The Sunyaev–Zel'dovich temperature of the intracluster medium

The relativistic Sunyaev–Zel'dovich (SZ) effect offers a method, independent of X-ray, for measuring the temperature of the intracluster medium (ICM) in the hottest systems. Here, using N -body/hydrodynamic simulations of three galaxy clusters, we compare the two quantities for a non-radiative ICM, and for one that is subject both to radiative cooling and to strong energy feedback from galaxies. Our study has yielded two interesting results. First, in all cases, the SZ temperature is hotter than the X-ray temperature and is within 10 per cent of the virial temperature of the cluster. Secondly, the mean SZ temperature is less affected by cooling and feedback than the X-ray temperature. Both these results can be explained by the SZ temperature being less sensitive to the distribution of cool gas associated with cluster substructure. A comparison of the SZ and X-ray temperatures (measured for a sample of hot clusters) would therefore yield interesting constraints on the thermodynamic structure of the intracluster gas.     

Bubbles, feedback and the intracluster medium: three-dimensional hydrodynamic simulations

We use a three-dimensional hydrodynamical code to simulate the effect of energy injection on cooling flows in the intracluster medium. Specifically, we compare a simulation of a 10¹⁵-M_⊙ cluster with radiative cooling only with a second simulation in which thermal energy is injected 31 kpc off-centre, over 64 kpc³ at a rate of     for 50 Myr. The heat injection forms a hot, low-density bubble which quickly rises, dragging behind it material from the cluster core. The rising bubble pushes with it a shell of gas which expands and cools. We find the appearance of the bubble in X-ray temperature and luminosity to be in good qualitative agreement with recent Chandra observations of cluster cores. Toward the end of the simulation, at 600 Myr, the displaced gas begins to fall back toward the core, and the subsequent turbulence is very efficient at mixing the low- and high-entropy gas. The result is that the cooling flow is disrupted for up to ∼ 50 Myr after the injection of energy ceases. Thus this mechanism provides a very efficient method for regulating cooling flows, if the injection events occur with a 1:1 duty cycle.     

Coulomb interactions in the intracluster medium

In this paper we discuss the effect of Coulomb collisions on the temperature profiles of the intracluster medium in clusters of galaxies, motivated by recent reports of negative temperature gradients in some clusters by Markevitch et al. The time-scale for electrons and protons to reach temperature equilibrium can exceed a few × 10⁹ years beyond radii of a megaparsec, if the intracluster gas is assumed to be at the usual cluster virial temperature. If a cluster merger has occurred within that time causing the protons, but not the electrons, to be rapidly heated then a small negative temperature gradient can result. This gradient is larger in clusters with higher temperatures and steeper density profiles.   Applying these considerations to the cluster of galaxies A2163, we conclude that, more plausibly, the observed gradient is due to a lack of hydrostatic equilibrium following a merger.     

Hydrodynamic simulations of merging clusters of galaxies

We present the results of high-resolution AP³M+SPH simulations of merging clusters of galaxies. We find that the compression and shocking of the core gas during a merger can lead to large increases in bolometric X-ray luminosities and emission-weighted temperatures of clusters. Cooling flows are completely disrupted during equal-mass mergers, with the mass deposition rate dropping to zero as the cores of the clusters collide. The large increase in the cooling time of the core gas strongly suggests that cooling flows will not recover from such a merger within a Hubble time. Mergers with subclumps having one eighth of the mass of the main cluster are also found to disrupt a cooling flow if the merger is head-on. However, in this case the entropy injected into the core gas is rapidly radiated away and the cooling flow restarts within a few Gyr of the merger. Mergers in which the subcluster has an impact parameter of 500 kpc do not disrupt the cooling flow, although the mass deposition rate is reduced by ∼30 per cent. Finally, we find that equal mass, off-centre mergers can effectively mix gas in the cores of clusters, while head on mergers lead to very little mixing. Gas stripped from the outer layers of subclumps results in parts of the outer layers of the main cluster being well mixed, although they have little effect on the gas in the core of the cluster. None of the mergers examined here resulted in the intracluster medium being well mixed globally.     

Hydrodynamical adaptive mesh refinement simulations of turbulent flows – II. Cosmological simulations of galaxy clusters

The development of turbulent gas flows in the intra-cluster medium and in the core of a galaxy cluster is studied by means of adaptive mesh refinement (AMR) cosmological simulations. A series of six runs was performed, employing identical simulation parameters but different criteria for triggering the mesh refinement. In particular, two different AMR strategies were followed, based on the regional variability of control variables of the flow and on the overdensity of subclumps, respectively. We show that both approaches, albeit with different results, are useful to get an improved resolution of the turbulent flow in the ICM. The vorticity is used as a diagnostic for turbulence, showing that the turbulent flow is not highly volume filling but has a large area-covering factor, in agreement with previous theoretical expectations. The measured turbulent velocity in the cluster core is larger than 200 km s⁻¹, and the level of turbulent pressure contribution to the cluster hydrostatic equilibrium is increased by using the improved AMR criteria.     

On viscosity, conduction and sound waves in the intracluster medium

Recent X-ray and optical observations of the Perseus cluster indicate that a combination of weak shocks at small radii  (≳20  kpc)  and viscous and conductive dissipation of sound waves at larger radii is responsible for heating the intracluster medium and can balance radiative cooling of cluster cores. We discuss this mechanism more generally and show how the specific heating and cooling rates vary with temperature and radius. It appears that this heating mechanism is most effective above  10⁷  K  , which allows for radiative cooling to proceed within normal galaxy formation but stifles the growth of very massive galaxies. The scaling of the wavelength of sound waves with cluster temperature and feedback in the system are investigated.     

Towards a holistic view of the heating and cooling of the intracluster medium

X-ray clusters are conventionally divided into two classes: 'cool core' (CC) clusters and 'non-cool core' (NCC) clusters. Yet relatively little attention has been given to the origins of this apparent dichotomy and, in particular, to the energetics and thermal histories of the two classes. We develop a model for the entropy profiles of clusters starting from the configuration established by gravitational shock heating and radiative cooling. At large radii, gravitational heating accounts for the observed profiles and their scalings well. However, at small and intermediate radii, radiative cooling and gravitational heating cannot be combined to explain the observed profiles of either CC or NCC clusters. The inferred entropy profiles of NCC clusters require that material is 'pre-heated' prior to cluster collapse in order to explain the absence of low-entropy (cool) material in these systems. We show that a similar modification is also required in CC clusters in order to match their entropy profiles at intermediate radii. In CC clusters, this modification is unstable, and an additional process is required to prevent cooling below a temperature of a few keV. We show that this can be achieved by adding a self-consistent active galactic nuclei (AGN) feedback loop in which the lowest entropy, most rapidly cooling material is heated and rises buoyantly to mix with material at larger radii. The resulting model does not require fine-tuning and is in excellent agreement with a wide variety of observational data from Chandra and XMM–Newton , including entropy and gas density profiles, the luminosity–temperature relation and high-resolution spectra. The spread in cluster core morphologies is seen to arise because of the steep dependence of the central cooling time on the initial level of pre-heating. Some of the other implications of this model are briefly discussed.     

Heating of the intracluster medium by quasar outflows

We study the possibility of quasar outflows in clusters and groups of galaxies heating the intracluster gas in order to explain the recent observation of excess entropy in this gas. We show that radio galaxies alone cannot provide the energy required to explain the observations but the inclusion of Broad Absorption Line (BAL) outflows can do so, and that in this scenario most of the heating takes place atz ∼ 1–4, the “preheating” epoch being at a lower redshift for lower mass clusters.     

Brief history of metal accumulation in the intracluster medium

We use models of the rates of Type Ia supernovae (SNe Ia) and core-collapsed supernovae, built in such a way that both are consistent with recent observational constraints at   z ≲ 1.6  and can reproduce the measured cosmic star formation rate, to recover the history of metal accumulation in the intracluster medium. We show that these SN rates, in unit of SN number per comoving volume and rest-frame year, provide on average a total amount of iron that is marginally consistent with the value measured in galaxy clusters in the redshift range 0–1, and a relative evolution with redshift that is in agreement with the observational constraints up to   z ≈ 1.2  . Moreover, we verify that the predicted metals-to-iron ratios reproduce the measurements obtained in nearby clusters through X-ray analysis, implying that (1) about half of the iron mass and ≳75 per cent of the nickel mass observed locally are produced by SN Ia ejecta, (2) the SN Ia contribution to the metal budget decreases steeply with redshift and by   z ≈ 1  is already less than half of the local amount, and (3) a transition in the abundance ratios relative to iron is present between redshifts ∼0.5 and 1.4, with core-collapsed SN products becoming dominant at higher redshifts.