X-ray Luminosity Temperature Research Articles

The XMM cluster survey: exploring scaling relations and completeness of the dark energy survey year 3 redMaPPer cluster catalogue

ABSTRACT We cross-match and compare characteristics of galaxy clusters identified in observations from two sky surveys using two completely different techniques. One sample is optically selected from the analysis of 3 years of Dark Energy Survey observations using the redMaPPer cluster detection algorithm. The second is X-ray selected from XMM observations analysed by the XMM Cluster Survey. The samples comprise a total area of 57.4 deg2, bounded by the area of four contiguous XMM survey regions that overlap the DES footprint. We find that the X-ray-selected sample is fully matched with entries in the redMaPPer catalogue, above λ > 20 and within 0.1 <$z$ <0.9. Conversely, only 38 per cent of the redMaPPer catalogue is matched to an X-ray extended source. Next, using 120 optically clusters and 184 X-ray-selected clusters, we investigate the form of the X-ray luminosity–temperature (LX –TX ), luminosity–richness (LX –λ), and temperature–richness (TX –λ) scaling relations. We find that the fitted forms of the LX –TX relations are consistent between the two selection methods and also with other studies in the literature. However, we find tentative evidence for a steepening of the slope of the relation for low richness systems in the X-ray-selected sample. When considering the scaling of richness with X-ray properties, we again find consistency in the relations (i.e. LX –λ and TX –λ) between the optical and X-ray-selected samples. This is contrary to previous similar works that find a significant increase in the scatter of the luminosity scaling relation for X-ray-selected samples compared to optically selected samples.

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.

The 3XMM/SDSS Stripe 82 Galaxy Cluster Survey – II. X-ray and optical properties of the cluster sample

ABSTRACT We present X-ray and optical properties of the optically confirmed galaxy cluster sample from the 3XMM/SDSS Stripe 82 cluster survey. The sample includes 54 galaxy clusters in the redshift range of 0.05–1.2, with a median redshift of 0.36. We first present the X-ray temperature and luminosity measurements that are used to investigate the X-ray luminosity–temperature relation. The slope and intercept of the relation are consistent with those published in the literature. Then, we investigate the optical properties of the cluster galaxies including their morphological analysis and the galaxy luminosity functions (GLFs). The morphological content of cluster galaxies is investigated as a function of cluster mass and distance from the cluster centre. No strong variation of the fraction of early- and late-type galaxies with cluster mass is observed. The fraction of early-type galaxies as a function of cluster radius varies as expected. The individual GLFs of red sequence galaxies were studied in the five ugriz bands for 48 clusters. The GLFs were then stacked in three mass bins and two redshift bins. Twenty clusters of the present sample are studied for the first time in X-rays, and all are studied for the first time in the optical range. Altogether, our sample appears to have X-ray and optical properties typical of ‘average’ cluster properties.

Halo Concentrations and the New Baseline X-Ray Luminosity–Temperature and Mass Relations of Galaxy Clusters

Abstract The standard self-similar model of galaxy cluster formation predicts that the X-ray luminosity–temperature (L X–T X) relation of galaxy clusters should have been L X ∝ T X 2 in absence of the baryonic physics, such as radiative cooling and feedback from stars and black holes. However, this baseline relation is predicted without considering the fact that the halo concentration and the characteristic density of clusters increases as their mass decreases, which is a consequence of hierarchical structure formation of the universe. Here, we show that the actual baseline relation should be L X ∝ T X α , where α ∼ 1.7, instead of α = 2, given the mass dependence of the concentration and the fundamental plane relation of galaxy clusters. Numerical simulations show that α ∼ 1.6, which is consistent with the prediction. We also show that the baseline luminosity–mass (L X–M Δ) relation should have been L X ∝ M Δ β , where β ∼ 1.1–1.2, in contrast with the conventional prediction (β = 4/3). In addition, some of the scatter in the L X–M Δ relation can be attributed to the scatter in the concentration–mass (c–M) relation. The confirmation of the shallow slope could be proof of hierarchical clustering. As an example, we show that the new baseline relations could be checked by studying the temperature or mass dependence of gas mass fraction of clusters. Moreover, the highest-temperature clusters would follow the shallow baseline relations if the influences of cool cores and cluster mergers are properly removed.

Anisotropy of the galaxy cluster X-ray luminosity–temperature relation

We introduce a new test to study the cosmological principle with galaxy clusters. Galaxy clusters exhibit a tight correlation between the luminosity and temperature of the X-ray-emitting intracluster medium. While the luminosity measurement depends on cosmological parameters through the luminosity distance, the temperature determination is cosmology-independent. We exploit this property to test the isotropy of the luminosity distance over the full extragalactic sky, through the normalization a of the LX–T scaling relation and the cosmological parameters Ωm and H0. To this end, we use two almost independent galaxy cluster samples: the ASCA Cluster Catalog (ACC) and the XMM Cluster Survey (XCS-DR1). Interestingly enough, these two samples appear to have the same pattern for a with respect to the Galactic longitude. More specifically, we identify one sky region within l ~ (−15°, 90°) (Group A) that shares very different best-fit values for the normalization of the LX–T relation for both ACC and XCS-DR1 samples. We use the Bootstrap and Jackknife methods to assess the statistical significance of these results. We find the deviation of Group A, compared to the rest of the sky in terms of a, to be ~2.7σ for ACC and ~3.1σ for XCS-DR1. This tension is not significantly relieved after excluding possible outliers and is not attributed to different redshift (z), temperature (T), or distributions of observable uncertainties. Moreover, a redshift conversion to the cosmic microwave background (CMB) frame does not have an important impact on our results. Using also the HIFLUGCS sample, we show that a possible excess of cool-core clusters in this region, is not able to explain the obtained deviations. Furthermore, we tested for a dependence of the results on supercluster environment, where the fraction of disturbed clusters might be enhanced, possibly affecting the LX–T relation. We indeed find a trend in the XCS-DR1 sample for supercluster members to be underluminous compared to field clusters. However, the fraction of supercluster members is similar in the different sky regions, so this cannot explain the observed differences, either. Constraining Ωm and H0 via the redshift evolution of LX–T and the luminosity distance via the flux–luminosity conversion, we obtain approximately the same deviation amplitudes as for a. It is interesting that the general observed behavior of Ωm for the sky regions that coincide with the CMB dipole is similar to what was found with other cosmological probes such as supernovae Ia. The reason for this behavior remains to be identified.

Suzaku and Chandra observations of the galaxy cluster RXC J1053.7+5453 with a radio relic

Abstract We present the results of Suzaku and Chandra observations of the galaxy cluster RXC J1053.7+5453 (z = 0.0704), which contains a radio relic. The radio relic is located at a distance of ∼540 kpc from the X-ray peak toward the west. We measured the temperature of this cluster for the first time. The resultant temperature in the center is ∼1.3 keV, which is lower than the value expected from the X-ray luminosity–temperature and the velocity dispersion–temperature relations. Though we did not find a significant temperature jump at the outer edge of the relic, our results suggest that the temperature decreases outward across the relic. Assuming the existence of the shock at the relic, its Mach number becomes M ≃ 1.4. A possible spatial variation of Mach number along the relic is suggested. Additionally, a sharp surface brightness edge is found at a distance of ∼160 kpc from the X-ray peak toward the west in the Chandra image. We performed X-ray spectral and surface brightness analyses around the edge with the Suzaku and Chandra data, respectively. The obtained surface brightness and temperature profiles suggest that this edge is not a shock but likely a cold front. Alternatively, it cannot be ruled out that thermal pressure is really discontinuous across the edge. In this case, if the pressure across the surface brightness edge is in equilibrium, other forms of pressure sources, such as cosmic-rays, are necessary. We searched for the non-thermal inverse Compton component in the relic region. Assuming a photon index Γ = 2.0, the resultant upper limit of the flux is 1.9 × 10−14 erg s−1 cm−2 for a 4.50 × 10−3 deg2 area in the 0.3–10 keV band, which implies that the lower limit of magnetic field strength becomes 0.7 μG.

The X-ray luminosity–temperature relation of a complete sample of low-mass galaxy clusters

We present \Chandra\ observations of 23 galaxy groups and low-mass galaxy clusters at $0.03<z<0.15$ with a median temperature of ~2keV. The sample is a statistically complete flux-limited subset of the 400 deg$^2$ survey. We investigated the scaling relation between X-ray luminosity ($L$) and temperature ($T$), taking selection biases fully into account. The logarithmic slope of the bolometric \LT\ relation was found to be $3.29\pm0.33$, consistent with values typically found for samples of more massive clusters. In combination with other recent studies of the \LT\ relation we show that there is no evidence for the slope, normalisation, or scatter of the \LT\ relation of galaxy groups being different than that of massive clusters. The exception to this is that in the special case of the most relaxed systems, the slope of the core-excised \LT\ relation appears to steepen from the self-similar value found for massive clusters to a steeper slope for the lower mass sample studied here. Thanks to our rigorous treatment of selection biases, these measurements provide a robust reference against which to compare predictions of models of the impact of feedback on the X-ray properties of galaxy groups.

On the structure of hot gas in haloes: implications for theLX–TXrelation and missing baryons

We present one-dimensional models of the hot gas in dark-matter halos, which both predict the existence of cool cores and explain their structure. Our models are directly applicable to semi-analytic models (SAMs) of galaxy formation. We have previously argued that filaments of cold (~10^4 K) gas condense out of the intracluster medium (ICM) in hydrostatic and thermal equilibrium when the ratio of the thermal instability timescale to the free-fall time $t_{TI}/t_{ff}$ falls below 5-10. This criterion corresponds to an upper limit on the density of the ICM and motivates a model in which a density core forms wherever $t_{TI}/t_{ff} \lesssim 10$. Consistent with observations and numerical simulations, this model predicts larger and more tenuous cores for lower-mass halos---while the core density in a cluster may be as large as ~ 0.1 cm^{-3}, the core density in the Galactic halo should not exceed ~ 10^{-4} cm^{-3}. We can also explain the large densities in smaller mass halos (galactic `coronae') if we include the contribution of the central galaxy to the gravitational potential. Our models produce a favorable match to the observational X-ray luminosity-temperature (Lx-Tx) relation. For halo masses $\lesssim 10^{13}$ Msun the core size approaches the virial radius. Thus, most of the baryons in such halos cannot be in the hot ICM, but either in the form of stars or in the form of hot gas beyond the virial radius. Because of the smaller mass in the ICM and much larger mass available for star formation, the majority of the baryons in low mass halos ($\lesssim 10^{13}$ Msun) can be expelled beyond the virial radius due to supernova feedback. This can account for the baryons `missing' from low mass halos, such as the Galactic halo.

Heating and enriching the intracluster medium

We present numerical simulations of galaxy clusters with stochastic heating from active galactic nuclei (AGN) that are able to reproduce the observed entropy and temperature profiles of non-cool-core (NCC) clusters. Our study uses N-body hydrodynamical simulations to investigate how star formation, metal production, black hole accretion and the associated feedback from supernovae and AGN heat and enrich diffuse gas in galaxy clusters. We assess how different implementations of these processes affect the thermal and chemical properties of the intracluster medium (ICM), using high-quality X-ray observations of local clusters to constrain our models. For the purposes of this study we have resimulated a sample of 25 massive galaxy clusters extracted from the Millennium Simulation. Sub-grid physics is handled using a semi-analytic model of galaxy formation, thus guaranteeing that the source of feedback in our simulations is a population of galaxies with realistic properties. We find that supernova feedback has no effect on the entropy and metallicity structure of the ICM, regardless of the method used to inject energy and metals into the diffuse gas. By including AGN feedback, we are able to explain the observed entropy and metallicity profiles of clusters, as well as the X-ray luminosity-temperature scaling relation for NCC systems. A stochastic model of AGN energy injection motivated by anisotropic jet heating - presented for the first time here - is crucial for this success. With the addition of metal-dependent radiative cooling, our model is also able to produce CC clusters, without overcooling of gas in dense, central regions.

TheXMMCluster Survey: evidence for energy injection at high redshift from evolution of the X-ray luminosity-temperature relation

We measure the evolution of the X-ray luminosity–temperature (LX − T) relation since z ∼ 1.5 using a sample of 211 serendipitously detected galaxy clusters with spectroscopic redshifts drawn from the XMM Cluster Survey first data release (XCS-DR1). This is the first study spanning this redshift range using a single, large, homogeneous cluster sample. Using an orthogonal regression technique, we find no evidence for evolution in the slope or intrinsic scatter of the relation since z ∼ 1.5, finding both to be consistent with previous measurements at z ∼ 0.1. However, the normalization is seen to evolve negatively with respect to the self-similar expectation: we find E−1(z) LX = 1044.67 ± 0.09(T/5)3.04 ± 0.16(1 + z)−1.5 ± 0.5, which is within 2σ of the zero evolution case. We see milder, but still negative, evolution with respect to self-similar when using a bisector regression technique. We compare our results to numerical simulations, where we fit simulated cluster samples using the same methods used on the XCS data. Our data favour models in which the majority of the excess entropy required to explain the slope of the LX − T relation is injected at high redshift. Simulations in which active galactic nucleus feedback is implemented using prescriptions from current semi-analytic galaxy formation models predict the positive evolution of the normalization, and differ from our data at more than 5σ. This suggests that more efficient feedback at high redshift may be needed in these models.

Self-similar scaling and evolution in the galaxy cluster X-ray luminosity-temperature relation

We investigate the form and evolution of the X-ray luminosity-temperature (LT) relation of a sample of 114 galaxy clusters observed with Chandra at 0.1<z<1.3. The clusters were divided into subsamples based on their X-ray morphology or whether they host strong cool cores. We find that when the core regions are excluded, the most relaxed clusters (or those with the strongest cool cores) follow an LT relation with a slope that agrees well with simple self-similar expectations. This is supported by an analysis of the gas density profiles of the systems, which shows self-similar behaviour of the gas profiles of the relaxed clusters outside the core regions. By comparing our data with clusters in the REXCESS sample, which extends to lower masses, we find evidence that the self-similar behaviour of even the most relaxed clusters breaks at around 3.5keV. By contrast, the LT slopes of the subsamples of unrelaxed systems (or those without strong cool cores) are significantly steeper than the self-similar model, with lower mass systems appearing less luminous and higher mass systems appearing more luminous than the self-similar relation. We argue that these results are consistent with a model of non-gravitational energy input in clusters that combines central heating with entropy enhancements from merger shocks. Such enhancements could extend the impact of central energy input to larger radii in unrelaxed clusters, as suggested by our data. We also examine the evolution of the LT relation, and find that while the data appear inconsistent with simple self-similar evolution, the differences can be plausibly explained by selection bias, and thus we find no reason to rule out self-similar evolution. We show that the fraction of cool core clusters in our (non-representative) sample decreases at z>0.5 and discuss the effect of this on measurements of the evolution in the LT relation.

Thermal instability and the feedback regulation of hot haloes in clusters, groups and galaxies

Observations of clusters and groups imply that such halos are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally-motivated heating prescriptions, we show that local thermal instability (TI) can produce a multi-phase medium---with ~ 10000 K cold filaments condensing out of the hot ICM---only when the ratio of the TI timescale in the hot plasma (t_{TI}) to the free-fall timescale (t_{ff}) satisfies t_{TI}/t_{ff} <~ 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling, and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of ~ 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling-flow is ~ 0.001 for clusters and decreases for lower mass halos; supernova heating may be energetically sufficient to balance cooling in galactic halos. We further argue that the ICM self-adjusts so that t_{TI}/t_{ff} >~ 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives t_{TI}/t_{ff} >~ 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminosity-temperature (L_X-T_X) relation. The high-velocity clouds observed in the Galactic halo can also be due to local TI producing multi-phase gas close to the virial radius.

Suzaku X-Ray Follow-Up Observation of Weak-Lensing-Detected Halos in the Field around ZwCl 0823.2+0425

Abstract We present the results of a Suzaku X-ray follow-up observation of weak-lensing-detected halos in the field around galaxy cluster ZwCl 0823.2$+$0425. We clearly detected X-ray emission associated with most of these halos, and determined their detailed physical parameters, such as the X-ray luminosity, temperature, and metal abundance, for the first time. We found that the X-ray luminosity–temperature relation for these halos agrees with the former typical results. With the mass determined from the weak gravitational lensing data, the mass–temperature relation for them was also investigated, and was found to be consistent with the prediction from a simple self-similar model and the results of previous studies with both lensing and X-ray data. We would like to emphasize that the self-similar scaling relation of the mass and the temperature is shown here for the first time using a weak-lensing selected sample, whereas previous studies of the mass scaling relation used X-ray-selected samples of clusters. Therefore, our study demonstrates the importance of X-ray follow-up observations of shear-selected clusters, and shows that a joint X-ray and lensing analysis will be crucial for clusters discovered by the forthcoming weak-lensing surveys, such as the one planned with Subaru/Hyper-Suprime-Cam.

A Dark Core in Abell 520

The rich cluster Abell 520 (z = 0.201) exhibits truly extreme and puzzling multiwavelength characteristics. It may best be described as a cosmic train wreck. It is a major merger showing abundant evidence for ram pressure stripping, with a clear offset in the gas distribution compared to the galaxies (as in the Bullet Cluster, 1E 0657-558). However, the most striking feature is a massive dark core (721 h70 M☉/L☉B) in our weak-lensing mass reconstruction. The core coincides with the central X-ray emission peak, but is largely devoid of galaxies. An unusually low mass-to-light ratio region lies 500 kpc to the east, and coincides with a shock feature visible in radio observations of the cluster. Although a displacement between the X-ray gas and the galaxy/dark matter distributions may be expected in a merger, a mass peak without galaxies cannot be easily explained within the current collisionless dark matter paradigm. Interestingly, the integrated gas mass fraction (≈0.15), mass-to-light ratio (220 h70 M☉/L☉B), and position on the X-ray luminosity-temperature and mass-temperature relations are unremarkable. Thus, gross properties and scaling relations are not always useful indicators of the dynamical state of clusters.

Nature versus nurture: the curved spine of the galaxy cluster X-ray luminosity–temperature relation

The physical processes that define the spine of the galaxy cluster X-ray luminosity?temperature (L?T) relation are investigated using a large hydrodynamical simulation of the universe. This simulation models the same volume and phases as the millennium simulation and has a linear extent of 500 h-1 Mpc. We demonstrate that mergers typically boost a cluster along but also slightly below the L?T relation. Due to this boost, we expect that all of the very brightest clusters will be near the peak of a merger. Objects from near the top of the L?T relation tend to have assembled much of their mass earlier than an average halo of similar final mass. Conversely, objects from the bottom of the relation are often experiencing an ongoing or recent merger.

Expectations for evolution of cluster scaling relations

Cluster observations with Chandra and XMM-Newton are beginning to reveal how the X-ray luminosity–temperature relation evolves with redshift. Some studies find that this evolution is consistent with the predictions of self-similar cluster models while others do not. While self-similar evolution may be plausible at low redshifts, it cannot continue to arbitrarily high redshifts because radiative cooling and the feedback from galaxy formation become increasingly more important at high redshifts. Likewise, the intracluster baryon fraction is likely to decline at high redshifts, owing to cooling and feedback processes. This article examines the predictions of self-similar models for clusters, which come in several different flavors, proposes some alternative scaling laws that account for radiative cooling and feedback in very a simplistic way, and compares those laws with the existing data.

Reexamination of the Galaxy Formation–regulated Gas Evolution Model in Groups and Clusters

As an alternative explanation of the entropy excess and the steepening of the X-ray luminosity-temperature relation in groups and clusters, the galaxy formation-regulated gas evolution (GG) model proposed recently by Bryan makes an attempt to incorporate the formation of galaxies into the evolution of gas without additional heating by nongravitational processes. This seems to provide a unified scheme for our understanding of the structures and evolution of both galaxies and gas in groups and clusters. In this paper, we present an extensive comparison of the X-ray properties of groups and clusters predicted by the GG model and those revealed by current X-ray observations, using various large data sources in the literature and also taking the observational selection effects into account. These include an independent check of the fundamental working hypothesis of the GG model, i.e., galaxy formation was less efficient in rich clusters than in groups, a new test of the radial gas distributions revealed by both the gas mass fraction and the X-ray surface brightness profiles, and an reexamination of the X-ray luminosity-temperature and entropy-temperature relations. In particular, it shows that the overall X-ray surface brightness profiles predicted by the GG model are very similar in shape, insensitive to the X-ray temperature, and the shallower X-ray surface brightness profiles seen at low-temperature systems may arise from the current observational selection effect. This can be used as the simplest approach to distinguishing between the GG model and the preheating scenario. The latter yields an intrinsically shallower gas distribution in groups than in rich clusters.

Expectations for Sunyaev‐Zeldovich Cluster Counts: Mass Function versus X‐Ray Luminosity Function

We present a comparison of the Sunyaev-Zeldovich (SZ) cluster counts predicted by the Press-Schechter (PS) mass function (MF) and the X-ray luminosity function (XLF) of clusters. The employment of the cluster XLF, together with the observationally determined X-ray luminosity-temperature (LX-T) relation, may allow us to estimate the SZ cluster counts in a more realistic manner, although such an empirical approach depends sensitively on our current knowledge of the dynamical properties of intracluster gas and its cosmic evolution. Using both the nonevolving and evolving XLFs of clusters suggested by X-ray observations, we calculate the expectations for SZ surveys of clusters with X-ray luminosity LX ≥ 3 × 1044 ergs s-1 and LX ≥ 1 × 1043 ergs s-1 in the 0.5-2.0 band, respectively. The nonevolving XLF results in a significant excess of SZ cluster counts at high redshifts as compared with the evolving XLF, while a slightly steeper LX-T relation than the observed one is needed to reproduce the distributions of SZ clusters predicted by the standard PS formalism. It is pointed out that uncertainties in the cosmological application of future SZ cluster surveys via the standard PS formalism should be carefully studied.

The LX--T relation and intracluster gas fractions of X-ray clusters

We re-examine the X-ray luminosity–temperature relation using a nearly homogeneous data set of 24 clusters selected for statistically accurate temperature measurements and absence of strong cooling flows. The data exhibit a remarkably tight power-law relation between bolometric luminosity and temperature with a slope 2.88 ± 0.15. With reasonable assumptions regarding cluster structure, we infer an upper limit on fractional variations in the intracluster gas fraction 〈(δ fgas fgas)2〉1/2≤ 15 per cent. A strictly homogeneous Ginga subset of 18 clusters places a more stringent limit of 9 per cent. Imaging data from the literature are employed to determine absolute values of fgas within spheres encompassing density contrasts δc=500 and 200 with respect to the critical density. Comparing binding mass estimates based on the virial theorem (VT) and the hydrostatic β-model (BM), we find a temperature-dependent discrepancy in fgas between the two methods caused by systematic variation of the outer slope parameter β with temperature. Mean values (for H0=50 km s−1 Mpc−1) range from f¯gas=0.10 for cool (T 4 keV) clusters using the BM at δc=200. There is evidence that cool clusters have a lower mean gas fraction than hot clusters, but it is not possible to assess the statistical significance of this effect in the present data set. The T dependence of the intracluster medium (ICM) density structure, coupled with the increase of the gas fraction with T in the VT approach, explains the steepening of the LX–T relation. The small variation about the mean gas fraction within this majority subpopulation of clusters presents an important constraint for theories of galaxy formation and supports arguments against an Einstein–de Sitter universe based on the population mean gas fraction and conventional, primordial nucleosynthesis. The apparent trend of lower gas fractions and more extended atmospheres in low-temperature systems is consistent with expectations of models incorporating the effects of galactic winds on the ICM.

The effect of supernova heating on cluster properties and constraints on galaxy formation models

Models of galaxy formation should be able to predict the properties of clusters of galaxies, in particular their gas fractions, metallicities, X-ray luminosity—temperature relation, temperature function and mass deposition rate function. Fitting these properties places important constaints on galaxy formation on all scales. By following gas processes in detail, our semi-analytic model (based on that of Nulsen & Fabian) is the only such model able to predict all of the above cluster properties. We use realistic gas fractions and gas density profiles, and as required by observations we break the self-similarity of cluster structure by including supernova heating of intracluster gas, the amount of which is indicated by the observed metallicities. We also highlight the importance of the mass deposition rate function as an independent and very sensitive probe of cluster structure.