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Zhimin Zhou

Publications and source records attributed to Zhimin Zhou.

At least 55 records · Page 3Linked to original sources
arXiv2023

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological $N$-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis. We also provide an optimized package for computing the power spectra and other two-point statistics of an arbitrary galaxy catalog as well as a pipeline for obtaining CV-reduced measurements on any of the AbacusSummit cubic box outputs. We make our scripts publicly available and report a speed improvement of $\sim$10 for a grid size of $N_{\rm mesh} = 256^3$ compared with \texttt{nbodykit}.

astro-ph.CO↗
arXiv2023

Unraveling emission line galaxy conformity at z~1 with DESI early data

Emission line galaxies (ELGs) are now the preeminent tracers of large-scale structure at z>0.8 due to their high density and strong emission lines, which enable accurate redshift measurements. However, relatively little is known about ELG evolution and the ELG-halo connection, exposing us to potential modeling systematics in cosmology inference using these sources. In this paper, we propose a physical picture of ELGs and improve ELG-halo connection modeling using a variety of observations and simulated galaxy models. We investigate DESI-selected ELGs in COSMOS data, and infer that ELGs are rapidly star-forming galaxies with a large fraction exhibiting disturbed morphology, implying that many of them are likely to be merger-driven starbursts. We further postulate that the tidal interactions from mergers lead to correlated star formation in central-satellite ELG pairs, a phenomenon dubbed "conformity." We argue for the need to include conformity in the ELG-halo connection using galaxy models such as IllustrisTNG, and by combining observations such as the DESI ELG auto-correlation, ELG cross-correlation with Luminous Red Galaxies (LRGs), and ELG-cluster cross-correlation. We also explore the origin of conformity using the UniverseMachine model and elucidate the difference between conformity and the well-known galaxy assembly bias effect.

astro-ph.CO↗
arXiv2023

Astrometric Calibration and Performance of the Dark Energy Spectroscopic Instrument Focal Plane

The Dark Energy Spectroscopic Instrument, consisting of 5020 robotic fiber positioners and associated systems on the Mayall telescope at Kitt Peak, Arizona, is carrying out a survey to measure the spectra of 40 million galaxies and quasars and produce the largest 3D map of the universe to date. The primary science goal is to use baryon acoustic oscillations to measure the expansion history of the universe and the time evolution of dark energy. A key function of the online control system is to position each fiber on a particular target in the focal plane with an accuracy of 11$μ$m rms 2-D. This paper describes the set of software programs used to perform this function along with the methods used to validate their performance.

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arXiv2023

The DESI One-Percent Survey: Evidence for Assembly Bias from Low-Redshift Counts-in-Cylinders Measurements

We explore the galaxy-halo connection information that is available in low-redshift samples from the early data release of the Dark Energy Spectroscopic Instrument (DESI). We model the halo occupation distribution (HOD) from z=0.1-0.3 using Survey Validation 3 (SV3; a.k.a., the One-Percent Survey) data of the DESI Bright Galaxy Survey (BGS). In addition to more commonly used metrics, we incorporate counts-in-cylinders (CiC) measurements, which drastically tighten HOD constraints. Our analysis is aided by the Python package, galtab, which enables the rapid, precise prediction of CiC for any HOD model available in halotools. This methodology allows our Markov chains to converge with much fewer trial points, and enables even more drastic speedups due to its GPU portability. Our HOD fits constrain characteristic halo masses tightly and provide statistical evidence for assembly bias, especially at lower luminosity thresholds: the HOD of central galaxies in $z\sim0.15$ samples with limiting absolute magnitude $M_r < -20.0$ and $M_r < -20.5$ samples is positively correlated with halo concentration with a significance of 99.9% and 99.5%, respectively. Our models also favor positive central assembly bias for the brighter $M_r < -21.0$ sample at $z\sim0.25$ (94.8% significance), but there is no significant evidence for assembly bias with the same luminosity threshold at $z\sim0.15$. We provide our constraints for each threshold sample's characteristic halo masses, assembly bias, and other HOD parameters. These constraints are expected to be significantly tightened with future DESI data, which will span an area 100 times larger than that of SV3.

astro-ph.CO↗
arXiv2023

Strong [O III] λ5007 Compact Galaxies Identified from SDSS DR16 and Their Scaling Relations

Green pea galaxies are a special class of star-forming compact galaxies with strong [O III]λ5007 and considered as analogs of high-redshift Lyα-emitting galaxies and potential sources for cosmic reionization. In this paper, we identify 76 strong [O III]λ5007 compact galaxies at z < 0.35 from DR1613 of the Sloan Digital Sky Survey. These galaxies present relatively low stellar mass, high star formation rate, and low metallicity. Both star-forming main sequence relation (SFMS) and mass-metallicity relation (MZR) are investigated and compared with green pea and blueberry galaxies collected from literature. It is found that our strong [O III] λ5007 compact galaxies share common properties with those compact galaxies with extreme star formation and show distinct scaling relations in respect to those of normal star-forming galaxies at the same redshift. The slope of SFMS is higher, indicates that strong [O III]λ5007 compact galaxies might grow faster in stellar mass. The lower MZR implies that they may be less chemically evolved and hence on the early stage of star formation. A further environmental investigation confirms that they inhabit relatively low-density regions. Future largescale spectroscopic surveys will provide more details on their physical origin and evolution.

astro-ph.GA↗
arXiv2023

Detecting and Characterizing Mg II absorption in DESI Survey Validation Quasar Spectra

We present findings of the detection of Magnesium II (Mg II, λ = 2796, 2803 Å) absorbers from the early data release of the Dark Energy Spectroscopic Instrument (DESI). DESI is projected to obtain spectroscopy of approximately 3 million quasars (QSOs), of which over 99% are anticipated to be at redshifts greater than z > 0.3, such that DESI would be able to observe an associated or intervening Mg II absorber illuminated by the background QSO. We have developed an autonomous supplementary spectral pipeline that detects these systems through an initial line-fitting process and then confirms the line properties using a Markov Chain Monte Carlo sampler. Based upon a visual inspection of the resulting systems, we estimate that this sample has a purity greater than 99%. We have also investigated the completeness of our sample in regard to both the signal-to-noise properties of the input spectra and the rest-frame equivalent width (W0) of the absorber systems. From a parent catalog containing 83,207 quasars, we detect a total of 23,921 Mg II absorption systems following a series of quality cuts. Extrapolating from this occurrence rate of 28.8% implies a catalog at the completion of the five-year DESI survey that will contain over eight hundred thousand Mg II absorbers. The cataloging of these systems will enable significant further research because they carry information regarding circumgalactic medium environments, the distribution of intervening galaxies, and the growth of metallicity across the redshift range 0.3 < z < 2.5.

astro-ph.GA↗
arXiv2023

Target Selection for the DESI Peculiar Velocity Survey

We describe the target selection and characteristics of the DESI Peculiar Velocity Survey, the largest survey of peculiar velocities (PVs) using both the fundamental plane (FP) and the Tully-Fisher (TF) relationship planned to date. We detail how we identify suitable early-type galaxies (ETGs) for the FP and suitable late-type galaxies (LTGs) for the TF relation using the photometric data provided by the DESI Legacy Imaging Survey DR9. Subsequently, we provide targets for 373 533 ETGs and 118 637 LTGs within the DESI 5-year footprint. We validate these photometric selections using existing morphological classifications. Furthermore, we demonstrate using survey validation data that DESI is able to measure the spectroscopic properties to sufficient precision to obtain PVs for our targets. Based on realistic DESI fiber assignment simulations and spectroscopic success rates, we predict the final DESI PV Survey will obtain $\sim$133 000 FP-based and $\sim$53 000 TF-based PV measurements over an area of 14 000 $\mathrm{deg^{2}}$. We forecast the ability of using these data to measure the clustering of galaxy positions and PVs from the combined DESI PV and Bright Galaxy Surveys (BGS), which allows for cancellation of cosmic variance at low redshifts. With these forecasts, we anticipate a $4\%$ statistical measurement on the growth rate of structure at $z<0.15$. This is over two times better than achievable with redshifts from the BGS alone. The combined DESI PV and BGS will enable the most precise tests to date of the time and scale dependence of large-scale structure growth at $z<0.15$.

astro-ph.CO↗
arXiv2023

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for Early DESI data

We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of Luminous Red Galaxies (LRG) data collected during the initial two months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel'dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, nontrivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable datasets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

astro-ph.CO↗
arXiv2023

The DESI One-Percent survey: constructing galaxy-halo connections for ELGs and LRGs using auto and cross correlations

In the current Dark Energy Spectroscopic Instrument (DESI) survey, emission line galaxies (ELGs) and luminous red galaxies (LRGs) are essential for mapping the dark matter distribution at $z \sim 1$. We measure the auto and cross correlation functions of ELGs and LRGs at $0.8 0.1$ $\mathrm{Mpc}\,h^{-1}$. We can also reproduce the auto correlations of ELGs at $r_{\mathrm{p}}>0.3$ $\mathrm{Mpc}\,h^{-1}$ ($s>1$ $\mathrm{Mpc}\,h^{-1}$) in real (redshift) space. Although our model has only seven parameters, we show that it can be extended to higher redshifts and reproduces the observed auto correlations of ELGs in the whole range of $0.8<z<1.6$, which enables us to generate a lightcone ELG mock for DESI. With the above model, we further derive halo occupation distributions (HODs) for ELGs which can be used to produce ELG mocks in coarse simulations without resolving subhalos.

astro-ph.GA↗
arXiv2023

Performance of the Quasar Spectral Templates for the Dark Energy Spectroscopic Instrument

Millions of quasar spectra will be collected by the Dark Energy Spectroscopic Instrument (DESI), leading to a four-fold increase in the number of known quasars. High accuracy quasar classification is essential to tighten constraints on cosmological parameters measured at the highest redshifts DESI observes ($z>2.0$). We present the spectral templates for identification and redshift estimation of quasars in the DESI Year 1 data release. The quasar templates are comprised of two quasar eigenspectra sets, trained on spectra from the Sloan Digital Sky Survey. The sets are specialized to reconstruct quasar spectral variation observed over separate yet overlapping redshift ranges and, together, are capable of identifying DESI quasars from $0.05 < z <7.0$. The new quasar templates show significant improvement over the previous DESI quasar templates regarding catastrophic failure rates, redshift precision and accuracy, quasar completeness, and the contamination fraction in the final quasar sample.

astro-ph.IM↗
arXiv2023

PROVABGS: The Probabilistic Stellar Mass Function of the BGS One-Percent Survey

We present the probabilistic stellar mass function (pSMF) of galaxies in the DESI Bright Galaxy Survey (BGS), observed during the One-Percent Survey. The One-Percent Survey was one of DESI's survey validation programs conducted from April to May 2021, before the start of the main survey. It used the same target selection and similar observing strategy as the main survey and successfully observed the spectra and redshifts of 143,017 galaxies in the $r < 19.5$ magnitude-limited BGS Bright sample and 95,499 galaxies in the fainter surface brightness and color selected BGS Faint sample over $z < 0.6$. We derive pSMFs from posteriors of stellar mass, $M_*$, inferred from DESI photometry and spectroscopy using the Hahn et al. (2022a; arXiv:2202.01809) PRObabilistic Value-Added BGS (PROVABGS) Bayesian SED modeling framework. We use a hierarchical population inference framework that statistically and rigorously propagates the $M_*$ uncertainties. Furthermore, we include correction weights that account for the selection effects and incompleteness of the BGS observations. We present the redshift evolution of the pSMF in BGS as well as the pSMFs of star-forming and quiescent galaxies classified using average specific star formation rates from PROVABGS. Overall, the pSMFs show good agreement with previous stellar mass function measurements in the literature. Our pSMFs showcase the potential and statistical power of BGS, which in its main survey will observe >100$\times$ more galaxies. Moreover, we present the statistical framework for subsequent population statistics measurements using BGS, which will characterize the global galaxy population and scaling relations at low redshifts with unprecedented precision.

astro-ph.GA↗
arXiv2023

The DESI One-Percent Survey: Exploring the Halo Occupation Distribution of Luminous Red Galaxies and Quasi-Stellar Objects with AbacusSummit

We present the first comprehensive Halo Occupation Distribution (HOD) analysis of the DESI One-Percent survey Luminous Red Galaxy (LRG) and Quasi-Stellar Object (QSO) samples. We constrain the HOD of each sample and test possible HOD extensions by fitting the redshift-space galaxy 2-point correlation functions in 0.15 < r < 32 Mpc/h in a set of fiducial redshift bins. We use AbacusSummit cubic boxes at Planck 2018 cosmology as model templates and forward model galaxy clustering with the AbacusHOD package. We achieve good fits with a standard HOD model with velocity bias, and we find no evidence for galaxy assembly bias or satellite profile modulation at the current level of statistical uncertainty. For LRGs in 0.4 < z < 0.6, we infer a satellite fraction of fsat = 11+-1%, a mean halo mass of log10 Mh = 13.40+0.02-0.02, and a linear bias of blin = 1.93+0.06-0.04. For LRGs in 0.6 < z < 0.8, we find fsat = 14+-1%, log10 Mh = 13.24+0.02-0.02, and blin = 2.08+0.03-0.03. For QSOs, we infer fsat = 3+8-2%, log10 Mh = 12.65+0.09-0.04, and blin = 2.63+0.37-0.26 in redshift range 0.8 < z < 2.1. Using these fits, we generate a large suite of high-fidelity galaxy mocks. We also study the redshift-evolution of the DESI LRG sample from z = 0.4 up to z = 1.1, revealing significant and interesting trends in mean halo mass, linear bias, and satellite fraction.

astro-ph.CO↗
arXiv2023

Target Selection and Sample Characterization for the DESI LOW-Z Secondary Target Program

We introduce the DESI LOW-Z Secondary Target Survey, which combines the wide-area capabilities of the Dark Energy Spectroscopic Instrument (DESI) with an efficient, low-redshift target selection method. Our selection consists of a set of color and surface brightness cuts, combined with modern machine learning methods, to target low-redshift dwarf galaxies ($z$ < 0.03) between $19 < r < 21$ with high completeness. We employ a convolutional neural network (CNN) to select high-priority targets. The LOW-Z survey has already obtained over 22,000 redshifts of dwarf galaxies (M$_* < 10^9$ M$_\odot$), comparable to the number of dwarf galaxies discovered in SDSS-DR8 and GAMA. As a spare fiber survey, LOW-Z currently receives fiber allocation for just ~50% of its targets. However, we estimate that our selection is highly complete: for galaxies at $z < 0.03$ within our magnitude limits, we achieve better than 95% completeness with ~1% efficiency using catalog-level photometric cuts. We also demonstrate that our CNN selections $z<0.03$ galaxies from the photometric cuts subsample at least ten times more efficiently while maintaining high completeness. The full five-year DESI program will expand the LOW-Z sample, densely mapping the low-redshift Universe, providing an unprecedented sample of dwarf galaxies, and providing critical information about how to pursue effective and efficient low-redshift surveys.

astro-ph.GA↗
arXiv2023

The Optical Corrector for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) is currently measuring the spectra of 40\,million galaxies and quasars, the largest such survey ever made to probe the nature of cosmological dark energy. The 4-meter Mayall telescope at Kitt Peak National Observatory has been adapted for DESI, including the construction of a 3.2-degree diameter prime focus corrector that focuses astronomical light onto a 0.8-meter diameter focal surface with excellent image quality over the DESI bandpass of 360-980nm. The wide-field corrector includes six lenses, as large as 1.1-meters in diameter and as heavy as 237\,kilograms, including two counter-rotating wedged lenses that correct for atmospheric dispersion over Zenith angles from 0 to 60 degrees. The lenses, cells, and barrel assembly all meet precise alignment tolerances on the order of tens of microns. The barrel alignment is maintained throughout a range of observing angles and temperature excursions in the Mayall dome by use of a hexapod, which is itself supported by a new cage, ring, and truss structure. In this paper we describe the design, fabrication, and performance of the new corrector and associated structure, focusing on how they meet DESI requirements. In particular we describe the prescription and specifications of the lenses, design choices and error budgeting of the barrel assembly, stray light mitigations, and integration and test at the Mayall telescope. We conclude with some validation highlights that demonstrate the successful corrector on-sky performance, and list some lessons learned during the multi-year fabrication phase.

astro-ph.IM↗
arXiv2023

Astrometric Calibration of the Beijing$-$Arizona Sky Survey

We present the astrometric calibration of the Beijing-Arizona Sky Survey (BASS). The BASS astrometry was tied to the International Celestial Reference Frame via the \emph{Gaia} Data Release 2 reference catalog. For effects that were stable throughout the BASS observations, including differential chromatic refraction and the low charge transfer efficiency of the CCD, we corrected for these effects at the raw image coordinates. Fourth-order polynomial intermediate longitudinal and latitudinal corrections were used to remove optical distortions. The comparison with the \emph{Gaia} catalog shows that the systematic errors, depending on color or magnitude, are less than 2 milliarcseconds (mas). The position systematic error is estimated to be about $-0.01\pm0.7$ mas in the region between 30 and 60 degrees of declination and up to $-0.07 \pm 0.9$ mas in the region north of declination 60 degrees.

astro-ph.IM↗
arXiv2023

Synthetic light cone catalogues of modern redshift and weak lensing surveys with AbacusSummit

The joint analysis of different cosmological probes, such as galaxy clustering and weak lensing, can potentially yield invaluable insights into the nature of the primordial Universe, dark energy and dark matter. However, the development of high-fidelity theoretical models that cover a wide range of scales and redshifts is a necessary stepping-stone. Here, we present public high-resolution weak lensing maps on the light cone, generated using the $N$-body simulation suite AbacusSummit in the Born approximation, and accompanying weak lensing mock catalogues, tuned via fits to the Early Data Release small-scale clustering measurements of the Dark Energy Spectroscopic Instrument (DESI). Available in this release are maps of the cosmic shear, deflection angle and convergence fields at source redshifts ranging from $z = 0.15$ to 2.45 with $Δz = 0.05$ as well as CMB convergence maps ($z \approx 1090$) for each of the 25 ${\tt base}$-resolution simulations ($L_{\rm box} = 2000\,h^{-1}{\rm Mpc}$, $N_{\rm part} = 6912^3$) as well as for the two ${\tt huge}$ simulations ($L_{\rm box} = 7500\,h^{-1}{\rm Mpc}$, $N_{\rm part} = 8640^3$) at the fiducial AbacusSummit cosmology ($Planck$ 2018). The pixel resolution of each map is 0.21 arcmin, corresponding to a HEALPiX $N_{\rm side}$ of 16384. The sky coverage of the ${\tt base}$ simulations is an octant until $z \approx 0.8$ (decreasing to about 1800 deg$^2$ at $z \approx 2.4$), whereas the ${\tt huge}$ simulations offer full-sky coverage until $z \approx 2.2$. Mock lensing source catalogues are sampled matching the ensemble properties of the Kilo-Degree Survey, Dark Energy Survey, and Hyper-Suprime Cam weak lensing datasets. The produced mock catalogues are validated against theoretical predictions for various clustering and lensing statistics such as galaxy clustering multipoles, galaxy-shear and shear-shear, showing excellent agreement.

astro-ph.CO↗
arXiv2023

SN 2016ije: An SN 2002es-like Type Ia Supernova Exploded in a Metal-poor and Low-surface Brightness Galaxy

We have conducted photometric and spectroscopic observations of the peculiar Type Ia supernova (SN Ia) 2016ije that was discovered through the Tsinghua-NAOC Transient Survey. This peculiar object exploded in the outskirts of a metal-poor, low-surface brightness galaxy (i.e., $M_{g}$ = $-$14.5 mag). Our photometric analysis reveals that SN 2016ije is subluminous ($M_{B,\rm{max}}$ = $-$17.65$\pm$0.06 mag) but exhibits relatively broad light curves ($Δm_{15}(B)$ = 1.35$\pm$0.14 mag), similar to the behavior of SN 2002es. Our analysis of the bolometric light curve indicates that only 0.14$\pm$0.04 $M_{\odot}$ of $^{56}$Ni was synthesized in the explosion of SN 2016ije, which suggests a less energetic thermonuclear explosion when compared to normal SNe Ia, and this left a considerable amount of unburned materials in the ejecta. Spectroscopically, SN 2016ije resembles other SN 2002es-like SNe Ia, except that the ejecta velocity inferred from its carbon absorption line ($\sim$ 4500 km s$^{-1}$) is much lower than that from silicon lines ($\sim$ 8300 km s$^{-1}$) at around the maximum light. Additionally, most of the absorption lines are broader than other 02es-like SNe Ia. These peculiarities suggest the presence of significant unburned carbon in the inner region and a wide line-forming region along the line of sight. These characteristics suggest that SN 2016ije might originate from the violent merger of a white dwarf binary system, when viewed near an orientation along the iron-group-element cavity caused by the companion star.

astro-ph.HE↗
arXiv2023

Planting a Lyman alpha forest on AbacusSummit

The full-shape correlations of the Lyman alpha (Ly$α$) forest contain a wealth of cosmological information through the Alcock-Paczyński effect. However, these measurements are challenging to model without robustly testing and verifying the theoretical framework used for analyzing them. Here, we leverage the accuracy and volume of the $N$-body simulation suite \textsc{AbacusSummit} to generate high-resolution Ly$α$ skewers and quasi-stellar object (QSO) catalogs. One of the main goals of our mocks is to aid in the full-shape Ly$α$ analysis planned by the Dark Energy Spectroscopic Instrument (DESI) team. We provide optical depth skewers for six of the fiducial cosmology base-resolution simulations ($L_{\rm box} = 2\,h^{-1}{\rm Gpc}$, $N = 6912^3$) at $z = 2.5$. We adopt a simple recipe based on the Fluctuating Gunn-Peterson Approximation (FGPA) for constructing these skewers from the matter density in an $N$-body simulation and calibrate it against the 1D and 3D Ly$α$ power spectra extracted from the hydrodynamical simulation IllustrisTNG (TNG; $L_{\rm box} = 205\,h^{-1}{\rm Mpc}$, $N = 2500^3$). As an important application, we study the non-linear broadening of the baryon acoustic oscillation (BAO) peak and show the cross-correlation between DESI-like QSOs and our Ly$α$ forest skewers. We find differences on small scales between the Kaiser approximation prediction and our mock measurements of the Ly$α$$\times$QSO cross-correlation, which would be important to account for in upcoming analyses. The \textsc{AbacusSummit} Ly$α$ forest mocks open up the possibility for improved modelling of cross correlations between Ly$α$ and cosmic microwave background (CMB) lensing and Ly$α$ and QSOs, and for forecasts of the 3-point Ly$α$ correlation function. Our catalogues and skewers are publicly available on Globus.

astro-ph.CO↗