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.     

Numerical simulations of rotating cooling flows in galaxy cluster environments

We have used 2D numerical simulations to study the evolution of galaxy cluster cooling flows undergoing a rotational perturbation. We show that such rotations in the intracluster medium may arise from cluster/subcluster mergers. Our galaxy cluster initial conditions involve spherically symmetric, steady-state cooling flows with varying mass-dropout strengths. The rotational perturbation serves to break the symmetry for each of the initial cooling flows, resulting in the formation of thin, gaseous disc-like structure extending radially out to ∼10 kpc. Disc-like structure formed for low mass-dropout strength simulations appears to contain cooling condensations whereas disc-like structure in higher mass-dropout strength simulations appears smooth. This is due to the influence of mass-dropout on the degree of cooling, which serves to reduce the strength of thermal instabilities by the removal of 'cold' gas from the flow. Morphological comparisons of the disc-like structure formed in our simulations are made to structure observed in the X-ray emitting gas of A4059. Comparisons of the gas dynamics within the disc-like structure are also made to the solid-body rotation profile observed from emission-line gas within the central galaxy of Hydra A. The influence of grid effects on the simulations is also discussed.     

Star formation and chemical evolution in smoothed particle hydrodynamics simulations: a statistical approach

In smoothed particle hydrodynamics (SPH) codes with a large number of particles, star formation as well as gas and metal restitution from dying stars can be treated statistically. This approach allows one to include detailed chemical evolution and gas re-ejection with minor computational effort. Here we report on a new statistical algorithm for star formation and chemical evolution, especially conceived for SPH simulations with large numbers of particles, and for parallel SPH codes.
For the sake of illustration, we also present two astrophysical simulations obtained with this algorithm, implemented into the Tree-SPH code by Lia & Carraro .
In the first simulation, we follow the formation of an individual disc-like galaxy, predict the final structure and metallicity evolution, and test resolution effects. In the second simulation we simulate the formation and evolution of a cluster of galaxies, to demonstrate the capabilities of the algorithm in investigating the chemo-dynamical evolution of galaxies and of the intergalactic medium in a cosmological context.     

Galaxy cluster mergers

We present the results of an Eulerian adaptive mesh refinement (AMR) hydrodynamical and N -body simulation in a Λ cold dark matter (ΛCDM) cosmology. The simulation incorporates common cooling and heating processes for a primordial gas. A specific halo finder has been designed and applied in order to extract a sample of galaxy clusters directly obtained from the simulation without considering any resimulating scheme. We have studied the evolutionary history of the cluster haloes, and classified them into three categories depending on the merger events they have undergone: major mergers, minor mergers and relaxed clusters. The main properties of each one of these classes and the differences among them are discussed. The collisions among galaxy clusters are produced naturally by the non-linear evolution in the simulated cosmological volume; no controlled collisions have been considered. We pay special attention to discuss the role of merger events as a source of feedback and reheating, and their effects on the existence of cool cores in galaxy clusters, as well as in the scaling relations.     

On the formation of cold fronts in massive mergers

Using adiabatic hydrodynamical simulations, we follow the evolution of two symmetric cold fronts forming in the remnant of a violent   z = 0.3  massive cluster merger. Because the fronts develop after the first passage of the two gas cores of the merging subclusters, and because they soon move ahead of their associated dark matter cores, both the structure and the location of our simulated cold fronts may correspond to a stage that is later than that of most cold fronts observed so far. The cold fronts are preceded by a roughly spherical shock that originates in the centre of the cluster and disappears in the outer regions after 1.6 Gyr. The cold fronts last longer, until   z ∼ 0  . We follow the spatial evolution of the gas of the subcluster cores, and find that a fraction of this gas is liberated in the intracluster medium after core passage, but mainly at apocentre, and that it does not fall back onto the cluster centre. Conversely, we trace back the low-temperature gas constituting the fronts and find that it is initially associated with the two dense cores of the merging clusters. In addition, we find some evidence for discontinuity of the gas velocity field across the edge of the forming cold fronts, suggesting the presence of a contact discontinuity there. In the light of other recent work, we then speculate on the physical mechanism resulting in the cold fronts. We suggest that sloshing induced by strongly varying ram pressure along the subcluster's orbit and/or spatial segregation between the dark matter and gas components of the cores of the subclusters results in strong tidal forces on the gas, and that these forces could be responsible for the deposition of part of the cold dense gas in the surrounding hot intracluster medium. This deposited gas then expands, cools down further, and constitutes the cold fronts.     

Stormy weather and cluster radio galaxies

New adaptive mesh refinement N-body+hydrodynamics numerical simulations are used to illustrate the complex and changing cluster environments in which many radio galaxies live and evolve. Groups and clusters of galaxies form at the intersections of filaments where they continue to accrete gas and dark matter to the present day. The accretion process produces shocks, turbulence, and transonic bulk flows forming a kind of stormy weather within the intracluster medium (ICM). Radio sources embedded within the stormy ICM form distorted, complex morphologies as observed in recent VLA cluster surveys. We show that the bending of wide-angle tailed radio sources can be understood as the result of recent cluster–subcluster mergers. We use new MHD simulations to illustrate how cluster radio halos can be formed by the shocks and turbulence produced during cluster mergers. Finally, we discuss new observations of distant Abell clusters that reveal a class of weak radio sources, probably starbursts, likely produced during the formation of the clusters as they accrete material from the supercluster environment.     

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.     

On the MHD Acceleration of Astrophysical Jets

We present a 2.5D magnetohydrodynamic (MHD) simulation of the acceleration of a collimated jet from a magnetized accretion disk. We employ a MHD Adaptive Mesh Refinement (AMR) code (FLASH—University of Chicago). Thanks to this tool we can follow the evolution of the system for many dynamical timescales with a high-spatial resolution. Assuming an initial condition in which a Keplerian disk, thus with no accretion motions, is threaded by a uniform poloidal magnetic field, we show how both the accretion flow and the acceleration of the outflow occur, and we present in detail which are the forces responsible for the jet launching and collimation. Our simulation also shows how the collimating forces due to the self-generated toroidal magnetic field can produce some peculiar knotty features.     

AGN effect on cooling flow dynamics

We analyzed the feedback of AGN jets on cooling flow clusters using three-dimensional AMR hydrodynamic simulations. We studied the interaction of the jet with the intracluster medium and creation of low X-ray emission cavities (Bubbles) in cluster plasma. The distribution of energy input by the jet into the system was quantified in its different forms, i.e. internal, kinetic and potential. We find that the energy associated with the bubbles, (pV+γ pV/(γ−1)), accounts for less than 10 percent of the jet energy.     

Parameter tests within cosmological simulations of galaxy formation

Numerical simulations of galaxy formation require a number of parameters. Some of these are intrinsic to the numerical integration scheme (e.g., the time-step), while others describe the physical model (e.g., the gas metallicity). In this paper we present results of a systematic exploration of the effects of varying a subset of these parameters on simulations of galaxy formation. We use N -body and 'Smoothed Particle Hydrodynamics' techniques to follow the evolution of cold dark matter and gas in a small volume. We compare a fiducial model with 24 different simulations, in which one parameter at a time is varied, focusing on properties such as the relative fraction of hot and cold gas, and the abundance and masses of galaxies. We find that for reasonable choices of numerical values, many parameters have relatively little effect on the galaxies, with the notable exception of the parameters that control the resolution of the simulation and the efficiency with which gas cools.     

Praesepe – two merging clusters?

A membership catalogue for Praesepe was compiled and split into four mass bins. A contour plot indicates the presence of a subcluster some 3 pc from the centre of the cluster, of approximately 30 M_⊙. A tidally truncated King profile was fitted to the remainder of the cluster and the tidal radius is found to be 12.1 pc; the mass of the cluster (excluding the subcluster) is 630 M_⊙. From the calculated velocity dispersions we find that the cluster appears to have too much kinetic energy and should be rapidly disintegrating. X-ray data suggest that there may be an age spread between the main core stars and the subcluster stars. This leads us to the conclusion that Praesepe is two merging clusters.     

Five young star clusters in the outer region of the Small Magellanic Cloud

Colour–magnitude diagrams in the Washington system are presented for the first time for five star clusters projected on to the outer region of the Small Magellanic Cloud (SMC). The clusters are found to have ages in the range 0.1–1.0 Gyr, as derived from the fit of isochrones with   Z = 0.004  . This sample increases substantially the number of young clusters in the outer SMC – particularly in the south-east quadrant – with well-derived parameters. We combine our results with those for other clusters in the literature to derive as large and homogeneous a data base as possible (totalling 49 clusters) in order to study global effects. We find no conclusive evidence for a dispersion in the cluster ages and metallicities as a function of their distance from the galaxy centre, in the SMC outer region. L 114 and 115, although very distant, are very young clusters, lying in the bridge of the SMC and therefore most likely formed during the interaction which formed this feature. We also find very good agreement between the cluster age–metallicity relation (AMR) and the prediction from a bursting model from Pagel & Tautvaišienė with a burst that occurred 3 Gyr ago. Comparing the present cluster AMR with that derived by Harris & Zaritsky for field stars in the main body of the SMC, we find that field stars and clusters underwent similar chemical enrichment histories during approximately the last couple of Gyr, but their chemical evolution was clearly different between 4 and 10 Gyr ago.     

Monte Carlo simulations of star clusters – IV. Calibration of the Monte Carlo code and comparison with observations for the open cluster M67

We outline the steps needed in order to incorporate the evolution of single and binary stars into a particular Monte Carlo code for the dynamical evolution of a star cluster. We calibrate the results against N -body simulations, and present models for the evolution of the old open cluster M67 (which has been studied thoroughly in the literature with N -body techniques). The calibration is done by choosing appropriate free code parameters. We describe, in particular, the evolution of the binary, white dwarf and blue straggler populations, though not all channels for blue straggler formation are represented yet in our simulations. Calibrated Monte Carlo runs show good agreement with results of N -body simulations not only for global cluster parameters, but also for, for example, binary fraction, luminosity function and surface brightness. Comparison of Monte Carlo simulations with observational data for M67 shows that it is possible to get reasonably good agreement between them. Unfortunately, because of the large statistical fluctuations of the numerical data and uncertainties in the observational data the inferred conclusions about the cluster initial conditions are not firm.     

Cluster magnetic fields from galactic outflows

We performed cosmological, magnetohydrodynamical simulations to follow the evolution of magnetic fields in galaxy clusters, exploring the possibility that the origin of the magnetic seed fields is galactic outflows during the starburst phase of galactic evolution. To do this, we coupled a semi-analytical model for magnetized galactic winds as suggested by Bertone, Vogt & Enßlin to our cosmological simulation. We find that the strength and structure of magnetic fields observed in galaxy clusters are well reproduced for a wide range of model parameters for the magnetized, galactic winds and do only weakly depend on the exact magnetic structure within the assumed galactic outflows. Although the evolution of a primordial magnetic seed field shows no significant differences to that of galaxy cluster fields from previous studies, we find that the magnetic field pollution in the diffuse medium within filaments is below the level predicted by scenarios with pure primordial magnetic seed field. We therefore conclude that magnetized galactic outflows and their subsequent evolution within the intracluster medium can fully account for the observed magnetic fields in galaxy clusters. Our findings also suggest that measuring cosmological magnetic fields in low-density environments such as filaments is much more useful than observing cluster magnetic fields to infer their possible origin.     

Dual black holes in merger remnants – I. Linking accretion to dynamics

We study the orbital evolution and accretion history of massive black hole (MBH) pairs in rotationally supported circumnuclear discs up to the point where MBHs form binary systems. Our simulations have high resolution in mass and space which, for the first time, makes it feasible to follow the orbital decay of a MBH either counter- or corotating with respect to the circumnuclear disc. We show that a moving MBH on an initially counter-rotating orbit experiences an 'orbital angular momentum flip' due to the gas-dynamical friction, i.e. it starts to corotate with the disc before a MBH binary forms. We stress that this effect can only be captured in very high resolution simulations. Given the extremely large number of gas particles used, the dynamical range is sufficiently large to resolve the Bondi–Hoyle–Lyttleton radii of individual MBHs. As a consequence, we are able to link the accretion processes to the orbital evolution of the MBH pairs. We predict that the accretion rate is significantly suppressed and extremely variable when the MBH is moving on a retrograde orbit. It is only after the orbital angular momentum flip has taken place that the secondary rapidly 'lights up' at which point both MBHs can accrete near the Eddington rate for a few Myr. The separation of the double nucleus is expected to be around ≲10 pc at this stage. We show that the accretion rate can be highly variable also when the MBH is corotating with the disc (albeit to a lesser extent) provided that its orbit is eccentric. Our results have significant consequences for the expected number of observable double active galactic nuclei at separations of ≲100 pc.     

Surveying the sky with the Arcminute MicroKelvin Imager: expected constraints on galaxy cluster evolution and cosmology

We discuss prospects for cluster detection via the Sunyaev–Zel'dovich (SZ) effect in a blank field survey with the interferometer array, the Arcminute MicroKelvin Imager (AMI). Clusters of galaxies selected in the SZ effect probe cosmology and structure formation with little observational bias, because the effect measures integrated gas pressure directly, and does so independently of cluster redshift.
We use hydrodynamical simulations in combination with the Press–Schechter expression to simulate SZ cluster sky maps. These are used with simulations of the observation process to gauge the expected SZ cluster counts. Even with a very conservative choice of parameters we find that AMI will discover at least several tens of clusters every year with     the numbers depend on factors such as the mean matter density, the density fluctuation power spectrum and cluster gas evolution. The AMI survey itself can distinguish between these to some degree, and parameter degeneracies are largely eliminated given optical and X-ray follow-up of these clusters; this will also permit direct investigation of cluster physics and what drives the evolution.     

Code Development of Three-Dimensional General Relativistic Hydrodynamics with AMR (Adaptive-Mesh Refinement) and Results from Special and General Relativistic Hydrodynamics

In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. This revised version was published online in July 2006 with corrections to the Cover Date.