Cooling Flow Problem Research Articles

Heating galaxy clusters with interacting dark matter

ABSTRACT The overcooling of cool core clusters is a persistent puzzle in the astrophysics of galaxy clusters. We propose that it may naturally be resolved via interactions between the baryons of the intracluster medium (ICM) and its dark matter (DM). DM–baryon interactions can inject heat into the ICM to offset bremsstrahlung cooling, but these interactions are also strongly constrained by existing experiments and astrophysical observations. We survey existing constraints and combine these with the energetic needs of an observed sample of cool core clusters. We find that a robust parameter space exists for baryon–DM scattering solutions to the cooling flow problem, provided that only a sub-component of DM interacts strongly with the baryons. Interestingly, baryon–DM scattering is a thermally stable heating source so long as the baryon temperature is greater than 1/3 to 1/2 the DM temperature, a condition that seems to be satisfied observationally.

Production efficiencies of sound waves in the intracluster medium driven by AGN jets

ABSTRACT Feedback from active galactic nuclei (AGNs) is believed to be the most promising solution to the cooling flow problem in cool-core clusters. Dissipation of sound waves is considered as one of the possible heating mechanisms; however, its relative contribution to heating remains unclear. To estimate the energy budget for heating, we perform 3D hydrodynamic simulations of AGN jet injections in a Perseus-like cluster and quantify the amount of energy stored in the forms of weak shocks and waves. We find that, for a single jet injection with typical parameters in cool-core clusters, ${\sim}9{{\ \rm per\ cent}}$ of the total jet energy is stored in compressional waves (including both shocks and waves). However, due to the destructive effects among randomly phased waves as well as the dissipation of shock energies, in our simulations including self-regulated AGN feedback, no more than $3{{\ \rm per\ cent}}$ of the total injected energy goes into compressional waves. We further separate the energy contribution from shocks and waves and find that, for a single outburst, the shocks can only contribute to ${\sim}20{-}30{{\ \rm per\ cent}}$ of the total compressional energy in the inner radii and quickly dissipate away. In the self-regulated case where shocks are repeatedly generated, shocks completely dominate over sound waves in the inner region and can still provide ${\sim}40{-}50{{\ \rm per\ cent}}$ of the total compressional energy at outer radii. Our results suggest that the production of sound waves is not as efficient as what was previously found, and thus sound wave dissipation may be a subdominant source of heating in cool-core clusters.

Constraining black hole feedback in galaxy clusters from X-ray power spectra

ABSTRACT Jets launched by the supermassive black holes in the centres of cool-core clusters are the most likely heat source to solve the cooling flow problem. One way for this heating to occur is through generation of a turbulent cascade by jet-inflated bubbles. Measurements of the X-ray intensity power spectra show evidence of this cascade in different regions of the cluster, constraining the role of driving mechanisms. We analyse feedback simulations of the Perseus cluster to constrain the effect of the jet activity on the intensity fluctuations and kinematics of the cluster atmosphere. We find that, within the inner 60 kpc, the power spectra of the predicted surface brightness fluctuations are broadly consistent with those measured by Chandra and that even a single episode of jet activity can generate a long-lasting imprint on the intensity fluctuations in the innermost region of the cluster. Active galactic nucleus (AGN)-driven motions within the same region approach the values reported by Hitomi during and right after the AGN episode. However, the line-of-sight velocity dispersion excited by the jet in simulations underpredicts the Hitomi measurement. This indicates that driving a volume-filling sustained level of turbulence requires several episodes of jet activity, and/or additional processes drive turbulence outside the 60-kpc sphere. This also suggests that sharp edges of the bubbles in the innermost region of the cluster contribute substantially to the intensity of fluctuations, consistent with the Perseus observations in the inner 30-kpc region. We discuss new diagnostics to decompose annular power spectra to constrain past episodes of jet activity.

On the Energy Coupling Efficiency of AGN Outbursts in Galaxy Clusters

Abstract Active galactic nucleus (AGN) jets are believed to be important in solving the cooling flow problem in the intracluster medium (ICM), while the detailed mechanism is still under debate. Here we present a systematic study on the energy coupling efficiency η cp, the fraction of AGN jet energy transferred to the ICM. We first estimate the values of η cp analytically in two extreme cases, which are further confirmed and extended with a parameter study of spherical outbursts in a uniform medium using hydrodynamic simulations. We find that η cp increases from ∼0.4 for a weak isobaric injection to ≳0.8 for a powerful point injection. For any given outburst energy, we find two characteristic outburst powers that separate these two extreme cases. We then investigate the energy coupling efficiency of AGN jet outbursts in a realistic ICM with hydrodynamic simulations, finding that jet outbursts are intrinsically different from spherical outbursts. For both powerful and weak jet outbursts, η cp is typically around 0.7–0.9, partly due to the nonspherical nature of jet outbursts, which produce backflows emanating from the hot spots, significantly enhancing the ejecta–ICM interaction. While for powerful outbursts a dominant fraction of the energy transferred from the jet to the ICM is dissipated by shocks, shock dissipation only accounts for ≲30% of the injected jet energy for weak outbursts. While both powerful and weak outbursts could efficiently heat cooling flows, powerful thermal-energy-dominated jets are most effective in delaying the onset of the central cooling catastrophe.

On the Cooling Flow Problem in the Gaseous Halo of the Milky Way

Abstract Theoretical and observational arguments suggest that there is a large amount of hot (∼106 K) diffuse gas residing in the Milky Way (MW) halo, but its total mass and spatial distribution are still unclear. In this work, we present a general model for the gas density distribution in the Galactic halo, and investigate the gas evolution under radiative cooling with a series of 2D hydrodynamic simulations. We find that the mass inflow rate in the developed cooling flow increases with gas metallicity and the total gas mass in the halo. For a fixed halo gas mass, the spatial gas distribution affects the onset time of the cooling catastrophe, which starts earlier when the gas distribution is more centrally peaked, but does not substantially affect the final mass inflow rate. The gravity from the Galactic bulge and disk affects gas properties in the inner regions, but has little effect on the final inflow rate either. We confirm our results by investigating cooling flows in several density models adopted from the literature, including the Navarro–Frenk–White (NFW) model, the cored-NFW model, the Maller & Bullock model, and the β model. Typical mass inflow rates in our simulations range from ∼5 M ⊙ yr−1 to ∼60 M ⊙ yr−1, and are much higher than the observed star formation rate in our Galaxy, suggesting that stellar and active galactic nucleus feedback processes may play important roles in the evolution of the MW and MW-type galaxies.

Cooling+Heating Flows in Galaxy Clusters: Turbulent Heating, Spectral Modeling, and Cooling Efficiency

Abstract The discrepancy between expected and observed cooling rates of X-ray emitting gas has led to the cooling-flow problem at the cores of clusters of galaxies. A variety of models have been proposed to model the observed X-ray spectra and resolve the cooling-flow problem, which involves heating the cold gas through different mechanisms. As a result, realistic models of X-ray spectra of galaxy clusters need to involve both heating and cooling mechanisms. In this paper, we argue that the heating timescale is set by the magnetohydrodynamic (MHD) turbulent viscous heating for the Intracluster plasma, parameterized by the Shakura–Sunyaev viscosity parameter, α. Using a cooling+heating flow model, we show that a value of α ≃ 0.05 (with 10% scatter) provides improved fits to the X-ray spectra of cooling flow, while at the same time, predicting reasonable cooling efficiency, . Our inferred values for α based on X-ray spectra are also in line with direct measurements of turbulent pressure in simulations and observations of galaxy clusters. This simple picture unifies astrophysical accretion, as a balance of MHD turbulent heating and cooling, across more than 16 orders of magnitudes in scale, from neutron stars to galaxy clusters.

Acoustic Disturbances in Galaxy Clusters

Abstract Galaxy cluster cores are pervaded by hot gas which radiates at far too high a rate to maintain any semblance of a steady state; this is referred to as the cooling flow problem. Of the many heating mechanisms that have been proposed to balance radiative cooling, one of the most attractive is the dissipation of acoustic waves generated by active galactic nuclei. Fabian et al. showed that if the waves are nearly adiabatic, wave damping due to heat conduction and viscosity must be well below standard Coulomb rates in order to allow the waves to propagate throughout the core. Because of the importance of this result, we have revisited wave dissipation under galaxy cluster conditions in a way that accounts for the self-limiting nature of dissipation by electron thermal conduction, allows the electron and ion temperature perturbations in the waves to evolve separately, and estimates kinetic effects by comparing to a semicollisionless theory. While these effects considerably enlarge the toolkit for analyzing observations of wavelike structures and developing a quantitative theory for wave heating, the drastic reduction of transport coefficients proposed in Fabian et al. remains the most viable path to acoustic wave heating of galaxy cluster cores.

Reversing cooling flows with AGN jets: shock waves, rarefaction waves and trailing outflows

The cooling flow problem is one of the central problems in galaxy clusters, and active galactic nucleus (AGN) feedback is considered to play a key role in offsetting cooling. However, how AGN jets heat and suppress cooling flows remains highly debated. Using an idealized simulation of a cool-core cluster, we study the development of central cooling catastrophe and how a subsequent powerful AGN jet event averts cooling flows, with a focus on complex gasdynamical processes involved. We find that the jet drives a bow shock, which reverses cooling inflows and overheats inner cool core regions. The shocked gas moves outward in a rarefaction wave, which rarefies the dense core and adiabatically transports a significant fraction of heated energy to outer regions. As the rarefaction wave propagates away, inflows resume in the cluster core, but a trailing outflow is uplifted by the AGN bubble, preventing gas accumulation and catastrophic cooling in central regions. Inflows and trailing outflows constitute meridional circulations in the cluster core. At later times, trailing outflows fall back to the cluster centre, triggering central cooling catastrophe and potentially a new generation of AGN feedback. We thus envisage a picture of cool cluster cores going through cycles of cooling-induced contraction and AGN-induced expansion. This picture naturally predicts an anti-correlation between the gas fraction (or X-ray luminosity) of cool cores and the central gas entropy, which may be tested by X-ray observations.

Cosmic-Ray Feedback Heating of the Intracluster Medium

Abstract Active galactic nuclei (AGNs) play a central role in solving the decades-old cooling-flow problem. Although there is consensus that AGNs provide the energy to prevent catastrophically large star formation, one major problem remains: How is the AGN energy thermalized in the intracluster medium (ICM)? We perform a suite of three-dimensional magnetohydrodynamical adaptive mesh refinement simulations of AGN feedback in a cool core cluster including cosmic rays (CRs). CRs are supplied to the ICM via collimated AGN jets and subsequently disperse in the magnetized ICM via streaming, and interact with the ICM via hadronic, Coulomb, and streaming instability heating. We find that CR transport is an essential model ingredient at least within the context of the physical model considered here. When streaming is included, (i) CRs come into contact with the ambient ICM and efficiently heat it, (ii) streaming instability heating dominates over Coulomb and hadronic heating, (iii) the AGN is variable and the atmosphere goes through low-/high-velocity dispersion cycles, and, importantly, (iv) CR pressure support in the cool core is very low and does not demonstrably violate observational constraints. However, when streaming is ignored, CR energy is not efficiently spent on the ICM heating and CR pressure builds up to a significant level, creating tension with the observations. Overall, we demonstrate that CR heating is a viable channel for the AGN energy thermalization in clusters and likely also in ellipticals, and that CRs play an important role in determining AGN intermittency and the dynamical state of cool cores.

LOCAL SIMULATIONS OF INSTABILITIES DRIVEN BY COMPOSITION GRADIENTS IN THE ICM

ABSTRACT The distribution of helium in the intracluster medium (ICM) permeating galaxy clusters is not well constrained due to the very high plasma temperature. Therefore, the plasma is often assumed to be homogeneous. A nonuniform helium distribution can, however, lead to biases when measuring key cluster parameters. This has motivated one-dimensional models that evolve the ICM composition assuming that the effects of magnetic fields can be parameterized or ignored. Such models for nonisothermal clusters show that helium can sediment in the cluster core, leading to a peak in concentration offset from the cluster center. The resulting profiles have recently been shown to be linearly unstable when the weakly collisional character of the magnetized plasma is considered. In this paper, we present a modified version of the MHD code Athena, which makes it possible to evolve a weakly collisional plasma subject to a gravitational field and stratified in both temperature and composition. We thoroughly test our implementation and confirm excellent agreement against several analytical results. In order to isolate the effects of composition, in this initial study we focus our attention on isothermal plasmas. We show that plasma instabilities, feeding off gradients in composition, can induce turbulent mixing and saturate by rearranging magnetic field lines and alleviating the composition gradient. Composition profiles that increase with radius lead to instabilities that saturate by driving the average magnetic field inclination to roughly 45°. We speculate that this effect may alleviate the core insulation observed in homogeneous settings, with potential consequences for the associated cooling flow problem.

INTERPLAY AMONG COOLING, AGN FEEDBACK, AND ANISOTROPIC CONDUCTION IN THE COOL CORES OF GALAXY CLUSTERS

ABSTRACT Feedback from the active galactic nuclei (AGNs) is one of the most promising heating mechanisms to circumvent the cooling-flow problem in galaxy clusters. However, the role of thermal conduction remains unclear. Previous studies have shown that anisotropic thermal conduction in cluster cool cores (CCs) could drive the heat-flux-driven buoyancy instabilities (HBIs) that reorient the field lines in the azimuthal directions and isolate the cores from conductive heating from the outskirts. However, how the AGN interacts with the HBI is still unknown. To understand these interwined processes, we perform the first 3D magnetohydrodynamic simulations of isolated CC clusters that include anisotropic conduction, radiative cooling, and AGN feedback. We find the following: (1) For realistic magnetic field strengths in clusters, magnetic tension can suppress a significant portion of HBI-unstable modes, and thus the HBI is either completely inhibited or significantly impaired, depending on the unknown magnetic field coherence length. (2) Turbulence driven by AGN jets can effectively randomize magnetic field lines and sustain conductivity at ∼1/3 of the Spitzer value; however, the AGN-driven turbulence is not volume filling. (3) Conductive heating within the cores could contribute to ∼10% of the radiative losses in Perseus-like clusters and up to ∼50% for clusters twice the mass of Perseus. (4) Thermal conduction has various impacts on the AGN activity and intracluster medium properties for the hottest clusters, which may be searched by future observations to constrain the level of conductivity in clusters. The distribution of cold gas and the implications are also discussed.

HST -COS SPECTROSCOPY OF THE COOLING FLOW IN A1795—EVIDENCE FOR INEFFICIENT STAR FORMATION IN CONDENSING INTRACLUSTER GAS

We present far-UV spectroscopy from the Cosmic Origins Spectrograph on the Hubble Space Telescope of a cool, star-forming filament in the core of Abell 1795. These data, which span 1025A - 1700A, allow for the simultaneous modeling of the young stellar populations and the intermediate-temperature (10^5.5 K) gas in this filament, which is far removed (~30 kpc) from the direct influence of the central AGN. Using a combination of UV absorption line indices and stellar population synthesis modeling, we find evidence for ongoing star formation, with the youngest stars having ages of 7.5 +/- 2.0 Myr and metallicities of 0.4 +/- 0.2 Zsun. The latter is consistent with the local metallicity of the intracluster medium. We detect the O VI (1038) line, measuring a flux of 4.0 +/- 0.9 x 10^-17 erg s^-1 cm^-2. The O VI (1032) line is redshifted such that it is coincident with a strong Galactic H2 absorption feature, and is not detected. The measured O VI (1038) flux corresponds to a cooling rate of 0.85 +/- 0.2 (stat) +/- 0.15 (sys) Msun/yr at ~10^5.5 K, assuming that the cooling proceeds isochorically, which is consistent with the classical X-ray luminosity-derived cooling rate in the same region. We measure a star formation rate of 0.11 +/- 0.02 Msun/yr from the UV continuum, suggesting that star formation is proceeding at 13 +/- 3% efficiency in this filament. We propose that this inefficient star formation represents a significant contribution to the larger-scale cooling flow problem.

PROBING THE EXTREME REALM OF ACTIVE GALACTIC NUCLEUS FEEDBACK IN THE MASSIVE GALAXY CLUSTER, RX J1532.9+3021

We present a detailed Chandra, XMM-Newton, VLA and HST analysis of one of the strongest cool core clusters known, RX J1532.9+3021 (z=0.3613). Using new, deep 90 ks Chandra observations, we confirm the presence of a western X-ray cavity or bubble, and report on a newly discovered eastern X-ray cavity. The total mechanical power associated with these AGN-driven outflows is (22+/-9)*10^44 erg/s, and is sufficient to offset the cooling, indicating that AGN feedback still provides a viable solution to the cooling flow problem even in the strongest cool core clusters. Based on the distribution of the optical filaments, as well as a jet-like structure seen in the 325 MHz VLA radio map, we suggest that the cluster harbours older outflows along the north to south direction. The jet of the central AGN is therefore either precessing or sloshing-induced motions have caused the outflows to change directions. There are also hints of an X-ray depression to the north aligned with the 325 MHz jet-like structure, which might represent the highest redshift ghost cavity discovered to date. We further find evidence of a cold front (r=65kpc) that coincides with the outermost edge of the western X-ray cavity and the edge of the radio mini-halo. The common location of the cold front with the edge of the radio mini-halo supports the idea that the latter originates from electrons being reaccelerated due to sloshing induced turbulence. Alternatively, its coexistence with the edge of the X-ray cavity may be due to cool gas being dragged out by the outburst. We confirm that the central AGN is highly sub-Eddington and conclude that a >10^10M_Sun or a rapidly spinning black hole is favoured to explain both the radiative-inefficiency of the AGN and the powerful X-ray cavities.

Solving the cooling flow problem through mechanical AGN feedback

AbstractUnopposed radiative cooling of plasma would lead to the cooling catastro‐phe, a massive inflow of condensing gas, manifest in the core of galaxies, groups and clusters. The last generation X‐ray telescopes, Chandra and XMM, have radically changed our view on baryons, indicating AGN heating as the balancing counterpart of cooling. This work reviews our extensive investigation on self‐regulated heating. We argue that the mechanical feedback, based on massive subrelativistic outflows, is the key to solving the cooling flow problem, i.e. dramatically quenching the cooling rates for several Gyr without destroying the cool‐core structure. Using a modified version of the 3D hydrocode FLASH, we show that bipolar AGN outflows can further reproduce fundamental observed features, such as buoyant bubbles, weak shocks, metals dredgeup, and turbulence. The latter is an essential ingredient to drive nonlinear thermal instabilities, which cause the formation of extended cold gas, a residual of the quenched cooling flow and, later, fuel for the feedback engine. Compared to clusters, groups and galaxies require a gentler mechanical feedback, in order to avoid catastro‐phic overheating. We highlight the essential characteristics for a realistic AGN feedback, with emphasis on observational consistency. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Stability analysis for cosmic-ray heating of cool cores in galaxy clusters

We study the heating of the cool cores in galaxy clusters by cosmic-rays (CRs) accelerated by the central active galactic nuclei (AGNs). We especially focus on the stability of the heating. The CRs stream with Alfv\'en waves in the intracluster medium (ICM) and heat the ICM. First, assuming that the heating and radiative cooling is balanced, we search steady state solutions for the ICM and CR profiles of clusters by solving a boundary value problem. The boundary conditions are set so that the solutions are consistent with observations of clusters. We find steady state solutions if the magnetic fields are strong enough and the association between the magnetic fields and the ICM is relatively weak. Then, we analyse the stability of the solutions via a Lagrangian perturbation analysis and find that the solutions are globally stable. We confirm the results by numerical simulations. Using the steady state solutions as the initial conditions, we follow the evolution of the profiles for 100 Gyr. We find that the profiles do not evolve on time scales much larger than cluster lifetimes. These results, as well as consistency with observations of radio mini-halos, suggest that the CR heating is a promising mechanism to solve the so-called "cooling flow problem".

COLD MOLECULAR GAS ALONG THE COOLING X-RAY FILAMENT IN A1795

We present the results of interferometric observations of the cool core of Abell 1795 at CO(1-0) using the Combined Array for Research in Millimeter-Wave Astronomy. In agreement with previous work, we detect a significant amount of cold molecular gas (3.9 +/- 0.4 x10^9 Msun) in the central ~10 kpc. We report the discovery of a substantial clump of cold molecular gas at clustercentric radius of 30 kpc (2.9 +/- 0.4 x10^9 Msun), coincident in both position and velocity with the warm, ionized filaments. We also place an upper limit on the H_2 mass at the outer edge of the star-forming filament, corresponding to a distance of 60 kpc (<0.9 x10^9 Msun). We measure a strong gradient in the HII/H_2 ratio as a function of radius, suggesting different ionization mechanisms in the nucleus and filaments of Abell1795. The total mass of cold molecular gas (\sim7x10^9 Msun) is roughly 30% of the classical cooling estimate at the same position, assuming a cooling time of 10^9 yr. Combining the cold molecular gas mass with the UV-derived star formation rate and the warm, ionized gas mass, the spectroscopically-derived X-ray cooling rate is fully accounted for and in good agreement with the cooling byproducts over timescales of \sim10^9 yr. The overall agreement between the cooling rate of the hot intracluster medium and the mass of the cool gas reservoir suggests that, at least in this system, the cooling flow problem stems from a lack of observable cooling in the more diffuse regions at large radii.

Mechanical AGN feedback: controlling the thermodynamical evolution of elliptical galaxies

A fundamental gap in the current understanding of galaxies concerns the thermodynamical evolution of the ordinary, baryonic matter. On one hand, radiative emission drastically decreases the thermal energy content of the interstellar plasma (ISM), inducing a slow cooling flow toward the centre. On the other hand, the active galactic nucleus (AGN) struggles to prevent the runaway cooling catastrophe, injecting huge amount of energy in the ISM. The present study intends to deeply investigate the role of mechanical AGN feedback in (isolated or massive) elliptical galaxies, extending and completing the mass range of tested cosmic environments. Our previously successful feedback models, in galaxy clusters and groups, demonstrated that AGN outflows, self-regulated by cold gas accretion, are able to properly quench the cooling flow, without destroying the cool core. Via 3D hydrodynamic simulations (FLASH 3.3), including also stellar evolution, we show that massive mechanical AGN outflows can indeed solve the cooling flow problem for the entire life of the galaxy, at the same time reproducing typical observational features and constraints, such as buoyant underdense bubbles, elliptical shock cocoons, sonic ripples, dredge-up of metals, subsonic turbulence, and extended filamentary or nuclear cold gas. In order to avoid overheating and totally emptying the isolated galaxy, the frequent mechanical AGN feedback should be less powerful and efficient (~1.e-4), compared to the heating required for more massive and bound ellipticals surrounded by the intragroup medium (efficiency ~1.e-3).

AGN feedback in galaxy groups: the delicate touch of self-regulated outflows

AGN heating, through massive subrelativistic outflows, might be the key to solve the long-lasting `cooling flow problem' in cosmological systems. In a previous paper, we showed that cold accretion feedback and, to a lesser degree, Bondi self-regulated models are in fact able to quench cooling rates for several Gyr, at the same time preserving the mainc ool core features, like observed density and temperature profiles. Is it true also for lighter systems, such as galaxy groups? The answer is globally yes, although with remarkable differences. Adopting a modified version of the AMR code FLASH 3.2, we found that successful 3D simulations with cold and Bondi models are almost convergent in the galaxy group environment, with mechanical efficiencies in the range 5.e-4 - 1.e-3 and 5.e-2 - 1.e-1, respectively. The evolutionary storyline of galaxy groups is dominated by a quasi-continuous gentle injection with sub-Eddington outflows (with mechanical power and velocity around 1.e44 erg/s and 1.e4 km/s). The cold and hybrid accretion models present, in addition, very short quiescence periods, followed by moderate outbursts (10 times the previous phase), which generate a series of 10-20 kpc size cavities with high density contrast, temperatures similar to the ambient medium and cold rims. After shock heating, a phase of turbulence promotes gas mixing and diffusion of metals, which peak along jet-axis (up to 40 kpc) during active phases. At this stage the tunnel, produced by the enduring outflow (hard to detect in the mock SBx maps), is easily fragmented, producing tiny buoyant bubbles, typically a few kpc in size. In contrast to galaxy clusters, the AGN self-regulated feedback has to be persistent, with a `delicate touch', rather than rare and explosive strokes. This evolutionary difference dictates in the end that galaxy groups are not scaled-down versions of clusters.

Gravitational quenching by clumpy accretion in cool-core clusters: convective dynamical response to overheating

Many galaxy clusters pose a "cooling-flow problem", where the observed X-ray emission from their cores is not accompanied by enough cold gas or star formation. A continuous energy source is required to balance the cooling rate over the whole core volume. We address the feasibility of a gravitational heating mechanism, utilizing the gravitational energy released by the gas that streams into the potential well of the cluster dark-matter halo. We focus here on a specific form of gravitational heating in which the energy is transferred to the medium thorough the drag exerted on inflowing gas clumps. Using spheri-symmetric hydro simulations with a subgrid representation of these clumps, we confirm our earlier estimates that in haloes >=10^13 solar masses the gravitational heating is more efficient than the cooling everywhere. The worry was that this could overheat the core and generate an instability that might push it away from equilibrium. However, we find that the overheating does not change the global halo properties, and that convection can stabilize the cluster by carrying energy away from the overheated core. In a typical rich cluster of 10^{14-15}solar masses, with ~5% of the accreted baryons in gas clumps of ~10^8 solar masses, we derive upper and lower limits for the temperature and entropy profiles and show that they are consistent with those observed in cool-core clusters. We predict the density and mass of cold gas and the level of turbulence driven by the clump accretion. We conclude that gravitational heating is a feasible mechanism for preventing cooling flows in clusters.

Astronomical constraints on properties of sterile neutrino dark matter

We consider sterile neutrinos as a component of dark matter in the Milky Way and clusters, and compare their rest mass, decay rate and the mixing angle. A radiative decaying rate of order Γ∼10−19 s−1 for sterile neutrino rest mass ms=18–19 keV can satisfactorily account for the cooling flow problem and heating source in Milky Way center simultaneously. Also, these ranges of decay rate and rest mass match the prediction of the mixing angle sin 22θ∼10−3 with a low reheating temperature in the inflation model, which enables the sterile-active neutrino oscillation to be visible in future experiments. However, decaying sterile neutrinos have to be ruled out as a major component of dark matter because of the high decay rate.