arXiv subjects

Etienne Burtin

Publications and source records attributed to Etienne Burtin.

At least 19 recordsLinked to original sources

arXiv2026

WST, the wide-field spectroscopic telescope: progress on the design of the instruments

WST, the Wide-field Spectroscopic Telescope is a proposed new facility that will provide a transformational gain in spectroscopic survey capability over existing facilities. The WST is a 12 metre class telescope equipped with instrumentation to provide simultaneous observations in both multiple-object spectroscopy and integral field spectroscopy modes. This paper will describe the status of the instruments being designed for the WST, the fibre positioner module, the low and high-resolution multiple object spectrographs, the integral field spectrograph, disperser technology, sustainable detector and cryostat technology, and the calibration system. An overview of the overall layout of the instruments within the WST facility will be provided.

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arXiv2026

The Wide-field Spectroscopic Telescope (WST): design trade-offs for the low-resolution multi-object spectrograph instrument

The Wide-field Spectroscopic Telescope (WST) is a planned 12-meter-class dedicated spectroscopic facility designed to address key scientific challenges through large spectroscopic surveys. This paper presents design and performance trade-offs for the Low-Resolution Multi-Object Spectrograph (MOS-LR) instrument. With a multiplex of 30,000 covering a field of view of 3.1 square degrees, this instrument will provide unprecedented survey efficiency, an order of magnitude beyond those of current facilities. Covering the 370 to 930 nm range at a resolving power of 3,000 with a sky-projected fiber diameter of 1 arcsec, this instrument faces extreme challenges in design, manufacturing, and maintenance. We present a systematic approach to trading off optical and mechanical design options, taking into account constraints such as volume and mass, but also projected availability of detectors and gratings etc.

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arXiv2026

The Wide-field Spectroscopic Telescope: optical designs for the low-resolution multi-object spectrographs

In MOS Low-Resolution mode, WST has a 'spectral etendue' per fiber (etendue x spectral resolution elements) twice as large as any existing MOS instrument, and a total spectral etendue ~20 times larger. Combined, these present enormous challenges for the spectrograph design. Initial designs were based on (a) a novel F/0.775 Folded Solid Schmidt camera with 6cm detectors, (b) an F/1.15 dioptric camera with 6cm detectors, and (c) an F/1.31 dioptric camera with 9cm detectors, all with YAG field-flatteners. However, the imperative of fast camera speed has greatly diminished, as the projected cost and read-noise of large format CMOS detectors is projected to decrease greatly. The adopted baseline solution has 4 dioptric F/1.64 cameras, each with two doublets, a YAG field lens and 9cm x 9cm detector. Theoretical image quality is 8 microns rms radius. The design seems readily athermalised, potentially allowing passive temperature control. Each spectrograph accepts 500+ fibers. Expected RoM costs (scaled from earlier designs) suggest a total cost <4M Euro per spectrograph.

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arXiv2025

The Impact of Spectroscopic Redshift Errors on Cosmological Measurements

Spectroscopic redshift errors, including redshift uncertainty and catastrophic failures, can bias cosmological measurements from galaxy redshift surveys at sub-percent level. In this work, we investigate their impact on the full-shape analysis using contaminated mock catalogs. We find that redshift uncertainty introduces a scale-dependent damping effect on the power spectrum, which is absorbed by counterterms in clustering model, keeping parameter biases below $5\%$. Catastrophic failures suppress the power spectrum amplitude by an approximately constant factor that scales with the catastrophic rate $f_c$. While this effect is negligible for DESI galaxy populations ($f_c=1\%$), the slitless-like errors, combining redshift uncertainty with $f_c=5\%$ catastrophics, introduce significant biases in cosmological constraints. In this case, we observe $6\%$ to $16\%$ shifts ($\sim2.2σ$ level) in estimating the fractional growth rate $df\equiv f/f^{\rm{fid}}$ and the log primordial amplitude $\ln(10^{10} A_{s})$. Applying the correction factor $(1-f_c)^2$ on the galaxy power spectrum mitigates the bias but weakens the parameter constraints due to new degeneracies. Alternatively, fixing $f_c$ to its expected value restores the constraining power with a modest bias of $1.0σ$. Our results indicate that for space-based slitless surveys such as \textit{Euclid}, at minimum accurate estimation of $f_c$ and its incorporation into the clustering model are essential to get unbiased cosmological inference. Extending to evolving dark energy and massive neutrino cosmologies, redshift errors do not bias the dark energy properties parametrized by $w_0$ and $w_a$, but can degrade constraints on the summed neutrino mass $\sum m_ν$ by up to 80% in the worst case.

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arXiv2025

Analytical and EZmock covariance validation for the DESI 2024 results

The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full Shape, two approaches are usually considered. First: analytical estimates of the covariance matrix use Gaussian approximations and (nonlinear) clustering measurements to estimate the matrix, which allows a relatively fast and computationally cheap way to generate matrices that adapt to an arbitrary clustering measurement. On the other hand, sample covariances are an empirical estimate of the matrix based on en ensemble of clustering measurements from fast and approximate simulations. While more computationally expensive due to the large amount of simulations and volume required, these allow us to take into account systematics that are impossible to model analytically. In this work we compare these two approaches in order to enable DESI's key analyses. We find that the configuration space analytical estimate performs satisfactorily in BAO analyses and its flexibility in terms of input clustering makes it the fiducial choice for DESI's 2024 BAO analysis. On the contrary, the analytical computation of the covariance matrix in Fourier space does not reproduce the expected measurements in terms of Full Shape analyses, which motivates the use of a corrected mock covariance for DESI's Full Shape analysis.

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arXiv2025

The Atacama Cosmology Telescope DR6 and DESI: Structure formation over cosmic time with a measurement of the cross-correlation of CMB Lensing and Luminous Red Galaxies

We present a high-significance cross-correlation of CMB lensing maps from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) with spectroscopically calibrated luminous red galaxies (LRGs) from the Dark Energy Spectroscopic Instrument (DESI). We detect this cross-correlation at a significance of 38$σ$; combining our measurement with the Planck Public Release 4 (PR4) lensing map, we detect the cross-correlation at 50$σ$. Fitting this jointly with the galaxy auto-correlation power spectrum to break the galaxy bias degeneracy with $σ_8$, we perform a tomographic analysis in four LRG redshift bins spanning $0.4 \le z \le 1.0$ to constrain the amplitude of matter density fluctuations through the parameter combination $S_8^\times = σ_8 \left(Ω_m / 0.3\right)^{0.4}$. Prior to unblinding, we confirm with extragalactic simulations that foreground biases are negligible and carry out a comprehensive suite of null and consistency tests. Using a hybrid effective field theory (HEFT) model that allows scales as small as $k_{\rm max}=0.6$ $h/{\rm Mpc}$, we obtain a 3.3% constraint on $S_8^\times = σ_8 \left(Ω_m / 0.3\right)^{0.4} = 0.792^{+0.024}_{-0.028}$ from ACT data, as well as constraints on $S_8^\times(z)$ that probe structure formation over cosmic time. Our result is consistent with the early-universe extrapolation from primary CMB anisotropies measured by Planck PR4 within 1.2$σ$. Jointly fitting ACT and Planck lensing cross-correlations we obtain a 2.7% constraint of $S_8^\times = 0.776^{+0.019}_{-0.021}$, which is consistent with the Planck early-universe extrapolation within 2.1$σ$, with the lowest redshift bin showing the largest difference in mean. The latter may motivate further CMB lensing tomography analyses at $z<0.6$ to assess the impact of potential systematics or the consistency of the $Λ$CDM model over cosmic time.

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arXiv2025

Cosmological constraints from the cross-correlation of DESI Luminous Red Galaxies with CMB lensing from Planck PR4 and ACT DR6

We infer the growth of large scale structure over the redshift range $0.4\lesssim z \lesssim 1$ from the cross-correlation of spectroscopically calibrated Luminous Red Galaxies (LRGs) selected from the Dark Energy Spectroscopic Instrument (DESI) legacy imaging survey with CMB lensing maps reconstructed from the latest Planck and ACT data. We adopt a hybrid effective field theory (HEFT) model that robustly regulates the cosmological information obtainable from smaller scales, such that our cosmological constraints are reliably derived from the (predominantly) linear regime. We perform an extensive set of bandpower- and parameter-level systematics checks to ensure the robustness of our results and to characterize the uniformity of the LRG sample. We demonstrate that our results are stable to a wide range of modeling assumptions, finding excellent agreement with a linear theory analysis performed on a restricted range of scales. From a tomographic analysis of the four LRG photometric redshift bins we find that the rate of structure growth is consistent with $Λ$CDM with an overall amplitude that is $\simeq5-7\%$ lower than predicted by primary CMB measurements with modest $(\sim2σ)$ statistical significance. From the combined analysis of all four bins and their cross-correlations with Planck we obtain $S_8 = 0.765\pm0.023$, which is less discrepant with primary CMB measurements than previous DESI LRG cross Planck CMB lensing results. From the cross-correlation with ACT we obtain $S_8 = 0.790^{+0.024}_{-0.027}$, while when jointly analyzing Planck and ACT we find $S_8 = 0.775^{+0.019}_{-0.022}$ from our data alone and $σ_8 = 0.772^{+0.020}_{-0.023}$ with the addition of BAO data. These constraints are consistent with the latest Planck primary CMB analyses at the $\simeq 1.6-2.2σ$ level, and are in excellent agreement with galaxy lensing surveys.

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arXiv2025

Constraining the phase shift of relativistic species in DESI BAOs

In the early Universe, neutrinos decouple quickly from the primordial plasma and propagate without further interactions. The impact of free-streaming neutrinos is to create a temporal shift in the gravitational potential that impacts the acoustic waves known as baryon acoustic oscillations (BAOs), resulting in a non-linear spatial shift in the Fourier-space BAO signal. In this work, we make use of and extend upon an existing methodology to measure the phase shift amplitude $β_ϕ$ and apply it to the DESI Data Release 1 (DR1) BAOs with an anisotropic BAO fitting pipeline. We validate the fitting methodology by testing the pipeline with two publicly available fitting codes applied to highly precise cubic box simulations and realistic simulations representative of the DESI DR1 data. We find further study towards the methods used in fitting the BAO signal will be necessary to ensure accurate constraints on $β_ϕ$ in future DESI data releases. Using DESI DR1, we present individual measurements of the anisotropic BAO distortion parameters and the $β_ϕ$ for the different tracers, and additionally a combined fit to $β_ϕ$ resulting in $β_ϕ = 2.7 \pm 1.7$. After including a prior on the distortion parameters from constraints using \textit{Planck} we find $β_ϕ = 2.7^{+0.60}_{-0.67} $ suggesting $β_ϕ > 0$ at 4.3$σ$ significance. This result may hint at a phase shift that is not purely sourced from the standard model expectation for $N_{\rm{eff}}$ or could be a upwards statistical fluctuation in the measured $β_ϕ$; this result relaxes in models with additional freedom beyond $Λ$CDM.

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arXiv2024

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Ly$α$ forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and eBOSS, offer independent measurements of baryon acoustic oscillation (BAO) measurements of angular-diameter distances and Hubble distances relative to the sound horizon, $r_d$, from eight different samples and six measurements of the growth rate parameter, $fσ_8$, from redshift-space distortions (RSD). This composite sample is the most constraining of its kind and allows us to perform a comprehensive assessment of the cosmological model after two decades of dedicated spectroscopic observation. We show that the BAO data alone are able to rule out dark-energy-free models at more than eight standard deviations in an extension to the flat, $Λ$CDM model that allows for curvature. When combined with Planck Cosmic Microwave Background (CMB) measurements of temperature and polarization the BAO data provide nearly an order of magnitude improvement on curvature constraints. The RSD measurements indicate a growth rate that is consistent with predictions from Planck primary data and with General Relativity. When combining the results of SDSS BAO and RSD with external data, all multiple-parameter extensions remain consistent with a $Λ$CDM model. Regardless of cosmological model, the precision on $Ω_Λ$, $H_0$, and $σ_8$, remains at roughly 1\%, showing changes of less than 0.6\% in the central values between models. The inverse distance ladder measurement under a o$w_0w_a$CDM yields $H_0= 68.20 \pm 0.81 \, \rm km\, s^{-1} Mpc^{-1}$, remaining in tension with several direct determination methods. (abridged)

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arXiv2024

The DESI One-Percent survey: exploring the Halo Occupation Distribution of Emission Line Galaxies with AbacusSummit simulations

The One-Percent survey of the Dark Energy Spectroscopic Instrument collected ~ 270k emission line galaxies (ELGs) at 0.8 < z < 1.6. The high completeness of the sample allowed the clustering to be measured down to scales never probed before, 0.04 Mpc/h in rp for the projected 2-point correlation function (2PCF) and 0.17 Mpc/h in galaxy pair separation s for the 2PCF monopole and quadrupole. The most striking feature of the measurements is a strong signal at the smallest scales, below 0.2 Mpc/h in rp and 1 Mpc/h in s. We analyze these data in the halo occupation distribution framework. We consider different distributions for central galaxies, a standard power law for satellites with no condition on the presence of a central galaxy and explore several extensions of these models. For all considered models, the mean halo mass of the sample is found to be log10 ~ 11.9. We obtain a satellite mean occupation function which agrees with physically motivated ELG models only if we introduce central-satellite conformity, meaning that the satellite occupation is conditioned by the presence of central galaxies of the same type. To achieve in addition a good modeling of the clustering between 0.1 and 1 Mpc/h in rp, we allow for ELG positioning outside of the halo virial radius and find 0.5% of ELGs residing in the outskirts of halos. Furthermore, the satellite velocity dispersion inside halos is found to be ~ 30% larger than that of the halo dark matter particles. These are the main findings of our work. We investigate assembly bias as a function of halo concentration, local density or local density anisotropies and observe no significant change in our results. We split the data sample in two redshift bins and report no significant evolution with redshift. Lastly, changing the cosmology in the modeling impacts only slightly our results.

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arXiv2023

First Detection of the BAO Signal from Early DESI Data

We present the first detection of the baryon acoustic oscillations (BAO) signal obtained using unblinded data collected during the initial two months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). From a selected sample of 261,291 Luminous Red Galaxies spanning the redshift interval 0.4 < z < 1.1 and covering 1651 square degrees with a 57.9% completeness level, we report a ~5 sigma level BAO detection and the measurement of the BAO location at a precision of 1.7%. Using a Bright Galaxy Sample of 109,523 galaxies in the redshift range 0.1 < z < 0.5, over 3677 square degrees with a 50.0% completeness, we also detect the BAO feature at ~3 sigma significance with a 2.6% precision. These first BAO measurements represent an important milestone, acting as a quality control on the optimal performance of the complex robotically-actuated, fiber-fed DESI spectrograph, as well as an early validation of the DESI spectroscopic pipeline and data management system. Based on these first promising results, we forecast that DESI is on target to achieve a high-significance BAO detection at sub-percent precision with the completed 5-year survey data, meeting the top-level science requirements on BAO measurements. This exquisite level of precision will set new standards in cosmology and confirm DESI as the most competitive BAO experiment for the remainder of this decade.

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arXiv2023

Halo Occupation Distribution of Emission Line Galaxies: fitting method with Gaussian Processes

The halo occupation distribution (HOD) framework is an empirical method to describe the connection between dark matter halos and galaxies, which is constrained by small scale clustering data. Efficient fitting procedures are required to scan the HOD parameter space. This paper describes such a method based on Gaussian Processes to iteratively build a surrogate model of the posterior of the likelihood surface from a reasonable amount of likelihood computations, typically two orders of magnitude less than standard Monte Carlo Markov chain algorithms. Errors in the likelihood computation due to stochastic HOD modelling are also accounted for in the method we propose. We report results of reproducibility, accuracy and stability tests of the method derived from simulation, taking as a test case star-forming emission line galaxies, which constitute the main tracer of the Dark Energy Spectroscopic Instrument and have so far a poorly constrained galaxy-halo connection from observational data.

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arXiv2023

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the growth rate of structure from the small-scale clustering of the luminous red galaxy sample

We measure the small-scale clustering of the Data Release 16 extended Baryon Oscillation Spectroscopic Survey Luminous Red Galaxy sample, corrected for fibre-collisions using Pairwise Inverse Probability weights, which give unbiased clustering measurements on all scales. We fit to the monopole and quadrupole moments and to the projected correlation function over the separation range $7-60\,h^{-1}$Mpc with a model based on the Aemulus cosmological emulator to measure the growth rate of cosmic structure, parameterized by $fσ_8$. We obtain a measurement of $fσ_8(z=0.737)=0.408\pm0.038$, which is $1.4σ$ lower than the value expected from 2018 Planck data for a flat $Λ$CDM model, and is more consistent with recent weak-lensing measurements. The level of precision achieved is 1.7 times better than more standard measurements made using only the large-scale modes of the same sample. We also fit to the data using the full range of scales $0.1-60\,h^{-1}$Mpc modelled by the Aemulus cosmological emulator and find a $4.5σ$ tension in the amplitude of the halo velocity field with the Planck+$Λ$CDM model, driven by a mismatch on the non-linear scales. This may not be cosmological in origin, and could be due to a breakdown in the Halo Occupation Distribution model used in the emulator. Finally, we perform a robust analysis of possible sources of systematics, including the effects of redshift uncertainty and incompleteness due to target selection that were not included in previous analyses fitting to clustering measurements on small scales.

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arXiv2022

The Completed SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: Growth rate of structure measurement from cosmic voids

We present a void clustering analysis in configuration-space using the completed Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 samples. These samples consist of Luminous Red Galaxies (LRG) combined with the high redshift tail of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) DR12 CMASS galaxies (called as LRG+CMASS sample), Emission Line Galaxies (ELG) and quasars (QSO). We build void catalogues from the three eBOSS DR16 samples using a ZOBOV-based algorithm, providing 2,814 voids, 1,801 voids and 4,347 voids in the LRG+CMASS, ELG and QSO samples, respectively, spanning the redshift range $0.6<z<2.2$. We measure the redshift space distortions (RSD) around voids using the anisotropic void-galaxy cross-correlation function and we extract the distortion parameter $β$. We test the methodology on realistic simulations before applying it to the data, and we investigate all our systematic errors on these mocks. We find $β^{\rm LRG}(z=0.74)=0.415\pm0.087$, $β^{\rm ELG}(z=0.85)=0.665\pm0.125$ and $β^{\rm QSO}(z=1.48)=0.313\pm0.134$, for the LRG+CMASS, ELG and QSO sample, respectively. The quoted errors include systematic and statistical contributions. In order to convert our measurements in terms of the growth rate $fσ_8$, we use consensus values of linear bias from the eBOSS DR16 companion papers~\citep{eBOSScosmo}, resulting in the following constraints: $fσ_8(z=0.74)=0.50\pm0.11$, $fσ_8(z=0.85)=0.52\pm0.10$ and $fσ_8(z=1.48)=0.30\pm0.13$. Our measurements are consistent with other measurements from eBOSS DR16 using conventional clustering techniques.

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arXiv2022

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from multi-tracer BAO analysis with galaxies and voids

We construct cosmic void catalogues with the DIVE void finder upon SDSS BOSS DR12 and eBOSS DR16 galaxy samples with BAO reconstruction applied, and perform a joint BAO analysis using different types of galaxies and the corresponding voids. The BAO peak is evident for the galaxy-galaxy, galaxy-void, and void-void correlation functions of all datasets, including the ones cross correlating luminous red galaxy and emission line galaxy samples. Two multi-tracer BAO fitting schemes are then tested, one combining the galaxy and void correlation functions with a weight applied to voids, and the other using a single BAO dilation parameter for all clustering measurements of different tracers. Both methods produce consistent results with mock catalogues, and on average ~10 per cent improvements of the BAO statistical uncertainties are observed for all samples, compared to the results from galaxies alone. By combining the clustering of galaxies and voids, the uncertainties of BAO measurements from the SDSS data are reduced by 5 to 15 per cent, yielding 0.9, 0.8, 1.1, 2.3, and 2.9 per cent constraints on the distance $D_{_{\rm V}}(z)$, at effective redshifts of 0.38, 0.51, 0.70, 0.77, and 0.85, respectively. When combined with BAO measurements from SDSS MGS, QSO, and Ly$α$ samples, as well as the BBN results, we obtain $H_0 = 67.58 \pm 0.91\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$, $Ω_{\rm m} = 0.290 \pm 0.015$, and $Ω_Λh^2 = 0.3241 \pm 0.0079$ in the flat-$Λ$CDM framework, where the 1$\,σ$ uncertainties are around 6, 6, and 17 per cent smaller respectively, compared to constraints from the corresponding anisotropic BAO measurements without voids and LRG-ELG cross correlations.

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arXiv2022

Combined full shape analysis of BOSS galaxies and eBOSS quasars using an iterative emulator

Standard full-shape clustering analyses in Fourier space rely on a fixed power spectrum template, defined at the fiducial cosmology used to convert redshifts into distances, and compress the cosmological information into the Alcock-Paczynski parameters and the linear growth rate of structure. In this paper, we propose an analysis method that operates directly in the cosmology parameter space and varies the power spectrum template accordingly at each tested point. Predictions for the power spectrum multipoles from the TNS model are computed at different cosmologies in the framework of $Λ\rm{CDM}$. Applied to the final eBOSS QSO and LRG samples together with the low-z DR12 BOSS galaxy sample, our analysis results in a set of constraints on the cosmological parameters $Ω_{\rm cdm}$, $H_0$, $σ_8$, $Ω_{\rm b}$ and $n_s$. To reduce the number of computed models, we construct an iterative process to sample the likelihood surface, where each iteration consists of a Gaussian process regression. This method is validated with mocks from N-body simulations. From the combined analysis of the (e)BOSS data, we obtain the following constraints: $σ_8=0.877\pm 0.049$ and $Ω_{\rm m}=0.304^{+0.016}_{-0.010}$ without any external prior. The eBOSS quasar sample alone shows a $3.1σ$ discrepancy compared to the Planck prediction.

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arXiv2021

Angular systematics-free cosmological analysis of galaxy clustering in configuration space

Galaxy redshift surveys are subject to incompleteness and inhomogeneous sampling due to the various constraints inherent to spectroscopic observations. This can introduce systematic errors on the summary statistics of interest, which need to be mitigated in cosmological analysis to achieve high accuracy. Standard practices involve applying weighting schemes based on completeness estimates across the survey footprint, possibly supplemented with additional weighting schemes accounting for density-dependent effects. In this work, we concentrate on pure angular systematics and describe an alternative approach consisting in analysing the galaxy two-point correlation function where angular modes are nulled. By construction, this procedure removes all possible known and unknown sources of angular observational systematics, but also part of the cosmological signal.We use a modified Landy-Szalay estimator for the two-point correlation function that relies on an additional random catalogue where angular positions are randomly drawn from the galaxy catalogue, and provide an analytical model to describe this modified statistic. We test the model by performing an analysis of the full anisotropic clustering in mock catalogues of luminous red and emission-line galaxies at 0.43 < z < 1.1. We find that the model fully accounts for the modified correlation function in redshift space, without introducing new nuisance parameters. The derived cosmological parameters from the analysis of baryon acoustic oscillations and redshift-space distortions display slightly larger statistical uncertainties, mostly for the growth rate of structure parameter fs8 that exhibits a 50% statistical error increase, but free from angular systematic error.

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arXiv2021

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body Mock Challenge for the eBOSS Emission Line Galaxy Sample

Cosmological growth can be measured in the redshift space clustering of galaxies targeted by spectroscopic surveys. Accurate prediction of clustering of galaxies will require understanding galaxy physics which is a very hard and highly non-linear problem. Approximate models of redshift space distortion (RSD) take a perturbative approach to solve the evolution of dark matter and galaxies in the universe. In this paper we focus on eBOSS emission line galaxies (ELGs) which live in intermediate mass haloes. We create a series of mock catalogues using haloes from the Multidark and {\sc Outer Rim} dark matter only N-body simulations. Our mock catalogues include various effects inspired by baryonic physics such as assembly bias and the characteristics of satellite galaxies kinematics, dynamics and statistics deviating from dark matter particles. We analyse these mocks using the TNS RSD model in Fourier space and the CLPT in configuration space. We conclude that these two RSD models provide an unbiased measurement of redshift space distortion within the statistical error of our mocks. We obtain the conservative theoretical systematic uncertainty of $3.3\%$, $1.8\%$ and $1.5\%$ in $fσ_8$, $α_{\parallel}$ and $α_{\bot}$ respectively for the TNS and CLPT models. We note that the estimated theoretical systematic error is an order of magnitude smaller than the statistical error of the eBOSS ELG sample and hence are negligible for the purpose of the current eBOSS ELG analysis.

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