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At least 289 records · Page 16

Galaxy assembly bias and large-scale distribution: a comparison between IllustrisTNG and a semi-analytic model

In this work, we compare large scale structure observables for stellar mass selected samples at z = 0, as predicted by two galaxy models, the hydrodynamical simulation IllustrisTNG and the Santa-Cruz semi-analytic model (SC-SAM). Although both models have been independently calibrated to match observations, rather than each other, we find good agreement between the two models for two-point clustering and galaxy assembly bias signatures. The models also show a qualitatively similar response of occupancy and clustering to secondary halo parameters other than mass, such as formation history and concentration, although with some quantitative differences. Thus, our results demonstrate that the galaxy–halo relationships in SC-SAM and TNG are quite similar to first order. However, we also find areas in which the models differ. For example, we note a strong correlation between halo gas content and environment in TNG, which is lacking in the SC-SAM, as well as differences in the occupancy predictions for low-mass haloes. Moreover, we show that higher order statistics, such as cumulants of the density field, help us to accurately describe the galaxy distribution and discriminate between models that show degenerate behaviour for two-point statistics. Our results suggest that SAMs are a promising cost-effective and intuitive method for generating mock catalogues for next generation cosmological surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Blast from the past: constraining progenitor models of SN 1972E

ABSTRACT We present a novel technique to study Type Ia supernovae (SNe Ia) by constraining surviving companions of historical extragalactic SN by combining archival photographic plates and Hubble Space Telescope(HST) imaging. We demonstrate this technique for Supernova 1972E, the nearest known SN Ia in 125 yr. Some models of SNe Ia describe a white dwarf with a non-degenerate companion that donates enough mass to trigger thermonuclear detonation. Hydrodynamic simulations and stellar evolution models show that these donor stars will survive the explosion, and show increased luminosity for at least a 1000 yr. Thus, late-time observations of the exact location of a supernova can constrain the presence of a surviving donor star and progenitor models. We find the explosion site of SN 1972E by analysing 17 digitized photographic plates taken with the European Southern Observatory 1-m Schmidt and 1 plate taken with the Cerro Tololo Inter-American Observatory 1.5-m telescope. Using the Gaia eDR3 catalogue to determine Supernova 1972E’s location yields: α = 13h39m52${_{.}^{\rm s}}$708 ± 0${_{.}^{\rm s}}$004 and δ = −31°40’9${_{.}^{\prime\prime}}$00 ± 0${_{.}^{\prime\prime}}$04 (ICRS). In 2005, HST/ACS imaged the host galaxy of SN 1972E with the F435W, F555W, and F814W filters covering the explosion site. The nearest detected source is offset by 3.0 times our positional precision, and is inconsistent with the colours expected of a surviving donor star. Thus, the limiting magnitude of the HST observation (F555W > 28 mag) rules out all He star companion models and the most luminous main-sequence companion model currently in the literature. The remaining main-sequence companion models could be tested with a 10 orbit HST exposure in the F606W filter.

Do, Aaron↗

Preliminary clustering properties of the DESI BGS bright targets using DR9 Legacy Imaging Surveys

ABSTRACT We characterize the selection cuts and clustering properties of a magnitude-limited sample of bright galaxies that is part of the Bright Galaxy Survey (BGS) of the Dark Energy Spectroscopic Instrument (DESI) using the ninth data release of the Legacy Imaging Surveys (DR9). We describe changes in the DR9 selection compared to the DR8 one and we also compare the DR9 selection in three distinct regions: BASS/MzLS in the north Galactic Cap (NGC), DECaLS in the NGC, and DECaLS in the south Galactic Cap (SGC). We investigate the systematics associated with the selection and assess its completeness by matching the BGS targets with the Galaxy and Mass Assembly (GAMA) survey. We measure the angular clustering for the overall bright sample (rmag ≤ 19.5) and as function of apparent magnitude and colour. This enables to determine the clustering strength r0 and slope γ by fitting a power-law model that can be used to generate accurate mock catalogues for this tracer. We use a counts-in-cells technique to explore higher order statistics and cross-correlations with external spectroscopic data sets in order to check the evolution of the clustering with redshift and the redshift distribution of the BGS targets using clustering redshifts. While this work validates the properties of the BGS bright targets, the final target selection pipeline and clustering properties of the entire DESI BGS will be fully characterized and validated with the spectroscopic data of Survey Validation.

79 ASTRONOMY AND ASTROPHYSICS↗

COMPASO : A new halo finder for competitive assignment to spherical overdensities

We describe a new method (compaso) for identifying groups of particles in cosmological N-body simulations. compaso builds upon existing spherical overdensity (SO) algorithms by taking into consideration the tidal radius around a smaller halo before competitively assigning halo membership to the particles. In this way, the compaso finder allows for more effective deblending of haloes in close proximity as well as the formation of new haloes on the outskirts of larger ones. This halo-finding algorithm is used in the abacussummit suite of N-body simulations, designed to meet the cosmological simulation requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. compaso is developed as a highly efficient on-the-fly group finder, which is crucial for enabling good load-balancing between the GPU and CPU and the creation of high-resolution merger trees. In this paper, we describe the halo-finding procedure and its particular implementation in abacus, accompanying it with a qualitative analysis of the finder. We test the robustness of the compaso catalogues before and after applying the cleaning method described in an accompanying paper and demonstrate its effectiveness by comparing it with other validation techniques. We then visualize the haloes and their density profiles, finding that they are well fit by the NFW formalism. Finally, we compare other properties such as radius–mass relationships and two-point correlation functions with that of another widely used halo finder, rockstar.

79 ASTRONOMY AND ASTROPHYSICS↗

MIGHTEE: total intensity radio continuum imaging and the COSMOS/XMM-LSS Early Science fields

ABSTRACT MIGHTEE is a galaxy evolution survey using simultaneous radio continuum, spectropolarimetry, and spectral line observations from the South African MeerKAT telescope. When complete, the survey will image ∼20 deg2 over the COSMOS, E-CDFS, ELAIS-S1, and XMM-Newton Large Scale Structure field (XMM-LSS) extragalactic deep fields with a central frequency of 1284 MHz. These were selected based on the extensive multiwavelength data sets from numerous existing and forthcoming observational campaigns. Here, we describe and validate the data processing strategy for the total intensity continuum aspect of MIGHTEE, using a single deep pointing in COSMOS (1.6 deg2) and a three-pointing mosaic in XMM-LSS (3.5 deg2). The processing includes the correction of direction-dependent effects, and results in thermal noise levels below 2 $\mathrm{\mu }$Jy beam−1 in both fields, limited in the central regions by classical confusion at ∼8 arcsec angular resolution, and meeting the survey specifications. We also produce images at ∼5 arcsec resolution that are ∼3 times shallower. The resulting image products form the basis of the Early Science continuum data release for MIGHTEE. From these images we extract catalogues containing 9896 and 20 274 radio components in COSMOS and XMM-LSS, respectively. We also process a close-packed mosaic of 14 additional pointings in COSMOS and use these in conjunction with the Early Science pointing to investigate methods for primary beam correction of broad-band radio images, an analysis that is of relevance to all full-band MeerKAT continuum observations, and wide-field interferometric imaging in general. A public release of the MIGHTEE Early Science continuum data products accompanies this article.

Heywood, I. (ORCID:0000000168645057)↗

encore : an O ( N g2) estimator for galaxy N -point correlation functions

ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ${\sim}100$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.

79 ASTRONOMY AND ASTROPHYSICS↗

Anomaly detection in the Zwicky Transient Facility DR3

We present results from applying the SNAD anomaly detection pipeline to the third public data release of the Zwicky Transient Facility (ZTF DR3). The pipeline is composed of three stages: feature extraction, search of outliers with machine learning algorithms, and anomaly identification with followup by human experts. Our analysis concentrates in three ZTF fields, comprising more than 2.25 million objects. A set of four automatic learning algorithms was used to identify 277 outliers, which were subsequently scrutinized by an expert. From these, 188 (68 per cent) were found to be bogus light curves – including effects from the image subtraction pipeline as well as overlapping between a star and a known asteroid, 66 (24 per cent) were previously reported sources whereas 23 (8 per cent) correspond to non-catalogued objects, with the two latter cases of potential scientific interest (e.g. one spectroscopically confirmed RS Canum Venaticorum star, four supernovae candidates, one red dwarf flare). Moreover, using results from the expert analysis, we were able to identify a simple bi-dimensional relation that can be used to aid filtering potentially bogus light curves in future studies. We provide a complete list of objects with potential scientific application so they can be further scrutinised by the community. These results confirm the importance of combining automatic machine learning algorithms with domain knowledge in the construction of recommendation systems for astronomy. Our code is publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

Photometric redshift estimation of BASS DR3 quasars by machine learning

ABSTRACT Correlating Beijing–Arizona Sky Survey (BASS) data release 3 (DR3) catalogue with the ALLWISE data base, the data from optical and infrared information are obtained. The quasars from Sloan Digital Sky Survey are taken as training and test samples while those from LAMOST are considered as external test sample. We propose two schemes to construct the redshift estimation models with XGBoost, CatBoost, and Random Forest. One scheme (namely one-step model) is to predict photometric redshifts directly based on the optimal models created by these three algorithms; the other scheme (namely two-step model) is to first classify the data into low- and high-redshift data sets, and then predict photometric redshifts of these two data sets separately. For one-step model, the performance of these three algorithms on photometric redshift estimation is compared with different training samples, and CatBoost is superior to XGBoost and Random Forest. For two-step model, the performances of these three algorithms on the classification of low and high redshift subsamples are compared, and CatBoost still shows the best performance. Therefore, CatBoost is regarded as the core algorithm of classification and regression in two-step model. In contrast to one-step model, two-step model is optimal when predicting photometric redshift of quasars, especially for high-redshift quasars. Finally, the two models are applied to predict photometric redshifts of all quasar candidates of BASS DR3. The number of high-redshift quasar candidates is 3938 (redshift ≥3.5) and 121 (redshift ≥4.5) by two-step model. The predicted result will be helpful for quasar research and follow-up observation of high-redshift quasars.

79 ASTRONOMY AND ASTROPHYSICS↗

Quenching, bursting, and galaxy shapes: colour transformation as a function of morphology

ABSTRACT Different mechanisms for quenching star formation in galaxies are commonly invoked in the literature, but the relative impact of each one at different cosmic epochs is still unknown. In particular, the relation between these processes and morphological transformation remains poorly understood. In this work, we measure the effectiveness of changes in star formation rates by analysing a new parameter, the Star Formation Acceleration (SFA), as a function of galaxy morphology. This methodology is capable of identifying both bursting and quenching episodes that occurred in the preceding 300 Myr. We use morphological classification catalogues based on Deep Learning techniques. Our final sample has ∼14 200 spirals and ∼2500 ellipticals. We find that elliptical galaxies in the transition region have median shorter quenching time-scales (τ < 1 Gyr) than spirals (τ ≥ 1 Gyr). This result conforms to the scenario in which major mergers and other violent processes play a fundamental role in galaxy evolution for most ellipticals, not only quenching star formation more rapidly but also playing a role in morphological transformation. We also find that ∼two-thirds of galaxies bursting in the green valley in our sample are massive spirals ($M_\star \ge 10^{11.0}\, \mathrm{M}_\odot$) with signs of disturbance. This is in accordance with the scenario where low-mass galaxies are losing their gas in an interaction with a massive galaxy: while the former is quenching, the last is being refueled and going through a burst, showing signs of recent interaction.

79 ASTRONOMY AND ASTROPHYSICS↗

SDSS-IV MaStar: theoretical atmospheric parameters for the MaNGA stellar library

ABSTRACT We calculate the fundamental stellar parameters effective temperature, surface gravity, and iron abundance – Teff, log g, [Fe/H] – for the final release of the Mapping Nearby Galaxies at APO (MaNGA) Stellar Library (MaStar), containing 59 266 per-visit-spectra for 24 290 unique stars at intermediate resolution (R ∼ 1800) and high S/N (median = 96). We fit theoretical spectra from model atmospheres by both MARCS and BOSZ-ATLAS9 to the observed MaStar spectra, using the full spectral fitting code pPXF. We further employ a Bayesian approach, using a Markov Chain Monte Carlo (MCMC) technique to map the parameter space and obtain uncertainties. Originally in this paper, we cross match MaStar observations with Gaia photometry, which enable us to set reliable priors and identify outliers according to stellar evolution. In parallel to the parameter determination, we calculate corresponding stellar population models to test the reliability of the parameters for each stellar evolutionary phase. We further assess our procedure by determining parameters for standard stars such as the Sun and Vega and by comparing our parameters with those determined in the literature from high-resolution spectroscopy (APOGEE and SEGUE) and from lower resolution matching template (LAMOST). The comparisons, considering the different methodologies and S/N of the literature surveys, are favourable in all cases. Our final parameter catalogue for MaStar cover the following ranges: 2592 ≤ Teff ≤ 32 983 K; −0.7 ≤ log g ≤ 5.4 dex; −2.9 ≤ [Fe/H] ≤ 1.0 dex and will be available with the last SDSS-IV Data Release, in 2021 December.

79 ASTRONOMY AND ASTROPHYSICS↗

Synthetic galaxy clusters and observations based on Dark Energy Survey Year 3 Data

ABSTRACT We develop a novel data-driven method for generating synthetic optical observations of galaxy clusters. In cluster weak lensing, the interplay between analysis choices and systematic effects related to source galaxy selection, shape measurement, and photometric redshift estimation can be best characterized in end-to-end tests going from mock observations to recovered cluster masses. To create such test scenarios, we measure and model the photometric properties of galaxy clusters and their sky environments from the Dark Energy Survey Year 3 (DES Y3) data in two bins of cluster richness $\lambda \in [30; 45)$, $\lambda \in [45; 60)$ and three bins in cluster redshift ($z\in [0.3; 0.35)$, $z\in [0.45; 0.5)$ and $z\in [0.6; 0.65)$. Using deep-field imaging data, we extrapolate galaxy populations beyond the limiting magnitude of DES Y3 and calculate the properties of cluster member galaxies via statistical background subtraction. We construct mock galaxy clusters as random draws from a distribution function, and render mock clusters and line-of-sight catalogues into synthetic images in the same format as actual survey observations. Synthetic galaxy clusters are generated from real observational data, and thus are independent from the assumptions inherent to cosmological simulations. The recipe can be straightforwardly modified to incorporate extra information, and correct for survey incompleteness. New realizations of synthetic clusters can be created at minimal cost, which will allow future analyses to generate the large number of images needed to characterize systematic uncertainties in cluster mass measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The DES view of the Eridanus supervoid and the CMB cold spot

ABSTRACT The Cold Spot is a puzzling large-scale feature in the Cosmic Microwave Background temperature maps and its origin has been subject to active debate. As an important foreground structure at low redshift, the Eridanus supervoid was recently detected, but it was subsequently determined that, assuming the standard ΛCDM model, only about 10–20 per cent of the observed temperature depression can be accounted for via its Integrated Sachs–Wolfe imprint. However, R ≳ 100 h−1Mpc supervoids elsewhere in the sky have shown ISW imprints AISW ≈ 5.2 ± 1.6 times stronger than expected from ΛCDM (AISW = 1), which warrants further inspection. Using the Year-3 redMaGiC catalogue of luminous red galaxies from the Dark Energy Survey, here we confirm the detection of the Eridanus supervoid as a significant underdensity in the Cold Spot’s direction at z < 0.2. We also show, with S/N ≳ 5 significance, that the Eridanus supervoid appears as the most prominent large-scale underdensity in the dark matter mass maps that we reconstructed from DES Year-3 gravitational lensing data. While we report no significant anomalies, an interesting aspect is that the amplitude of the lensing signal from the Eridanus supervoid at the Cold Spot centre is about 30 per cent lower than expected from similar peaks found in N-body simulations based on the standard ΛCDM model with parameters Ωm = 0.279 and σ8 = 0.82. Overall, our results confirm the causal relation between these individually rare structures in the cosmic web and in the CMB, motivating more detailed future surveys in the Cold Spot region.

79 ASTRONOMY AND ASTROPHYSICS↗

Automated algorithms to build active galactic nucleus classifiers

ABSTRACT We present a machine learning model to classify active galactic nuclei (AGNs) and galaxies (AGN-galaxy classifier) and a model to identify type 1 (optically unabsorbed) and type 2 (optically absorbed) AGN (type 1/2 classifier). We test tree-based algorithms, using training samples built from the X-ray Multi-Mirror Mission–Newton (XMM–Newton) catalogue and the Sloan Digital Sky Survey (SDSS), with labels derived from the SDSS survey. The performance was tested making use of simulations and of cross-validation techniques. With a set of features including spectroscopic redshifts and X-ray parameters connected to source properties (e.g. fluxes and extension), as well as features related to X-ray instrumental conditions, the precision and recall for AGN identification are 94 and 93 per cent, while the type 1/2 classifier has a precision of 74 per cent and a recall of 80 per cent for type 2 AGNs. The performance obtained with photometric redshifts is very similar to that achieved with spectroscopic redshifts in both test cases, while there is a decrease in performance when excluding redshifts. Our machine learning model trained on X-ray features can accurately identify AGN in extragalactic surveys. The type 1/2 classifier has a valuable performance for type 2 AGNs, but its ability to generalize without redshifts is hampered by the limited census of absorbed AGN at high redshift.

Falocco, S. (ORCID:0000000299841103)↗

The large-scale environment of thermonuclear and core-collapse supernovae

ABSTRACT The new generation of wide-field time-domain surveys has made it feasible to study the clustering of supernova (SN) host galaxies in the large-scale structure (LSS) for the first time. We investigate the LSS environment of SN populations, using 106 dark matter density realisations with a resolution of ∼3.8 Mpc, constrained by the 2M+ + galaxy survey. We limit our analysis to redshift z < 0.036, using samples of 498 thermonuclear and 782 core-collapse SNe from the Zwicky Transient Facility’s Bright Transient Survey and Census of the Local Universe catalogues. We detect clustering of SNe with high significance; the observed clustering of the two SNe populations is consistent with each other. Further, the clustering of SN hosts is consistent with that of the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey DR12 spectroscopic galaxy sample in the same redshift range. Using a tidal shear classifier, we classify the LSS into voids, sheets, filaments, and knots. We find that both SNe and SDSS galaxies are predominantly found in sheets and filaments. SNe are significantly under-represented in voids and over-represented in knots compared to the volume fraction in these structures. This work opens the potential for using forthcoming wide-field deep SN surveys as a complementary LSS probe.

Astronomy & Astrophysics↗

The incidence of X-ray selected AGN in nearby galaxies

ABSTRACT We present the identification and analysis of an unbiased sample of active galactic nuclei (AGN) that lie within the local galaxy population. Using the MPA-JHU catalogue (based on SDSS DR8) and 3XMM DR7 we define a parent sample of 25 949 local galaxies (z ≤ 0.33). After confirming that there was strictly no AGN light contaminating stellar mass and star-formation rate calculations, we identified 917 galaxies with central, excess X-ray emission likely originating from an AGN. We analysed their optical emission lines using the BPT diagnostic and confirmed that such techniques are more effective at reliably identifying sources as AGN in higher mass galaxies: rising from 30 per cent agreement in the lowest mass bin to 93 per cent in the highest. We then calculated the growth rates of the black holes powering these AGN in terms of their specific accretion rates (∝LX/M*). Our sample exhibits a wide range of accretion rates, with the majority accreting at rates $\le 0.5\ \mathrm{ per \, cent}$ of their Eddington luminosity. Finally, we used our sample to calculate the incidence of AGN as a function of stellar mass and redshift. After correcting for the varying sensitivity of 3XMM, we split the galaxy sample by stellar mass and redshift and investigated the AGN fraction as a function of X-ray luminosity and specific black hole accretion rate. From this we found the fraction of galaxies hosting AGN above a fixed specific accretion rate limit of 10−3.5 is constant (at $\approx 1\ \mathrm{ per \, cent}$) over stellar masses of 8 < log M*/M⊙ < 12 and increases (from $\approx 1\ \mathrm{ per \, cent}$ to 10 per cent) with redshift.

79 ASTRONOMY AND ASTROPHYSICS↗

Scaling pair count to next galaxy surveys

ABSTRACT Counting pairs of galaxies or stars according to their distance is at the core of real-space correlation analyses performed in astrophysics and cosmology. Upcoming galaxy surveys (LSST, Euclid) will measure properties of billions of galaxies challenging our ability to perform such counting in a minute-scale time relevant for the usage of simulations. The problem is only limited by efficient access to the data, hence belongs to the big data category. We use the popular Apache Spark framework to address it and design an efficient high-throughput algorithm to deal with hundreds of millions to billions of input data. To optimize it, we revisit the question of non-hierarchical sphere pixelization based on cube symmetries and develop a new one dubbed the ‘Similar Radius Sphere Pixelization’ (SARSPix) with very close to square pixels. It provides the most adapted indexing over the sphere for all distance-related computations. Using LSST-like fast simulations, we compute autocorrelation functions on tomographic bins containing between a hundred million to one billion data points. In each case, we achieve the construction of a standard pair-distance histogram in about 2 min, using a simple algorithm that is shown to scale, over a moderate number of nodes (16–64). This illustrates the potential of this new techniques in the field of astronomy where data access is becoming the main bottleneck. They can be easily adapted to other use-cases as nearest-neighbours search, catalogue cross-match or cluster finding. The software is publicly available from https://github.com/astrolabsoftware/SparkCorr.

79 ASTRONOMY AND ASTROPHYSICS↗

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

ABSTRACT We study the connection of matter density and its tracers from the probability density function (PDF) perspective. One aspect of this connection is the conditional expectation value 〈δtracer|δm〉 when averaging both tracer and matter density over some scale. We present a new way to incorporate a Lagrangian bias expansion of this expectation value into standard frameworks for modelling the PDF of density fluctuations and counts-in-cells statistics. Using N-body simulations and mock galaxy catalogues we confirm the accuracy of this expansion and compare it to the more commonly used Eulerian parametrization. For haloes hosting typical luminous red galaxies, the Lagrangian model provides a significantly better description of 〈δtracer|δm〉 at second order in perturbations. A second aspect of the matter-tracer connection is shot-noise, i.e. the scatter of tracer density around 〈δtracer|δm〉. It is well known that this noise can be significantly non-Poissonian and we validate the performance of a more general, two-parameter shot-noise model for different tracers and simulations. Both parts of our analysis are meant to pave the way for forthcoming applications to survey data.

Friedrich, Oliver↗

The impact of tomographic redshift bin width errors on cosmological probes

ABSTRACT Systematic errors in the galaxy redshift distribution n(z) can propagate to systematic errors in the derived cosmology. We characterize how the degenerate effects in tomographic bin widths and galaxy bias impart systematic errors on cosmology inference using observational data from the Deep Lens Survey. For this we use a combination of galaxy clustering and galaxy–galaxy lensing. We present two end-to-end analyses from the catalogue level to parameter estimation. We produce an initial cosmological inference using fiducial tomographic redshift bins derived from photometric redshifts, then compare this with a result where the redshift bins are empirically corrected using a set of spectroscopic redshifts. We find that the derived parameter S8 ≡ σ8(Ωm/.3)1/2 decreases from $0.841^{+0.062}_{-0.061}$ to $0.781^{0.061}_{0.054}$ upon correcting the n(z) errors in the second method.

79 ASTRONOMY AND ASTROPHYSICS↗