arXiv subjects

R. Glenn Morris

Publications and source records attributed to R. Glenn Morris.

At least 37 records · Page 2Linked to original sources

arXiv2023

Improved noise performance from the next-generation buried-channel p-Mosfet SiSeROs

The Single electron Sensitive Read Out (SiSeRO) is a novel on-chip charge detector output stage for charge-coupled device (CCD) image sensors. Developed at MIT Lincoln Laboratory, this technology uses a p-MOSFET transistor with a depleted internal gate beneath the transistor channel. The transistor source-drain current is modulated by the transfer of charge into the internal gate. At Stanford, we have developed a readout module based on the drain current of the on-chip transistor to characterize the device. In our earlier work, we characterized a number of first prototype SiSeROs with the MOSFET transistor channels at the surface layer. An equivalent noise charge (ENC) of around 15 electrons root mean square (RMS) was obtained. In this work, we examine the first buried-channel SiSeRO. We have achieved substantially improved noise performance of around 4.5 electrons root mean square (RMS) and a full width half maximum (FWHM) energy resolution of 132 eV at 5.9 keV, for a readout speed of 625 kpixel/s. We also discuss how digital filtering techniques can be used to further improve the SiSeRO noise performance. Additional measurements and device simulations will be essential to further mature the SiSeRO technology. This new device class presents an exciting new technology for the next-generation astronomical X-ray telescopes requiring fast, low-noise, radiation-hard megapixel imagers with moderate spectroscopic resolution.

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arXiv2023

The Concentration-Mass Relation of Massive, Dynamically Relaxed Galaxy Clusters: Agreement Between Observations and $Λ$CDM Simulations

The relationship linking a galaxy cluster's total mass with the concentration of its mass profile and its redshift is a fundamental prediction of the Cold Dark Matter (CDM) paradigm of cosmic structure formation. However, confronting those predictions with observations is complicated by the fact that simulated clusters are not representative of observed samples where detailed mass profile constraints are possible. In this work, we calculate the Symmetry-Peakiness-Alignment (SPA) morphology metrics for maps of X-ray emissivity from THE THREE HUNDRED project hydrodynamical simulations of galaxy clusters at four redshifts, and thereby select a sample of morphologically relaxed, simulated clusters, using observational criteria. These clusters have on average earlier formation times than the full sample, confirming that they are both morphologically and dynamically more relaxed than typical. We constrain the concentration-mass-redshift relation of both the relaxed and complete sample of simulated clusters, assuming power-law dependences on mass ($κ_m$) and $1+z$ ($κ_ζ$), finding $κ_m = -0.12 \pm 0.07$ and $κ_ζ= -0.27 \pm 0.19$ for the relaxed subsample. From an equivalently selected sample of massive, relaxed clusters observed with ${\it Chandra}$, we find $κ_m = -0.12 \pm 0.08$ and $κ_ζ= -0.48 \pm 0.19$, in good agreement with the simulation predictions. The simulated and observed samples also agree well on the average concentration at a pivot mass and redshift providing further validation of the $Λ$CDM paradigm in the properties of the largest gravitationally collapsed structures observed. This also represents the first clear detection of decreasing concentration with redshift, a longstanding prediction of simulations, in data.

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arXiv2023

The Evolution and Mass Dependence of Galaxy Cluster Pressure Profiles at 0.05 $\le z \le$ 0.60 and $4 \times 10^{14}$ M$_{\odot}$ $\le \textrm{M}_{500} \le 30 \times 10^{14}$ M$_{\odot}$

We have combined X-ray observations from Chandra with Sunyaev-Zel'dovich (SZ) effect data from Planck and Bolocam to measure intra-cluster medium pressure profiles from 0.03R$_{500}$ $\le$ R $\le$ 5R$_{500}$ for a sample of 21 low-$z$ galaxy clusters with a median redshift $\langle z \rangle = 0.08$ and a median mass $\langle \textrm{M}_{500} \rangle = 6.1 \times 10^{14}$ M$_{\odot}$ and a sample of 19 mid-$z$ galaxy clusters with $\langle z \rangle = 0.50$ and $\langle \textrm{M}_{500} \rangle = 10.6 \times 10^{14}$ M$_{\odot}$. The mean scaled pressure in the low-$z$ sample is lower at small radii and higher at large radii, a trend that is accurately reproduced in similarly selected samples from The300 simulations. This difference appears to be primarily due to dynamical state at small radii, evolution at intermediate radii, and a combination of evolution and mass dependence at large radii. Furthermore, the overall flattening of the mean scaled pressure profile in the low-$z$ sample compared to the mid-$z$ sample is consistent with expectations due to differences in mass accretion rate and the fractional impact of feedback mechanisms. In agreement with previous studies, the fractional scatter about the mean scaled pressure profile reaches a minimum of $\simeq 20$ per cent near 0.5R$_{500}$. This scatter is consistent between the low-$z$ and mid-$z$ samples at all radii, suggesting it is not strongly impacted by sample selection, and this general behavior is reproduced in The300 simulations. Finally, analytic functions that approximately describe the mass and redshift trends in mean pressure profile shape are provided.

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arXiv2022

Chandra measurements of gas homogeneity and turbulence at intermediate radii in the Perseus Cluster

We present a Chandra study of surface brightness fluctuations in the diffuse intracluster medium of the Perseus Cluster. Our study utilizes deep, archival imaging of the cluster core as well as a new mosaic of 29 short 5 ks observations extending in 8 different directions out to radii of r_500 ~ 2.2r_2500. Under the assumption that the distribution of densities at a given radius is log-normally distributed, two important quantities can be derived from the width of the log-normal density distribution on a given spatial scale: the density bias, which is equal to the square root of the clumping factor C; and the one-component turbulent velocity, v_(k, 1D). We forward-model all contributions to the measured surface brightness, including astrophysical and particle background components, and account for the Poisson nature of the measured signal. Measuring the distribution of surface brightness fluctuations in 1 arcmin^2 regions, spanning the radial range 0.3-2.2 r_2500 (7.8-57.3 arcmin), we find a small to moderate average density bias of around 3% at radii below 1.6r_2500. We also infer an average turbulent velocity at these radii of v_1D <400 km s^-1. Direct confirmation of our results on turbulent velocities inferred from surface brightness fluctuations should be possible using the X-ray calorimeter spectrometers to be flown aboard the XRISM and Athena. observatories.

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arXiv2022

Development and characterization of a fast and low noise readout for the next generation X-ray CCDs

The broad energy response, low electronic read noise, and good energy resolution have made X-ray Charge-Coupled Devices (CCDs) an obvious choice for developing soft X-ray astronomical instruments over the last half century. They also come in large array formats with small pixel sizes which make them a potential candidate for the next generation astronomical X-ray missions. However, the next generation X-ray telescopic experiments propose for significantly larger collecting area compared to the existing observatories in order to explore the low luminosity and high redshift X-ray universe which requires these detectors to have an order of magnitude faster readout. In this context, the Stanford University (SU) in collaboration with the Massachusetts Institute of Technology (MIT) has initiated the development of fast readout electronics for X-ray CCDs. At SU, we have designed and developed a fast and low noise readout module with the goal of achieving a readout speed of 5 Mpixel/s. We successfully ran a prototype CCD matrix of 512 $\times$ 512 pixels at 4 Mpixels/s. In this paper, we describe the details of the readout electronics and report the performance of the detectors at these readout speeds in terms of read noise and energy resolution. In the future, we plan to continue to improve performance of the readout module and eventually converge to a dedicated ASIC based readout system to enable parallel read out of large array multi-node CCD devices.

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arXiv2021

First results on SiSeRO (Single electron Sensitive Read Out) devices -- a new X-ray detector for scientific instrumentation

We present an evaluation of a novel on-chip charge detector, called the Single electron Sensitive Read Out (SiSeRO), for charge-coupled device (CCD) image sensor applications. It uses a p-MOSFET transistor at the output stage with a depleted internal gate beneath the p-MOSFET. Charge transferred to the internal gate modulates the source-drain current of the transistor. We have developed a drain current readout module to characterize the detector. The prototype sensor achieves a charge/current conversion gain of 700 pA per electron, an equivalent noise charge (ENC) of 15 electrons (e-) root mean square (RMS), and a full width half maximum (FWHM) of 230 eV at 5.9 keV. In this paper, we discuss the SiSeRO working principle, the readout module developed at Stanford, and the first characterization test results of the SiSeRO prototypes. While at present only a proof-of-concept experiment, in the near future we plan to use next generation sensors with improved noise performance and an enhanced readout module. In particular, we are developing a readout module enabling Repetitive Non-Destructive Readout (RNDR) of the charge, which can in principle yield sub-electron ENC performance. With these developments, we eventually plan to build a matrix of SiSeRO amplifiers to develop an active pixel sensor with an on-chip ASIC-based readout system. Such a system, with fast readout speeds and sub-electron noise, could be effectively utilized in scientific applications requiring fast and low-noise spectro-imagers.

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arXiv2021

The History of Metal Enrichment Traced by X-ray Observations of High Redshift Galaxy Clusters

We present the analysis of deep X-ray observations of 10 massive galaxy clusters at redshifts $1.05 < z < 1.71$, with the primary goal of measuring the metallicity of the intracluster medium (ICM) at intermediate radii, to better constrain models of the metal enrichment of the intergalactic medium. The targets were selected from X-ray and Sunyaev-Zel'dovich (SZ) effect surveys, and observed with both the \textit{XMM-Newton} and \textit{Chandra} satellites. For each cluster, a precise gas mass profile was extracted, from which the value of $r_{500}$ could be estimated. This allows us to define consistent radial ranges over which the metallicity measurements can be compared. In general, the data are of sufficient quality to extract meaningful metallicity measurements in two radial bins, $r<0.3r_{500}$ and $0.3<r/r_{500}<1.0$. For the outer bin, the combined measurement for all ten clusters, $Z/Z_{\odot} = 0.21 \pm 0.09$, represents a substantial improvement in precision over previous results. This measurement is consistent with, but slightly lower than, the average metallicity of 0.315 Solar measured at intermediate-to-large radii in low-redshift clusters. Combining our new high-redshift data with the previous low-redshift results allows us to place the tightest constraints to date on models of the evolution of cluster metallicity at intermediate radii. Adopting a power law model of the form $Z \propto \left(1+z\right)^γ$, we measure a slope $γ= -0.5^{+0.4}_{-0.3}$, consistent with the majority of the enrichment of the ICM having occurred at very early times and before massive clusters formed, but leaving open the possibility that some additional enrichment in these regions may have occurred since a redshift of 2.

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arXiv2021

Measuring $H_0$ using X-ray and SZ effect observations of dynamically relaxed galaxy clusters

We use a sample of 14 massive, dynamically relaxed galaxy clusters to constrain the Hubble Constant, $H_0$, by combining X-ray and Sunyaev-Zel'dovich (SZ) effect signals measured with Chandra, Planck and Bolocam. This is the first such analysis to marginalize over an empirical, data-driven prior on the overall accuracy of X-ray temperature measurements, while our restriction to the most relaxed, massive clusters also minimizes astrophysical systematics. For a cosmological-constant model with $Ω_m = 0.3$ and $Ω_Λ = 0.7$, we find $H_0 = 67.3^{+21.3}_{-13.3}$ km/s/Mpc, limited by the temperature calibration uncertainty (compared to the statistically limited constraint of $H_0 = 72.3^{+7.6}_{-7.6}$ km/s/Mpc). The intrinsic scatter in the X-ray/SZ pressure ratio is found to be $13 \pm 4$ per cent ($10 \pm 3$ per cent when two clusters with significant galactic dust emission are removed from the sample), consistent with being primarily due to triaxiality and projection. We discuss the prospects for reducing the dominant systematic limitation to this analysis, with improved X-ray calibration and/or precise measurements of the relativistic SZ effect providing a plausible route to per cent level constraints on $H_0$.

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arXiv2020

Deep XMM-Newton Observations of the Most Distant SPT-SZ Galaxy Cluster

We present results from a 577 ks XMM-Newton observation of SPT-CL J0459-4947, the most distant cluster detected in the South Pole Telescope 2500 square degree (SPT-SZ) survey, and currently the most distant cluster discovered through its Sunyaev-Zel'dovich effect. The data confirm the cluster's high redshift, $z=1.71 \pm 0.02$, in agreement with earlier, less precise optical/IR photometric estimates. From the gas density profile, we estimate a characteristic mass of $M_{500}=(1.8 \pm 0.2) \times 10^{14}M_{Sun}$; cluster emission is detected above the background to a radius of $\sim 2.2 r_{500}$, or approximately the virial radius. The intracluster gas is characterized by an emission-weighted average temperature of $7.2 \pm 0.3$ keV and metallicity with respect to Solar of $0.37 \pm 0.08$. For the first time at such high redshift, this deep data set provides a measurement of metallicity outside the cluster center; at radii $r > 0.3 r_{500}$, we find it to be $0.33 \pm 0.17$, in good agreement with precise measurements at similar radii in the most nearby clusters, supporting an early enrichment scenario in which the bulk of the cluster gas is enriched to a universal metallicity prior to cluster formation, with little to no evolution thereafter. The leverage provided by the high redshift of this cluster tightens by a factor of 2 constraints on evolving metallicity models, when combined with previous measurements at lower redshifts.

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arXiv2019

Improved Cosmological Constraints from SDSS redMaPPer Clusters via X-ray Follow-up of a Complete Subsample of Systems

We improve upon the cosmological constraints derived from the abundance and weak-lensing data of redMaPPer clusters detected in the Sloan Digital Sky Survey (SDSS). Specifically, we derive gas mass data using Chandra X-ray follow-up of a complete sample of the 30 richest SDSS redMaPPer clusters with $z\in[0.1,0.3]$, and use these additional data to improve upon the original analysis by Costanzi et al. (2019b). We simultaneously fit for the parameters of the richness-mass relation, the cluster gas mass-mass relation, and cosmology. By including our X-ray cluster sample in the SDSS cluster cosmology analysis, we measure $Ω_{\rm m} = 0.25 \pm 0.04$ and $σ_8 = 0.85^{+0.06}_{-0.08}$. These constraints represent a 25.5% and 29.8% reduction in the size of the 68% confidence intervals of $Ω_{\rm m}$ and $σ_8$ respectively, relative to the constraints published in Costanzi et al. (2019b). Our cosmological constraints are in agreement with early universe results from Planck. As a byproduct of our analysis, we also perform an independent calibration of the amplitude of the $\langle M_{\rm gas}^{\rm true}|M_{\rm 500c}\rangle$ scaling relation. Our calibration is consistent with and of comparable precision to that of Mantz et al. (2016b).

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arXiv2019

Ellipticity of Brightest Cluster Galaxies as tracer of halo orientation and weak-lensing mass bias

Weak-lensing measurements of the masses of galaxy clusters are commonly based on the assumption of spherically symmetric density profiles. Yet, the cold dark matter model predicts the shapes of dark matter halos to be triaxial. Halo triaxiality, and the orientation of the major axis with respect to the line of sight, are expected to be the leading cause of intrinsic scatter in weak-lensing mass measurements. The shape of central cluster galaxies (Brightest Cluster Galaxies; BCGs) is expected to follow the shape of the dark matter halo. Here we investigate the use of BCG ellipticity as predictor of the weak-lensing mass bias in individual clusters compared to the mean. Using weak lensing masses $M^{\rm WL}_{500}$ from the Weighing the Giants project, and $M_{500}$ derived from gas masses as low-scatter mass proxy, we find that, on average, the lensing masses of clusters with the roundest / most elliptical 25% of BCGs are biased $\sim 20$% high / low compared to the average, as qualitatively predicted by the cold dark matter model. For cluster cosmology projects utilizing weak-lensing mass estimates, the shape of the BCG can thus contribute useful information on the effect of orientation bias in weak lensing mass estimates as well as on cluster selection bias.

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arXiv2017

Center-Excised X-ray Luminosity as an Efficient Mass Proxy for Future Galaxy Cluster Surveys

The cosmological constraining power of modern galaxy cluster catalogs can be improved by obtaining low-scatter mass proxy measurements for even a small fraction of sources. In the context of large upcoming surveys that will reveal the cluster population down to the group scale and out to high redshifts, efficient strategies for obtaining such mass proxies will be valuable. In this work, we use high-quality weak lensing and X-ray mass estimates for massive clusters in current X-ray selected catalogs to revisit the scaling relations of the projected, center-excised X-ray luminosity ($L_{ce}$), which previous work suggests correlates tightly with total mass. Our data confirm that this is the case, with $L_{ce}$ having an intrinsic scatter at fixed mass comparable to that of gas mass, temperature or $Y_X$. Compared to these other proxies, however, $L_{ce}$ is less susceptible to systematic uncertainties due to background modeling, and can be measured precisely with shorter exposures. This opens up the possibility of using $L_{ce}$ to estimate masses for large numbers of clusters discovered by new X-ray surveys (e.g. eROSITA) directly from the survey data, as well as for clusters discovered at other wavelengths, with relatively short follow-up observations. We describe a simple procedure for making such estimates from X-ray surface brightness data, and comment on the spatial resolution required to apply this method as a function of cluster mass and redshift. We also explore the potential impact of Chandra and XMM-Newton follow-up observations over the next decade on dark energy constraints from new cluster surveys.

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arXiv2017

The Metallicity of the Intracluster Medium Over Cosmic Time: Further Evidence for Early Enrichment

We use Chandra X-ray data to measure the metallicity of the intracluster medium (ICM) in 245 massive galaxy clusters selected from X-ray and Sunyaev-Zel'dovich (SZ) effect surveys, spanning redshifts $0<z<1.2$. Metallicities were measured in three different radial ranges, spanning cluster cores through their outskirts. We explore trends in these measurements as a function of cluster redshift, temperature, and surface brightness "peakiness" (a proxy for gas cooling efficiency in cluster centers). The data at large radii (0.5--1 $r_{500}$) are consistent with a constant metallicity, while at intermediate radii (0.1-0.5 $r_{500}$) we see a late-time increase in enrichment, consistent with the expected production and mixing of metals in cluster cores. In cluster centers, there are strong trends of metallicity with temperature and peakiness, reflecting enhanced metal production in the lowest-entropy gas. Within the cool-core/sharply peaked cluster population, there is a large intrinsic scatter in central metallicity and no overall evolution, indicating significant astrophysical variations in the efficiency of enrichment. The central metallicity in clusters with flat surface brightness profiles is lower, with a smaller intrinsic scatter, but increases towards lower redshifts. Our results are consistent with other recent measurements of ICM metallicity as a function of redshift. They reinforce the picture implied by observations of uniform metal distributions in the outskirts of nearby clusters, in which most of the enrichment of the ICM takes place before cluster formation, with significant later enrichment taking place only in cluster centers, as the stellar populations of the central galaxies evolve.

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arXiv2017

Weighing the Giants V: Galaxy Cluster Scaling Relations

We present constraints on the scaling relations of galaxy cluster X-ray luminosity, temperature and gas mass (and derived quantities) with mass and redshift, employing masses from robust weak gravitational lensing measurements. These are the first such results obtained from an analysis that simultaneously accounts for selection effects and the underlying mass function, and directly incorporates lensing data to constrain total masses. Our constraints on the scaling relations and their intrinsic scatters are in good agreement with previous studies, and reinforce a picture in which departures from self-similar scaling laws are primarily limited to cluster cores. However, the data are beginning to reveal new features that have implications for cluster astrophysics and provide new tests for hydrodynamical simulations. We find a positive correlation in the intrinsic scatters of luminosity and temperature at fixed mass, which is related to the dynamical state of the clusters. While the evolution of the nominal scaling relations over the redshift range $0.0<z<0.5$ is consistent with self similarity, we find tentative evidence that the luminosity and temperature scatters respectively decrease and increase with redshift. Physically, this likely related to the development of cool cores and the rate of major mergers. We also examine the scaling relations of redMaPPer richness and Compton $Y$ from Planck. While the richness--mass relation is in excellent agreement with recent work, the measured $Y$--mass relation departs strongly from that assumed in the Planck cluster cosmology analysis. The latter result is consistent with earlier comparisons of lensing and Planck scaling-relation-derived masses.

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arXiv2016

Cosmology and Astrophysics from Relaxed Galaxy Clusters V: Consistency with Cold Dark Matter Structure Formation

This is the fifth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises 40 clusters identified as being dynamically relaxed and hot in Papers I and II of this series. Here we use constraints on cluster mass profiles from X-ray data to test some of the basic predictions of cosmological structure formation in the Cold Dark Matter (CDM) paradigm. We present constraints on the concentration--mass relation for massive clusters, finding a power-law mass dependence with a slope of $κ_m=-0.16\pm0.07$, in agreement with CDM predictions. For this relaxed sample, the relation is consistent with a constant as a function of redshift (power-law slope with $1+z$ of $κ_ζ=-0.17\pm0.26$), with an intrinsic scatter of $σ_{\ln c}=0.16\pm0.03$. We investigate the shape of cluster mass profiles over the radial range probed by the data (typically $\sim50$kpc--1Mpc), and test for departures from the simple Navarro, Frenk & White (NFW) form, for which the logarithmic slope of the density profile tends to $-1$ at small radii. Specifically, we consider as alternatives the generalized NFW (GNFW) and Einasto parametrizations. For the GNFW model, we find an average value of (minus) the logarithmic inner slope of $β=1.02\pm0.08$, with an intrinsic scatter of $σ_β=0.22\pm0.07$, while in the Einasto case we constrain the average shape parameter to be $α=0.29\pm0.04$ with an intrinsic scatter of $σ_α=0.12\pm0.04$. Our results are thus consistent with the simple NFW model on average, but we clearly detect the presence of intrinsic, cluster-to-cluster scatter about the average.

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arXiv2016

Cosmology and Astrophysics from Relaxed Galaxy Clusters III: Thermodynamic Profiles and Scaling Relations

This is the third in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises 40 clusters identified as being dynamically relaxed and hot (i.e., massive) in Papers I and II of this series. Here we consider the thermodynamics of the intracluster medium, in particular the profiles of density, temperature and related quantities, as well as integrated measurements of gas mass, average temperature, total luminosity and center-excluded luminosity. We fit power-law scaling relations of each of these quantities as a function of redshift and cluster mass, which can be measured precisely and with minimal bias for these relaxed clusters using hydrostatic arguments. For the thermodynamic profiles, we jointly model the density and temperature and their intrinsic scatter as a function of radius, thus also capturing the behavior of the gas pressure and entropy. For the integrated quantities, we also jointly fit a multidimensional intrinsic covariance. Our results reinforce the view that simple hydrodynamical models provide a good description of relaxed clusters outside their centers, but that additional heating and cooling processes are important in the inner regions (radii $r < 0.5r_{2500} \approx 0.15r_{500}$). The thermodynamic profiles remain regular, with small intrinsic scatter, down to the smallest radii where deprojection is straightforward ($\sim 20$ kpc); within this radius, even the most relaxed systems show clear departures from spherical symmetry. Our results suggest that heating and cooling are continuously regulated in a tight feedback loop, allowing the cluster atmosphere to remain stratified on these scales.

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arXiv2015

New constraints on $f(R)$ gravity from clusters of galaxies

The abundance of massive galaxy clusters is a powerful probe of departures from General Relativity (GR) on cosmic scales. Despite current stringent constraints placed by stellar and galactic tests, on larger scales alternative theories of gravity such as $f(R)$ can still work as effective theories. Here we present constraints on two popular models of $f(R)$, Hu-Sawicki and "designer", derived from a fully self-consistent analysis of current samples of X-ray selected clusters and accounting for all the covariances between cosmological and astrophysical parameters. Using cluster number counts in combination with recent data from the cosmic microwave background (CMB) and the CMB lensing potential generated by large scale structures, as well as with other cosmological constraints on the background expansion history and its mean matter density, we obtain the upper bounds $\log_{10}|f_{R0}| < 4.79$ and $\log_{10}B_0 < 3.75$ at the 95.4 per cent confidence level, for the Hu-Sawicki (with $n=1$) and designer models, respectively. The robustness of our results derives from high quality cluster growth data for the most massive clusters known out to redshifts $z \sim 0.5$, a tight control of systematic uncertainties including an accurate and precise mass calibration from weak gravitational lensing data, and the use of the full shape of the halo mass function over the mass range of our data.

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arXiv2015

Cosmology and Astrophysics from Relaxed Galaxy Clusters I: Sample Selection

This is the first in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here we present a new, automated method for identifying relaxed clusters based on their morphologies in X-ray imaging data. While broadly similar to others in the literature, the morphological quantities that we measure are specifically designed to provide a fair basis for comparison across a range of data quality and cluster redshifts, to be robust against missing data due to point-source masks and gaps between detectors, and to avoid strong assumptions about the cosmological background and cluster masses. Based on three morphological indicators - Symmetry, Peakiness and Alignment - we develop the SPA criterion for relaxation. This analysis was applied to a large sample of cluster observations from the Chandra and ROSAT archives. Of the 361 clusters which received the SPA treatment, 57 (16 per cent) were subsequently found to be relaxed according to our criterion. We compare our measurements to similar estimators in the literature, as well as projected ellipticity and other image measures, and comment on trends in the relaxed cluster fraction with redshift, temperature, and survey selection method. Code implementing our morphological analysis will be made available on the web.

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