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S. Pires

Publications and source records attributed to S. Pires.

At least 37 records · Page 2Linked to original sources
arXiv2023

Euclid preparation. XXXII. Evaluating the weak lensing cluster mass biases using the Three Hundred Project hydrodynamical simulations

The photometric catalogue of galaxy clusters extracted from ESA Euclid data is expected to be very competitive for cosmological studies. Using state-of-the-art hydrodynamical simulations, we present systematic analyses simulating the expected weak lensing profiles from clusters in a variety of dynamic states and at wide range of redshifts. In order to derive cluster masses, we use a model consistent with the implementation within the Euclid Consortium of the dedicated processing function and find that, when jointly modelling mass and the concentration parameter of the Navarro-Frenk-White halo profile, the weak lensing masses tend to be, on average, biased low by 5-10% with respect to the true mass, up to z=0.5. Using a fixed value for the concentration $c_{200} = 3$, the mass bias is diminished below 5%, up to z=0.7, along with its relative uncertainty. Simulating the weak lensing signal by projecting along the directions of the axes of the moment of inertia tensor ellipsoid, we find that orientation matters: when clusters are oriented along the major axis, the lensing signal is boosted, and the recovered weak lensing mass is correspondingly overestimated. Typically, the weak lensing mass bias of individual clusters is modulated by the weak lensing signal-to-noise ratio, related to the redshift evolution of the number of galaxies used for weak lensing measurements: the negative mass bias tends to be larger toward higher redshifts. However, when we use a fixed value of the concentration parameter, the redshift evolution trend is reduced. These results provide a solid basis for the weak-lensing mass calibration required by the cosmological application of future cluster surveys from Euclid and Rubin.

astro-ph.CO↗
arXiv2023

Euclid: Cosmology forecasts from the void-galaxy cross-correlation function with reconstruction

We investigate the cosmological constraints that can be expected from measurement of the cross-correlation of galaxies with cosmic voids identified in the Euclid spectroscopic survey, which will include spectroscopic information for tens of millions of galaxies over $15\,000$ deg$^2$ of the sky in the redshift range $0.9\leq z<1.8$. We do this using simulated measurements obtained from the Flagship mock catalogue, the official Euclid mock that closely matches the expected properties of the spectroscopic data set. To mitigate anisotropic selection-bias effects, we use a velocity field reconstruction method to remove large-scale redshift-space distortions from the galaxy field before void-finding. This allows us to accurately model contributions to the observed anisotropy of the cross-correlation function arising from galaxy velocities around voids as well as from the Alcock-Paczynski effect, and we study the dependence of constraints on the efficiency of reconstruction. We find that Euclid voids will be able to constrain the ratio of the transverse comoving distance $D_{\rm M}$ and Hubble distance $D_{\rm H}$ to a relative precision of about $0.3\%$, and the growth rate $fσ_8$ to a precision of between $5\%$ and $8\%$ in each of four redshift bins covering the full redshift range. In the standard cosmological model, this translates to a statistical uncertainty $ΔΩ_\mathrm{m}=\pm0.0028$ on the matter density parameter from voids, better than can be achieved from either Euclid galaxy clustering and weak lensing individually. We also find that voids alone can measure the dark energy equation of state to $6\%$ precision.

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arXiv2023

Euclid: Identification of asteroid streaks in simulated images using deep learning

Up to 150000 asteroids will be visible in the images of the ESA Euclid space telescope, and the instruments of Euclid offer multiband visual to near-infrared photometry and slitless spectra of these objects. Most asteroids will appear as streaks in the images. Due to the large number of images and asteroids, automated detection methods are needed. A non-machine-learning approach based on the StreakDet software was previously tested, but the results were not optimal for short and/or faint streaks. We set out to improve the capability to detect asteroid streaks in Euclid images by using deep learning. We built, trained, and tested a three-step machine-learning pipeline with simulated Euclid images. First, a convolutional neural network (CNN) detected streaks and their coordinates in full images, aiming to maximize the completeness (recall) of detections. Then, a recurrent neural network (RNN) merged snippets of long streaks detected in several parts by the CNN. Lastly, gradient-boosted trees (XGBoost) linked detected streaks between different Euclid exposures to reduce the number of false positives and improve the purity (precision) of the sample. The deep-learning pipeline surpasses the completeness and reaches a similar level of purity of a non-machine-learning pipeline based on the StreakDet software. Additionally, the deep-learning pipeline can detect asteroids 0.25-0.5 magnitudes fainter than StreakDet. The deep-learning pipeline could result in a 50% increase in the number of detected asteroids compared to the StreakDet software. There is still scope for further refinement, particularly in improving the accuracy of streak coordinates and enhancing the completeness of the final stage of the pipeline, which involves linking detections across multiple exposures.

astro-ph.EP↗
arXiv2023

Fast multiscale galaxy cluster detection with weak lensing: towards a mass-selected sample

The sensitivity and wide area reached by ongoing and future wide-field optical surveys allows for the detection of an increasing number of galaxy clusters uniquely through their weak lensing (WL) signal. This motivates the development of new methods to analyse the unprecedented volume of data faster and more efficiently. Here we introduce a new multi-scale WL detection method based on application of wavelet filters to the convergence maps. We compare our results to those obtained from four commonly-used single scale approaches based on the application of aperture mass filters to the shear in real and Fourier space. The method is validated on Euclid-like mocks from the DUSTGRAIN-pathfinder simulations. We introduce a new matching procedure that takes into account the theoretical signal-to-noise of detection by WL and the filter size. We perform a complete analysis of the filters, and a comparison of the purity and the completeness of the resulting detected catalogues. We show that equivalent results are obtained when the detection is undertaken in real and Fourier space, and when the algorithms are applied to the shear and the convergence. We show that the multiscale method applied to the convergence is faster and more efficient at detecting clusters than single scale methods applied to the shear. We obtained an increase of 25% in the number of detections while maintaining the same purity compared to the most up-to-date aperture mass filter. We analyse the detected catalogues and quantify the efficiency of the matching procedure, showing in particular that less than 5% of the detections from the multiscale method can be ascribed to line-of-sight alignments. The method is well-adapted to the more sensitive, wider-area, optical surveys that will be available in the near future, and paves the way to cluster samples that are as near as possible to being selected by total matter content.

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arXiv2023

Euclid Preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of $Euclid$-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic ($Ω_{\rm m}$, $σ_8$) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a $4.5$ times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with $Euclid$. The data used in this analysis are publicly released with the paper.

astro-ph.CO↗
arXiv2023

Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes

$\textit{Euclid}$ will provide a powerful compilation of data including spectroscopic redshifts, the angular clustering of galaxies, weak lensing cosmic shear, and the cross-correlation of these last two photometric observables. In this study we extend recently presented $\textit{Euclid}$ forecasts into the Hu-Sawicki $f(R)$ cosmological model, a popular extension of the Hilbert-Einstein action that introduces an universal modified gravity force in a scale-dependent way. Our aim is to estimate how well future $\textit{Euclid}$ data will be able to constrain the extra parameter of the theory, $f_{R0}$, for the range in which this parameter is still allowed by current observations. For the spectroscopic probe, we use a phenomenological approach for the scale dependence of the growth of perturbations in the terms related to baryon acoustic oscillations and redshift-space distortions. For the photometric observables, we use a fitting formula that captures the modifications in the non-linear matter power spectrum caused by the $f(R)$ model. We show that, in an optimistic setting, and for a fiducial value of $f_{R0} = 5 \times 10^{-6}$, $\textit{Euclid}$ alone will be able to constrain the additional parameter $\log f_{R0}$ at the $3\%$ level, using spectroscopic galaxy clustering alone; at the $1.4\%$ level, using the combination of photometric probes on their own; and at the $1\%$ level, using the combination of spectroscopic and photometric observations. This last constraint corresponds to an error of the order of $6 \times 10^{-7}$ at the $1σ$ level on the model parameter $f_{R0} = 5 \times 10^{-6}$. We report also forecasted constraints for $f_{R0} = 5 \times 10^{-5}$ and $f_{R0} = 5 \times 10^{-7}$ and show that in the optimistic scenario, $\textit{Euclid}$ will be able to distinguish these models from $Λ\mathrm{CDM}$ at more than 3$σ$. (abridged)

astro-ph.CO↗
arXiv2023

Euclid: Validation of the MontePython forecasting tools

The Euclid mission of the European Space Agency will perform a survey of weak lensing cosmic shear and galaxy clustering in order to constrain cosmological models and fundamental physics. We expand and adjust the mock Euclid likelihoods of the MontePython software in order to match the exact recipes used in previous Euclid Fisher matrix forecasts for several probes: weak lensing cosmic shear, photometric galaxy clustering, the cross-correlation between the latter observables, and spectroscopic galaxy clustering. We also establish which precision settings are required when running the Einstein-Boltzmann solvers CLASS and CAMB in the context of Euclid. For the minimal cosmological model, extended to include dynamical dark energy, we perform Fisher matrix forecasts based directly on a numerical evaluation of second derivatives of the likelihood with respect to model parameters. We compare our results with those of other forecasting methods and tools. We show that such MontePython forecasts agree very well with previous Fisher forecasts published by the Euclid Collaboration, and also, with new forecasts produced by the CosmicFish code, now interfaced directly with the two Einstein-Boltzmann solvers CAMB and CLASS. Moreover, to establish the validity of the Gaussian approximation, we show that the Fisher matrix marginal error contours coincide with the credible regions obtained when running Monte Carlo Markov Chains with MontePython while using the exact same mock likelihoods. The new Euclid forecast pipelines presented here are ready for use with additional cosmological parameters, in order to explore extended cosmological models.

astro-ph.CO↗
arXiv2023

Euclid preparation. XXIV. Calibration of the halo mass function in $Λ(ν)$CDM cosmologies

Euclid's photometric galaxy cluster survey has the potential to be a very competitive cosmological probe. The main cosmological probe with observations of clusters is their number count, within which the halo mass function (HMF) is a key theoretical quantity. We present a new calibration of the analytic HMF, at the level of accuracy and precision required for the uncertainty in this quantity to be subdominant with respect to other sources of uncertainty in recovering cosmological parameters from Euclid cluster counts. Our model is calibrated against a suite of N-body simulations using a Bayesian approach taking into account systematic errors arising from numerical effects in the simulation. First, we test the convergence of HMF predictions from different N-body codes, by using initial conditions generated with different orders of Lagrangian Perturbation theory, and adopting different simulation box sizes and mass resolution. Then, we quantify the effect of using different halo-finder algorithms, and how the resulting differences propagate to the cosmological constraints. In order to trace the violation of universality in the HMF, we also analyse simulations based on initial conditions characterised by scale-free power spectra with different spectral indexes, assuming both Einstein--de Sitter and standard $Λ$CDM expansion histories. Based on these results, we construct a fitting function for the HMF that we demonstrate to be sub-percent accurate in reproducing results from 9 different variants of the $Λ$CDM model including massive neutrinos cosmologies. The calibration systematic uncertainty is largely sub-dominant with respect to the expected precision of future mass-observation relations; with the only notable exception of the effect due to the halo finder, that could lead to biased cosmological inference.

astro-ph.CO↗
arXiv2023

Euclid: Calibrating photometric redshifts with spectroscopic cross-correlations

Cosmological constraints from key probes of the Euclid imaging survey rely critically on the accurate determination of the true redshift distributions, $n(z)$, of tomographic redshift bins. We determine whether the mean redshift, $ $, of ten Euclid tomographic redshift bins can be calibrated to the Euclid target uncertainties of $σ( )<0.002\,(1+z)$ via cross-correlation, with spectroscopic samples akin to those from the Baryon Oscillation Spectroscopic Survey (BOSS), Dark Energy Spectroscopic Instrument (DESI), and Euclid's NISP spectroscopic survey. We construct mock Euclid and spectroscopic galaxy samples from the Flagship simulation and measure small-scale clustering redshifts up to redshift $z<1.8$ with an algorithm that performs well on current galaxy survey data. The clustering measurements are then fitted to two $n(z)$ models: one is the true $n(z)$ with a free mean; the other a Gaussian Process modified to be restricted to non-negative values. We show that $ $ is measured in each tomographic redshift bin to an accuracy of order 0.01 or better. By measuring the clustering redshifts on subsets of the full Flagship area, we construct scaling relations that allow us to extrapolate the method performance to larger sky areas than are currently available in the mock. For the full expected Euclid, BOSS, and DESI overlap region of approximately 6000 deg$^{2}$, the uncertainties attainable by clustering redshifts exceeds the Euclid requirement by at least a factor of three for both $n(z)$ models considered, although systematic biases limit the accuracy. Clustering redshifts are an extremely effective method for redshift calibration for Euclid if the sources of systematic biases can be determined and removed, or calibrated-out with sufficiently realistic simulations. We outline possible future work, in particular an extension to higher redshifts with quasar reference samples.

astro-ph.CO↗
arXiv2023

Euclid preparation: XXVIII. Modelling of the weak lensing angular power spectrum

This work considers which higher-order effects in modelling the cosmic shear angular power spectra must be taken into account for Euclid. We identify which terms are of concern, and quantify their individual and cumulative impact on cosmological parameter inference from Euclid. We compute the values of these higher-order effects using analytic expressions, and calculate the impact on cosmological parameter estimation using the Fisher matrix formalism. We review 24 effects and find the following potentially need to be accounted for: the reduced shear approximation, magnification bias, source-lens clustering, source obscuration, local Universe effects, and the flat Universe assumption. Upon computing these explicitly, and calculating their cosmological parameter biases, using a maximum multipole of $\ell=5000$, we find that the magnification bias, source-lens clustering, source obscuration, and local Universe terms individually produce significant ($\,>0.25σ$) cosmological biases in one or more parameters, and accordingly must be accounted for. In total, over all effects, we find biases in $Ω_{\rm m}$, $Ω_{\rm b}$, $h$, and $σ_{8}$ of $0.73σ$, $0.28σ$, $0.25σ$, and $-0.79σ$, respectively, for flat $Λ$CDM. For the $w_0w_a$CDM case, we find biases in $Ω_{\rm m}$, $Ω_{\rm b}$, $h$, $n_{\rm s}$, $σ_{8}$, and $w_a$ of $1.49σ$, $0.35σ$, $-1.36σ$, $1.31σ$, $-0.84σ$, and $-0.35σ$, respectively; which are increased relative to the $Λ$CDM due to additional degeneracies as a function of redshift and scale.

astro-ph.CO↗
arXiv2022

Euclid preparation: XXII. Selection of Quiescent Galaxies from Mock Photometry using Machine Learning

The Euclid Space Telescope will provide deep imaging at optical and near-infrared wavelengths, along with slitless near-infrared spectroscopy, across ~15,000 sq deg of the sky. Euclid is expected to detect ~12 billion astronomical sources, facilitating new insights into cosmology, galaxy evolution, and various other topics. To optimally exploit the expected very large data set, there is the need to develop appropriate methods and software. Here we present a novel machine-learning based methodology for selection of quiescent galaxies using broad-band Euclid I_E, Y_E, J_E, H_E photometry, in combination with multiwavelength photometry from other surveys. The ARIADNE pipeline uses meta-learning to fuse decision-tree ensembles, nearest-neighbours, and deep-learning methods into a single classifier that yields significantly higher accuracy than any of the individual learning methods separately. The pipeline has `sparsity-awareness', so that missing photometry values are still informative for the classification. Our pipeline derives photometric redshifts for galaxies selected as quiescent, aided by the `pseudo-labelling' semi-supervised method. After application of the outlier filter, our pipeline achieves a normalized mean absolute deviation of ~< 0.03 and a fraction of catastrophic outliers of ~< 0.02 when measured against the COSMOS2015 photometric redshifts. We apply our classification pipeline to mock galaxy photometry catalogues corresponding to three main scenarios: (i) Euclid Deep Survey with ancillary ugriz, WISE, and radio data; (ii) Euclid Wide Survey with ancillary ugriz, WISE, and radio data; (iii) Euclid Wide Survey only. Our classification pipeline outperforms UVJ selection, in addition to the Euclid I_E-Y_E, J_E-H_E and u-I_E,I_E-J_E colour-colour methods, with improvements in completeness and the F1-score of up to a factor of 2. (Abridged)

astro-ph.IM↗
arXiv2022

Euclid: Cosmological forecasts from the void size function

The Euclid mission $-$ with its spectroscopic galaxy survey covering a sky area over $15\,000 \ \mathrm{deg}^2$ in the redshift range $0.9<z<1.8\ -$ will provide a sample of tens of thousands of cosmic voids. This paper explores for the first time the constraining power of the void size function on the properties of dark energy (DE) from a survey mock catalogue, the official Euclid Flagship simulation. We identify voids in the Flagship light-cone, which closely matches the features of the upcoming Euclid spectroscopic data set. We model the void size function considering a state-of-the art methodology: we rely on the volume conserving (Vdn) model, a modification of the popular Sheth & van de Weygaert model for void number counts, extended by means of a linear function of the large-scale galaxy bias. We find an excellent agreement between model predictions and measured mock void number counts. We compute updated forecasts for the Euclid mission on DE from the void size function and provide reliable void number estimates to serve as a basis for further forecasts of cosmological applications using voids. We analyse two different cosmological models for DE: the first described by a constant DE equation of state parameter, $w$, and the second by a dynamic equation of state with coefficients $w_0$ and $w_a$. We forecast $1σ$ errors on $w$ lower than $10\%$, and we estimate an expected figure of merit (FoM) for the dynamical DE scenario $\mathrm{FoM}_{w_0,w_a} = 17$ when considering only the neutrino mass as additional free parameter of the model. The analysis is based on conservative assumptions to ensure full robustness, and is a pathfinder for future enhancements of the technique. Our results showcase the impressive constraining power of the void size function from the Euclid spectroscopic sample, both as a stand-alone probe, and to be combined with other Euclid cosmological probes.

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arXiv2022

Euclid preparation. XXVII. Covariance model validation for the 2-point correlation function of galaxy clusters

Aims. We validate a semi-analytical model for the covariance of real-space 2-point correlation function of galaxy clusters. Methods. Using 1000 PINOCCHIO light cones mimicking the expected Euclid sample of galaxy clusters, we calibrate a simple model to accurately describe the clustering covariance. Then, we use such a model to quantify the likelihood analysis response to variations of the covariance, and investigate the impact of a cosmology-dependent matrix at the level of statistics expected for the Euclid survey of galaxy clusters. Results. We find that a Gaussian model with Poissonian shot-noise does not correctly predict the covariance of the 2-point correlation function of galaxy clusters. By introducing few additional parameters fitted from simulations, the proposed model reproduces the numerical covariance with 10 per cent accuracy, with differences of about 5 per cent on the figure of merit of the cosmological parameters $Ω_{\rm m}$ and $σ_8$. Also, we find that the cosmology-dependence of the covariance adds valuable information that is not contained in the mean value, significantly improving the constraining power of cluster clustering. Finally, we find that the cosmological figure of merit can be further improved by taking mass binning into account. Our results have significant implications for the derivation of cosmological constraints from the 2-point clustering statistics of the Euclid survey of galaxy clusters.

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arXiv2022

Euclid preparation: XX. The Complete Calibration of the Color-Redshift Relation survey: LBT observations and data release

The Complete Calibration of the Color-Redshift Relation survey (C3R2) is a spectroscopic programme designed to empirically calibrate the galaxy color-redshift relation to the Euclid depth (I_E=24.5), a key ingredient for the success of Stage IV dark energy projects based on weak lensing cosmology. A spectroscopic calibration sample as representative as possible of the galaxies in the Euclid weak lensing sample is being collected, selecting galaxies from a self-organizing map (SOM) representation of the galaxy color space. Here, we present the results of a near-infrared H- and K-bands spectroscopic campaign carried out using the LUCI instruments at the LBT. For a total of 251 galaxies, we present new highly-reliable redshifts in the 1.3<= z <=1.7 and 2<= z<=2.7 ranges. The newly-determined redshifts populate 49 SOM cells which previously contained no spectroscopic measurements and almost double the occupation numbers of an additional 153 SOM cells. A final optical ground-based observational effort is needed to calibrate the missing cells in particular in the redshift range 1.7<= z<=2.7 that lack spectroscopic calibration. In the end, Euclid itself will deliver telluric-free NIR spectra that can complete the calibration.

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arXiv2022

KiDS & Euclid: Cosmological implications of a pseudo angular power spectrum analysis of KiDS-1000 cosmic shear tomography

We present a tomographic weak lensing analysis of the Kilo Degree Survey Data Release 4 (KiDS-1000), using a new pseudo angular power spectrum estimator (pseudo-$C_{\ell}$) under development for the ESA Euclid mission. Over 21 million galaxies with shape information are divided into five tomographic redshift bins, ranging from 0.1 to 1.2 in photometric redshift. We measured pseudo-$C_{\ell}$ using eight bands in the multipole range $76<\ell<1500$ for auto- and cross-power spectra between the tomographic bins. A series of tests were carried out to check for systematic contamination from a variety of observational sources including stellar number density, variations in survey depth, and point spread function properties. While some marginal correlations with these systematic tracers were observed, there is no evidence of bias in the cosmological inference. B-mode power spectra are consistent with zero signal, with no significant residual contamination from E/B-mode leakage. We performed a Bayesian analysis of the pseudo-$C_{\ell}$ estimates by forward modelling the effects of the mask. Assuming a spatially flat $Λ$CDM cosmology, we constrained the structure growth parameter $S_8 = σ_8(Ω_{\rm m}/0.3)^{1/2} = 0.754_{-0.029}^{+0.027}$. When combining cosmic shear from KiDS-1000 with baryon acoustic oscillation and redshift space distortion data from recent Sloan Digital Sky Survey (SDSS) measurements of luminous red galaxies, as well as the Lyman-$α$ forest and its cross-correlation with quasars, we tightened these constraints to $S_8 = 0.771^{+0.006}_{-0.032}$. These results are in very good agreement with previous KiDS-1000 and SDSS analyses and confirm a $\sim 3σ$ tension with early-Universe constraints from cosmic microwave background experiments.

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arXiv2022

Euclid preparation: XIX. Impact of magnification on photometric galaxy clustering

We investigate the importance of lensing magnification for estimates of galaxy clustering and its cross-correlation with shear for the photometric sample of Euclid. Using updated specifications, we study the impact of lensing magnification on the constraints and the shift in the estimation of the best fitting cosmological parameters that we expect if this effect is neglected. We follow the prescriptions of the official Euclid Fisher matrix forecast for the photometric galaxy clustering analysis and the combination of photometric clustering and cosmic shear. The slope of the luminosity function (local count slope), which regulates the amplitude of the lensing magnification, and the galaxy bias have been estimated from the Euclid Flagship simulation.We find that magnification significantly affects both the best-fit estimation of cosmological parameters and the constraints in the galaxy clustering analysis of the photometric sample. In particular, including magnification in the analysis reduces the 1$σ$ errors on $Ω_{\text{m},0}, w_{0}, w_a$ at the level of 20-35%, depending on how well we will be able to independently measure the local count slope. In addition, we find that neglecting magnification in the clustering analysis leads to shifts of up to 1.6$σ$ in the best-fit parameters. In the joint analysis of galaxy clustering, cosmic shear, and galaxy-galaxy lensing, magnification does not improve precision, but it leads to an up to 6$σ$ bias if neglected. Therefore, for all models considered in this work, magnification has to be included in the analysis of galaxy clustering and its cross-correlation with the shear signal ($3\times2$pt analysis) for an accurate parameter estimation.

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arXiv2022

Euclid: Fast two-point correlation function covariance through linear construction

We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy-Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (data-to-random objects ratio M>>1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs of size M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of these. We validate the method with PINOCCHIO simulations in range r = 20-200 Mpc/h, and show that the covariance estimate is unbiased. With M = 50 and with 2 Mpc/h bins, the theoretical speed-up of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and derive a formula for the covariance of covariance.

astro-ph.CO↗
arXiv2022

Euclid: Covariance of weak lensing pseudo-$C_\ell$ estimates. Calculation, comparison to simulations, and dependence on survey geometry

An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-$C_\ell$ estimates of tomographic cosmic shear power spectra. Using two existing publicly available codes in combination, we calculate the full covariance matrix, including mode-coupling contributions arising from both partial sky coverage and non-linear structure growth. For three different sky masks, we compare the theoretical covariance matrix to that estimated from publicly available N-body weak lensing simulations, finding good agreement. We find that as a more extreme sky cut is applied, a corresponding increase in both Gaussian off-diagonal covariance and non-Gaussian super-sample covariance is observed in both theory and simulations, in accordance with expectations. Studying the different contributions to the covariance in detail, we find that the Gaussian covariance dominates along the main diagonal and the closest off-diagonals, but further away from the main diagonal the super-sample covariance is dominant. Forming mock constraints in parameters describing matter clustering and dark energy, we find that neglecting non-Gaussian contributions to the covariance can lead to underestimating the true size of confidence regions by up to 70 per cent. The dominant non-Gaussian covariance component is the super-sample covariance, but neglecting the smaller connected non-Gaussian covariance can still lead to the underestimation of uncertainties by 10--20 per cent. A real cosmological analysis will require marginalisation over many nuisance parameters, which will decrease the relative importance of all cosmological contributions to the covariance, so these values should be taken as upper limits on the importance of each component.

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