Temperature Decrement Research Articles

Experimental and FEA Investigations on the Fracture Properties of Pipe Structures Under Internal Pressure in DBTT Region

The fracture behavior of pipes with penetrating cracks was experimentally investigated with the results of the load-deflection curves and crack length. J-R curves were obtained from the testing results for different temperatures. With the decrement in temperature, the critical J integral decreases and the tearing modulus increases. An updated continuum damage model was proposed, in which the fracture energy density as a function of the stress triaxiality, temperature and strain rate in the transition region was taken as the critical damage factor. The uni-axial tension experiments at different temperatures were carried out to obtain the basic material properties and the critical fracture energy density, to verify the validity of the damage model. Based on detailed finite element analyses with the proposed updated continuum damage model, the loading level of pipes with penetrating cracks was estimated and compared with the experimental results, meanwhile the fracture processes of the pipeline structure in the ductile-brittle-transition-temperature region were reproduced. It has been shown that the fracture process in the transition region strongly depends on both the stress and strain state, and can be effectively predicted using the continuum damage models incorporating with the stress state effect.

AN X-RAY/OPTICAL STUDY OF THE COMPLEX DYNAMICS OF THE CORE OF THE MASSIVE INTERMEDIATE-REDSHIFT CLUSTER MACSJ0717.5+3745

Using CHANDRA, we investigate the spatial temperature distribution of the intracluster medium (ICM) within 700 kpc of the center of the massive merging cluster MACSJ0717.5+3745 at z = 0.55. Combining the X-ray evidence with information about the distribution and velocities of the cluster galaxies near the core provides us with a snapshot of the three-dimensional geometry and dynamics of one of the most complex clusters studied to date. We find MACSJ0717.5+3745 to be an active triple merger with ICM temperatures exceeding 20 keV. Although radial velocity information and X-ray/optical offsets indicate that all three mergers proceed along distinctly different directions, the partial alignment of the merger axes points to a common origin in the large-scale filament south-east of the cluster core. Clear decrements in the ICM temperature observed near two of these subclusters identify the respective X-ray surface brightness peaks as remnants of cool cores; the compactness and low temperature of 5.7 keV of one of these features suggest that the respective merger, a high-velocity collision at 3,000 km s−1, is still in its very early stages. Looking beyond the triple merger, we find the large-scale filament to not only provide a spatial as well as temporal arrow for the interpretation of the dynamics of the merger events near the cluster core, but we also find tantalizing, if circumstantial, evidence for direct, large-scale heating of the ICM by contiguous infall of low-density gas from the filament.

Thermal properties of glasses based on Bi2O3 for Pb free solder glasses

With the aim of developing Pb-free Bi2O3-based new solder glasses; glass forming region, glass transition temperature, crystallization temperature, thermal expansion, and water resistance of Bi2O3-BaO-B2O3 ternary glass system were investigated. The roles of Bi2O3 in this ternary glass were also discussed. The results showed that glass transition temperature and thermal expansion coefficients of the ternary glasses were in similar range as compared to those solder glass consisting PbO. The water resistance of ternary glass was almost the same as compared to window glass, but it is higher than solder glass containing PbO. The glass transition temperature of ternary glass was dependent on average bond strength. Our results also showed that as the amount of Bi2O3 increased, the average bond strength was decreased which lead to decrement of glass transition temperature. These results suggested that Bi2O3 plays an important role as glass network former in the glass system.

The CMB cold spot: texture, cluster or void?

ABSTRACT The non-Gaussian cold spot found in the WMAP data has created controversyabout its origin. Here we calculate the Bayesian posterior probability ratios for threedifferent models that could explain the cold spot. A recent work claimed that theSpot could be caused by a cosmic texture, while other papers suggest that it couldbe due to the gravitational effect produced by an anomalously large void. Also theSunyaev-Zeldovich effect caused by a cluster is taken into account as a possible origin.We perform a template fitting on a 20 ◦ radius patch centered at Galactic coordi-nates (b = −57 ◦ ,l = 209 ◦ ) and calculate the posterior probability ratios for the voidand Sunyaev-Zeldovich models, comparing the results to those obtained with texture.Taking realistic priors for the parameters, the texture interpretation is favored, whilethe void and Sunyaev-Zeldovich hypotheses are discarded. The temperature decre-ment produced by voids or clusters is negligible considering realistic values for theparameters.Key words: methods: data analysis - cosmic microwave background

Distribution and escape of molecular hydrogen in Titan's thermosphere and exosphere

We present an in‐depth study of the distribution and escape of molecular hydrogen (H2) on Titan, based on the global average H2 distribution at altitudes between 1000 and 6000 km, extracted from a large sample of Cassini/Ion and Neutral Mass Spectrometer (INMS) measurements. Below Titan's exobase, the observed H2 distribution can be described by an isothermal diffusion model, with a most probable flux of (1.37 ± 0.01) × 1010 cm−2 s−1, referred to the surface. This is a factor of ∼3 higher than the Jeans flux of 4.5 × 109 cm−2 s−1, corresponding to a temperature of 152.5 ± 1.7 K, derived from the background N2 distribution. The H2 distribution in Titan's exosphere is modeled with a collisionless approach, with a most probable exobase temperature of 151.2 ± 2.2 K. Kinetic model calculations in the 13‐moment approximation indicate a modest temperature decrement of several kelvin for H2, as a consequence of the local energy balance between heating/cooling through thermal conduction, viscosity, neutral collision, and adiabatic outflow. The variation of the total energy flux defines an exobase level of ∼1600 km, where the perturbation of the Maxwellian velocity distribution function, driven primarily by the heat flow, becomes strong enough to raise the H2 escape flux considerably higher than the Jeans value. Nonthermal processes may not be required to interpret the H2 escape on Titan. In a more general context, we suggest that the widely used Jeans formula may significantly underestimate the actual thermal escape flux and that a gas kinetic model in the 13‐moment approximation provides a better description of thermal escape in planetary atmospheres.

Outdoor test method to determine the thermal behavior of solar domestic water heating systems

The dynamics of the market, the generation of new promotion programs, fiscal incentives and many other factors are to be considered for the massive application of solar domestic water heating systems (SDWHS) mainly of the compact thermosiphon type, makes it necessary to choose simple and inexpensive procedure tests that permit to know their characteristic thermal behaviors without an official standard being necessary. Moreover, it allows the comparison among systems and offers enough and reliable information to consumers and manufacturers. In most developing countries, an official national standard for SDWHS is not available, therefore it is necessary to adopt an international test procedure in which the cost and time of implementation is very important. In this work, a simple and inexpensive test method to determine the thermal behavior of SDWHS is proposed. Even though these procedure tests do not have an official standard structure they permit, by comparing different solar systems under identical solar, ambient, and initial conditions, the experimental determination of: (a) the maximum available volume of water for solar heating; (b) water temperature increment and available thermal energy at the end of the day; (c) temperature profiles (stratification) and the average temperature in the storage tank after it is homogenized; (d) the average global thermal efficiency; (e) water temperature decrement and energy lost overnight; and (f) the relationship between hot water volume and solar collector area as function of the average heating temperature. An additional proposed test permits to know the heat losses caused by the reverse flow in the collector loop. These tests will be carried out independently of the configuration between the solar collector and the storage tank, the way the fluid circulates and the type of thermal exchange. The results of this procedure test can be very useful, firstly, for the local solar manufacturers’ equipment in order to design and optimize its products comparing their systems against a reference system under identical test conditions and secondly, by the consumers in order to select the most suitable system. The resulting experimental data for a particular thermosiphon system is presented and discussed.

The Association Between Acetaminophen Concentrations in the Cerebrospinal Fluid and Temperature Decline in Febrile Infants

The objective of this study consisting of a prospective cohort of febrile infants was to describe the correlation between cerebrospinal fluid (CSF) acetaminophen (paracetamol) concentrations and changes in body temperature in febrile infants. Infants, one week to one year of age, with rectal temperature >or=38.0 degrees C, treated with acetaminophen were studied if they underwent a lumbar puncture (LP). Patients received 15 mg/kg of acetaminophen 30 minutes to 4 hours before lumbar puncture was performed. Rectal temperature was documented before acetaminophen administration and at the time of lumbar puncture. Plasma and CSF acetaminophen levels were determined using high-pressure liquid chromatography. Thirty-one infants were studied. In a nonlinear regression, the relationship among acetaminophen concentrations in the CSF, time, and temperature differences is best described by a Lorentzian distribution. The model suggests that a peak effect on temperature is achieved at CSF concentration of 11.9 microg/mL and 182 minutes after acetaminophen administration (P<0.001 and P<0.001, respectively r=0.9 adjusted r square=0.78). Temperature decrement in young febrile infants, treated with acetaminophen, correlates with time and acetaminophen concentrations in the CSF. High concentrations of acetaminophen in the CSF, exceeding a certain level, are not associated with greater temperature decrement.

Preliminary Sunyaev-Zel'dovich observations of galaxy clusters with OCRA-p

We present 30 GHz Sunyaev Zel'dovich (SZ) observations of a sample of four galaxy clusters with a prototype of the One Centimetre Receiver Array (OCRA-p) which is mounted on the Torun 32-m telescope. The clusters (Cl0016+16, MS0451.6-0305, MS1054.4-0321 and Abell 2218) are popular SZ targets and serve as commissioning observations. All four are detected with clear significance (4-6 sigma) and values for the central temperature decrements are in good agreement with measurements reported in the literature. We believe that systematic effects are successfully suppressed by our observing strategy. The relatively short integration times required to obtain these results demonstrate the power of OCRA-p and its successors for future SZ studies.

21-cm Radiation: A New Probe of Variation in the Fine-Structure Constant

We investigate the effect of variation in the value of the fine-structure constant (alpha) at high redshifts (recombination > z > 30) on the absorption of the cosmic microwave background (CMB) at 21 cm hyperfine transition of the neutral atomic hydrogen. We find that the 21 cm signal is very sensitive to the variations in alpha and it is so far the only probe of the fine-structure constant in this redshift range. A change in the value of alpha by 1% changes the mean brightness temperature decrement of the CMB due to 21 cm absorption by >5% over the redshift range z < 50. There is an effect of similar magnitude on the amplitude of the fluctuations in the brightness temperature. The redshift of maximum absorption also changes by approximately 5%.

Drying characteristics of porous material immersed in a bed of hygroscopic porous particles fluidized under reduced pressure

A relatively large wet material was immersed in a fluidized bed of hygroscopic porous particle (silica gel beads) under reduced pressure. And then the drying characteristics were compared with those in the case of inert particle (glass beads). The comparison of drying characteristics is performed experimentally and theoretically. In calculation, the water transfer from the sample to the fluidized bed was considered. The calculation results are in good agreement with the experimental data. The effects of the operational conditions (the pressure in the drying chamber and the temperature of the drying gas) on the drying characteristics were also examined in both fluidizing particles. The drying finishes earlier in the case of hygroscopic porous particle than in the case of inert particle regardless of pressure in the drying chamber, since the water transfer from the sample facilitates the drying in the case of hygroscopic porous particles. The temperature decrement in drying appears in the case of inert particle. This phenomenon is also observed in the case of hygroscopic porous particle, but the decrement degree of the temperature is much smaller than that in the case of inert particle. The difference of the minimum temperature in the sample in drying between the cases of hygroscopic porous particle and inert particle is very slight for different pressures in the drying chamber.

One-Dimensional Shape Memory Alloy Model Applicable to Any Status of Stress and Temperature

The transformation kinetics formulation is the principal factor underlying the constitutive model of shape memory alloys. Therefore, the transformation kinetics formulation, which is applicable to any status of stress and temperature, is essential for predicting the material behavior of SMAs. In this work, we show that the transformation kinetics of the Brinson model, which is the most widely used 1-dimensional model, has shortcomings under certain stress and temperature histories. In addition, we propose a modified transformation kinetics model that can be used for any stress or temperature conditions. The martensite transformation kinetics is modified so that the transformation from austenite into temperature-induced martensite, due to the decrement of temperature, is coupled with a transformation from austenite or temperature-induced martensite into stress-induced martensite, due to the increment of the stress. Through this modification, the suggested model can simulate the behavior of shape memory alloy materials under arbitrarily changed circumstances at every stress-temperature region.

Temperature profiles of a representative sample of nearby X-ray galaxy clusters

Context. A study of the structural and scaling properties of the temperature distribution of the hot, X-ray emitting intra-cluster medium of galaxy clusters, and its dependence on dynamical state, can give insights into the physical processes governing the formation and evolution of structure. Aims. Accurate temperature measurements are a pre-requisite for a precise knowledge of the thermodynamic properties of the intra-cluster medium. Methods. We analyse the X-ray temperature profiles from XMM-Newton observations of 15 nearby (z < 0.2) clusters, drawn from a statistically representative sample. The clusters cover a temperature range from 2.5 keV to 8.5 keV, and present a variety of X-ray morphologies. We derive accurate projected temperature profiles to ∼0.5 R 200 , and compare structural properties (outer slope, presence of cooling core) with a quantitative measure of the X-ray morphology as expressed by power ratios. We also compare the results to recent cosmological numerical simulations. Results. Once the temperature profiles are scaled by an average cluster temperature (excluding the central region) and the estimated virial radius, the profiles generally decline in the region 0.1 R 200 ≤ R ≤ 0.5 R 200 . The central regions show the largest scatter, attributable mostly to the presence of cool core clusters. There is good agreement with numerical simulations outside the core regions. We find no obvious correlations between power ratio and outer profile slope. There may however be a weak trend with the existence of a cool core, in the sense that clusters with a central temperature decrement appear to be slightly more regular. Conclusions. The present results lend further evidence to indicate that clusters are a regular population, at least outside the core region.

The Sunyaev‐Zel’dovich Effect in a Sample of 31 Clusters: A Comparison between the X‐Ray Predicted andWMAPObserved Cosmic Microwave Background Temperature Decrement

The WMAP Q-, V-, and W-band radial profiles of temperature deviation of the cosmic microwave background (CMB) were constructed for a sample of 31 randomly selected nearby clusters of galaxies in directions of Galactic latitude > 30°. The profiles were compared in detail with the expected CMB Sunyaev-Zel'dovich effect (SZE) caused by these clusters, with the hot gas properties of each cluster inferred observationally by applying gas temperatures as measured by ASCA to isothermal β-models of the ROSAT X-ray surface brightness profiles, with the WMAP point-spread function fully taken into consideration. After co-adding the 31 cluster fields to significantly reduce the systematic and random uncertainties, it appears that WMAP detected the SZE in all three bands. Quantitatively, however, the observed SZE only accounts for about 1/4 of the expected decrement. The discrepancy represents too much unexplained extra flux: in the W band, the detected SZE corresponds on average to 5.6 times less X-ray gas mass within a 10' radius than the mass value given by the ROSAT β-model. We critically examined how the X-ray prediction of the SZE may depend on our uncertainties in the density and temperature of the hot intracluster plasma, and emission by cluster radio sources. Although our comparison between the detected and expected SZE levels is subject to a margin of error, the fact remains that the average observed SZE depth and profile are consistent with those of the primary CMB anisotropy, i.e., the overall WMAP temperature decrement among the 31 rich clusters is too shallow to necessitate an interpretation in terms of an additional effect like the SZE. A unique aspect of this SZE investigation is that because all the data being analyzed are in the public domain, our work is readily open to scrutiny by others.

The Baryonic Matter at Supercluster Scales: The Case of Corona Borealis Supercluster

AbstractSuperclusters of galaxies are the largest gravitationally bound structures of the Universe. Numerical simulations indicate that a significant fraction of baryonic matter could be located in supercluster (SC) scales in the form of a warm/hot plasma. The sensitivity and resolution of the VSA interferometer at Teide observatory allow us to search for evidence of the Sunyaev-Zeldovich effect (SZE). We have published evidence for such a plasma towards the center of the Corona Borealis Supercluster (CrB-SC), Génova-Santos et al. (2005). Two large decrements in the intensity of the signal measured by VSA at 33 GHz (CrB-B and H) subtending an angle of about 25' could be indicative of a concentration of baryonic matter comparable to thousands of galaxies. This matter could be in the form of a plasma of temperature ~105 − 107 K where no clusters of galaxies have been identified. No other similar spots have been found in the VSA fields observed to measure the CMB primordial power spectrum of fluctuations, Rubiño-Martin et al. (2003), and suggests that this is indeed a very particular feature of the CrB-SC of galaxies. Additional data obtained with the MITO telescope of CrB-H also support this VSA finding Battistelli et al. (2006), and could be related to warm/hot plasma in the SC. We would expect a galaxy population to be associated with such a plasma, as it is well known to occur in clusters of galaxies where the SZE has been measured, Lancaster et al. (2005). However, the absence of X-ray emission in the ROSAT images in the CrB-SC SZ spots suggests that if there is a galaxy population linked to the plasma it may have a peculiar spatial distribution. We obtained photometry of CrB-SC region using the data base from SDSS DR4, covering a total of 15o2 in the CrB-SC area. We built a catogue with 121251 galaxies down a selection criterion based on galaxies colours 0.2 ≤ r − i ≤ 0.6 and δ(g, r, i) ≤ |0.2| errors. In order to study the behaviour of differents regions in the CrB-SC, four regions were measured that belongs it, two regions not associated with overdensity, A2065, and CrB-H with 30' radius for each ones. The completeness magnitude is R ≤ 21. A photometric study produced colour-magnitude diagrams where we can detect evidence that many of these galaxies belong to the same system. The excess in the number density of galaxies appears to be larger in CrB-H where the strongest CMB temperature decrement was found. The number of galaxies in it is a factor ~1.5 lower than A2065 and ~2.5 highest that the SC background field. This resembles the typical number of galaxies in clusters of galaxies. However, it appears these galaxies are more broadly distributed than in the well known clusters of this SC. It is possible that the hot plasma causing the SZ spot is indeed associated with a new large concentration of galaxies unidentified in the SC.

Measuring the Three‐dimensional Structure of Galaxy Clusters. II. Are Clusters of Galaxies Oblate or Prolate?

The intrinsic shape of galaxy clusters can be obtained through a combination of X-ray and Sunyaev-Zeldovich effect observations once cosmological parameters are assumed to be known. In this paper we discuss the feasibility of modeling galaxy clusters as either prolate or oblate ellipsoids. We analyze the intracluster medium distribution for a sample of 25 X-ray-selected clusters, with measured Sunyaev-Zeldovich temperature decrements. A mixed population of prolate and oblate ellipsoids of revolution fits the data well, with prolate shapes preferred by ~60%-76%. We observe an excess of clusters nearly aligned along the line of sight, with respect to what is expected from a randomly oriented cluster population, which might imply the presence of a selection bias in our sample. We also find signs that a more general triaxial morphology might better describe the morphology of galaxy clusters. Additional constraints from gravitational lensing could disentangle the degeneracy between an ellipsoidal and a triaxial morphology, and could also allow an unbiased determination of the Hubble constant.

Comptonization of cosmic microwave background photons in dwarf spheroidal galaxies

We present theoretical modelling of the electron distribution produced by annihilating neutralino dark matter in dwarf spheroidal galaxies (dSphs). In particular, we follow up the idea of Colafrancesco and find that such electrons distort the cosmic microwave background (CMB) by the Sunyaev-Zeldovich (SZ) effect. For an assumed neutralino mass of 10 GeV and beam size of 1 arcsec, the SZ temperature decrement is of the order of nano-Kelvin for dSph models with a soft core. By contrast, it is of the order of micro-Kelvin for the strongly cusped dSph models favoured by some cosmological simulations. Although this is out of reach of current instruments, it may well be detectable by future mm telescopes, such as the Atacama Large Millimetre Array. We also show that the upscattered CMB photons have energies within reach of upcoming X-ray observatories, but that the flux of such photons is too small to be detectable now. None the less, we conclude that searching for the dark matter induced SZ effect is a promising way of constraining the dark distribution in dSphs, especially if the particles are light.

Spectral indications of thermal Sunyaev-Zel'dovich effect in ARCHEOPS and WMAP data

In this paper, we present a joint cross-correlation analysis of the Archeops CMB maps at 143 and 217 GHz and the WMAP CMB maps at 41, 61 and 94 GHz with sky templates of projected galaxy density constructed from the 2MASS Extended Source catalog. These templates have been divided in patches sorted in decreasing galaxy density with a fixed number of pixels (we considered patches having 32, 64 and 128 pixels) and the cross correlation has been performed independently for each of these patches. We find that the densest patch shows a strong temperature decrement in the Q, V, W bands of WMAP and in the 143 GHz channel of Archeops, but not in the 217 GHz channel. Furthermore, we find that the spectral behavior of the amplitude of this decrement is compatible with that expected for the non-relativistic thermal Sunyaev-Zel'dovich effect, and is incompatible (at 4.5 sigma level) with the null hypothesis of having only CMB, noise and a dust component (nu^2) in those pixels. We find that the first 32-pixel sized patch samples the cores of 11 known massive nearby galaxy clusters. Under the assumption that the decrement found in this patch is due entirely to the thermal Sunyaev-Zel'dovich effect, we obtain an average comptonization parameter for those sources of y = (0.41 +- 0.08) x 10^(-4) at 13 arcmin angular scales. This value is compatible at 1 sigma with the expectation, y = 0.49 x 10^(-4), from a model of the cluster flux number counts based on the standard Lambda-CDM cosmology. The observed value of y is slightly diluted when computed for the first patch of 64 and 128 pixels, presumably due to the inclusion of less massive clusters, and the dilution factor inferred is also compatible with the quoted model.

Detection and Fundamental Applications of Individual First Galaxies

First galaxies formed within halos of mass M=E7.5-E9 Msun at z=30-40 in the standard cold dark matter (CDM) universe may each display an extended hydrogen 21-cm absorption halo against the cosmic microwave background with a brightness temperature decrement of del T=-(100-150)mK at a radius 0.3 < r < 3.0 comoving Mpc, corresponding to an angular size of 10-100 arcseconds. A 21-cm tomographic survey in the redshift shell z=30-40 (at 35-45MHz), which could be carried out by the next generation of radio telescopes, is expected to be able to detect millions of first galaxies and may prove exceedingly profitable in enabling (at least) four fundamental applications for cosmology and galaxy formation. First, it may yield direct information on star formation physics in first galaxies. Second, it could provide a unique and sensitive probe of small-scale power in the standard cosmological model hence physics of dark matter and inflation. Third, it would allow for an independent, perhaps cleaner characterization of interesting features on large scales in the power spectrum such as the baryonic oscillations. Finally, possibly the most secure, each 21-cm absorption halo is expected to be highly spherical and faithfully follow the Hubble flow. By applying the Alcock-Paczynski test to a significant sample of first galaxies, one may be able to determine the dark energy equation of state with an accuracy likely only limited by the accuracy with which the matter density can be determined independently.

A theoretical study on the behavior of simulated annealing leading to a new cooling schedule

This paper presents an empirical study on the efficiency of the simulated annealing (SA) algorithm. It considers various parameters such as landscape and neighborhood. The need for a better understanding of SA, with the additional goal of implementing the algorithm efficiently, motivated this study. The method selected to conduct that study was to carry out experiments to obtain practical data, which could be utilized to carry out a theoretical study simultaneously. Experiments on such a stochastic algorithm as SA were initiated following the observation that it is possible to calculate the exact probability for SA to reach any point in the landscape, provided that the number of solutions and the number of neighbors per solution are small enough. An efficient development of a SA simulator has enabled us to study the influence of the tuning of all the main parameters of SA as well as theoretical concepts such as thermodynamic equilibrium and optimal temperature decrement rules. Interesting results have been obtained in the field of adaptive cooling schedules that enable us to demonstrate that the classical cooling schedules are all equivalent. Finally a new schedule has been proposed that exhibits some useful properties. The proposed cooling schedule has been successfully implemented in the SA algorithm to solve the well known traveling salesman problem.

AGN Heating, Thermal Conduction, and the Sunyaev‐Zel'dovich Effect in Galaxy Groups and Clusters

We investigate in detail the role of active galactic nuclei (AGNs) in the physical state of the gas in galaxy groups and clusters, and the implications for anisotropy in the cosmic microwave background (CMB) from the Sunyaev-Zel'dovich (SZ) effect. We have recently shown that AGNs can significantly change the entropy of the intracluster medium (ICM) and explain the observations of excess entropy in groups and clusters. AGNs are assumed to deposit energy via buoyant bubbles that expand as they rise in the cluster atmosphere and do P dV work on the ICM. Here we include the effect of thermal conduction and find that the resulting profiles of temperature and entropy are consistent with observations. Unlike previously proposed models, our model predicts that isentropic cores are not an inevitable consequence of preheating. The model also reproduces the observational trend for the density profiles to flatten in lower mass systems. We deduce the energy (Eagn) required to explain the entropy observations as a function of mass of groups and clusters (Mcluster) and show that Eagn ∝ M with α ~ 1.5. We demonstrate that the entropy measurements, in conjunction with our model, can be translated into constraints on the cluster-black hole mass relation. The inferred relation is nonlinear and has the form Mbh ∝ M. This scaling is an analog and extension of a similar relation between the black hole mass and the galactic halo mass that holds on smaller scales. In addition, we study the implications of these results for the thermal SZ effect. We show that the central decrement of the CMB temperature is reduced due to the enhanced entropy of the ICM and that the decrement predicted from the plausible range of energy input from the AGN is consistent with available data on the SZ decrement. We also estimate the Poisson contribution to the angular power spectrum of the CMB from the SZ effect due to AGN heating. We show that AGN heating, combined with the observational constraints on entropy, leads to suppression of higher multipole moments in the power spectrum, and we find that this effect is stronger than previously thought. The suppression in the power spectrum in our model is due to depletion of gas from the central regions that is more efficient in low-mass clusters and groups than in massive clusters.