arXiv subjects

Francisco Prada

Publications and source records attributed to Francisco Prada.

At least 37 records · Page 2Linked to original sources

arXiv2026

The 3D clustering of Lyman Alpha Emitters measured with DESI

We present a clustering analysis of Lyman-$α$ emitters (LAEs) using spectroscopic observations from the Dark Energy Spectroscopic Instrument (DESI) of candidates selected from the Blanco/DECam Intermediate-Band Imaging Survey (IBIS). We measure the two-point correlation function and the power spectrum, including cross-correlations with DESI quasars. Using both analytical and halo occupation distribution (HOD) simulation-based modeling, we find a linear bias of $b \sim 2.31$--$2.62$ for LAEs over the redshift range $2.26 < z < 3.41$. The analytical modeling also provides constraints on the strength of radiative transfer effects, while the HOD analysis characterizes the LAE-halo connection across multiple models. Finally, we quantify the magnitude of non-perturbative clustering effects such as Fingers of God in the LAE population, providing essential input for the accurate modeling of LAE-based cosmological analyses in forthcoming high-redshift surveys such as DESI-II.

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arXiv2026

Signatures of a Tidally Induced Spiral Arm at the Anticenter of the Milky Way and a Kinematically Extended Anticenter Stream Using DESI DR2

Using the Dark Energy Spectroscopic Instrument Milky Way Survey (DESI MWS), we examine the 6D space of the anticenter region of the stellar disk (150$^\circ$ $<$ Galactic longitude $<$ 220$^\circ$) using 61,883 main-sequence turnoff stars. We focus on two well-known stellar overdensities in the anticenter, the Monoceros Ring (MRi) and Anticenter Stream (ACS). We find that the MRi overdensity has kinematics consistent with a tidally induced spiral arm, a type of dynamic spiral arm created by an interaction with a satellite galaxy, most likely the Sagittarius dwarf spheroidal galaxy (Sgr). We use the kinematics of the MRi to calculate the two most recent passage times of Sgr are 0.25 $\pm$ 0.09 Gyrs and 1.10 $\pm$ 0.23 Gyrs from the present day. We validate that the ACS is kinematically decoupled from the MRi because they are moving in opposite radial and vertical directions. We find that the kinematics associated with the ACS are not confined to our defined overdensity. The features we see in the ACS region are likely part of a broader distribution of stars with the same kinematic signature as detected in other places, like the vertical wave in the outer disk and phase spiral.

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arXiv2026

Disentangling the Distant Stellar Halo Using K-Giants in the DESI Year 3 Data

We present a sample of 88,959 K-giants from DESI Milky Way Survey Year 3 data, which we use to characterize the chemo-dynamical properties of the stellar halo at Galactocentric distances of 12 to ~100 kpc. Using HDBSCAN, we identify five prominent stellar halo substructures: Aleph, the Sagittarius stream, Gaia Sausage-Enceladus (GSE), Cetus-Palca and the Orphan-Chenab stream. We present the properties of each of these structures as they appear in our catalog, and examine how uncertainties on distance affect the characterization of substructure with this approach. We also examine regions associated with previously reported overdensities (such as the Virgo Overdensities and the Sagittarius spur) that we do not recover with HDBSCAN. The size and distance range of our catalog allows us to explore in detail the residual stellar halo, comprising stars that we do not associate with any substructure. We find that samples of ~2000 outer halo stars with both highly prograde and highly retrograde angular momenta have similar metallicity distribution functions (MDFs), which do not resemble the MDFs of either GSE or Sagittarius. Both the prograde and retrograde residual halo MDFs are bimodal, with a metal-poor peak at [Fe/H] ~ -2 and a metal-rich peak at [Fe/H] ~ -1.3 (prograde) or -1.5 (retrograde). The MDF for lower angular momentum residual halo K-giants does not show clear evidence for a metal-poor peak, and broadly resembles the MDF of GSE, even at much lower binding energies than GSE itself. We discuss possible interpretations of these findings for GSE accretion scenarios.

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arXiv2026

Satellite Metallicity Enhancement I: Suppressed Star Formation, Stellar Mass Loss, and Enriched Inflow of DESI and EAGLE Galaxies around Massive Clusters

Environmental effects are a primary driver of elevated gas-phase metallicities in galaxies around massive clusters, but the underlying physical mechanisms for this satellite metallicity enhancement (SME) are still unclear. Using the Dark Energy Spectroscopic Instrument (DESI) Data Release 1, we present the first measurement of the average SME as a function of projected cluster-centric distance. The resulting profile reveals three distinct regimes: a steep decline from the cluster center, a plateau near the cluster boundary, and an extended downturn across several cluster radii. Remarkably, the complex shape and amplitude of this observed SME profile are successfully reproduced in the EAGLE cosmological simulation. Drawing insights from EAGLE, we develop a novel satellite chemical evolution model to decompose the observed SME into physical contributions from suppressed star formation, stellar mass loss, and enriched gas inflow. Our analysis shows that continuous accretion of enriched intracluster medium dominates the SME plateau within the cluster virial radius, while mass loss and quenching jointly drive the rapid metallicity decline in the cluster core. Our method disentangles the impacts of three environmental processes on galactic chemical enrichment in the cosmic web, providing a powerful framework for understanding cluster galaxy evolution with current and future spectroscopic surveys.

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arXiv2026

Constraining the Galactic bar using the M92 stellar stream

Stellar streams are excellent probes of the gravitational potential in which they evolve. In the Milky Way (MW), globular cluster (GC) streams are routinely used to infer properties about time-dependent perturbations of the underlying potential. This implies that streams with Galactocentric radii small enough to be perturbed by the MW bar should offer constraints on it, such as its pattern speed, which currently has a wide range of values reported in the literature and is important when studying stellar kinematics. The GC M92 has a small pericentre and should be affected by the bar. It has a diffuse stellar stream, but confirming stream members has previously been hindered by a lack of spectroscopic data. In this paper, we use Dark Energy Spectroscopic Instrument (DESI) observations together with photometric and astrometric data to obtain spectroscopic members of the M92 stream for the first time. We identify a clear spatial distribution and gradients in distance moduli, proper motions, and radial velocities that confirm the stream's existence. We compare the observed stream to mock streams generated in different barred potentials and estimate the MW bar's pattern speed $Ω= 29.1^{+0.7}_{-0.4}$ km s$^{-1}$ kpc$^{-1}$ and $\dot Ω= 0.7^{+3.5}_{-2.3}$ km s$^{-1}$ kpc$^{-1}$ Gyr$^{-1}$. This is the first time a stellar stream is used to probabilistically infer these bar properties, and it opens up an exciting realm of inner Galactic potential characterisation using stellar streams.

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arXiv2026

Galaxies at z > 10: ΛCDM predicts increased Star Formation Efficiency

We show that the rest-frame UV statistics and global properties of galaxies at 7 <= z <= 14 are naturally reproduced within the standard ΛCDM framework when galaxy formation is modeled with UniverseMachine applied to the high-resolution Uchuu N-body simulation. Our model matches the UV luminosity functions over five magnitudes and reproduces the evolution of the UV (and inferred star formation rate) density once internal dust attenuation is included. Comparisons with spectroscopically confirmed JWST/HST galaxies show good agreement with the stellar mass-SFR and stellar mass-UV luminosity relations. In contrast, earlier claims of insufficient stellar masses at z=8 are inconsistent with our model and are likely driven by systematic uncertainties, including AGN contamination, dust attenuation, and the lack of JWST/MIRI constraints. A key prediction is that the star-formation efficiency increases with redshift at fixed halo mass, reaching 2-3 percent of baryons converted into stars by z=10-12. These results demonstrate that current JWST observations of early galaxy populations can be explained within the ΛCDM framework.

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arXiv2026

Constraining primordial non-Gaussianity from DESI DR1 quasars and Planck PR4 CMB Lensing

We present the first measurement of local-type primordial non-Gaussianity from the cross-correlation between $1.2$ million spectroscopically confirmed quasars from the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI) and the Planck PR4 CMB lensing reconstructions. The analysis is performed in three tomographic redshift bins covering $0.8 < z < 3.5$, covering a sky fraction of $\sim 20\%$. We adopt a catalog-based pseudo-$C_\ell$ estimator and apply linear imaging weights validated on noiseless mocks. Compared to previous analyses using photometric quasar samples, our results benefit from the high purity of the DESI spectroscopic sample, the reduced noise of PR4 lensing, and the absence of excess large-scale power in the spectroscopic quasar auto-correlation. Fitting simultaneously for the non-Gaussianity parameter $f_{\mathrm{NL}}$ and the linear bias amplitude in each redshift bin, we obtain $f_{\mathrm{NL}} = 2^{+28}_{-34}$ for a response parameter $p=1.6$, and $f_{\mathrm{NL}} = 6^{+20}_{-24}$ for $p=1.0$. These results improve the constraints on $f_{\mathrm{NL}}$ by $\sim 35\%$ compared to the previous analysis based on the Legacy Imaging Survey DR9. Additionally, we derive an optimal weighting scheme to maximize the constraining power. In this case, and assuming $p=1.6$, we obtain $f_\mathrm{NL}=19^{+25}_{-31}$. Our results demonstrate the statistical power of DESI quasars for probing inflationary physics, and highlight the promise of future DESI data releases.

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arXiv2026

A Natural $\gtrsim 100\times$ Telescope: Discovery of the Strongly Lensed Type II SN 2025mkn at $z=1.37$

We present the discovery of SN 2025mkn, a gravitationally lensed Type II supernova. First detected as a blue transient in ZTF, 0.83$^{\prime\prime}$ from a $z=0.42$ elliptical galaxy, follow-up SNIFS/UH2.2m and LRIS/Keck spectra revealed absorption lines at $z=1.371$. Later JWST NIRCam imaging shows that the bright transient is a close pair of point sources separated by $\sim 0.07^{\prime\prime}$, and a 30 times fainter counterimage opposite the lens, for which NIRSpec reveals strong H$α$ emission also at $z=1.371$. The light curves and spectra are consistent with the Type II supernova source being magnified $\gtrsim 100$ times, with $\sim 250$ required to reconcile its luminosity with that of nearby events such as SN 2023ixf. Lens models are consistent with such high magnifications, and always show that the faint image arrived first (undetected in earlier ZTF imaging), consistent with the later spectral phase of this fainter image. A fourth image is also predicted and possibly detected in the NIRSpec data. Light-curve-based time-delay measurements are not possible due to the first image being the faintest; however, the resolved NIRSpec spectra offer a future opportunity for time-delay cosmography through supernova phase measurements.

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arXiv2026

The velocity field of our Milky Way outer stellar halo based on DESI DR2

Using 64,000 halo K giants from Dark Energy Spectroscopic Instrument (DESI) second Data Release (DR2), we decompose the Milky Way (MW) stellar halo between 3 and 160 kpc into metal-rich (MR) and metal-poor (MP) components via a Gaussian mixture model (GMM). The two populations are nearly equal in number but chemically and kinematically distinct: MR stars occupy highly radial orbits with velocity anisotropy of beta ~0.94 and metallicity dispersion sigma([Fe/H]) ~0.17 dex, without obvious dependence on distance, and are mainly contributed by Gaia-Sausage/Enceladus (GSE) debris. MR component dominates the inner 30 kpc and re-emerges beyond 50 kpc, implying GSE debris can extend to ~70-80 kpc. MP stars exhibit a weaker radial bias of beta ~0.46, decreasing to -0.5 beyond 80 kpc, and with a larger metallicity dispersion of sigma([Fe/H]) ~0.46 dex, showing signatures of multiple minor mergers. Both components exhibit net prograde rotation at ~10-30 kpc with a stronger azimuthal signal in the MP population. The non-equilibrium motions of the outer halo (>50 kpc) are quantified with a dipole-plus-contraction velocity field. We find that the outer halo is simultaneously contracting (~-19 km/s, distance-independent) and subject to reflex motions (increases from -19 to -44 km/s with radius), reflecting the perturbation from the Large Magellanic Cloud (LMC). We also confirm a linear dependence of mean polar velocity for the outer stellar halo on the dipole velocity field, a direct consequence of the LMC and MW interaction. Our results provide a quantitative distance-resolved description of the MW's last major accretion event and its ongoing response to the first infall of the LMC.

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arXiv2026

Nonlinear Information from DESI Luminous Red Galaxies: An Emulator-Based Analysis of Pre- and Post-Reconstruction Power Spectra

We present joint measurements of the pre- and post-reconstruction power spectra, $P_{\rm pre}$ and $P_{\rm post}$, together with their cross-power spectrum, $P_{\rm cross}$, for the Luminous Red Galaxies (LRGs) in the DESI Data Release 1 (DR1). We jointly analyse these observables with an emulator-based full-shape modeling framework, thereby, for the first time, we extract complementary nonlinear information from the galaxy density field before and after reconstruction in real survey data. Specifically, including $P_{\rm post}$ and $P_{\rm cross}$ in addition to $P_{\rm pre}$ (hereafter $P_{\rm all}$) yields an improvement of approximately $18$-$27\%$ in the $σ_8$ constraint in both $Λ$CDM and $w$CDM, depending on the redshift bin, relative to the $P_{\rm pre}$-only analysis with the cosmic microwave background distance priors (hereafter CMB). In $w$CDM, the joint CMB+$P_{\rm all}$ analysis can tighten the constraints on $w$ by approximately $5$-$15\%$ across the two LRG redshift bins, compared to the CMB+$P_{\rm pre}$ combination. Further incorporating the Type Ia supernova dataset and comparing the cosmological constraints in $w$CDM from each individual power-spectrum component with those from the full combination, we find that $P_{\rm all}$ consistently provides the tightest constraints. From the joint CMB+$P_{\rm all}$+DES-Dovekie dataset, we obtain $Ω_m = 0.314 \pm 0.0048$ and $w = -0.988 \pm 0.023$ for the \texttt{LRG1} sample, and $Ω_m = 0.318 \pm 0.0046$ and $w = -0.988 \pm 0.025$ for \texttt{LRG2}. These results demonstrate that combining pre- and post-reconstruction power spectra with their cross-correlation enables DESI to harvest additional nonlinear information, leading to tighter constraints on cosmological parameters.

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arXiv2026

Bayesian Component Separation for DESI LAE Automated Spectroscopic Redshifts and Photometric Targeting

Lyman Alpha Emitters (LAEs) are valuable high-redshift cosmological probes traditionally identified using specialized narrow-band photometric surveys. In ground-based spectroscopy, it can be difficult to distinguish the sharp LAE peak from residual sky emission lines using automated methods, leading to misclassified redshifts. We present a Bayesian spectral component separation technique to automatically determine spectroscopic redshifts for LAEs while marginalizing over sky residuals. We use visually inspected spectra of LAEs obtained using the Dark Energy Spectroscopic Instrument (DESI) to create a data-driven prior and can determine redshift by jointly inferring sky residual, LAE, and residual components for each individual spectrum. We demonstrate this method on 881 spectroscopically observed $z = 2-4$ DESI LAE candidate spectra and determine their redshifts with $>$90% accuracy when validated against visually inspected redshifts. Using the $Δχ^2$ value from our pipeline as a proxy for detection confidence, we then explore potential survey design choices and implications for targeting LAEs with medium-band photometry. This method allows for scalability and accuracy in determining redshifts from DESI spectra, and the results provide recommendations for LAE targeting in anticipation of future high-redshift spectroscopic surveys.

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arXiv2026

Detection of the Pairwise Kinematic Sunyaev-Zel'dovich Effect and Pairwise Velocity with DESI DR1 Galaxies and ACT DR6 and Planck CMB Data

We present a 9.3-sigma detection of the pairwise kinematic Sunyaev-Zeldovich (kSZ) effect by combining a sample of 913,286 Luminous Red Galaxies (LRGs) from the Dark Energy Spectroscopic Instrument Data Release 1 (DESI DR1) catalog and co-added Atacama Cosmology Telescope (ACT DR6) and Planck cosmic microwave background (CMB) temperature maps. This represents the highest-significance pairwise kSZ measurement to date. The analysis uses three ACT CMB temperature maps: co-added 150 GHz, total frequency maps, and a component-separated Internal Linear Combination (ILC) map, all of which cover 19,000 square degrees of the sky from Advanced ACTPol observations conducted between 2017 and 2022. Comparison of the results of these three maps serves as a consistency check for potential foreground contamination that may depend on the observation frequency. An estimate of the best-fit mass-averaged optical depth is obtained by comparing the pairwise kSZ curve with the linear-theory prediction of the pairwise velocity under the best-fit Planck cosmology, and is compared with predictions from simulations. This estimate serves as a reference point for future comparisons with thermal SZ-derived optical depth measurements for the same DESI cluster samples, which will be presented in a companion paper. Finally, we employ a machine-learning approach trained on simulations to estimate the optical depth for 456,803 DESI LRG-identified clusters within the simulated mass range (greater than about 1e13 solar masses). These are combined with the measured kSZ signal to infer the individual cluster peculiar velocities, providing the opportunity to constrain the behavior of gravity and the dark sector over a range of cosmic scales and epochs.

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arXiv2026

Extremely Metal-Poor Galaxies in DESI DR1: Connections to Galaxies in the Early Universe

Extremely Metal-Poor Galaxies (XMPGs), defined as having metallicities below 10\% of the solar value, are considered possible local analogs to primordial systems and offer a unique window into early galaxy evolution. This study presents a large-scale search for XMPGs using data from the Dark Energy Spectroscopic Instrument DR1, systematically evaluating their resemblance to high-redshift galaxies. From a parent sample of over 14 million galaxies, we identify 656 (551 new) confirmed XMPGs and 767 (670 new) high-quality candidates via the direct $T_{\mathrm{e}}$ method. Results reveal that XMPGs follow a distinct star-forming main sequence (SFMS) that is elevated and shallower than that of the comparing star-forming galaxies. Notably, at higher stellar masses ($M_{\star} > 10^{7.5} M_{\odot}$), the XMPG SFMS converges with the sequence observed in high-redshift galaxies by James Webb Space Telescope (JWST), indicating that mature XMPGs sustain star formation rates comparable to their primordial counterparts. Furthermore, XMPGs consistently deviate below the local fundamental metallicity relation, mirroring high-redshift galaxy behavior. These findings demonstrate that XMPGs not only exhibit low metallicities but also preserve scaling relations characteristic of the early Universe, confirming their potential value as local laboratories for studying early galaxy formation processes.

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arXiv2026

The Extremely Large Telescope Interferometer

The ELTI concept capitalizes on recent breakthroughs in large-format SPAD (Single-Photon Avalanche Diode) imaging sensors, combining them with the unprecedented collecting area and segmented architecture of the ELT to deliver a fundamentally new observational capability for the 2040s: visible-light intensity interferometry with ELT-scale angular resolution and quantum-limited temporal sampling. By uniting three transformative innovations - segmented sub-pupil beam combination, megapixel SPAD arrays with picosecond time resolution, and high-dispersion spectroscopy - ELTI opens an entirely new region of observational parameter space in angular resolution, spectral bandwidth, and temporal precision. This capability enables true milliarcsecond imaging of stellar surfaces, direct probes of extreme-gravity and strong electromagnetic-field environments around compact objects, precision studies of accretion physics, and even the potential detection of Earth-sized exoplanets through minute visibility modulations. ELTI thus positions the ELT as the world-leading facility for ultra-high-resolution optical astronomy in the coming decades.

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arXiv2026

The Milky Way stellar halo is twisted and doubly broken: insights from DESI DR2 Milky Way Survey observation

Using K giants from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI) Milky Way (MW) Survey, we measure the shape, orientation, radial profile, and density anisotropies of the MW stellar halo over 8 kpc$<r_\mathrm{GC}<200$ kpc. We identify a triaxial stellar halo (axes ratio $10:8:7$), 43 degrees tilted from the disk, showing two break radii at $\sim16$ kpc and $\sim76$ kpc, likely associated with Gaia-Sausage/Enceladus (GSE) and Large Magellanic Cloud (LMC), respectively. The inner stellar halo ($<30$ kpc) is oblate and aligned with the disk, whereas the outer stellar halo becomes prolate and perpendicular to the disk, consistent with the Vast Polar Structure of MW satellites. The twisted halo may arise from the disk-halo angular momentum shift triggered by the infall of a massive satellite. The anisotropic density distribution of the stellar halo is also measured, with successful re-identification of the Hercules-Aquila Cloud South/North (HAC-N/-S) and Virgo overdensities (VOD). Break radii are found at 15/30 kpc for VOD/HAC-N(-S). We identify the LMC transient density wake with a break radius at 60 kpc in the Pisces overdensity region. We also find new observational evidence of the LMC collective density wake, by showing a break radius at $\sim$100 kpc in the northern Galactic cap with a clear density peak at 90 kpc. In the end, we found that more metal-poor halo stars are more radially extended. Our results provide important clues to the assembly and evolution of the MW stellar halo under the standard cosmic structure formation framework.

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arXiv2026

First Detection of the Baryon Acoustic Oscillation (BAO) Feature in the 3-Point Correlation Function of DESI DR1 Luminous Red Galaxies

We present the first detection of the 3-Point Correlation Function (3PCF) Baryon Acoustic Oscillation (BAO) signal from the DESI Data Release 1 (DR1) sample of Luminous Red Galaxies (LRGs), which contains over 2.1 million galaxies. Our analysis is based on a tree-level redshift-space bispectrum template, which is then transformed to position space using the Fast Fourier Transform on Logarithmic scales (FFTLog) algorithm. We detect the BAO feature with a significance of approximately $8.1σ$ using the EZmock covariance matrix and $8.5σ$ using the analytical covariance matrix, for the full LRG redshift range ($0.4<z<1.1$), denoted as the $z_{\rm full}$ sample. We use the Abacus altMTL mocks, the most precise DESI DR1 mock catalogs currently available, to validate our model. We find that our model fits the mocks well, with a small offset of $0.6\%$ in the recovered BAO scale, which we treat as a systematic error due to modeling. We measure the angle-averaged distance, $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.88 \pm 0.27$ ($1.72\%$ precision) when using the covariance matrix estimated from EZmocks and $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.72 \pm 0.18$ ($1.12\%$ precision) when using the analytical Gaussian covariance matrix. Our results show excellent agreement with the DESI DR1 2PCF BAO measurements as well. We also explore several other ways to estimate the error and find between $1.7$--$2.2\%$ precision on the BAO scale from the EZmock covariance matrix and between $1.1$--$1.5\%$ precision from the analytical covariance matrix. This work represents the first detection of the BAO feature in the DESI 3PCF, establishing its ability to probe the expansion history of the Universe with future DESI 3PCF measurements.

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arXiv2026

Measurements of the Thermal Sunyaev-Zel'dovich Effect with ACT and DESI Luminous Red Galaxies

Cosmic Microwave Background (CMB) photons scatter off the free-electron gas in galaxies and clusters, allowing us to use the CMB as a backlight to probe the gas in and around low-redshift galaxies. The thermal Sunyaev-Zel'dovich effect, sourced by hot electrons in high-density environments, measures the thermal pressure of the target objects, shedding light on halo thermodynamics and galaxy formation and providing a path toward understanding the baryon distribution around cosmic structures. We use a combination of high-resolution CMB maps from the Atacama Cosmology Telescope (ACT) and photometric luminous red galaxy (LRG) catalogues from the Dark Energy Spectroscopic Instrument (DESI) to measure the thermal Sunyaev-Zel'dovich signal in four redshift bins from $z=0.4$ to $z=1.2$, with a combined detection significance of 19$σ$ when stacking on the fiducial CMB Compton-$y$ map. We discuss possible sources of contamination, finding that residual dust emission associated with the target galaxies is important and limits current analyses. We discuss several mitigation strategies and quantify the residual modelling uncertainty. This work complements closely related measurements of the kinematic Sunyaev-Zel'dovich and weak lensing of the same galaxies.

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arXiv2026

A redshift-independent theoretical halo mass function validated with Uchuu simulations

We present a new theoretical framework for the halo mass function (HMF) that accurately predicts the abundance of dark matter haloes across an exceptionally wide range in mass and redshift. Building on a generalised Press & Schechter model and triaxial collapse (GPS+), we predict the HMF in terms of the variance of the linear density field, with only a weak explicit dependence on halo mass and no explicit dependence on redshift. The GPS+ model naturally provides the correct normalization and high-mass behaviour without requiring empirical fitting. We calibrate and validate the GPS+ model using the Uchuu N-body simulation suite, which combines large cosmological volume and high mass resolution under Planck cosmology. Using six simulations with up to 300 realizations, we obtain precision HMF measurements spanning halo masses in the range 6.5 < log($M_{\rm 200m}$/[h$^{-1}$ $M_{\odot}$]) <16 over 0 < z < 20, with reduced cosmic variance. Across this full domain, the GPS+ model reproduces the simulated HMF with deviations typically below 10-20%. Comparison with the Sheth-Tormen (ST) model shows similar performance at z < 2, but markedly improved agreement at higher redshifts, where ST can deviate by 70-80% while our model remains within ~20%. Finally, we assess the impact of the halo mass definition: adopting the evolving virial overdensity of Bryan & Norman (1998) worsens agreement at low redshift and high masses, whereas M200m yields a more universal, nearly redshift-independent HMF.

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