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At least 55 records · Page 3

Dark Energy Survey Year 6 Results: Redshift Calibration of the Weak Lensing Source Galaxies

Determining the distribution of redshifts for galaxies in wide-field photometric surveys is essential for robust cosmological studies of weak gravitational lensing. We present the methodology, calibrated redshift distributions, and uncertainties of the final Dark Energy Survey Year 6 (Y6) weak lensing galaxy data, divided into four redshift bins centered at $\langle z \rangle = [0.414, 0.538, 0.846, 1.157]$. We combine independent information from two methods on the full shape of redshift distributions: optical and near-infrared photometry within an improved Self-Organizing Map $p(z)$ (SOMPZ) framework, and cross-correlations with spectroscopic galaxy clustering measurements (WZ), which we demonstrate to be consistent both in terms of the redshift calibration itself and in terms of resulting cosmological constraints within 0.1$σ$. We describe the process used to produce an ensemble of redshift distributions that account for several known sources of uncertainty. Among these, imperfection in the calibration sample due to the lack of faint, representative spectra is the dominant factor. The final uncertainty on mean redshift in each bin is $σ_{\langle z\rangle} = [0.012, 0.008,0.009, 0.024]$. We ensure the robustness of the redshift distributions by leveraging new image simulations and a cross-check with galaxy shape information via the shear ratio (SR) method.

Yin, B. [Duke U.] (ORCID:0009000656049980)↗

Anisotropic effective redshift and evolving clustering amplitude

A typical galaxy survey geometry results in galaxy pairs of different separation and angle to the line-of-sight having different distributions in redshift and consequently a different effective redshift. However, clustering measurements are analysed assuming that the clustering is representative of that at a single effective redshift. Here, we investigate the impact of variations in the galaxy-pair effective redshift on the large-scale clustering measured in galaxy surveys. We find that galaxy surveys spanning a large redshift range have different effective redshifts as a function of both pair separation and angle. Furthermore, when considering tracers whose clustering amplitude evolves strongly with redshift, this combination can result in an additional scale-dependent clustering anisotropy. We demonstrate the size of this effect on the eBOSS DR16 Quasar sample and show that, while the impact on monopole is negligible, neglecting this effect can result in a tilt of ~ 4% and ~40% in quadrupole and hexadecapole, respectively, on scales ~1 h -1 Gpc. We discuss strategies to mitigate this effect when making

79 ASTRONOMY AND ASTROPHYSICS↗

The Dark Energy Survey Year 3 high-redshift sample: selection, characterization, and analysis of galaxy clustering

ABSTRACT The fiducial cosmological analyses of imaging surveys like DES typically probe the Universe at redshifts z < 1. We present the selection and characterization of high-redshift galaxy samples using DES Year 3 data, and the analysis of their galaxy clustering measurements. In particular, we use galaxies that are fainter than those used in the previous DES Year 3 analyses and a Bayesian redshift scheme to define three tomographic bins with mean redshifts around z ∼ 0.9, 1.2, and 1.5, which extend the redshift coverage of the fiducial DES Year 3 analysis. These samples contain a total of about 9 million galaxies, and their galaxy density is more than 2 times higher than those in the DES Year 3 fiducial case. We characterize the redshift uncertainties of the samples, including the usage of various spectroscopic and high-quality redshift samples, and we develop a machine-learning method to correct for correlations between galaxy density and survey observing conditions. The analysis of galaxy clustering measurements, with a total signal to noise S/N ∼ 70 after scale cuts, yields robust cosmological constraints on a combination of the fraction of matter in the Universe Ωm and the Hubble parameter h, $\Omega _m h = 0.195^{+0.023}_{-0.018}$, and 2–3 per cent measurements of the amplitude of the galaxy clustering signals, probing galaxy bias and the amplitude of matter fluctuations, bσ8. A companion paper (in preparation) will present the cross-correlations of these high-z samples with cosmic microwave background lensing from Planck and South Pole Telescope, and the cosmological analysis of those measurements in combination with the galaxy clustering presented in this work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DESI complete calibration of the colour–redshift relation (DC3R2): results from early DESI data

We present initial results from the Dark Energy Spectroscopic Instrument (DESI) complete calibration of the colour–redshift relation (DC3R2) secondary target survey. Our analysis uses 230 k galaxies that overlap with KiDS-VIKING ugriZYJHK s photometry to calibrate the colour–redshift relation and to inform photometric redshift (photo-z) inference methods of future weak lensing surveys. Together with emission line galaxies (ELGs), luminous red galaxies (LRGs), and the Bright Galaxy Survey (BGS) that provide samples of complementary colour, the DC3R2 targets help DESI to span 56 percent of the colour space visible to Euclid and LSST with high confidence spectroscopic redshifts. The effects of spectroscopic completeness and quality are explored, as well as systematic uncertainties introduced with the use of common Self-Organizing Maps trained on different photometry than the analysis sample. We further examine the dependence of redshift on magnitude at fixed colour, important for the use of bright galaxy spectra to calibrate redshifts in a fainter photometric galaxy sample. We find that noise in the KiDS-VIKING photometry introduces a dominant, apparent magnitude dependence of redshift at fixed colour, which indicates a need for carefully chosen deep drilling fields, and survey simulation to model this effect for future weak lensing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Archetype-based Redshift Estimation for the Dark Energy Spectroscopic Instrument Survey

We present a computationally efficient galaxy archetype-based redshift estimation and spectral classification method for the Dark Energy Survey Instrument (DESI) survey. The DESI survey currently relies on a redshift fitter and spectral classifier using a linear combination of principal component analysis–derived templates, which is very efficient in processing large volumes of DESI spectra within a short time frame. However, this method occasionally yields unphysical model fits for galaxies and fails to adequately absorb calibration errors that may still be occasionally visible in the reduced spectra. Our proposed approach improves upon this existing method by refitting the spectra with carefully generated physical galaxy archetypes combined with additional terms designed to absorb data reduction defects and provide more physical models to the DESI spectra. We test our method on an extensive data set derived from the survey validation (SV) and Year 1 (Y1) data of DESI. Our findings indicate that the new method delivers marginally better redshift success for SV tiles while reducing catastrophic redshift failure by 10%–30%. At the same time, results from millions of targets from the main survey show that our model has relatively higher redshift success and purity rates (0.5%–0.8% higher) for galaxy targets while having similar success for QSOs. These improvements also demonstrate that the main DESI redshift pipeline is generally robust. Additionally, it reduces the false-positive redshift estimation by 5%–40% for sky fibers. We also discuss the generic nature of our method and how it can be extended to other large spectroscopic surveys, along with possible future improvements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Predicting the Redshift 2 H-Alpha Luminosity Function Using [OIII] Emission Line Galaxies

Upcoming space-based surveys such as Euclid and WFIRST-AFTA plan to measure Baryonic Acoustic Oscillations (BAOs) in order to study dark energy. These surveys will use IR slitless grism spectroscopy to measure redshifts of a large number of galaxies over a significant redshift range. In this paper, we use the WFC3 Infrared Spectroscopic Parallel Survey (WISP) to estimate the expected number of H-alpha emitters observable by these future surveys. WISP is an ongoing Hubble Space Telescope slitless spectroscopic survey, covering the 0.8 - 1.65 micrometers wavelength range and allowing the detection of H-alpha emitters up to z approximately equal to 1.5 and [OIII] emitters to z approximately equal to 2.3. We derive the H-alpha-[OIII] bivariate line luminosity function for WISP galaxies at z approximately equal to 1 using a maximum likelihood estimator that properly accounts for uncertainties in line luminosity measurement, and demonstrate how it can be used to derive the H-alpha luminosity function from exclusively fitting [OIII] data. Using the z approximately equal to 2 [OIII] line luminosity function, and assuming that the relation between H-alpha and [OIII] luminosity does not change significantly over the redshift range, we predict the H-alpha number counts at z approximately equal to 2 - the upper end of the redshift range of interest for the future surveys. For the redshift range 0.7 less than z less than 2, we expect approximately 3000 galaxies per sq deg for a flux limit of 3 x 10(exp −16) ergs per sec per sq cm (the proposed depth of Euclid galaxy redshift survey) and approximately 20,000 galaxies per sq deg for a flux limit of approximately 10(exp −16) ergs per sec per sq cm (the baseline depth of WFIRST galaxy redshift survey).

Redshift↗

Extending empirical constraints on the SZ–mass scaling relation to higher redshifts via HST weak lensing measurements of nine clusters from the SPT-SZ survey at z ≳ 1

We present a Hubble Space Telescope (HST) weak gravitational lensing study of nine distant and massive galaxy clusters with redshifts 1.0 ≲ z ≲ 1.7 (z median = 1.4) and Sunyaev Zel’dovich (SZ) detection significance ξ > 6.0 from the South Pole Telescope Sunyaev Zel’dovich (SPT-SZ) survey. We measured weak lensing galaxy shapes in HST/ACS F606W and F814W images and used additional observations from HST/WFC3 in F110W and VLT/FORS2 in U HIGH to preferentially select background galaxies at z ≳ 1.8, achieving a high purity. We combined recent redshift estimates from the CANDELS/3D-HST and HUDF fields to infer an improved estimate of the source redshift distribution. We measured weak lensing masses by fitting the tangential reduced shear profiles with spherical Navarro-Frenk-White (NFW) models. We obtained the largest lensing mass in our sample for the cluster SPT-CL J2040—4451, thereby confirming earlier results that suggest a high lensing mass of this cluster compared to X-ray and SZ mass measurements. Combining our weak lensing mass constraints with results obtained by previous studies for lower redshift clusters, we extended the calibration of the scaling relation between the unbiased SZ detection significance ζ and the cluster mass for the SPT-SZ survey out to higher redshifts. We found that the mass scale inferred from our highest redshift bin (1.2 < z < 1.7) is consistent with an extrapolation of constraints derived from lower redshifts, albeit with large statistical uncertainties. Thus, our results show a similar tendency as found in previous studies, where the cluster mass scale derived from the weak lensing data is lower than the mass scale expected in a PlanckνΛCDM (i.e. νΛ cold dark matter) cosmology given the SPT-SZ cluster number counts.

79 ASTRONOMY AND ASTROPHYSICS↗

The first high-redshift cavity power measurements of cool-core galaxy clusters with the International LOFAR Telescope

Radio-mode feedback associated with the active galactic nuclei (AGNs) at the cores of galaxy clusters injects a large amount of energy into the intracluster medium (ICM), offsetting radiative losses through X-ray emission. This mechanism prevents the ICM from rapidly cooling down and fueling extreme starburst activity as it accretes onto the central galaxies, and it is therefore a key ingredient in the evolution of galaxy clusters. However, the influence and mode of feedback at high redshifts (z ∼ 1) remains largely unknown. Low-frequency sub-arcsecond-resolution radio observations taken with the International LOFAR Telescope have demonstrated their ability to assist X-ray observations with constraining the energy output from the AGNs (or “cavity power”) in galaxy clusters, thereby enabling research at higher redshifts than before. In this pilot project, we tested this hybrid method on a high-redshift (0.6 < z < 1.3) sample of 13 galaxy clusters for the first time with the aim of verifying the performance of this method at these redshifts and providing the first estimates of the cavity power associated with the central AGN for a sample of distant clusters. We were able to detect clear radio lobes in three out of 13 galaxy clusters at redshifts of 0.7 < z < 0.9, and we used these detections in combination with ICM pressures surrounding the radio lobes obtained from standard profiles to calculate the corresponding cavity powers of the AGNs. Combining our results with the literature, the current data appear to suggest that the average cavity power peaked at a redshift ofz ∼ 0.4 and slowly decreases toward higher redshifts. However, we require more and tighter constraints on the cavity volume and a better understanding of our observational systematics to confirm any deviation of the cavity power trend from a constant level.

Astronomy & Astrophysics↗

Dark Energy Survey Year 3 results: marginalization over redshift distribution uncertainties using ranking of discrete realizations

ABSTRACT Cosmological information from weak lensing surveys is maximized by sorting source galaxies into tomographic redshift subsamples. Any uncertainties on these redshift distributions must be correctly propagated into the cosmological results. We present hyperrank, a new method for marginalizing over redshift distribution uncertainties, using discrete samples from the space of all possible redshift distributions, improving over simple parametrized models. In hyperrank, the set of proposed redshift distributions is ranked according to a small (between one and four) number of summary values, which are then sampled, along with other nuisance parameters and cosmological parameters in the Monte Carlo chain used for inference. This approach can be regarded as a general method for marginalizing over discrete realizations of data vector variation with nuisance parameters, which can consequently be sampled separately from the main parameters of interest, allowing for increased computational efficiency. We focus on the case of weak lensing cosmic shear analyses and demonstrate our method using simulations made for the Dark Energy Survey (DES). We show that the method can correctly and efficiently marginalize over a wide range of models for the redshift distribution uncertainty. Finally, we compare hyperrank to the common mean-shifting method of marginalizing over redshift uncertainty, validating that this simpler model is sufficient for use in the DES Year 3 cosmology results presented in companion papers.

79 ASTRONOMY AND ASTROPHYSICS↗

Photometric redshifts from SDSS images with an interpretable deep capsule network

ABSTRACT Studies of cosmology, galaxy evolution, and astronomical transients with current and next-generation wide-field imaging surveys like the Rubin Observatory Legacy Survey of Space and Time are all critically dependent on estimates of photometric redshifts. Capsule networks are a new type of neural network architecture that is better suited for identifying morphological features of the input images than traditional convolutional neural networks. We use a deep capsule network trained on ugriz images, spectroscopic redshifts, and Galaxy Zoo spiral/elliptical classifications of ∼400 000 Sloan Digital Sky Survey galaxies to do photometric redshift estimation. We achieve a photometric redshift prediction accuracy and a fraction of catastrophic outliers that are comparable to or better than current methods for SDSS main galaxy sample-like data sets (r ≤ 17.8 and zspec ≤ 0.4) while requiring less data and fewer trainable parameters. Furthermore, the decision-making of our capsule network is much more easily interpretable as capsules act as a low-dimensional encoding of the image. When the capsules are projected on a two-dimensional manifold, they form a single redshift sequence with the fraction of spirals in a region exhibiting a gradient roughly perpendicular to the redshift sequence. We perturb encodings of real galaxy images in this low-dimensional space to create synthetic galaxy images that demonstrate the image properties (e.g. size, orientation, and surface brightness) encoded by each dimension. We also measure correlations between galaxy properties (e.g. magnitudes, colours, and stellar mass) and each capsule dimension. We publicly release our code, estimated redshifts, and additional catalogues at https://biprateep.github.io/encapZulate-1.

79 ASTRONOMY AND ASTROPHYSICS↗

Analysis of the impact of broad absorption lines on quasar redshift measurements with synthetic observations

ABSTRACT Accurate quasar classifications and redshift measurements are increasingly important to precision cosmology experiments. Broad absorption line (BAL) features are present in 15–20 per cent of all quasars, and these features can introduce systematic redshift errors, and in extreme cases produce misclassifications. We quantitatively investigate the impact of BAL features on quasar classifications and redshift measurements with synthetic spectra that were designed to match observations by the Dark Energy Spectroscopic Instrument (DESI) survey. Over the course of 5 yr, DESI aims to measure spectra for 40 million galaxies and quasars, including nearly three million quasars. Our synthetic quasar spectra match the signal-to-noise ratio and redshift distributions of the first year of DESI observations, and include the same synthetic quasar spectra both with and without BAL features. We demonstrate that masking the locations of the BAL features decreases the redshift errors by about 1 per cent and reduces the number of catastrophic redshift errors by about 80 per cent. We conclude that identifying and masking BAL troughs should be a standard part of the redshift determination step for DESI and other large-scale spectroscopic surveys of quasars.

(galaxies:) quasars: absorption↗

Evaluating cosmological biases using photometric redshifts for Type Ia Supernova cosmology with the Dark Energy Survey Supernova Program

Cosmological analyses with Type Ia Supernovae (SNe Ia) have traditionally been reliant on spectroscopy for both classifying the type of supernova and obtaining reliable redshifts to measure the distance–redshift relation. While obtaining a host-galaxy spectroscopic redshift for most SNe is feasible for small-area transient surveys, it will be too resource intensive for upcoming large-area surveys such as the Vera Rubin Observatory Legacy Survey of Space and Time, which will observe on the order of millions of SNe. Here, we use data from the Dark Energy Survey (DES) to address this problem with photometric redshifts (photo-z) inferred directly from the SN light curve in combination with Gaussian and full p(z) priors from host-galaxy photo-z estimates. Using the DES 5-yr photometrically classified SN sample, we consider several photo-z algorithms as host-galaxy photo-z priors, including the Self-Organizing Map redshifts (SOMPZ), Bayesian Photometric Redshifts (BPZ), and Directional-Neighbourhood Fitting (DNF) redshift estimates employed in the DES 3 × 2 point analyses. With detailed catalogue-level simulations of the DES 5-yr sample, we find that the simulated w can be recovered within ±0.02 when using SN+SOMPZ or DNF prior photo-z, smaller than the average statistical uncertainty for these samples of 0.03. With data, we obtain biases in w consistent with simulations within ~1σ for three of the five photo-z variants. We further evaluate how photo-z systematics interplay with photometric classification and find classification introduces a subdominant systematic component. This work lays the foundation for next-generation fully photometric SNe Ia cosmological analyses.

(cosmology:) dark energy↗

The DECADE cosmic shear project II: photometric redshift calibration of the source galaxy sample

We present the photometric redshift characterization and calibration for the Dark Energy Camera All Data Everywhere (DECADE) weak lensing dataset: a catalog of 107 million galaxies observed by the Dark Energy Camera (DECam) in the northern Galactic cap. The redshifts are estimated from a combination of wide-field photometry, deep-field photometry with associated redshift estimates, and a transfer function between the wide field and deep field that is estimated using a source injection catalog. We construct four tomographic bins for the galaxy catalog, and estimate the redshift distribution, $n(z)$, within each one using the Self-organizing Map Photo-Z (SOMPZ) methodology. Our estimates include the contributions from sample variance, zeropoint calibration uncertainties, and redshift biases, as quantified for the deep-field dataset. The total uncertainties on the mean redshifts are $σ_{\langle}$$_z$$_{\rangle} ≈ 0.01$. The SOMPZ estimates are then compared to those from the clustering redshift method, obtained by cross-correlating our source galaxies with galaxies in spectroscopic surveys, and are shown to be consistent with each other.

Anbajagane, D. [Univ. of Chicago, IL (United State↗

Simulating Continuum-based Redshift Measurement in the Roman’s High Latitude Spectroscopic Survey

We investigate the capability of the Nancy Grace Roman Space Telescope’s (Roman) Wide-Field Instrument G150 slitless grism to detect red, quiescent galaxies based on the current reference survey. We simulate dispersed images for Roman reference High-Latitude Spectroscopic Survey (HLSS) and analyze two-dimensional spectroscopic data using the grism Redshift and Line Analysis (Grizli) software. This study focus on assessing Roman grism’s capability for continuum-level redshift measurement for a redshift range of 0.5 ≤ z ≤ 2.5. The redshift recovery is assessed by setting three requirements of: σ z = $\frac{|z–z_{true}|}{1+z}$ ≤ 0.01, signal-to-noise ratio≥ 5 and the presence of a single dominant peak in redshift likelihood function. We find that, for quiescent galaxies, the reference HLSS can reach a redshift recovery completeness of ≥50% for F158 magnitude brighter than 20.2 mag. We also explore how different survey parameters, such as exposure time and the number of exposures, influence the accuracy and completeness of redshift recovery, providing insights that could optimize future survey strategies and enhance the scientific yield of the Roman in cosmological research.

Astronomical simulations↗

The magnitude-redshift relation for 561 Abell clusters

The Hubble diagram for the 561 Abell clusters with measured redshifts has been examined using Abell's (1958) corrected photo-red magnitudes for the tenth-ranked cluster member (m10). After correction for the Scott effect and K dimming, the data are in good agreement with a linear magnitude-redshift relation with a slope of 0.2 out to z = 0.1. New redshift data are also presented for 20 Abell clusters. Abell's m10 is suitable for redshift estimation for clusters with m10 of no more than 16.5. At fainter m10, the number of foreground galaxies expected within an Abell radius is large enough to make identification of the tenth-ranked galaxy difficult. Interlopers bias the estimated redshift toward low values at high redshift. Leir and van den Bergh's (1977) redshift estimates suffer from this same bias but to a smaller degree because of the use of multiple cluster parameters. Constraints on deviations of cluster velocities from the mean cosmological flow require greater photometric accuracy than is provided by Abell's m10 magnitudes.

Postman, M.↗

An archival study of IUE observations of low redshift quasars

The emission line and continuum characteristics of a sample of 18 low redshift QSOs from the IUE Archives are presented. The spectral index is found to have a mean value of 1.22, which is considerably steeper than the index of the same spectral region for high redshift QSOs. The line ratios L alpha/H beta and C IV/L alpha for the sample, 9.4 + or - 1.9 and 0.61 + or - .06, respectively, are consistent with the values of the photoionization models. When the low redshift sample is extended with Seyfert galaxies, intermediate redshift QSOs and high redshift QSOs, the equivalent width of L alpha and CIV anticorrelates with the luminosity at 1450 A. The slope of the anticorrelation is seen to be steeper for the higher redshift samples than for the lower redshift samples.

Cheng, F. H.↗

High redshift QSOs and the x ray background

ROSAT pointed observations were made of 9 QSO's from the Large Bright Quasar Survey (LBQS). The LBQS is based on machine measurement of objective prism plates taken with the UK Schmidt Telescope. Software has been used to select QSO's by both color and by the presence of spectral features and continuum breaks. The probability of detection can be calculated as a function of magnitude, redshift and spectral features, and the completeness of the survey can be accurately estimated. Nine out of 1040 QSO's in the LBQS have z greater than 3. The observations will provide an important data point in the X-ray luminosity function of QSO's at high redshift. The QSO's with z greater than 3 span less than a magnitude in M(sub B), so can be combined as a homogeneous sample. This analysis is only possible with a sample drawn from a large and complete catalog such as the LBQS. Four of the 9 QSO's that were observed with the ROSAT PSPC for this proposal were detected, including one of the most luminous X-ray sources ever observed. The April 1992 version of the PROS DETECT package was used to reduce the data. The results have been used to search for evolution of the X-ray properties of QSO's in redshift. The 9 QSO's lie in the range -28.7 less than M(sub B) less than -27.8. When combined with data for 16 QSO's in a similar luminosity range at lower redshift correlations with luminosity and redshift can be separated out. The LBQS sample also yields a new constraint on the contribution of high redshift QSO's to the X-ray background. An initial requirement is knowledge of the X-ray properties (alpha(sub OX)) as a function of redshift. Integration over the evolving luminosity function of the LBQS then gives the QSO contribution to the source counts.

Impey, Chris↗

Redshift distortions of galaxy correlation functions

To examine how peculiar velocities can affect the two-, three-, and four-point redshift correlation functions, we evaluate volume-average correlations for configurations that emphasize and minimize redshift distortions for four different volume-limited samples from each of the CfA, SSRS, and IRAS redshift catalogs. We present the results as the correlation length r(sub 0) and power index gamma of the two-point correlations, bar-xi(sub 0) = (r(sub 0)/r)(exp gamma), and as the hierarchical amplitudes of the three- and four-point functions, S(sub 3) = bar-xi(sub 3)/bar-xi(exp 2)(sub 2) and S(sub 4) = bar-xi(sub 4)/bar-xi(exp 3)(sub 2). We find a characteristic distortion for bar-xi(sub 2), the slope gamma is flatter and the correlation length is larger in redshift space than in real space; that is, redshift distortions 'move' correlations from small to large scales. At the largest scales (up to 12 Mpc), the extra power in the redshift distribution is compatible with Omega(exp 4/7)/b approximately equal to 1. We estimate Omega(exp 4/7)/b to be 0.53 +/- 0.15, 1.10 +/- 0.16, and 0.84 +/- 0.45 for the CfA, SSRS, and IRAS catalogs. Higher order correlations bar-xi(sub 3) and bar-xi(sub 4) suffer similar redshift distortions but in such a way that, within the accuracy of our ananlysis, the normalized amplitudes S(sub 3) and S(sub 4) are insensitive to this effect. The hierarchical amplitudes S(sub 3) and S(sub 4) are constant as a function of scale between 1 and 12 Mpc and have similar values in all samples and catalogs, S(sub 3) approximately equal to 2 and S(sub 4) approximately equal to 6, despite the fact that bar-xi(sub 2), bar-xi(sub 3), and bar-xi(sub 4) differ from one sample to another by large factors (up to a factor of 4 in bar-xi(sub 2), 8 for bar-xi(sub 3), and 12 for bar-xi(sub 4)). The agreement between the independent estimations of S(sub 3) and S(sub 4) is remarkable given the different criteria in the selection of galaxies and also the difference in the resulting range of densities, luminosities, and locations between samples.

Fry, J. N.↗