An analytic investigation of the scatter in the integrated X-ray properties of galaxy groups and clusters
We revisit the scaling relationships between the dark matter mass and observed X-ray luminosity and temperature of galaxy clusters and groups in the local Universe. Specifically, we compare recent observations with analytic models of the intracluster medium in which the gas entropy distribution has been shifted by a variable amount, K o , to investigate the origin of the scatter in these scaling relations, and its influence on the luminosity and temperature functions. We find that variations in halo concentration or formation epoch (which might determine the time available for low-entropy gas to cool out) are insufficient to explain the amount of scatter in the mass and X-ray luminosity (M-L) relation. Instead, a range of entropy floors at a fixed halo mass, spanning approximately ∼50-700 keV cm 2 , is required to match the data. This range is likely related to the variance in heating and/or cooling efficiency from halo to halo. We demonstrate that these models are consistent with the observed temperature and luminosity functions of clusters, with a normalization of σ 8 ∼ 0.8 in agreement with Wilkinson Microwave Anisotropy Probe (WMAP) measurements (for h = 0.7 and Ω m = 0.3); in particular, the scatter in the M-L relation has an important influence on the shape of the luminosity function, and must be accounted for to provide a consistent result. Finally, we present predictions for the redshift evolution of these scaling relations and luminosity/temperature functions. Comparison with recent data at z < 0.7 shows reasonable agreement with a model that assumes a median entropy floor of K = 200 keV cm 2 . When observations are extended to group scales (kT ≤ 1 keV). this evolution will have the potential to discriminate between an entropy floor that is independent of redshift (e.g. in a preheating scenario) and one that depends on the cooling time of the halo.

title: Revisiting the baryon fractions of galaxy clusters: a comparison with WMAP 3-yr results
abstract: The universal baryonic mass fraction (Ω b /Ω m ) can be sensitively constrained using X-ray observations of galaxy clusters. In this paper, we compare the baryonic mass fraction inferred from measurements of the cosmic microwave background with the gas mass fractions (f gas ) of a large sample of clusters taken from the recent literature. In systems cooler than 4 keV, /gas declines as the system temperature decreases. However, in higher temperature systems, f gas (r 500 ) converges to≈(0.12 ± 0.02) (h /0.72) -1.5 , where the uncertainty reflects the systematic variations between clusters at r 500· This is significantly lower than the maximum-likelihood value of the baryon fraction from the recently released Wilkinson Microwave Anisotropy Probe (WMAP) 3-yr results. We investigate possible reasons for this discrepancy, including the effects of radiative cooling and non-gravitational heating, and conclude that the most likely solution is that Ω m is higher than the best-fitting WMAP value (we find Ω m =0.36 +0.11 ¯0.08 , but consistent at the 2σ level. Degeneracies within the WMAP data require that σ 8 must also be greater than the maximum likelihood value for consistency between the data sets.

title: New Tests of the Cluster Entropy Floor Hypothesis
abstract: Recent efforts to account for the observed X-ray luminosity - temperature relation of galaxy clusters has led to suggestions that the ICM has an apparent ``entropy floor'' at or above the level of 300 keV cm^2. Here, we propose new tests based on the thermal Sunyaev-Zeldovich effect and on the cluster gas mass - temperature trend (from X-ray data) to probe the level of excess entropy in the ICM. We show that these new tests lend further support to the case for a high entropy floor in massive clusters.

title: The Sunyaev–Zeldovich background
abstract: The cosmic background due to the Sunyaev–Zeldovich (SZ) effect is expected to be the largest signal at mm and cm wavelengths at a resolution of a few arcminutes. We investigate some simple statistics of SZ maps and their scaling with the normalization of the matter power spectrum, σ8, as well as the effects of the unknown physics of the intracluster medium on these statistics. We show that the SZ background provides a significant background for SZ cluster searches, with the onset of confusion occurring around 1014 h−1 M⊙ in a cosmology-dependent way, where confusion is defined as typical errors in recovered flux larger than 20 per cent. The confusion limit corresponds to the mass at which there are roughly 10 clusters per square degree, with this number nearly independent of cosmology and cluster gas physics. Typical errors grow quickly as lower mass objects are included in the catalogue. 
 
 
 
We also point out that there is nothing in particular about the rms of the filtered map that makes it especially well suited for capturing aspects of the SZ effect, and other indicators of the one-point SZ probability distribution function are at least as well suited for the task. For example, the full width at half-maximum of the one-point probability distribution has a field-to-field scatter that is about 60 per cent that of the rms. 
 
 
 
The simplest statistics of SZ maps are largely unaffected by cluster physics such as preheating, although the impact of preheating is clear by eye in the maps. Studies aimed at learning about the physics of the intracluster medium will apparently require more specialized statistical indicators.

title: The impact of mergers on relaxed X‐ray clusters – III. Effects on compact cool cores
abstract: We use the simulations presented in Poole et al. to examine the effects of mergers on the properties of cool cores in X-ray clusters. Motivated by recent Chandra and XMM-Newton observations, we propose a scheme for classifying the morphology of clusters based on their surface brightness and entropy profiles. Three dominant morphologies emerge: two hosting compact cores and central temperatures which are cool [CCC (compact cool core) systems] or warm [CWC (compact warm core) systems] and one hosting extended cores which are warm [EWC (extended warm core) systems]. In the cases we have studied, CCC states are disrupted only after direct collisions with merging cluster cores. This can happen in head-on collisions or during second pericentric passage in off-axis mergers. By the time they are relaxed, our remnant cores have generally been heated to warm core (CWC or EWC) states but subsequently recover CCC states by the end of the simulation. The only case resulting in a long-lived EWC state is a slightly off-axis 3:1 merger for which the majority of shock heating occurs during the accretion of a low-entropy stream formed from the disruption of the secondary's cool core. Since t dyn « t cool for all our relaxing merger remnant cores, compression prevents their core temperatures from falling until after they relax to the compact states allowed by their remnant central entropies. This naturally explains the population of relaxed CWC systems observed in recent Chandra and XMM-Newton observations with no need to invoke active galactic nuclei feedback. The morphological segregation in the L x -T x scaling relation noted by McCarthy et al. is qualitatively reflected in the results of our mergers as well. However, none of the cases we have studied produces systems with sufficiently high central entropies to account for the most underluminous EWC systems observed. Lastly, mergers do not efficiently mix the intracluster medium in our simulations. As a result, merging systems which initially host central metallicity gradients do not yield merger remnants with flat metallicity profiles. Taken together, these results suggest that once formed, compact core systems are remarkably stable against disruption from mergers. It remains to be demonstrated exactly how the sizable observed population of extended core systems was formed.

title: Modelling shock heating in cluster mergers – I. Moving beyond the spherical accretion model
abstract: The thermal history of the intracluster medium (ICM) is complex. Heat input from cluster mergers, from active galactic nuclei (AGN) and from winds in galaxies offsets and may even prevent the cooling of the ICM. Consequently, the processes that set the temperature and density structure of the ICM play a key role in determining how galaxies form. In this paper, we focus on the heating of the ICM during cluster mergers, with the eventual aim of incorporating this mechanism into semi-analytic models for galaxy formation. 
 
 
 
We generate and examine a suite of non-radiative hydrodynamic simulations of mergers in which the initial temperature and density structure of the systems are set using realistic scaling laws. Our collisions cover a range of mass ratios and impact parameters, and consider both systems composed entirely of gas (these reduce the physical processes involved), and systems comprising a realistic mixture of gas and dark matter. We find that the heating of the ICM can be understood relatively simply by considering evolution of the gas entropy during the mergers. The increase in this quantity in our simulations closely corresponds to that predicted from scaling relations based on the increase in cluster mass. 
 
 
 
We examine the physical processes that succeed in generating the entropy in order to understand why previous analytical approaches failed. We find the following. (i) The energy that is thermalized during the collision greatly exceeds the kinetic energy available when the systems first touch. The smaller system penetrates deep into the gravitational potential before it is disrupted. (ii) For systems with a large mass ratio, most of the energy is thermalized in the massive component. The heating of the smaller system is minor and its gas sinks to the centre of the final system. This contrasts with spherically symmetric analytical models in which accreted material is simply added to the outer radius of the system. (iii) The bulk of the entropy generation occurs in two distinct episodes. The first episode occurs following the collision of the cores, when a large shock wave is generated that propagates outwards from the centre. This causes the combined system to expand rapidly and overshoot hydrostatic equilibrium. The second entropy generation episode occurs as this material is shock heated as it recollapses. Both heating processes play an important role, contributing approximately equally to the final entropy. This revised model for entropy generation improves our physical understanding of cosmological gas simulations.

title: Simple Realistic Treatment of Nuclear Direct-Interaction Processes
abstract: Physical arguments are used to predict qualitatively the effect on direct-interaction differential cross sections of the distortion of the wave functions of the scattered particle. These qualitative predictions are confirmed by calculations using a simple but fairly realistic model for the wave function distortion in ($\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}$) scattering. The model used is based on examination of the properties of optical model wave functions. Good fits to experimental data are found using the model for ($\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}$) scattering in the energy range 20-40 Mev for scattering angles less than 90\ifmmode^\circ\else\textdegree\fi{}. Features of direct-interaction processes involving nucleons are interpreted in terms of a focus in the optical model wave functions for these particles, but detailed calculations are not presented.

title: Optical Model in the Interior of the Nucleus
abstract: It is shown how phase relationships between partial waves in the optical model result in focusing effects which are largest for surface partial waves. In the case of very low incident energies where the wavelength of a partial wave is large compared to the nuclear surface thickness, it is shown how the phase relationships may enable surfaceand volume-reaction mechanisms for a direct reaction to be distinguished by looking at gross features of the argular distribution. Thus, low-energy direct interactions may be used as a probe for the nuclear interior.

title: Observing electron motion in solids
abstract: We describe an experimental technique that allows for the direct determination of the motion (i.e., the momentum) of electrons in atoms, molecules, and solids. This ({ital e},2{ital e}) technique centers on a fast electron`s ejecting a second electron from a target. Precise spectroscopy of both electrons` final energies and momenta provides very significant information on the second electron`s initial state. Decades of past ({ital e},2{ital e}) studies on single-molecule states have now progressed into studies of condensed matter. The interpretation of these experiments is mediated in this colloquium by analysis of intermediate models in the form of chainlike molecules.

title: Distorted wave theory of the 50 MeV (p, 2p) reaction
abstract: An attempt is made to answer the question whether distorting potentials that give really good fits to elastic scattering cross sections and total reaction cross sections for experiments in the relevant two-body subsystems can correctly give positions of maxima and minima in the (p, 2p) angular correlation. The 50 MeV energy range is chosen because the angular correlation is very sensitive to the distortion. It is found that the positions are correctly reproduced by good elastic scattering parameters for the reaction 89 Y(p, 2p) 88 Sr, Q = 7.44 MeV, at 46 MeV. The shortcoming of the distorted wave theory at this energy, as at higher energies, is that the calculated ratio of the cross section at small angles to that at large angles is too large. Apart from this serious defect, the shape of the angular correlation for 12 C(p, 2p) 11 B, Q = 16 MeV, at 50 MeV is also encouraging. Previous studies suggest that the defect can be corrected if a better description of the p-p t -matrix is used in the distorted wave theory.

title: A high-resolution electron momentum spectroscopy and density functional theory study into the complete valence electronic structure of allene
abstract: A study of the electronic structure of the complete valence shell of allene (1,2-propadiene) is reported. New high-resolution binding-energy spectra were measured in the energy regime 6–34.5 eV over a range of different target electron momenta, so that momentum distributions (MDs) could be determined for each molecular orbital. These data supersede the low-resolution work of Braidwood et al. [ (1994) 2075–2087], and also clarify some ambiguities with the earlier results. Theoretical MDs were calculated using a plane wave impulse approximation (PWIA) model for the reaction mechanism and density functional theory (DFT) for the wave function. Three basis sets, at the local spin density (LSD) approximation level and, additionally, incorporating nonlocal corrections such as the generalized gradient approximation (GGA), were studied. A critical comparison between the experimental and theoretical MDs was made, and it allowed us to determine the “optimum” wave function for allene from the basis sets we considered. This wave function is then used to derive allene's chemically interesting molecular properties. A summary of some of these results and a comparison of them with those of other workers is also presented with the level of agreement typically being good.