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.     

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.     

Simulation of radio plasma in clusters of galaxies

We present three-dimensional hydrodynamical simulations of buoyant gas in a typical cluster environment. In these simulations, hot matter was injected continuously into a small region offset from the cluster centre. In agreement with previous analytic estimates, we found that the bubbles evolve very differently depending on the rate of energy injection. Using tracer particles we computed the efficiency of the bubbles to stir the intracluster medium (ICM) and find that recurrent low-power sources are more effective in mixing the inner cluster region than rarer large outbursts. Moreover, we computed radio maps of the bubbles based on different assumptions about the magnetic field. In the radio band the bubbles closely resemble FR I sources. For the bubbles to be detectable for long enough to account for FR I sources, we found that reacceleration has to take place. The bubbles are generally difficult to detect, both in the radio and in the X-ray band. Thus it is possible to hide a significant amount of energy in the form of bubbles in clusters.     

Sunyaev–Zel'dovich profiles and scaling relations: modelling effects and observational biases

We use high-resolution hydrodynamic resimulations to investigate the properties of the thermal Sunyaev–Zel'dovich (SZ) effect from galaxy clusters. We compare results obtained using different physical models for the intracluster medium (ICM), and show how they modify the SZ emission in terms of cluster profiles and scaling relations. We also produce realistic mock observations to verify whether the results from hydrodynamic simulations can be confirmed. We find that SZ profiles depend marginally on the modelled physical processes, while they exhibit a strong dependence on cluster mass. The central and total SZ emission strongly correlates with the cluster X-ray luminosity and temperature. The logarithmic slopes of these scaling relations differ from the self-similar predictions by less than 0.2; the normalization of the relations is lower for simulations including radiative cooling. The observational test suggests that SZ cluster profiles are unlikely to be able to probe the ICM physics. The total SZ decrement appears to be an observable much more robust than the central intensity, and we suggest using the former to investigate scaling relations.     

Sound waves excitation by jet-inflated bubbles in clusters of galaxies

We show that repeated sound waves in the intracluster medium (ICM) can be excited by a single inflation episode of an opposite bubble pair. To reproduce this behaviour in numerical simulations, the bubbles should be inflated by jets, rather than being injected artificially as already full-blown bubbles. The multiple sound waves are excited by the motion of the bubble–ICM boundary that is caused by vortices inside the inflated bubbles and the backflow ('cocoon') of the ICM around the bubble. These sound waves form a structure that can account for the ripples observed in the Perseus cooling flow cluster. We inflate the bubbles using slow massive jets either with a very wide opening angle or that are narrow and precessing. The wide jets (or collimated fast winds) are slow in the sense that they are highly subrelativistic,   v _j∼ 0.01 c – 0.1 c   , and they are massive in the sense that the pair of bubbles carries back to the ICM a large fraction of the cooling mass, i.e.  ∼1–50 M_⊙ yr⁻¹  . We use a two-dimensional axisymmetric (referred to as 2.5D) hydrodynamical numerical code ( vh-1 ).     

Are 'Bondi–Hoyle wakes' detectable in clusters of galaxies?

In clusters of galaxies, the reaction of the intracluster medium (ICM) to the motion of the co-existing galaxies in the cluster triggers the formation of unique features, which trace their position and motion. Galactic wakes, for example, are an apparent result of the ICM/galaxy interactions, and they constitute an important tool for deciphering the motion of the cluster galaxies.
In this paper we investigate whether Bondi–Hoyle accretion can create galactic wakes by focusing the ICM behind moving galaxies. The solution of the equations that describe this physical problem provides us with observable quantities along the wake at any time of its lifetime. We also investigate which are the best environmental conditions for the detectability of such structures in the X-ray images of clusters of galaxies.
We find that significant Bondi–Hoyle wakes can only be formed in low-temperature clusters, and that they are more pronounced behind slow-moving, relatively massive galaxies. The scalelength of these elongated structures is not very large: in the most favourable conditions a Bondi–Hoyle wake in a cluster at the redshift of z =0.05 is 12 arcsec long. However, the X-ray emission of the wake is noticeably strong: the X-ray flux can reach ∼30 times the flux of the surrounding medium. Such features will be easily detectable in the X-ray images of nearby, relatively poor clusters of galaxies by the Chandra and XMM-Newton satellites.     

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.     

Morphology of flows and buoyant bubbles in the Virgo cluster

There is growing evidence that the active galactic nuclei (AGN) associated with the central elliptical galaxy in clusters of galaxies are playing an important role in the evolution of the intracluster medium (ICM) and clusters themselves. We use high-resolution three-dimensional simulations to study the interaction of the cavities created by AGN outflows (bubbles) with the ambient ICM. The gravitational potential of the cluster is modelled using the observed temperature and density profiles of the Virgo cluster. We demonstrate the importance of the hydrodynamical Kutta–Zhukovsky forces associated with the vortex ring structure of the bubbles, and discuss possible effects of diffusive processes on their evolution.     

The effect of formation redshifts on the cluster mass–temperature relation

I employ an ensemble of hydrodynamical simulations and the xspec mekal emission model to reproduce observable spectral and flux-weighted temperatures for 24 clusters. Each cluster is imaged at 16 points in its history, which allows the investigation of evolutionary effects on the mass–temperature relation. In the zero-redshift scaling relations, I find no evidence for a relationship between cluster temperature and formation epoch for those clusters that acquired 75 per cent of their final mass since a redshift of 0.6. This result holds for both observable and intrinsic intracluster medium temperatures, and implies that halo formation epochs are not an important variable in analysis of observable cluster temperature functions.     

Hydrodynamical simulations of cluster formation with central AGN heating

We analyse a hydrodynamical simulation model for the recurrent heating of the central intra-cluster medium (ICM) by active galactic nuclei (AGN). Besides the self-gravity of the dark matter and gas components, our approach includes the radiative cooling and photoheating of the gas, as well as a subresolution multiphase model for star formation and supernova feedback. Additionally, we incorporate a periodic heating mechanism in the form of hot, buoyant bubbles, injected into the intragalactic medium (IGM) during the active phases of the accreting central AGN. We use simulations of isolated cluster haloes of different masses to study the bubble dynamics and heat transport into the IGM. We also apply our model to self-consistent cosmological simulations of the formation of galaxy clusters with a range of masses. Our numerical schemes explore a variety of different assumptions for the spatial configuration of AGN-driven bubbles, for their duty cycles and for the energy injection mechanism, in order to obtain better constraints on the underlying physical picture. We argue that AGN heating can substantially affect the properties of both the stellar and gaseous components of clusters of galaxies. Most importantly, it alters the properties of the central dominant (cD) galaxy by reducing the mass deposition rate of freshly cooled gas out of the ICM, thereby offering an energetically plausible solution to the cooling-flow problem. At the same time, this leads to reduced or eliminated star formation in the central cD galaxy, giving it red stellar colours as observed.     

Galaxies in clusters: the observational characteristics of bow shocks, wakes and tails

The dynamical signatures of the interaction between galaxies in clusters and the intracluster medium (ICM) can potentially yield significant information about the structure and dynamical history of clusters. To develop our understanding of this phenomenon we present results from numerical modelling of the galaxy–ICM interaction, as the galaxy moves through the cluster. The simulations have been performed for a broad range of ICM temperatures ( kT _cl=1, 4 and 8 keV), representative of poor clusters or groups through to rich clusters.
There are several dynamical features that can be identified in these simulations. For supersonic galaxy motion, a leading bow shock is present, and also a weak gravitationally focused wake or tail behind the galaxy (analogous to Bondi–Hoyle accretion). For galaxies with higher mass replenishment rates and a denser interstellar medium (ISM), the dominant feature is a dense ram-pressure stripped tail. In line with other simulations, we find that the ICM/galaxy–ISM interaction can result in complex time-dependent dynamics, with ram-pressure stripping occurring in an episodic manner.
In order to facilitate this comparison between the observational consequences of dynamical studies and X-ray observations we have calculated synthetic X-ray flux and hardness maps from these simulations. These calculations predict that the ram-pressure stripped tail will usually be the most visible feature, though in nearby galaxies the bow shock preceding the galaxy should also be apparent in deeper X-ray observations. We briefly discuss these results and compare them with X-ray observations of galaxies where there is evidence of such interactions.     

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.     

Galactic winds and circulation of the interstellar medium in dwarf galaxies

We study, through 2D hydrodynamical simulations, the feedback of a starburst on the ISM of typical gas-rich dwarf galaxies. The main goal is to address the circulation of the ISM and metals following the starburst. We assume a single-phase rotating ISM in equilibrium in the galactic potential generated by a stellar disc and a spherical dark halo. The starburst is assumed to occur in a small volume in the centre of the galaxy, and it generates a mechanical power of 3.8×10³⁹ or 3.8×10⁴⁰ erg s⁻¹ for 30 Myr. We find, in accordance with previous investigations, that the galactic wind is not very effective in removing the ISM. The metal-rich stellar ejecta, however, can be efficiently expelled from the galaxy and dispersed in the intergalactic medium.
Moreover, we find that the central region of the galaxy is always replenished with cold and dense gas a few 100 million years after the starburst, achieving the requisite for a new star formation event in ≈0.5–1 Gyr. The hydrodynamical evolution of galactic winds is thus consistent with the episodic star formation regime suggested by many chemical evolution studies.
We also discuss the X-ray emission of these galaxies and find that the observable (emission-averaged) abundance of the hot gas underestimates the real one if thermal conduction is effective. This could explain the very low hot-gas metallicities estimated in starburst galaxies.     

Reconciling optical and X-ray mass estimates: the case of the elliptical galaxy NGC 3379

NGC 3379 is a well-studied nearby elliptical for which optical investigations have claimed a little dark matter content, or even no dark matter. Recently, its total mass profile M ( r ) has been derived by exploiting Chandra observations of its extended and X-ray emitting interstellar medium, based on the hypothesis of hydrostatic equilibrium for the hot gas. The resulting total mass within the effective radius R _e has been claimed to be a few times larger than that found by optical studies. Here, we show that part of the discrepancy can be due to an underestimate of the optically derived mass, and the remaining discrepancy of a factor of ∼2 can be explained by deviations from hydrostatic equilibrium of the hot gas. By using hydrodynamical simulations tailored to reproduce the observed hot gas properties of NGC 3379, and by assuming as input for the simulations the total mass profile derived optically, we show that (i) the hot gas at the present time has X-ray properties consistent with those observed only if it is outflowing over most of the galactic body, and (ii) an overestimate of M of the same size found in the recent X-ray analysis is recovered when assuming hydrostatic equilibrium. We also show that the hot gas is outflowing even for a dark matter fraction within R _e as large as derived with the standard X-ray procedure based on the hydrostatic equilibrium assumption, which shows the unapplicability of the method for this galaxy. Finally, we find that the whole range of dark mass amount and distribution allowed for by optical studies is compatible with a hot gas flow with the observed X-ray properties.     

Modelling star formation and feedback in simulations of interacting galaxies

We discuss a heuristic model to implement star formation and feedback in hydrodynamical simulations of galaxy formation and evolution. In this model, gas is allowed to cool radiatively and to form stars at a rate given by a simple Schmidt-type law. We assume that supernova feedback results in turbulent motions of gas below resolved scales, a process that can pressurize the diffuse gaseous medium effectively, even if it lacks substantial thermal support. Ignoring the complicated detailed physics of the feedback processes, we try to describe their net effect on the interstellar medium with a fiducial second reservoir of internal energy, which accounts for the kinetic energy content of the gas on unresolved scales. Applying the model to three-dimensional, fully self-consistent models of isolated disc galaxies, we show that the resulting feedback loop can be modelled with smoothed particle hydrodynamics such that converged results can be reached with moderate numerical resolution. With an appropriate choice of the free parameters, Kennicutt's phenomenological star formation law can be reproduced over many orders of magnitude in gas surface density. We also apply the model to mergers of equal-mass disc galaxies, typically resulting in strong nuclear starbursts. Confirming previous findings, the presence of a bulge can delay the onset of the starburst from the first encounter of the galaxies until their final coalescence. The final density profiles of the merger remnants are consistent with de Vaucouleurs profiles, except for the innermost region, where the newly created stars give rise to a luminous core with stellar densities that may be in excess of those observed in the cores of most elliptical galaxies. By comparing the isophotal shapes of collisionless and dissipative merger simulations we show that dissipation leads to isophotes that are more discy than those of corresponding collisionless simulations.     

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.     

Temperature and abundance profiles of hot gas in galaxy groups – II. Implications for feedback and ICM enrichment

We investigate the history of galactic feedback and chemical enrichment within a sample of 15 X-ray bright groups of galaxies, on the basis of the inferred Fe and Si distributions in the hot gas and the associated metal masses produced by core-collapse and Type Ia supernovae (SNe). Most of these cool-core groups show a central Fe and Si excess, which can be explained by prolonged enrichment by SN Ia and stellar winds in the central early-type galaxy alone, but with tentative evidence for additional processes contributing to core enrichment in hotter groups. Inferred metal mass-to-light ratios inside r ₅₀₀ show a positive correlation with total group mass but are generally significantly lower than in clusters, due to a combination of lower global intracluster medium (ICM) abundances and gas-to-light ratios in groups. This metal deficiency is present for products from both SN Ia and SN II, and suggests that metals were either synthesized, released from galaxies or retained within the ICM less efficiently in lower mass systems. We explore possible causes, including variations in galaxy formation and metal release efficiency, cooling out of metals, and gas and metal loss via active galactic nuclei (AGN) – or starburst-driven galactic winds from groups or their precursor filaments. Loss of enriched material from filaments coupled with post-collapse AGN feedback emerges as viable explanations, but we also find evidence for metals to have been released less efficiently from galaxies in cooler groups and for the ICM in these to appear chemically less evolved, possibly reflecting more extended star formation histories in less massive systems. Some implications for the hierarchical growth of clusters from groups are briefly discussed.     

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.     

The photoionization effect of the ultraviolet background on the colour–magnitude relation of elliptical galaxies

We have examined the effects of the ultraviolet background radiation (UVB) on the colour–magnitude relation (CMR) of elliptical galaxies in clusters of galaxies in the hierarchical clustering scenario by using a semi-analytic model of galaxy formation. In our model the UVB photoionizes gas in dark haloes and suppresses the cooling of the diffuse hot gas on to galaxy discs. By using a semi-analytic model without the effect of the UVB, Kauffmann & Charlot found that the CMR can be reproduced by strong supernova heating because such supernova feedback suppresses the chemical enrichment in galaxies, especially for small galaxies. We find that the CMR also becomes bluer because of the UVB, in a different way from the effect of supernova feedback. While supernova feedback suppresses the chemical enrichment by a similar mechanism to galactic winds, the UVB suppresses the cooling of the hot gas. This induces suppression of the metallicity of the intracluster medium (ICM). In our model we find that the existence of the UVB can plausibly account for an observed ICM metallicity that is equal to nearly 0.3 times the solar value, and that in this case we can reproduce the CMR and the metallicity of the ICM simultaneously.