The impact of mergers on relaxed X-ray clusters – I. Dynamical evolution and emergent transient structures
We report on the analysis of a suite of smoothed particle hydrodynamics simulations (incorporating cooling and star formation) of mergers involving idealized X-ray clusters whose initial conditions resemble relaxed clusters with cool compact cores observed by Chandra and XMM. The simulations sample the most-interesting, theoretically plausible, range of impact parameters and progenitor mass ratios. We find that all mergers evolve via a common progression. We illustrate this progression in the projected gas density, X-ray surface brightness, Sunyaev-Zel'dovich, temperature, and gas-entropy maps. Several different classes of transient 'cold front' like features can arise over the course of a merger. Each class is distinguished by a distinct morphological signature and physical cause. We find that all these classes are present in Chandra and XMM observations of merging systems and propose a naming scheme for these features: 'comet-like' tails, bridges, plumes, streams and edges. In none of the cases considered do the initial cool compact cores of the primary and the secondary get destroyed during the course of the mergers. Instead, the two remnant cores eventually combine to form a new core that, depending on the final mass of the remnant, can have a greater cooling efficiency than either of its progenitors. We quantify the evolving morphology of our mergers using centroid variance, power ratios and offset between the X-ray and the projected mass maps. We find that the centroid variance best captures the dynamical state of the cluster. It also provides an excellent indicator of how far the system is from virial and hydrostatic equilibrium. Placing the system at z = 0.1, we find that all easily identified observable traces of the secondary disappear from a simulated 50-ks Chandra image following the second pericentric passage. The system, however, takes an additional ∼2 Gyr to relax and virialize. Observationally, the only reliable indicator of a system in this state is the smoothness of its X-ray surface brightness isophotes, not temperature fluctuations. Temperature fluctuations at the level of AT/T ∼20 per cent, can persist in the final systems well past the point of virialization, suggesting that the existence of temperature fluctuations, in and of themselves, does not necessarily indicate a disturbed or unrelaxed system.

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: 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: 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: 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: 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: Continuum in the atomic optical model
abstract: The optical potential in principle gives a complete description of the effect of the target continuum on an electron-scattering problem truncated to a discrete set of channels. A momentum-space form for the optical potential has been derived and computed for the continuum in various approximations for the case of hydrogen. The total ionization cross section is excellently reproduced in the weak-coupling approximation above 100 eV by the most detailed model, and is tolerable as low as 50 eV.

title: Theory of (p,2p) reactions at medium energies
abstract: A new and effective means of calculating matrix elements relevant to direct interactions is introduced and applied to a distorted-wave t matrix approximation analysis of the /sup 12/C(p,2p9/sup 11/B and /sup 16/O(p,2p)/sup 15/N reactions at 45-50 MeV incident energy. A realistic separable two-body t matrix has been employed and core polarization, whereby the final state is generated after excitation of giant resonance target states, has been included. The integrals involved in the matrix elements were calculated analytically by making a parametrization of the distorted scattering wave functions, the nucleon-nucleon interaction, and the bound state wave function, the parameters being chosen in accordance with elastic (p,p) and inelastic (p,p') data and realistic shell model wave functions. The results indicate the inadequacy of a distorted-wave t-matrix approximation analysis at these energies.

title: Analytic distorted waves for intermediate-energy alpha particles

title: Core Excitation in a Stripping Reaction