Galaxy Cluster Scaling Relations Research Articles

Examining the local Universe isotropy with galaxy cluster velocity dispersion scaling relations

Context. In standard cosmology, the Universe is assumed to be statistically homogeneous and isotropic. This assumption suggests that the expansion rate of the Universe, as measured by the Hubble parameter, should be the same in all directions. However, our recent study based on galaxy clusters finds an apparent angular variation of approximately 9% in the Hubble constant, H0, across the sky. In the study, the authors utilised galaxy cluster scaling relations between various cosmology-dependent cluster properties and a cosmology-independent property, i.e. the temperature of the intracluster gas (T). A position-dependent systematic bias of T measurements can, in principle, result in an overestimation of apparent H0 variations. Therefore, it is crucial to confirm or exclude this possibility. Aims. In this work, we search for directional T measurement biases by examining the relationship between the member galaxy velocity dispersion and gas temperature (σv − T) of galaxy clusters. Both measurements are independent of any cosmological assumptions and do not suffer from the same potential systematic biases. Additionally, we search for apparent H0 angular variations independently of T by analysing the relations between the X-ray luminosity and Sunyaev-Zeldovich signal with the velocity dispersion, LX − σv and YSZ − σv. Methods. To study the angular variation of scaling relation parameters, we determined the latter for different sky patches across the extra-galactic sky. We constrained the possible directional T bias using the σv − T relation, as well as the apparent H0 variations using the LX − σv and YSZ − σv relations. We utilised Monte Carlo simulations of isotropic cluster samples to quantify the statistical significance of any observed anisotropies. We calculated and rigorously took into account a correlation of LX and YSZ residuals. Results. No significant directional T measurement biases are found from the σv − T anisotropy study. The probability that the previously observed H0 anisotropy is caused by a directional T bias is only 0.002%. On the other hand, from the joint analysis of the LX − σv and YSZ − σv relations, the maximum variation of H0 is found in the direction of (295 ° ±71 ° , − 30 ° ±71 ° ) with a statistical significance of 3.64σ, fully consistent with our previous results. Conclusions. Our findings, based on the analysis of new scaling relations utilising a completely independent cluster property, σv, strongly corroborate the previously detected anisotropy of galaxy cluster scaling relations. The underlying cause, for example, H0 angular variation or large-scale bulk flows of matter, remains to be identified.

Bayesian recalibration of Planck galaxy cluster scaling relations including relativistic Sunyaev-Zel’dovich corrections

Abstract We investigate the impact of relativistic SZ corrections on Planck measurements of massive galaxy clusters, finding that they have a significant impact at the $\approx$ 5–15% and up to $\approx$ 3 $\sigma$ level. We investigate the possibility of constraining temperature directly from these SZ measurements but find that only weak constraints are possible for the most significant detections; for most clusters, an external temperature measurement is required to correctly measure integrated Compton-y. We also investigate the impact of profile shape assumptions and find that these have a small but non-negligible impact on measured Compton-y, at the $\approx$ 5% level. Informed by the results of these investigations, we recalibrate the Planck SZ observable-mass scaling relation, using the updated NPIPE data release and a larger sample of X-ray mass estimates. Along with the expected change in the high-mass end of the scaling relation, which does not impact Planck mass estimation, we also find hints of a low-mass deviation, but this requires better understanding of the selection function in order to confirm.

CODEX: Role of velocity substructure in the scaling relations of galaxy clusters

Context. The use of galaxy clusters as cosmological probes relies on a detailed understanding of their properties. They define cluster selection and ranking linked to a cosmologically significant cluster mass function. Previous studies have employed small samples of clusters, concentrating on achieving the first calibrations of cluster properties with mass, while the diversity of cluster properties has been revealed via detailed studies. Aims. The large spectroscopic follow-up on the CODEX cluster sample with SDSS and NOT enables a detailed study of hundreds of clusters, lifting the limitations of previous samples. We aim to update the spectroscopic cluster identification of CODEX by running the spectroscopic group finder on the follow-up spectroscopy results and connecting the dynamical state of clusters to their scaling relations. Methods. We implemented a reproducible spectroscopic membership determination and cleaning procedures, based on the redMaPPer membership, running the spectroscopic group finder on the follow-up spectroscopy results and cleaning the membership for spectroscopic outliers. We applied the Anderson-Darling test for velocity substructure and analysed its influence on the scaling relations. We also tested the effect of the X-ray-to-optical centre offset on the scaling relations. Results. We report on the scaling relations between richness, X-ray luminosity, and velocity dispersion for a complete sample of clusters with at least 15 members. Clusters with velocity substructure exhibit enhanced velocity dispersion for a given richness and are characterized by 2.5 times larger scatter. Clusters that have a strong offset in X-ray-to-optical centres have comparable scaling relations as clusters with substructure. We demonstrate that there is a consistency in the parameters of the scaling relations for the low- and high-richness galaxy clusters. Splitting the clusters by redshift, we note a decrease in scatter with redshift in all scaling relations. We localize the redshift range where a high scatter is observed to z < 0.15, which is in agreement with the literature results on the scatter. We note that the increase in scatter for both high- and low-luminosity clusters is z < 0.15, suggesting that both cooling and the resulting active galactic nucleus feedback are at the root of this scatter.

Rhapsody-Csimulations – anisotropic thermal conduction, black hole physics, and the robustness of massive galaxy cluster scaling relations

ABSTRACTWe present the Rhapsody-C simulations that extend the Rhapsody-G suite of massive galaxy clusters at the $M_{\rm vir}\sim 10^{15}\, {\rm M}_{\odot }$ scale with cosmological magneto-hydrodynamic zoom-in simulations that include anisotropic thermal conduction, modified supermassive black hole (SMBH) feedback, new SMBH seeding, and the SMBH orbital decay model. These modelling improvements have a dramatic effect on the SMBH growth, star formation, and gas depletion in the proto-clusters. We explore the parameter space of the models and report their effect on both star formation and the thermodynamics of the intracluster medium (ICM) as observed in X-ray and SZ observations. We report that the star formation in proto-clusters is strongly impacted by the choice of the SMBH seeding as well as the orbital decay of SMBHs. The feedback from AGNs is substantially boosted by the SMBH decay; its time evolution and impact range differ noticeably depending on the AGN energy injection scheme used. Compared to a mass-weighted injection whose energy remains confined close to the central SMBHs, a volume-weighted thermal energy deposition allows to heat the ICM out to large radii that severely quenches the star formation in proto-clusters. By flattening out temperature gradients in the ICM, anisotropic thermal conduction can reduce star formation early on but weakens and delays the AGN activity. Despite the dissimilarities found in the stellar and gaseous content of our haloes, the cluster scaling relations we report are surprisingly insensitive to the subresolution models used and are in good agreement with recent observational and numerical studies.

Larger H0 values in the CMB dipole direction

Based on the assumption that quasars (QSOs) and gamma-ray bursts (GRBs) represent standardizable candles, we provide evidence that the Hubble constant ${H}_{0}$ adopts larger values in hemispheres aligned with the cosmic microwave background (CMB) dipole direction. If substantiated, this trend signals a departure from Friedmann-Lema\^{\i}tre-Robertson-Walker cosmology. In particular, QSOs show a definite trend, whereas our findings in GRBs are consistent with an isotropic universe, but we show in a sample of GRBs calibrated with type Ia supernovae (SNe) that this conclusion may change as one focuses on GRBs more closely (mis)aligned with the CMB dipole direction. The statistical significance in QSOs alone is $\ensuremath{\gtrsim}2\ensuremath{\sigma}$, and when combined with similar trends in strong lensing, type Ia SNe, and calibrated GRBs, this increases to $\ensuremath{\sim}3\ensuremath{\sigma}$. Our findings are consistent with reported discrepancies in the cosmic dipole and anisotropies in galaxy cluster scaling relations. The reported variations in ${H}_{0}$ across the sky suggest that Hubble tension may be a symptom of a deeper cosmological malaise.

The eROSITA Final Equatorial-Depth Survey (eFEDS)

We present the first weak-lensing mass calibration and X-ray scaling relations of galaxy clusters and groups selected in the eROSITA Final Equatorial Depth Survey (eFEDS) observed by Spectrum Roentgen Gamma/eROSITA over a contiguous footprint with an area of ≈140 deg2, using the three-year (S19A) weak-lensing data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. In this work, we study a sample of 434 optically confirmed galaxy clusters (and groups) at redshift 0.01 ≲z ≲1.3 with a median of 0.35, of which 313 systems are uniformly covered by the HSC survey to enable the extraction of the weak-lensing shear observable. In a Bayesian population modeling, we perform a blind analysis for the weak-lensing mass calibration by simultaneously modeling the observed count rateηand the shear profileg+of individual clusters through the count-rate-to-mass-and-redshift (η-M500-z) relation and the weak-lensing-mass-to-mass-and-redshift (MWL-M500-z) relation, respectively, while accounting for the bias in these observables using simulation-based calibrations. As a result, the count-rate-inferred and lensing-calibrated cluster mass is obtained from the joint modeling of the scaling relations, as the ensemble mass spanning a range of 1013h-1M⊙≲M500≲ 1015h-1M⊙with a median of ≈1014h-1M⊙for the eFEDS sample. With the mass calibration, we further model the X-ray observable-to-mass-and-redshift relations, including the rest-frame soft-band and bolometric luminosity (LXandLb), the emission-weighted temperatureTX, the mass of intra-cluster mediumMg, and the mass proxyYX, which is the product ofTXandMg. Except forLXwith a steeper dependence on the cluster mass at a statistically significant level, we find that the other X-ray scaling relations all show a mass trend that is statistically consistent with the self-similar prediction at a level of ≲1.7σ. Meanwhile, all these scaling relations show no significant deviation from the self-similarity in their redshift scaling. Moreover, no significant redshift-dependent mass trend is present. This work demonstrates the synergy between the eROSITA and HSC surveys in preparation for the forthcoming first-year eROSITA cluster cosmology.

A Hydro-particle-mesh Code for Efficient and Rapid Simulations of the Intracluster Medium

Abstract We introduce the cosmological HYPER code based on an innovative hydro-particle-mesh (HPM) algorithm for efficient and rapid simulations of gas and dark matter. For the HPM algorithm, we update the approach of Gnedin & Hui to expand the scope of its application from the lower-density intergalactic medium (IGM) to the higher-density intracluster medium (ICM). While the original algorithm tracks only one effective particle species, the updated version separately tracks the gas and dark matter particles, as they do not exactly trace each other on small scales. For the approximate hydrodynamics solver, the pressure term in the gas equations of motion is calculated using robust physical models. In particular, we use a dark matter halo model, ICM pressure profile, and IGM temperature–density relation, all of which can be systematically varied for parameter-space studies. We show that the HYPER simulation results are in good agreement with the halo model expectations for the density, temperature, and pressure radial profiles. Simulated galaxy cluster scaling relations for Sunyaev–Zel’dovich (SZ) and X-ray observables are also in good agreement with mean predictions, with scatter comparable to that found in hydrodynamic simulations. HYPER also produces lightcone catalogs of dark matter halos and full-sky tomographic maps of the lensing convergence, SZ effect, and X-ray emission. These simulation products are useful for testing data analysis pipelines, generating training data for machine learning, understanding selection and systematic effects, and for interpreting astrophysical and cosmological constraints.

Super interacting dark sector: An improvement on self-interacting dark matter via scaling relations of galaxy clusters

Self-interacting dark matter is known as one of the most appropriate candidates for dark matter. Due to its excellent success in removing many astrophysical problems, particularly in small scale structure, studying this model has taken on added significance. In this paper, we focus on the results of two previously performed simulations of cluster sized halos with self-interacting dark matter and introduce a new function for the density profile of galaxy clusters, which can perfectly describe the result of these simulations. This density profile helps to find a velocity dispersion profile and also a relation between cluster mass and concentration parameter. Using these relations, we investigate two scaling relations of galaxy clusters, namely mass-velocity dispersion and mass-temperature relations. The scaling relations reveal that in the self-interacting dark matter model, halos are more massive than what the standard non-interacting model predicts for any fixed temperature. We also study the mass-temperature relation for a hybrid interacting model, which is a combination of self-interacting dark matter idea with another model of the dark sector in which dark matter particle mass is determined according to its interaction with dark energy. This super interacting dark sector (SIDS) model can change the mass-temperature relation to a modified form that has the same result as a non-interacting model. Finally, we provide quantitative expressions which can describe the constants of this interacting model with the value of cross-section per unit mass of dark matter particles.

Cosmological implications of the anisotropy of ten galaxy cluster scaling relations

The hypothesis that the late Universe is isotropic and homogeneous is adopted by most cosmological studies, including studies of galaxy clusters. The cosmic expansion rateH0is thought to be spatially constant, while bulk flows are often presumed to be negligible compared to the Hubble expansion, even at local scales. The effects of bulk flows on the redshift–distance conversion are hence usually ignored. Any deviation from this consensus can strongly bias the results of such studies, and thus the importance of testing these assumptions cannot be understated. Scaling relations of galaxy clusters can be effectively used for this testing. In previous works, we observed strong anisotropies in cluster scaling relations, whose origins remain ambiguous. By measuring many different cluster properties, several scaling relations with different sensitivities can be built. Nearly independent tests of cosmic isotropy and large bulk flows are then feasible. In this work, we make use of up to 570 clusters with measured properties at X-ray, microwave, and infrared wavelengths to construct ten different cluster scaling relations and test the isotropy of the local Universe; to our knowedge, we present five of these scaling relations for the first time. Through rigorous and robust tests, we ensure that our analysis is not prone to generally known systematic biases and X-ray absorption issues. By combining all available information, we detect an apparent 9% spatial variation in the localH0between (l, b)∼(280°−35°+35°, −15°−20°+20°) and the rest of the sky. The observed anisotropy has a nearly dipole form. Using isotropic Monte Carlo simulations, we assess the statistical significance of the anisotropy to be > 5σ. This result could also be attributed to a ∼900 km s−1bulk flow, which seems to extend out to at least ∼500 Mpc. These two effects will be indistinguishable until more high-zclusters are observed by future all-sky surveys such as eROSITA.

The Dynamical State of the Frontier Fields Galaxy Cluster Abell 370

Abstract We study the dynamics of Abell 370 (A370), a highly massive Hubble Frontier Fields galaxy cluster, using self-consistent three-dimensional N-body/hydrodynamical simulations. Our simulations are constrained by X-ray, optical spectroscopic and gravitational lensing, and Sunyaev–Zel’dovich (SZ) effect observations. Analyzing archival Chandra observations of A370 and comparing the X-ray morphology to the latest gravitational lensing mass reconstruction, we find offsets of ∼30 and ∼100 kpc between the two X-ray surface brightness peaks and their nearest mass surface density peaks, suggesting that it is a merging system, in agreement with previous studies. Based on our dedicated binary cluster merger simulations, we find that initial conditions of the two progenitors with virial masses of and , an infall velocity of 3500 km s−1, and an impact parameter of 100 kpc can explain the positions and the offsets between the peaks of the X-ray emission and mass surface density, the amplitude of the integrated SZ signal, and the observed relative line-of-sight velocity. Moreover, our best model reproduces the observed velocity dispersion of cluster member galaxies, which supports the large total mass of A370 derived from weak lensing. Our simulations strongly suggest that A370 is a post major merger after the second core passage in the infalling phase, just before the third core passage. In this phase, the gas has not settled down in the gravitational potential well of the cluster, which explains why A370 does not follow closely the galaxy cluster scaling relations.

Cosmology dependence of galaxy cluster scaling relations

ABSTRACT The abundance of galaxy clusters as a function of mass and redshift is a well known powerful cosmological probe, which relies on underlying modelling assumptions on the mass-observable relations (MOR). Some of the MOR parameters can be constrained directly from multi-wavelength observations, as the normalization at some reference cosmology, the mass-slope, the redshift evolution, and the intrinsic scatter. However, the cosmology dependence of MORs cannot be tested with multi-wavelength observations alone. We use magneticum simulations to explore the cosmology dependence of galaxy cluster scaling relations. We run fifteen hydrodynamical cosmological simulations varying Ωm, Ωb, h0, and σ8 (around a reference cosmological model). The MORs considered are gas mass, baryonic mass, gas temperature, Y and velocity dispersion as a function of virial mass. We verify that the mass and redshift slopes and the intrinsic scatter of the MORs are nearly independent of cosmology with variations significantly smaller than current observational uncertainties. We show that the gas mass and baryonic mass sensitively depends only on the baryon fraction, velocity dispersion, and gas temperature on h0, and Y on both baryon fraction and h0. We investigate the cosmological implications of our MOR parametrization on a mock catalogue created for an idealized eROSITA-like experiment. We show that our parametrization introduces a strong degeneracy between the cosmological parameters and the normalization of the MOR. Finally, the parameter constraints derived at different overdensity (Δ500c), for X-ray bolometric gas luminosity, and for different subgrid physics prescriptions are shown in the appendix.

Probing cosmic isotropy with a new X-ray galaxy cluster sample through theLX–Tscaling relation

The isotropy of the late Universe and consequently of the X-ray galaxy cluster scaling relations is an assumption greatly used in astronomy. However, within the last decade, many studies have reported deviations from isotropy when using various cosmological probes; a definitive conclusion has yet to be made. New, effective and independent methods to robustly test the cosmic isotropy are of crucial importance. In this work, we use such a method. Specifically, we investigate the directional behavior of the X-ray luminosity-temperature (LX–T) relation of galaxy clusters. A tight correlation is known to exist between the luminosity and temperature of the X-ray-emitting intracluster medium of galaxy clusters. While the measured luminosity depends on the underlying cosmology through the luminosity distanceDL, the temperature can be determined without any cosmological assumptions. By exploiting this property and the homogeneous sky coverage of X-ray galaxy cluster samples, one can effectively test the isotropy of cosmological parameters over the full extragalactic sky, which is perfectly mirrored in the behavior of the normalizationAof theLX–Trelation. To do so, we used 313 homogeneously selected X-ray galaxy clusters from the Meta-Catalogue of X-ray detected Clusters of galaxies. We thoroughly performed additional cleaning in the measured parameters and obtain core-excised temperature measurements for all of the 313 clusters. The behavior of theLX–Trelation heavily depends on the direction of the sky, which is consistent with previous studies. Strong anisotropies are detected at a ≳4σconfidence level toward the Galactic coordinates (l, b) ∼ (280°, − 20°), which is roughly consistent with the results of other probes, such as Supernovae Ia. Several effects that could potentially explain these strong anisotropies were examined. Such effects are, for example, the X-ray absorption treatment, the effect of galaxy groups and low redshift clusters, core metallicities, and apparent correlations with other cluster properties, but none is able to explain the obtained results. Analyzing 105bootstrap realizations confirms the large statistical significance of the anisotropic behavior of this sky region. Interestingly, the two cluster samples previously used in the literature for this test appear to have a similar behavior throughout the sky, while being fully independent of each other and of our sample. Combining all three samples results in 842 different galaxy clusters with luminosity and temperature measurements. Performing a joint analysis, the final anisotropy is further intensified (∼5σ), toward (l, b) ∼ (303°, − 27°), which is in very good agreement with other cosmological probes. The maximum variation ofDLseems to be ∼16 ± 3% for different regions in the sky. This result demonstrates that X-ray studies that assume perfect isotropy in the properties of galaxy clusters and their scaling relations can produce strongly biased results whether the underlying reason is cosmological or related to X-rays. The identification of the exact nature of these anisotropies is therefore crucial for any statistical cluster physics or cosmology study.

SZ Scaling Relations of Galaxy Groups and Clusters Near the North Ecliptic Pole

SZ scaling relations have been used to test the self-similar prediction for massive galaxy clusters, but little attention has been given to individual galaxy groups. We investigate the scaling relations of galaxy groups and clusters near the North Ecliptic Pole using X-ray and SZ observations. This region of the sky is where both the ROSAT and Planck satellites achieved their deepest observations, permitting the investigation of lower mass systems. Our sample consists of 62 X-ray detected groups and clusters, spanning a mass range of $10^{13.4}M_{\odot}<~M_{500}<10^{15}M_{\odot}$ and redshifts of $0.03\lesssim z \lesssim 0.82$. We extract the total SZ flux from unresolved Planck data and estimate the fraction of the SZ flux within $R_{500}$ assuming two different pressure profiles. The SZ scaling relations were derived using a Bayesian technique that accounts for censored data. We find a power law slope of $1.73^{+0.19}_{-0.18}$ for the $Y_{SZ}-M_{500}$ relation which is consistent with the self-similar prediction of 5/3. The slope of $0.89^{+0.09}_{-0.08}$ for the $Y_{SZ}-L_{X,500}$ relation is in agreement with other observational studies but not the self-similar prediction of 5/4, and the $Y_{SZ}-Y_{X}$ relation lies below the 1:1 relation when the slope is fixed to unity. The determined scaling relations are dependent on the selected pressure profile, so resolved data are needed to determine the effects of AGN feedback. In addition, we find a number of potential cluster candidates in the Planck Compton maps that were not identified in our X-ray sample.

The redshift evolution of X-ray and Sunyaev–Zel’dovich scaling relations in the fable simulations

Abstract We study the redshift evolution of the X-ray and Sunyaev–Zel’dovich (SZ) scaling relations for galaxy groups and clusters in the fable suite of cosmological hydrodynamical simulations. Using an expanded sample of 27 high-resolution zoom-in simulations, together with a uniformly sampled cosmological volume to sample low-mass systems, we find very good agreement with the majority of observational constraints up to z ∼ 1. We predict significant deviations of all examined scaling relations from the simple self-similar expectations. While the slopes are approximately independent of redshift, the normalizations evolve positively with respect to self-similarity, even for commonly used mass proxies such as the YX parameter. These deviations are due to a combination of factors, including more effective active galactic nuclei feedback in lower mass haloes, larger binding energy of gas at a given halo mass at higher redshifts, and larger non-thermal pressure support from kinetic motions at higher redshifts. Our results have important implications for cluster cosmology from upcoming SZ surveys such as SPT-3G, ACTpol, and CMB-S4, as relatively small changes in the observable–mass scaling relations (within theoretical uncertainties) have a large impact on the predicted number of high-redshift clusters and hence on our ability to constrain cosmology using cluster abundances. In addition, we find that the intrinsic scatter of the relations, which agrees well with most observational constraints, increases at lower redshifts and for lower mass systems. This calls for a more complex parametrization than adopted in current observational studies to be able to accurately account for selection biases.

LoCuSS: scaling relations between galaxy cluster mass, gas, and stellar content

We present a simultaneous analysis of galaxy cluster scaling relations between weak-lensing mass and multiple cluster observables, across a wide range of wavelengths, that probe both gas and stellar content. Our new hierarchical Bayesian model simultaneously considers the selection variable alongside all other observables in order to explicitly model intrinsic property covariance and account for selection effects. We apply this method to a sample of 41 clusters at $0.15<z<0.30$, with a well-defined selection criteria based on RASS X-ray luminosity, and observations from Chandra / XMM, SZA, Planck, UKIRT, SDSS and Subaru. These clusters have well-constrained weak-lensing mass measurements based on Subaru / Suprime-Cam observations, which serve as the reference masses in our model. We present 30 scaling relation parameters for 10 properties. All relations probing the intracluster gas are slightly shallower than self-similar predictions, in moderate tension with prior measurements, and the stellar fraction decreases with mass. K-band luminosity has the lowest intrinsic scatter with a 95th percentile of 0.16, while the lowest scatter gas probe is gas mass with a fractional intrinsic scatter of $0.16 \pm 0.03$. We find no distinction between the core-excised X-ray or high-resolution Sunyaev-Zel'dovich relations of clusters of different central entropy, but find with modest significance that higher entropy clusters have higher stellar fractions than their lower entropy counterparts. We also report posterior mass estimates from our likelihood model.

The Three Hundred project: a large catalogue of theoretically modelled galaxy clusters for cosmological and astrophysical applications

We introduce the the three hundred project, an endeavour to model 324 large galaxy clusters with full-physics hydrodynamical re-simulations. Here we present the data set and study the differences to observations for fundamental galaxy cluster properties and scaling relations. We find that the modelled galaxy clusters are generally in reasonable agreement with observations with respect to baryonic fractions and gas scaling relations at redshift |$z$| = 0. However, there are still some (model-dependent) differences, such as central galaxies being too massive, and galaxy colours (g − r) being bluer (about 0.2 dex lower at the peak position) than in observations. The agreement in gas scaling relations down to |$10^{13}{{\, h^{-1}\, {\rm {M_{\odot }}}}}$| between the simulations indicates that particulars of the sub-grid modelling of the baryonic physics only has a weak influence on these relations. We also include – where appropriate – a comparison to three semi-analytical galaxy formation models as applied to the same underlying dark-matter-only simulation. All simulations and derived data products are publicly available.

The extended ROSAT-ESO Flux-Limited X-ray Galaxy Cluster Survey (REFLEX II)

The mass function of galaxy clusters is a sensitive tracer of the gravitational evolution of the cosmic large-scale structure and serves as an important census of the fraction of matter bound in large structures. We obtain the mass function by fitting the observed cluster X-ray luminosity distribution from the REFLEX galaxy cluster survey to models of cosmological structure formation. We marginalise over uncertainties in the cosmological parameters as well as those of the relevant galaxy cluster scaling relations. The mass function is determined with an uncertainty less than 10% in the mass range 3 x 10^12 to 5 x 10^14 M$_\odot$. For the cumulative mass function we find a slope at the low mass end consistent with a value of -1, while the mass rich end cut-off is milder than a Schechter function with an exponential term exp($- M^\delta$) with $\delta$ smaller than 1. Changing the Hubble parameter in the range $H_0 = 67 - 73 km s^-1 Mpc^{-1}$ or allowing the total neutrino mass to have a value between 0 - 0.4 eV causes variations less than the uncertainties. We estimate the fraction of mass locked up in galaxy clusters: about 4.4% of the matter in the Universe is bound in clusters (inside $r_200$) with a mass larger than 10^14 M$_\odot$ and 14% to clusters and groups with a mass larger than 10^13 M$_\odot$ at the present Universe. We also discuss the evolution of the galaxy cluster population with redshift. Our results imply that there is hardly any clusters with a mass > 10^15 M$_\odot$ above a redshift of z = 1.

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.

Galaxy cluster scaling relations measured with APEX-SZ

We present thermal Sunyaev-Zel'dovich effect (SZE) measurements for 42 galaxy clusters observed at 150 GHz with the APEX-SZ experiment. For each cluster, we model the pressure profile and calculate the integrated Comptonization $Y$ to estimate the total thermal energy of the intracluster medium (ICM). We compare the measured $Y$ values to X-ray observables of the ICM from the literature (cluster gas mass $M_{\rm{gas}}$, temperature $T_X$, and $Y_X =M_{\rm{gas}}T_X$) that relate to total cluster mass. We measure power law scaling relations, including an intrinsic scatter, between the SZE and X-ray observables for three subsamples within the set of 42 clusters that have uniform X-ray analysis in the literature. We observe that differences between these X-ray analyses introduce significant variability into the measured scaling relations, particularly affecting the normalization. For all three subsamples, we find results consistent with a self-similar model of cluster evolution dominated by gravitational effects. Comparing to predictions from numerical simulations, these scaling relations prefer models that include cooling and feedback in the ICM. Lastly, we measure an intrinsic scatter of $\sim28$ per cent in the $Y-Y_X\,$ scaling relation for all three subsamples.

Weak-lensing-inferred scaling relations of galaxy clusters in the RCS2: mass-richness, mass-concentration, mass-bias, and more

We study a sample of ~10^4 galaxy clusters in the redshift range 0.2<z<0.8 with masses M_200 > 5x10^13 h_70^-1 M_sun, discovered in the second Red-sequence Cluster Survey (RCS2). The depth and excellent image quality of the RCS2 enable us to detect the cluster-mass cross-correlation up to z~0.7. To obtain cluster masses, concentrations and halo biases, we fit a cluster halo model simultaneously to the lensing signal and to the projected density profile of red-sequence cluster members, as the latter provides tight constraints on the cluster miscentring distribution. We parametrise the mass-richness relation as M_200 = A x (N_200/20)^alpha, and find A = (15.0 +- 0.8) x 10^13 h_70^-1 M_sun and alpha = 0.73 +- 0.07 at low redshift (0.2<z<0.35). At intermediate redshift (0.35<z<0.55), we find a higher normalisation, which points at a fractional increase of the richness towards lower redshift caused by the build-up of the red-sequence. The miscentring distribution is well constrained. Only ~30% of our BCGs coincide with the peak of the dark matter distribution. The distribution of the remaining BCGs are modelled with a 2D-Gaussian, whose width increases from 0.2 to 0.4 h_70^-1 Mpc towards higher masses; the ratio of width and r_200 is constant with mass and has an average value of 0.44 +- 0.01. The mass-concentration and mass-bias relation agree fairly well with literature results at low redshift, but have a higher normalisation at higher redshifts, which may be due to selection and projection effects. The concentration of the satellite distribution decreases with mass and is correlated with the concentration of the halo.