Can simulations reproduce the observed temperature–mass relation for clusters of galaxies?

It has become increasingly apparent that traditional hydrodynamical simulations of galaxy clusters are unable to reproduce the observed properties of galaxy clusters, in particular overpredicting the mass corresponding to a given cluster temperature. Such overestimation may lead to systematic errors in results using galaxy clusters as cosmological probes, such as constraints on the density perturbation normalization σ ₈. In this paper we demonstrate that inclusion of additional gas physics, namely radiative cooling and a possible pre-heating of gas prior to cluster formation, is able to bring the temperature–mass relation in the innermost parts of clusters into good agreement with recent determinations by Allen, Schmidt & Fabian using Chandra data.     

Ram-pressure stripping of disc galaxies orbiting in clusters – II. Galactic wakes

We present 3D hydrodynamical simulations of ram-pressure stripping of a disc galaxy orbiting in a galaxy cluster. In this paper, we focus on the properties of the galaxies' tails of stripped gas. The galactic wakes show a flaring width, where the flaring angle depends on the gas disc's cross-section with respect to the galaxy's direction of motion. The velocity in the wakes shows a significant turbulent component of a few     . The stripped gas is deposited in the cluster rather locally, i.e. within     from where it was stripped. We demonstrate that the most important quantity governing the tail density, length and gas mass distribution along the orbit is the galaxy's mass-loss per orbital length. This in turn depends on the ram pressure as well as the galaxy's orbital velocity.
For a sensitivity limit of     in projected gas density, we find typical tail lengths of     . Such long tails are seen even at large distances (0.5 to     ) from the cluster centre. At this sensitivity limit, the tails show little flaring, but a width similar to the gas disc's size.
Morphologically, we find good agreement with the H  i tails observed in the Virgo cluster by Chung et al. 2007 . However, the observed tails show a much smaller velocity width than predicted from the simulation. The few known X-ray and Hα tails are generally much narrower and much straighter than the tails in our simulations. Thus, additional physics like a viscous intracluster medium (ICM), the influence of cooling and tidal effects may be needed to explain the details of the observations.
We discuss the hydrodynamical drag as a heat source for the ICM but conclude that it is not likely to play an important role, especially not in stopping cooling flows.     

A ROSAT study of the cores of clusters of galaxies — I. Cooling flows in an X-ray flux-limited sample

This is the first part of a study of the detailed X-ray properties of the cores of nearby clusters. We have used the flux-limited sample of 55 clusters listed by Edge et al., and archival and proprietary data from the ROSAT observatory. In this paper an X-ray spatial analysis based on the surface-brightness-deprojection technique is applied to the clusters in the sample with the aim of studying their cooling flow properties. We determine the fraction of cooling flows in this sample to be 70–90 per cent, and estimate the contribution of the flow region to the cluster X-ray luminosity. We show that the luminosity within a strong cooling flow can account for up to 70 per cent of a cluster X-ray bolometric luminosity. Our analysis indicates that about 40 per cent of the clusters in the sample have flows depositing more than 100 M⊙ yr⁻¹ throughout the cooling region, and that these possibly have been undisturbed for many Gyr, confirming that cooling flows are the natural state of cluster cores. New cooling flows in the sample are presented, and previously ambiguous ones are clarified. We have constructed a catalogue of some intracluster medium properties for the clusters in this sample. The profiles of the mass deposited from cooling flows are analysed, and evidence is presented for the existence of breaks in some of the profiles. Comparison is made to recent optical and radio data. We cross-correlate our sample with the Green Bank, NVSS and FIRST surveys, and with the volume-limited sample of brightest cluster galaxies presented by Lauer &38; Postman. Although weak trends exist, no strong correlation between optical magnitude or radio power of the brightest cluster galaxy and the strength of the flow is found.     

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.     

Hydrodynamics and stability of galactic cooling flows

Using numerical techniques we study the global stability of cooling flows in X-ray luminous giant elliptical galaxies. As an unperturbed equilibrium state we choose the hydrostatic gas recycling model. Non-equilibrium radiative cooling, stellar mass loss, heating by type Ia supernovae, distributed mass deposition and thermal conductivity are included. Although the recycling model reproduces the basic X-ray observables, it appears to be unstable with respect to the development of inflow or outflow. In spherical symmetry the inflows are subject to a central cooling catastrophe, while the outflows saturate in a form of a subsonic galactic wind. Two-dimensional axisymmetric random velocity perturbations of the equilibrium model trigger the onset of a cooling catastrophe, which develops in an essentially non-spherical way. The simulations show a patchy pattern of mass deposition and the formation of hollow gas jets, which penetrate through the outflow down to the galaxy core. The X-ray observables of such a hybrid gas flow mimic those of the equilibrium recycling model, but the gas temperature exhibits a central depression. The mass deposition rate M ˙ consists of two contributions of similar size: (i) a hydrostatic one resembling that of the equilibrium model, and (ii) a dynamical one which is related to the jets and is more concentrated towards the centre. For a model galaxy, like NGC 4472, our 2D simulations predict M ˙ ≈ 2 M⊙ yr⁻¹ within the cooling radius for the advanced non-linear stage of the instability. We discuss the implications of these results to Hα nebulae and star formation in cooling flow galaxies and emphasize the need for high-resolution 3D simulations.     

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.     

The first galaxies: assembly, cooling and the onset of turbulence

We investigate the properties of the first galaxies at   z ≳ 10  with highly resolved numerical simulations, starting from cosmological initial conditions and taking into account all relevant primordial chemistry and cooling. A first galaxy is characterized by the onset of atomic hydrogen cooling, once the virial temperature exceeds  ≃10⁴ K  , and its ability to retain photoheated gas. We follow the complex accretion and star formation history of a  ≃5 × 10⁷ M_⊙  system by means of a detailed merger tree and derive an upper limit on the number of Population III (Pop III) stars formed prior to its assembly. We investigate the thermal and chemical evolution of infalling gas and find that partial ionization at temperatures  ≳10⁴ K  catalyses the formation of  H₂  and hydrogen deuteride, allowing the gas to cool to the temperature of the cosmic microwave background. Depending on the strength of radiative and chemical feedback, primordial star formation might be dominated by intermediate-mass Pop III stars formed during the assembly of the first galaxies. Accretion on to the nascent galaxy begins with hot accretion, where gas is accreted directly from the intergalactic medium and shock heated to the virial temperature, but is quickly accompanied by a phase of cold accretion, where the gas cools in filaments before flowing into the parent halo with high velocities. The latter drives supersonic turbulence at the centre of the galaxy and could lead to very efficient chemical mixing. The onset of turbulence in the first galaxies thus likely marks the transition to Pop II star formation.     

Radio profile instability in the millisecond pulsar PSR J0437−4715 resulting from spiky emission

We report the discovery of a 40 arcsec long X-ray filament in the core of the cluster of galaxies Abell 1795. The feature coincides with an H α +N  ii filament found by Cowie et al. in the early 1980s and resolved into at least two U -band filaments by McNamara et al. in the mid-1990s. The (emission-weighted) temperature of the X-ray emitting gas along the filament is 2.5–3 keV, as revealed by X-ray colour ratios. The deprojected temperature will be less. A detailed temperature map of the core of the cluster presented. The cD galaxy at the head of the filament is probably moving through or oscillating in the cluster core. The radiative cooling time of the X-ray emitting gas in the filament is about     which is similar to the age of the filament obtained from its length and velocity. This suggests that the filament is produced by cooling of the gas from the intracluster medium. The filament, much of which is well separated from the body of the cD galaxy and its radio source, is potentially of great importance in helping to understand the energy and ionization source of the optical nebulosity common in cooling flows.     

The hydrodynamics of dead radio galaxies

We present a numerical investigation of dead, or relic, radio galaxies and the environmental impact that radio galaxy activity has on the host galaxy or galaxy cluster. We perform axisymmetric hydrodynamical calculations of light, supersonic, back-to-back jets propagating in a β -model galaxy/cluster atmosphere. We then shut down the jet activity and let the resulting structure evolve passively. The dead source undergoes an initial phase of pressure driven expansion until it achieves pressure equilibrium with its surroundings. Thereafter, buoyancy forces drive the evolution and lead to the formation of two oppositely directed plumes that float high into the galaxy/cluster atmosphere. These plumes entrain a significant amount of low entropy material from the galaxy/cluster core and lift it high into the atmosphere. An important result is that a large fraction (at least half) of the energy injected by the jet activity is thermalized in the interstellar medium (ISM)/intracluster medium (ICM) core. The whole ISM/ICM atmosphere inflates in order to regain hydrostatic equilibrium. This inflation is mediated by an approximately spherical disturbance which propagates into the atmosphere at the sound speed. The fact that such a large fraction of the injected energy is thermalized suggests that radio galaxies may have an important role in the overall energy budget of rich ISM/ICM atmospheres. In particular, they may act as a strong and highly time-dependent source of negative feedback for galaxy/cluster cooling flows.     

Cooling flows in clusters of galaxies

Summary X-ray images and spectra of clusters of galaxies show strong evidence for cooling flows. In many clusters, the hot gas in the core is cooling at rates of 100Myr^–1 and greater. Few traces of the cooled gas have been observed, but it probably forms into low-mass stars (perhaps brown dwarf or even Jupiter-mass objects). X-ray surface-brightness profiles show that the cooling gas is highly inhomogeneous. Overdense gas cools rapidly to form cooled clumps distributed throughout the flow, with little of the gas ever reaching the cluster centre. Cooled and cooling clumps are disrupted because of their motion relative to the remainder of the gas, tending to produce small cooled fragments and, ultimately, low-mass stars. Large molecular clouds, which are the sites of massive star formation in our galaxy, do not occur in the outer parts of cooling flows. There is evidence of larger gas clumps and the formation of more massive stars in the central few kpc of some cooling flows. It is argued that cooling flows efficiently form dark matter. This has wider implications for the formation of dark matter in massive galaxies.     

Supersonic motions of galaxies in clusters

We study motions of galaxies in galaxy clusters formed in the concordance Λ cold dark matter cosmology. We use high-resolution cosmological simulations that follow the dynamics of dark matter and gas and include various physical processes critical for galaxy formation: gas cooling, heating and star formation. Analysing the motions of galaxies and the properties of intracluster gas in a sample of eight simulated clusters at z = 0, we study the velocity dispersion profiles of the dark matter, gas and galaxies. We measure the mean velocity of galaxy motions and gas sound speed as a function of radius and calculate the average Mach number of galaxy motions. The simulations show that galaxies, on average, move supersonically with the average Mach number of ≈1.4, approximately independent of the cluster-centric radius. The supersonic motions of galaxies may potentially provide an important source of heating for the intracluster gas by driving weak shocks and via dynamical friction, although these heating processes appear to be inefficient in our simulations. We also find that galaxies move slightly faster than the dark matter particles. The magnitude of the velocity bias,   b _v ≈ 1.1  , is, however, smaller than the bias estimated for subhaloes in dissipationless simulations. Interestingly, we find velocity bias in the tangential component of the velocity dispersion, but not in the radial component. Finally, we find significant random bulk motions of gas. The typical gas velocities are of order ≈20–30 per cent of the gas sound speed. These random motions provide about 10 per cent of the total pressure support in our simulated clusters. The non-thermal pressure support, if neglected, will bias measurements of the total mass in the hydrostatic analyses of the X-ray cluster observations.     

Morphology and evolution of simulated and optical clusters: a comparative analysis

We have made a comparative study of morphological evolution in simulated dark matter (DM) haloes and X-ray brightness distribution, and in optical clusters. Samples of simulated clusters include star formation with supernovae feedback, radiative cooling and simulation in the adiabatic limit at three different redshifts,   z = 0.0, 0.10  and 0.25. The optical sample contains 208 Abell, Corwin & Olowin (ACO) clusters within redshift,   z ≤ 0.25  . Cluster morphology, within 0.5 and 1.0 h ⁻¹ Mpc from cluster centre, is quantified by multiplicity and ellipticity.
We find that the distribution of the DM haloes in the adiabatic simulation appears to be more elongated than the galaxy clusters. Radiative cooling brings halo shapes in excellent agreement with observed clusters; however, cooling along with feedback mechanism makes the haloes more flattened.
Our results indicate relatively stronger structural evolution and more clumpy distributions in observed clusters than in the structure of simulated clusters, and slower increase in simulated cluster shapes compared to those in the observed one.
Within   z ≤ 0.1  , we note an interesting agreement in the shapes of clusters obtained from the cooling simulations and observation. We also note that the different samples of observed clusters differ significantly in morphological evolution with redshift. We highlight a few possibilities responsible for the discrepancy in morphological evolution of simulated and observed clusters.     

Spiral structure formed in a pair of interacting galaxies

The formation of spiral structure in a galaxy, as a result of the gravitational perturbation caused by a permanent companion, is studied. It is found that spiral structure appears only when a resonance exists between the rotational frequency of the stars in the galaxy and the rotational frequency of the companion galaxy. The number of spiral arms depends strongly on the particular resonance. In the case where the companion moves in an elliptic orbit, spiral arms are formed when a resonance, inside the galactic body, exists in almost all the parts of the orbit or, at least, in the largest part of it.     

AGN feedback through sound wave dissipation

We investigate the possibility of explaining the observed ripples in the X-ray gas in the Perseus and Virgo clusters through natural oscillations of a perturbed radio cocoon. Such a perturbation would result from an expanding overpressured cocoon of radio plasma overshooting its pressure equilibrium point with the cluster gas. The oscillations are heavily acoustically damped, and energy injection rates required to sustain them are consistent with observed AGN powers. Viscous dissipation of sound waves generated by these oscillations heats the cluster gas. By comparing our model with observations in Perseus and Virgo, we reproduce the observed ripple separations and amplitudes. Spitzer viscosity is largely sufficient in explaining the gas density profile, suggesting that thermal conductivity is likely to be heavily suppressed. In the central regions, viscous heating can suppress cooling flows on timescales exceeding the radio source lifetime.     

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.     

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.     

Populating a cluster of galaxies – I. Results at

We simulate the assembly of a massive rich cluster and the formation of its constituent galaxies in a flat, low-density universe. Our most accurate model follows the collapse, the star formation history and the orbital motion of all galaxies more luminous than the Fornax dwarf spheroidal, while dark halo structure is tracked consistently throughout the cluster for all galaxies more luminous than the SMC. Within its virial radius this model contains about     dark matter particles and almost 5000 distinct dynamically resolved galaxies. Simulations of this same cluster at a variety of resolutions allow us to check explicitly for numerical convergence both of the dark matter structures produced by our new parallel N -body and substructure identification codes, and of the galaxy populations produced by the phenomenological models we use to follow cooling, star formation, feedback and stellar aging. This baryonic modelling is tuned so that our simulations reproduce the observed properties of isolated spirals outside clusters. Without further parameter adjustment our simulations then produce a luminosity function, a mass-to-light ratio, luminosity, number and velocity dispersion profiles, and a morphology–radius relation which are similar to those observed in real clusters. In particular, since our simulations follow galaxy merging explicitly, we can demonstrate that it accounts quantitatively for the observed cluster population of bulges and elliptical galaxies.     

The haloes of merger remnants

We perform collisionless N -body simulations of 1:1 galaxy mergers, using models which include a galaxy halo, disc and bulge, focusing on the behaviour of the halo component. The galaxy models are constructed without recourse to a Maxwellian approximation. We investigate the effect of varying the galaxies' orientation, their mutual orbit and the initial velocity anisotropy or cusp strength of the haloes upon the remnant halo density profiles and shape, as well as on the kinematics. We observe that the halo density profile (determined as a spherical average, an approximation we find appropriate) is exceptionally robust in mergers, and that the velocity anisotropy of our remnant haloes is nearly independent of the orbits or initial anisotropy of the haloes. The remnants follow the halo anisotropy – local density slope (β–γ) relation suggested by Hansen & Moore in the inner parts of the halo, but β is systematically lower than this relation predicts in the outer parts. Remnant halo axis ratios are strongly dependent on the initial parameters of the haloes and on their orbits. We also find that the remnant haloes are significantly less spherical than those described in studies of simulations which include gas cooling.     

Active galactic nuclei heating in the centres of galaxy groups: a statistical study

We present gas temperature, density, entropy and cooling time profiles for the cores of a sample of 15 galaxy groups observed with Chandra . We find that the entropy profiles follow a power-law profile down to very small fractions of R ₅₀₀. Differences between the gas profiles of groups with radio-loud and radio-quiet brightest group galaxies are only marginally significant, and there is only a small difference in the   L _X: T _X  relations, for the central regions we study with Chandra , between the radio-loud and radio-quiet objects in our sample, in contrast to the much larger difference found on scales of the whole group in earlier work. However, there is evidence, from splitting the sample based on the mass of the central black holes, that repeated outbursts of active galactic nuclei (AGN) activity may have a long-term cumulative effect on the entropy profiles. We argue that, to first order, energy injection from radio sources does not change the global structure of the gas in the cores of groups, although it can displace gas on a local level. In most systems, it appears that AGN energy injection serves primarily to counter the effects of radiative cooling, rather than being responsible for the similarity breaking between groups and clusters.