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J. Silber

Publications and source records attributed to J. Silber.

At least 37 records · Page 2Linked to original sources

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.

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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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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.

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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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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.

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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$+Ω_\mathrm{K}$.

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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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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.

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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.

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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.

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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.

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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.

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Peering down the barrel with DESI DR2: 10 000+ inflows at $z$ < 0.6 reveal how galaxies accrete cold gas

Direct observational constraints on how galaxies acquire their gas remain remarkably limited, hindering our understanding of the baryon cycle. We present a search for down-the-barrel NaI D absorption towards 15.6 million galaxies at $z < 0.6$ in DESI Data Release 2. We use Bayesian evidence ratios to assess whether the absorption requires additional components tracing interstellar gas distinct from the systemic component of the galaxy. We construct a catalogue of 50 088 (27 420) galaxies with moderate (strong) evidence for down-the-barrel absorption. The inferred absorption components are broadly distributed in velocity, with approximately 50% at $v_{\rm flow} < -50$ km/s, 30% within 50 km/s of the systemic velocity and the remaining 20% at $v_{\rm flow} > 50$ km/s. We find strong evidence for a large population of low-velocity, infalling absorbers with velocities $\sim$20 km/s in edge-on galaxies, consistent with radial inflows predicted in simulations. The stronger correlation in early-type galaxies between inflow velocity and stellar velocity dispersion, compared to that with stellar mass, suggests that a portion of these inflows may be associated with accreting satellites. These results reveal the multiple pathways in which galaxies accrete gas at redshift $z < 0.6$ for the first time in a statistically significant sample.

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Measuring local primordial non-Gaussianity from the clustering of DESI DR1 LRGs and QSOs

We report the first measurement of primordial non-Gaussianity (PNG), parameterized by $f_{\mathrm{NL}}$, in the configuration space two-point correlation function (2pcf). We employ simulation based modeling and a novel approach for the mitigation of imaging systematics. We apply this method to samples of luminous red galaxies (LRG) and quasars (QSO) observed by the Dark Energy Spectroscopic Instrument (DESI) during the first year of its observations (DR1). The observed 68\% CL interval on $f_{\mathrm{NL}}$ is $-3^{+22}_{-21}$ using LRGs, and $ 0^{+17}_{-16}$ using QSOs. The joint measurement yields $f_{\mathrm{NL}} = -3^{+12}_{-12}$ at $\ [68\%]$ CL. Our pipeline imposes a Gaussian prior on the value of $p$ (which defines the PNG bias via the Universality relation), with $p_{\rm LRG} = 1.0 \pm 0.1$ and $p_{\rm QSO} = 1.6\pm 0.1$. The observed constraining power of DESI tracers significantly exceeds that of previous large-scale structure (LSS) surveys, and encouragingly, approaches the sensitivity of CMB probes of PNG.

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

We present cosmological constraints from the combination of DESI DR1 full-shape measurements, including for the LRG bispectrum, and DESI DR2 BAO data. The joint analysis accounts for cross-covariance using mocks, while ShapeFit compression mitigates prior volume effects that hinder beyond-$Λ$CDM analyses. In $Λ$CDM, the bispectrum (P+B) shifts $σ_8$ up by $1.1σ$ and $S_8$ by $1.2σ$, reducing their uncertainties by $26\%$ and $28\%$, respectively. For $w_0w_a$CDM, DESI-only analyses with the bispectrum shift dark energy parameters toward $Λ$CDM, staying consistent with a cosmological constant within $1σ$. 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 DESI+CMB+DES-Dovekie gives $3.1σ$, driven primarily by the CMB. The bispectrum consistently weakens evidence for time-varying dark energy relative to power-spectrum-only analyses. The bispectrum also enhances sensitivity to massive neutrinos: in DESI-only analysis, the power-spectrum-only posterior for $\sum m_ν$ is consistent with zero, whereas adding the bispectrum yields a mean of $0.26\pm0.17$~eV and a $95\%$ upper limit of $0.57$~eV, shifting the peak into the positive region and agreeing with oscillation lower bounds. For modified gravity, the bispectrum further constrains $μ_0 = 0.12\pm0.49$ from DESI-only data, consistent with general relativity. Our analysis shows that accounting for cross-dataset covariances and avoiding prior volume effects yields robust constraints, with the bispectrum raising amplitude parameters and tightening their uncertainties.

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Quality Assessment of Spectroscopic Data Reduction Pipelines Using Artificial Intelligence: Scrutinizing Data Release 2 from the DESI Survey

Large spectroscopic surveys now collect data at a scale that makes traditional visual inspection impractical. We present an unsupervised pipeline for spectroscopic quality assessment that requires no labeled training data. The method combines Uniform Manifold Approximation and Projection for dimensionality reduction with Friends-of-Friends clustering to isolate anomalous spectra for targeted review. We apply this pipeline to 58,291,334 spectra across 14,199 tiles from DESI Data Release 2, processing each tile independently to produce a tile-level outlier catalog. In each tile, the pipeline separates a dense core of typical spectra from small, isolated components and singletons, yielding a total of 1,095,816 outlier candidates. The mean tile-level outlier fraction is about 1.96 percent overall, with values of 0.76 percent and 2.36 percent for the dark and bright main-survey programs, respectively. From the visual inspection of 391 outlier candidates from the dark and bright programs of the main survey, we find that 66.8 percent exhibit identifiable spectral anomalies consistent with known reduction and calibration effects. By contrast, only 4.1 percent carry a non-zero quality flag from the standard reduction pipeline. This shows that the method provides a complementary quality-assessment layer to existing pipeline diagnostics and recovers a substantial population of problematic spectra that standard diagnostics miss. Extrapolating to the main-survey catalog, we estimate that approximately 218,000 candidate outliers are free of identifiable reduction artifacts and may correspond to genuine atypical spectra in the context of DESI. The pipeline is scalable, reproducible, and directly comparable across successive data releases, making it a practical quality-assurance monitor for DESI and future multi-object spectroscopic surveys.

astro-ph.IM↗

DESI Data Release 2 ELGs: Property-dependent subsamples, imaging systematics, and clustering

Using emission-line galaxies (ELGs) from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2, we evaluate a property-dependent correction to imaging systematics. We derive systematic weights following the same linear regression method used for other DESI tracers, but do so separately on ELG subsamples to provide a physically-informed alternative to the fiducial, neural-network-based approach. In doing so, we show that the deeper imaging in the Dark Energy Survey (DES) footprint leads to a higher overall number density but a lack of targets with extreme $g-r$ and $r-z$ colors. ELGs in the DES region also show a distinct redshift distribution when subsampled by position in the $g-r$ vs. $r-z$ plane. To address these effects, we implement a separate treatment of the DES footprint within the DESI catalog production pipeline, which is generally well-motivated and, in some cases, imperative for accurate clustering measurements. With DES treated separately, we find that property-dependent systematic weights further mitigate spurious clustering signal in $\sim$10% of subsamples, while the fiducial scheme remains optimal for the full sample.

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Tomography of the gamma-ray sky from cross-correlation with DESI DR2 and unWISE galaxies

We study the origin of extragalactic gamma-ray emission observed by Fermi-LAT, using the cross-correlation of the gamma-ray sky with maps of large-scale structure provided by the DESI and unWISE surveys. Tomographic cross-correlation reveals the bias-weighted redshift distributions of gamma-ray sources. We first illustrate this method by cross-correlating detected gamma-ray point sources with large-scale structure. We find a significant cross-correlation and infer a point source redshift distribution broadly consistent with the distribution of identified optical counterparts previously reported in the literature, as well as a similar linear bias ($b \approx 2$) to massive galaxies that host bright active galactic nuclei. We then study the clustering of the Fermi unresolved gamma-ray background (UGRB), both in auto-correlation and in cross-correlation with large-scale structure. We detect the cross-correlation of the UGRB and LSS at $\sim 10σ$ in total, with highly significant detections from both DESI and unWISE. Our measurements suggest that the redshift distribution of the UGRB is broadly consistent with the redshift distribution of detected point sources. Additionally, we find a relatively weak amplitude for the cross-correlation with large-scale structure at z < 2, suggesting a significant fraction of the UGRB does not come from z < 2 large-scale structure. A natural candidate is contamination of from residual Galactic emission, and our best estimate of the contamination level derived from the UGRB auto-spectrum suggests that the mean bias of UGRB sources is indeed quite similar to the bias of detected Fermi point sources. However, we cannot exclude additional emission from gamma-ray sources at high redshift, z > 2, and we suggest that cross-correlation with tracers at z > 2, including CMB lensing, would be the ideal way to determine the fraction of z > 2 emission.

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