main survey, which includes $\sim $2.5 million stars, and the backup program, which includes $\sim $ 1 million stars. The combined magnitude range for the stars in the catalogue extends from ${\it Gaia}$ G $\sim 12$ to G $\sim 21$. For the magnitude range $17.5<G<21$ this catalogue represents a factor of 10 increase in the number of stars with radial velocity and abundance measurements compared to existing surveys. Despite DESI's resolution (R $\sim 2500-5000$), the median radial velocity uncertainty for stars in the catalogue is better than 1 km s$^{-1}$. The stellar parameters and abundances of stars in DESI are measured by two independent pipelines, and after applying a temperature-dependent calibration, [Fe/H] abundances of high signal-to-noise stars are accurate to better than $\sim$ 0.1 dex when compared to high-resolution surveys. The catalogue probes different Galactic components including a particularly large number of distant stars: tens of thousands of stars further than 10 kpc, and thousands further than 50 kpc. The catalogue also contains several thousand extremely metal-poor stars with ${\rm [Fe/H]}<-3$. The released sample of stars includes measurements for thousands of stars that are members of dwarf galaxies, open and globular clusters as well as members of several dozen stellar streams. The next public DESI data release is expected in less than two years and will contain three times as many stars as DR1.

astro-ph.GA↗
arXiv2026

Full calibration of the tomographic redshift distribution from the HSC PDR3 Shape Catalog with DESI

The calibration of tomographic redshift distributions is essential for cosmological analysis of weak lensing data. In this work, we calibrate all four tomographic bins of the Hyper Suprime Camera (HSC) weak lensing catalog with the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 and 2 using the clustering redshifts technique. We include z > 1.2 redshift sources such as emission line galaxies (ELG) and quasars (QSO) sources in our calibration, which were not available in the previous HSC calibration (Rau et al. 2022), allowing a complete calibration of all the redshift bins. We find the first tomographic bin exhibits a small shift towards low redshifts. The second bin is in good agreement with the photometric calibration, while third and fourth bin exhibit a shift towards higher redshifts. However, these shifts are considerably smaller than the shifts obtained in the HSC Year 3 cosmic shear analyses. We evaluate the impact of galaxy bias and magnification effects from all the samples on the measurements, finding them to be small, and we propose corrections to reduce them further. Specifically, we relax the assumption of linear bias and only assume no redshift evolution of the cross-correlation coefficient, allowing us to leverage smaller clustering scales. We model the redshift distributions with splines and compare our results to previous analyses as well as to other parameterizations found in literature. For the two high-redshift tomographic bins, we find the shifts to higher redshifts with respect to the measurements performed in Rau+2022 to be $Δz_3=-0.043^{+0.022}_{-0.020}$ and $Δz_4=-0.050^{+0.012}_{-0.012}$.

astro-ph.CO↗
arXiv2026

Lyman Break Galaxy selection and redshift measurement with supervised contrastive learning

Some of the next steps for high-precision cosmology lie within the high-redshift, high-density universe. Spectroscopic survey experiments such as the Dark Energy Spectroscopic Instrument (DESI)'s second phase DESI Run 2 will shift towards probing Lyman Break Galaxy (LBG) populations from z$\sim$2 to z$\sim$4.5. For this faint sample, spectroscopic redshift measurement and sample decontamination remains a challenge, even after target selection. We propose an approach based on supervised weighted contrastive learning, in order to both learn a redshift representation for spectra and decontaminate the sample from quasars and low redshift emission line galaxies. This strategy generalizes the contrastive learning loss approach with continuous relationship weights, such that the network simultaneously learns redshift and classification tasks. The model shows stronger outlier classification and comparable redshift identification performances when compared to the previous network used for DESI (a modified version of QuasarNET) on the same dataset. In particular, contrastive learning is well suited to the small, visually-inspected sample used for training and testing, especially given the multi-task nature of this work.

astro-ph.CO↗
arXiv2026

DESI DR2 Results IV: Alcock-Paczyński Measurements from the Lyman Alpha Forest and Cosmological Constraints

We present Alcock-Paczyński (AP) measurements from the full shape of Lyman-$α$ (Ly$α$) forest correlation functions measured from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI). Our measurements include information from the Ly$α$ forest auto-correlation and its cross-correlation with quasars. We constrain the AP effect with $1\%$ precision at an effective redshift $z_\mathrm{eff}=2.33$, which is twice as tight as the Baryon Acoustic Oscillation (BAO) constraint from the same data. When using the joint Ly$α$ AP and BAO results, we measure the ratios $D_\text{H}(z_\mathrm{eff})/r_\text{d}=8.600 \pm 0.066$ and $D_\text{M}(z_\mathrm{eff})/r_\text{d}=39.32 \pm 0.33$, where $D_\text{M}$ is the transverse comoving distance, $D_\text{H}$ is the Hubble distance, and $r_\text{d}$ is the sound horizon at the drag epoch. Assuming $Λ$CDM, Ly$α$ forest measurements combined with a nucleosynthesis prior produce a constraint on the Hubble constant $H_0=66.5\pm1.3\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The Ly$α$ AP result corresponds to a matter fraction constraint $Ω_\text{m}=0.325\pm0.018$ in $Λ$CDM, which is $1.4σ$ higher than DESI BAO. This impacts the DESI results relative to the Cosmic Microwave Background (CMB), slightly reducing their discrepancy from $2.4σ$ to $2.2σ$. We present updated constraints on extended models using the joint DESI DR2 BAO and Ly$α$ forest full shape data, together with external data sets. When considering a time-evolving dark energy equation of state parametrized by $w_0$ and $w_a$, we find it is preferred over $Λ$CDM at $2.7σ$ for the combination of DESI and CMB data, and at $3.2σ$ when also including supernovae. With the new Ly$α$ AP measurement, DESI provides its most precise anchor for the expansion history at $z > 1$ in the matter-dominated Universe.

astro-ph.CO↗
arXiv2026

Validation of the DESI DR2 Ly$α$ forest full-shape analysis

We present the validation of the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) Lyman-$α$ (Ly$α$) forest full-shape analysis. This analysis combines three-dimensional Ly$α$ forest auto-correlations and cross-correlations with quasars to extract information from both the baryon acoustic oscillation (BAO) feature and the broadband clustering signal, with primary emphasis on the Alcock-Paczynski (AP) measurement. Compared to the DESI DR1 analysis, the DR2 validation uses substantially larger and more realistic mock datasets, including CoLoRe 2LPT and AbacusSummit Ly$α$ forest simulations. The modeling framework is also improved through analytic marginalization over small scales ($<10$ $h^{-1}$Mpc) and the impact of ultraviolet background fluctuations. The validation program was completed prior to unblinding and defines quantitative requirements for the cosmological parameters of interest, which are evaluated using hundreds of mock realizations. We further test the analysis through independent fits to the auto- and cross-correlations, multiple catalog splits, and a broad suite of analysis and modeling variations applied to both mocks and blinded observational data. We find that the BAO and AP parameters satisfy all validation requirements and remain stable across all tests. In contrast, mock studies reveal a significant bias in the inferred growth-rate parameter $fσ_8$, leading us to exclude this measurement from the final analysis. The consistency across mocks, data splits, and robustness tests demonstrates that the DR2 Ly$α$ full-shape analysis provides a reliable and substantially improved broadband AP measurement over previous Ly$α$ forest studies.

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