Engineering topics

Moodley, Kavilan

Publications and source records attributed to Moodley, Kavilan.

At least 37 records · Page 2

DOE OSTI2020

Atacama Cosmology Telescope: Component-separated maps of CMB temperature and the thermal Sunyaev-Zel’dovich effect

Optimal analyses of many signals in the cosmic microwave background (CMB) require map-level extraction of individual components in the microwave sky, rather than measurements at the power spectrum level alone. To date, nearly all map-level component separation in CMB analyses has been performed exclusively using satellite data. In this paper, we implement a component separation method based on the internal linear combination (ILC) approach which we have designed to optimally account for the anisotropic noise (in the 2D Fourier domain) often found in ground-based CMB experiments. Using this method, we combine multi-frequency data from the Planck satellite and the Atacama Cosmology Telescope Polarimeter (ACTPol) to construct the first wide-area, arcminute-resolution component-separated maps (≈ 2100 sq. deg.) of the CMB temperature anisotropy and the thermal Sunyaev-Zel'dovich (tSZ) effect sourced by the inverse-Compton scattering of CMB photons off hot, ionized gas. Our ILC pipeline allows for explicit deprojection of various contaminating signals, including a modified blackbody approximation of the cosmic infrared background (CIB) spectral energy distribution. The cleaned CMB maps will be a useful resource for CMB lensing reconstruction, kinematic SZ cross-correlations, and primordial non-Gaussianity studies. Here, the tSZ maps will be used to study the pressure profiles of galaxies, groups, and clusters through cross-correlations with halo catalogs, with dust contamination controlled via CIB deprojection. The data products described in this paper are available on LAMBDA.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Atacama Cosmology Telescope: Constraints on cosmic birefringence

We present new constraints on anisotropic birefringence of the cosmic microwave background polarization using two seasons of data from the Atacama Cosmology Telescope covering 456 square degrees of sky. The birefringence power spectrum, measured using a curved-sky quadratic estimator, is consistent with zero. Our results provide the tightest current constraint on birefringence over a range of angular scales between 5 arc minutes and 9°. Here, we improve previous upper limits on the amplitude of a scale-invariant birefringence power spectrum by a factor of between 2 and 3. Assuming a nearly massless axion field during inflation, our result is equivalent to a 2σ upper limit on the Chern-Simons coupling constant between axions and photons of g αγ < 4.0 × 10 –2 /H I , where H I is the inflationary Hubble scale.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2017

Two-Season Atacama Cosmology Telescope Polarimeter Lensing Power Spectrum

We report a measurement of the power spectrum of cosmic microwave background (CMB) lensing from two seasons of Atacama Cosmology Telescope polarimeter (ACTPol) CMB data. The CMB lensing power spectrum is extracted from both temperature and polarization data using quadratic estimators. We obtain results that are consistent with the expectation from the best-fit Planck CDM model over a range of multipoles L 80-2100, with an amplitude of lensing A(sub lens) = 1.06 +/- 0.15 stat +/- 0.06 sys relative to Planck. Our measurement of the CMB lensing power spectrum gives sigma 8 omega m(sup 0.25) = 0.643 +/- 0.054; including baryon acoustic oscillation scale data, we constrain the amplitude of density fluctuations to be sigma 8 = 0.831 +/- 0.053. We also update constraints on the neutrino mass sum. We verify our lensing measurement with a number of null tests and systematic checks, finding no evidence of significant systematic errors. This measurement relies on a small fraction of the ACTPol data already taken; more precise lensing results can therefore be expected from the full ACTPol data set.

Shewin, Blake D.↗

NASA NTRS2017

The Atacama Cosmology Telescope: Two-Season ACTPol Spectra and Parameters

We present the temperature and polarization angular power spectra measuredby the Atacama Cosmology Telescope Polarimeter (ACTPol). We analyze night-time datacollected during 2013-14 using two detector arrays at 149 GHz, from 548 deg(exp. 2) of sky onthe celestial equator. We use these spectra, and the spectra measured with the MBAC camera on ACT from 2008-10, in combination with Planck and WMAP data to estimate cosmological parameters from the temperature, polarization, and temperature-polarization cross-correlations. We find the new ACTPol data to be consistent with the CDM model. The ACTPol temperature-polarization cross-spectrum now provides stronger constraints on multiple parameters than the ACTPol temperature spectrum, including the baryon density, the acoustic peak angular scale, and the derived Hubble constant. The new ACTPol dataprovide information on damping tail parameters. The joint uncertainty on the number of neutrino species and the primordial helium fraction is reduced by 20% when adding ACTPol to Planck temperature data alone.

Louis, Thibaut↗

NASA NTRS2017

Cosmological Parameters From Pre-Planck CMB Measurements: A 2017 Update

We present cosmological constraints from the combination of the full mission nine-year WMAP release and small-scale temperature data from the pre-Planck Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT) generation of instruments. This is an update of the analysis presented in Calabrese et al. [Phys. Rev. D 87, 103012 (2013)], and highlights the impact on CDM cosmology of a 0.06 eV massive neutrino which was assumed in the Planck analysis but not in the ACTSPT analyses and a Planck-cleaned measurement of the optical depth to reionization. We show that cosmological constraints are now strong enough that small differences in assumptions about reionization and neutrino mass give systematic differences which are clearly detectable in the data. We recommend that these updated results be used when comparing cosmological constraints from WMAP, ACT and SPT with other surveys or with current and future full-mission Planck cosmology. Cosmological parameter chains are publicly available on the NASAs LAMBDA data archive.

Calabrese, Erminia↗

NASA NTRS2016

Evidence for the Thermal Sunyaev Zeldovich Effect Associated with Quasar Feedback

Using a radio-quiet subsample of the Sloan Digital Sky Survey spectroscopic quasar catalogue, spanning redshifts 0.5-3.5, we derive the mean millimetre and far-infrared quasar spectral energy distributions (SEDs) via a stacking analysis of Atacama Cosmology Telescope and Herschel-Spectral and Photometric Imaging REceiver data. We constrain the form of the far-infrared emission and find 3 sigma-4 sigma evidence for the thermal Sunyaev-Zel'dovich (SZ) effect, characteristic of a hot ionized gas component with thermal energy (6.2 plus or minus 1.7) × 10 (exp 60) erg. This amount of thermal energy is greater than expected assuming only hot gas in virial equilibrium with the dark matter haloes of (1-5) × 10(exp 12) h(exp −1) solar mass that these systems are expected to occupy, though the highest quasar mass estimates found in the literature could explain a large fraction of this energy. Our measurements are consistent with quasars depositing up to (14.5 +/- 3.3)tau (sub 8)(exp -1) per cent of their radiative energy into their circumgalactic environment if their typical period of quasar activity is tau(sub 8) x 108 yr. For high quasar host masses, approximately 10(exp 13) h(exp −1) solar mass, this percentage will be reduced. Furthermore, the uncertainty on this percentage is only statistical and additional systematic uncertainties enter at the 40 per cent level. The SEDs are dust dominated in all bands and we consider various models for dust emission. While sufficiently complex dust models can obviate the SZ effect, the SZ interpretation remains favoured at the 3 sigma-4 sigma level for most models.

Sunyaev-Zeldovich (SZ)↗

NASA NTRS2015

First Measurement of the Cross-Correlation of CMB Lensing and Galaxy Lensing

We measure the cross-correlation of cosmic microwave background (CMB) lensing convergence maps derived from Atacama Cosmology Telescope data with galaxy lensing convergence maps as measured by the Canada-France-Hawaii Telescope Stripe 82 Survey. The CMB-galaxy lensing cross power spectrum is measured for the first time with a significance of 4.2σ, which corresponds to a 12% constraint on the amplitude of density fluctuations at redshifts ∼0.9. With upcoming improved lensing data, this novel type of measurement will become a powerful cosmological probe, providing a precise measurement of the mass distribution at intermediate redshifts and serving as a calibrator for systematic biases in weak lensing measurements.

CMB-galzxy lensing cross power spectrum↗

NASA NTRS2014

The Atacama Cosmology Telescope: Dusty Star-Forming Galaxies and Active Galactic Nuclei in the Southern Survey

We present a catalogue of 191 extragalactic sources detected by the Atacama Cosmology Telescope (ACT) at 148 and/or 218 GHz in the 2008 Southern survey. Flux densities span 14 -1700 mJy, and we use source spectral indices derived using ACT-only data to divide our sources into two subpopulations: 167 radio galaxies powered by central active galactic nuclei (AGN) and 24 dusty star-forming galaxies (DSFGs). We cross-identify 97 per cent of our sources (166 of the AGN and 19 of the DSFGs) with those in currently available catalogues. When combined with flux densities from the Australia Telescope 20 GHz survey and follow-up observations with the Australia Telescope Compact Array, the synchrotron-dominated population is seen to exhibit a steepening of the slope of the spectral energy distribution from 20 to 148 GHz, with the trend continuing to 218 GHz. The ACT dust-dominated source population has a median spectral index, A(sub 148-218), of 3.7 (+0.62 or −0.86), and includes both local galaxies and sources with redshift around 6. Dusty sources with no counterpart in existing catalogues likely belong to a recently discovered subpopulation of DSFGs lensed by foreground galaxies or galaxy groups.

dusty star-forming galaxies (DSFGs)↗

NASA NTRS2014

The Atacama Cosmology Telescope: Dusty Star-Forming Galaxies and Active Galactic Nuclei in the Southern Survey

We present a catalogue of 191 extragalactic sources detected by the Atacama Cosmology Telescope (ACT) at 148 and/or 218 GHz in the 2008 Southern survey. Flux densities span 14 - 1700 mJy, and we use source spectral indices derived using ACT-only data to divide our sources into two subpopulations: 167 radio galaxies powered by central active galactic nuclei (AGN) and 24 dusty star-forming galaxies (DSFGs). We cross-identify 97 per cent of our sources (166 of the AGN and 19 of the DSFGs) with those in currently available catalogues. When combined with flux densities from the Australia Telescope 20 GHz survey and follow-up observations with the Australia Telescope Compact Array, the synchrotron-dominated population is seen to exhibit a steepening of the slope of the spectral energy distribution from 20 to 148 GHz, with the trend continuing to 218 GHz. The ACT dust-dominated source population has a median spectral index, alpha(sub 148−218), of 3.7 +0.62/-0.86), and includes both local galaxies and sources with redshift around 6. Dusty sources with no counterpart in existing catalogues likely belong to a recently discovered subpopulation of DSFGs lensed by foreground galaxies or galaxy groups.

Telescope↗

NASA NTRS2013

First Measurement of the Cross-Correlation of CMB Lensing and Galaxy Lensing

We measure the cross-correlation of cosmic microwave background lensing convergence maps derived from Atacama Cosmology Telescope data with galaxy lensing convergence maps as measured by the Canada-France-Hawaii Telescope Stripe 82 Survey. The CMB-galaxy lensing cross power spectrum is measured for the first time with a significance of 3.2σ, which corresponds to a 16% constraint on the amplitude of density fluctuations at redshifts ~ 0.9. With upcoming improved lensing data, this novel type of measurement will become a powerful cosmological probe, providing a precise measurement of the mass distribution at intermediate redshifts and serving as a calibrator for systematic biases in weak lensing measurements.

Hand, Nick↗

NASA NTRS2013

The Atacama Cosmology Telescope: Beam Measurements and the Microwave Brightness Temperatures of Uranus and Saturn

We describe the measurement of the beam profiles and window functions for the Atacama Cosmology Telescope (ACT), which operated from 2007 to 2010 with kilopixel bolometer arrays centered at 148, 218, and 277 GHz. Maps of Saturn are used to measure the beam shape in each array and for each season of observations. Radial profiles are transformed to Fourier space in a way that preserves the spatial correlations in the beam uncertainty to derive window functions relevant for angular power spectrum analysis. Several corrections are applied to the resulting beam transforms, including an empirical correction measured from the final cosmic microwave background (CMB) survey maps to account for the effects of mild pointing variation and alignment errors. Observations of Uranus made regularly throughout each observing season are used to measure the effects of atmospheric opacity and to monitor deviations in telescope focus over the season. Using the WMAP-based calibration of the ACT maps to the CMB blackbody, we obtain precise measurements of the brightness temperatures of the Uranus and Saturn disks at effective frequencies of 149 and 219 GHz. For Uranus we obtain thermodynamic brightness temperatures T(149/U) = 106.7 +/- 2.2 K and T(219/U) = 100.1 +/- 3.1 K. For Saturn, we model the effects of the ring opacity and emission using a simple model and obtain resulting (unobscured) disk temperatures of T(149/S) = 137.3 +/- 3.2 K and T(219/S) = 137.3 +/- 4.7 K.

Atacama Cosmology Telescope (ACT)↗

NASA NTRS2013

The Atacama Cosmology Telescope: Dusty Star-Forming Galaxies and Active Galactic Nuclei in the Southern Survey

We present a catalog of 191 extragalactic sources detected by the Atacama Cosmology Telescope (ACT) at 148 GHz and/or 218GHz in the 2008 Southern survey. Flux densities span 14-1700mJy, and we use source spectral indices derived using ACT-only data to divide our sources into two sub-populations: 167 radio galaxies powered by central active galactic nuclei (AGN), and 24 dusty star-forming galaxies (DSFGs). We cross-identify 97% of our sources (166 of the AGN and 19 of the DSFGs) with those in currently available catalogs. When combined with flux densities from the Australian Telescope 20 GHz survey and follow-up observations with the Australia Telescope Compact Array, the synchrotron-dominated population is seen to exhibit a steepening of the slope of the spectral energy distribution from 20 to 148GHz, with the trend continuing to 218GHz. The ACT dust-dominated source population has a median spectral index, alpha(sub 148−218), of 3.7+0.62 or −0.86, and includes both local galaxies and sources with redshifts as great as 5.6. Dusty sources with no counterpart in existing catalogs likely belong to a recently discovered subpopulation of DSFGs lensed by foreground galaxies or galaxy groups.

millimeter: galaxies↗

NASA NTRS2012

The Atacama Cosmology Telescope: Cross-Correlation of Cosmic Microwave Background Lensing and Quasars

We measure the cross-correlation of Atacama cosmology telescope cosmic microwave background (CMB) lensing convergence maps with quasar maps made from the Sloan Digital Sky Survey DR8 SDSS-XDQSO photometric catalog. The CMB lensing quasar cross-power spectrum is detected for the first time at a significance of 3.8 sigma, which directly confirms that the quasar distribution traces the mass distribution at high redshifts z > 1. Our detection passes a number of null tests and systematic checks. Using this cross-power spectrum, we measure the amplitude of the linear quasar bias assuming a template for its redshift dependence, and find the amplitude to be consistent with an earlier measurement from clustering; at redshift z ap 1.4, the peak of the distribution of quasars in our maps, our measurement corresponds to a bias of b = 2.5 +/- 0.6. With the signal-to-noise ratio on CMB lensing measurements likely to improve by an order of magnitude over the next few years, our results demonstrate the potential of CMB lensing crosscorrelations to probe astrophysics at high redshifts.

CMB lensing quasar cross-power spectrum↗

NASA NTRS2012

Power-Law Template for Infrared Point-Source Clustering

We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub −n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ν(sup Beta)B(ν, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.

cosmic background radiation↗

NASA NTRS2012

The Atacama Cosmology Telescope: ACT-CL J0102-4915 'EL GORDO', A Massive Merging Cluster at Redshift 0.87

We present a detailed analysis from new multi-wavelength observations of the exceptional galaxy cluster ACT-CL J0102−4915, likely the most massive, hottest, most X-ray luminous and brightest Sunyaev-Zel'dovich (SZ) effect cluster known at redshifts greater than 0.6. The Atacama Cosmology Telescope (ACT) collaboration discovered ACT-CL J0102−4915 as the most significant Sunyaev-Zeldovich (SZ) decrement in a sky survey area of 755 square degrees. Our VLT/FORS2 spectra of 89 member galaxies yield a cluster redshift, z = 0.870, and velocity dispersion, sigma(sub gal) = 1321+/-106 km s−1. Our Chandra observations reveal a hot and X-ray luminous system with an integrated temperature of T(sub X) = 14.5+/-1.0 keV and 0.5-2.0 keV band luminosity of L(sub X) = (2.19+/-0.11)×10(sup 45) h(sup −2)(sub 70) erg s−1. We obtain several statistically consistent cluster mass estimates; using empirical mass scaling relations with velocity dispersion, X-ray Y(sub X), and integrated SZ distortion, we estimate a cluster mass of M(sub 200a) = (2.16+/-0.32)×1015 h(sup −1)(sub 70) solar mass. We constrain the stellar content of the cluster to be less than 1% of the total mass, using Spitzer IRAC and optical imaging. The Chandra and VLT/FORS2 optical data also reveal that ACT-CL J0102−4915 is undergoing a major merger between components with a mass ratio of approximately 2 to 1. The X-ray data show significant temperature variations from a low of 6.6+/-0.7 keV at the merging low-entropy, high-metallicity, cool core to a high of 22+/-6 keV. We also see a wake in the X-ray surface brightness and deprojected gas density caused by the passage of one cluster through the other. Archival radio data at 843 MHz reveal diffuse radio emission that, if associated with the cluster, indicates the presence of an intense double radio relic, hosted by the highest redshift cluster yet. ACT-CL J0102−4915 is possibly a high-redshift analog of the famous Bullet Cluster. Such a massive cluster at this redshift is rare, although consistent with the standard ΛCDM cosmology in the lower part of its allowed mass range. Massive, highredshift mergers like ACT-CL J0102−4915 are unlikely to be reproduced in the current generation of numerical N-body cosmological simulations.

cosmology observations↗

NASA NTRS2012

The Atacama Cosmology Telescope: Relation Between Galaxy Cluster Optical Richness and Sunyaev-Zel'dovich Effect

We present the measured Sunyaev-Zel'dovich (SZ) flux from 474 optically-selected MaxBCG clusters that fall within the Atacama Cosmology Telescope (ACT) Equatorial survey region. The ACT Equatorial region used in this analysis covers 510 square degrees and overlaps Stripe 82 of the Sloan Digital Sky Survey. We also present the measured SZ flux stacked on 52 X-ray-selected MCXC clusters that fall within the ACT Equatorial region and an ACT Southern survey region covering 455 square degrees. We find that the measured SZ flux from the X-ray-selected clusters is consistent with expectations. However, we find that the measured SZ flux from the optically-selected clusters is both significantly lower than expectations and lower than the recovered SZ flux measured by the Planck satellite. Since we find a lower recovered SZ signal than Planck, we investigate the possibility that there is a significant offset between the optically-selected brightest cluster galaxies (BCGs) and the SZ centers, to which ACT is more sensitive due to its finer resolution. Such offsets can arise due to either an intrinsic physical separation between the BCG and the center of the gas concentration or from misidentification of the cluster BCG. We find that the entire discrepancy for both ACT and Planck can be explained by assuming that the BCGs are offset from the SZ maxima with a uniform random distribution between 0 and 1.5 Mpc. In contrast, the physical separation between BCGs and X-ray peaks for an X-ray-selected subsample of MaxBCG clusters shows a much narrower distribution that peaks within 0.2 Mpc. We conclude that while offsets between BCGs and SZ peaks may be an important component in explaining the discrepancy, it is likely that a combination of factors is responsible for the ACT and Planck measurements. Several effects that can lower the SZ signal equally for both ACT and Planck, but not explain the difference in measured signals, include a larger percentage of false detections in the MaxBCG sample, a lower normalization of the mass-richness relation, radio or infrared galaxy contamination of the SZ flux, and a low intrinsic SZ signal. In the latter two cases, the effects would need to be preferentially more significant in the optically-selected MaxBCG sample than in the MCXC X-ray sample.

Sehgal, Neelima↗

NASA NTRS2011

The Atacama Cosmology Telescope: ACT-CL J0102-4215 "El Gordo," a Massive Merging Cluster at Redshift 0.87

We present a detailed analysis from new multi-wavelength observations of the exceptional galaxy cluster ACT-CL J0102-4915, likely the most massive, hottest, most X-ray luminous and brightest Sunyaev-Zel'dovich (SZ) effect cluster known at redshifts greater than 0.6. The Atacama Cosmology Telescope (ACT) collaboration discovered ACT-CL J0102-4915 as the most significant Sunyaev-Zeldovich (SZ) decrement in a sky survey area of 755 square degrees. Our VLT/FORS2 spectra of 89 member galaxies yield a cluster redshift, z = 0.870, and velocity dispersion, sigma(gal) +/- 1321 106 km s-1. Our Chandra observations reveal a hot and X-ray luminous system with an integrated temperature of T(X) = 14:5 +/- 0:1 keV and 0.5 2.0 keV band luminosity of L(X) = (2:19 0:11) 1045 h(exp -2)70erg s-1. We obtain several statistically consistent cluster mass estimates; using empirical mass scaling relations with velocity dispersion, X-ray Y(X) , and integrated SZ distortion, we estimate a cluster mass of M(200) = (2:16 +/- 0:32) 10(exp 15) h(exp-1) 70M compared to the Sun. We constrain the stellar content of the cluster to be less than 1% of the total mass, using Spitzer IRAC and optical imaging. The Chandra and VLT/FORS2 optical data also reveal that ACT-CL J0102-4915 is undergoing a major merger between components with a mass ratio of approximately 2 to 1. The X-ray data show significant temperature variations from a low of 6:6 +/- 0:7 keV at the merging low-entropy, high-metallicity, cool core to a high of 22 +/- 6 keV. We also see a wake in the X-ray surface brightness and deprojected gas density caused by the passage of one cluster through the other from which we estimate a merger speed of around 1300 km s(exp -1) for an assumed merger timescale of 1 Gyr. ACTCL J0102-4915 is possibly a high-redshift analog of the famous Bullet Cluster. Such a massive cluster at this redshift is rare, although consistent with the standard CDM cosmology in the lower part of its allowed mass range. Massive, high-redshift mergers like ACT-CL J0102-4915 are unlikely to be reproduced in the current generation of numerical N-body cosmological simulations.

Menanteau, Felipe↗

NASA NTRS2011

The Atacama Cosmology Telescope: High-Resolution Sunyaev-Zeldovich Array Observations of ACT SZE-Selected Clusters from the Equatorial Strip

We present follow-up observations with the Sunyaev-Zel'dovich Array (SZA) of optically-confirmed galaxy clusters found in the equatorial survey region of the Atacama Cosmology Telescope (ACT): ACT-CL J0022-0036, ACT-CL J2051+0057, and ACT-CL J2337+0016. ACT-CL J0022-0036 is a newly-discovered, massive ( approximately equals 10(exp 15) Solar M), high-redshift (z = 0.81) cluster revealed by ACT through the Sunyaev-Zeldovich effect (SZE). Deep, targeted observations with the SZA allow us to probe a broader range of cluster spatial scales, better disentangle cluster decrements from radio point source emission, and derive more robust integrated SZE flux and mass estimates than we can with ACT data alone. For the two clusters we detect with the SZA we compute integrated SZE signal and derive masses from the SZA data only. ACT-CL J2337+0016, also known as Abell 2631, has archival Chandra data that allow an additional X-ray-based mass estimate. Optical richness is also used to estimate cluster masses and shows good agreement with the SZE and X-ray-based estimates. Based on the point sources detected by the SZA in these three cluster fields and an extrapolation to ACT's frequency, we estimate that point sources could be contaminating the SZE decrement at the approx < 20% level for some fraction of clusters.

galaxies↗