Multiphase smoothed-particle hydrodynamics

We adapt the smoothed-particle hydrodynamics (SPH) technique to allow a multiphase fluid in which SPH particles of widely differing density may be freely intermixed. Applications include modelling of galaxy formation and cooling flows.     

On the soft X-ray spectrum of cooling flows

Strong evidence for cooling flows has been found in low-resolution X-ray imaging and spectra of many clusters of galaxies. However, high-resolution X-ray spectra of several clusters from the Reflection Grating Spectrometer on XMM-Newton now show a soft X-ray spectrum inconsistent with a simple cooling flow. The main problem is a lack of the emission lines expected from gas cooling below 1–2 keV. Lines from gas at about 2–3 keV are observed, even in a high-temperature cluster such as A1835, indicating that gas is cooling down to about 2–3 keV, but is not found at lower temperatures. Here we discuss several solutions to the problem: heating, mixing, differential absorption and inhomogeneous metallicity. Continuous or sporadic heating creates further problems, including the targeting of the heat at the cooler gas and also the high total energy required. So far there is no clear observational evidence for widespread heating, or shocks, in cluster cores, except in radio lobes which occupy only part of the volume. Alternatively, if the metals in the intracluster medium are not uniformly spread but are clumped, then little line emission is expected from the gas cooling below 1 keV. The low-metallicity part cools without line emission, whereas the strengths of the soft X-ray lines from the metal-rich gas depend on the mass fraction of that gas and not on the abundance, since soft X-ray line emission dominates the cooling function below 2 keV.     

Self-similar shocked accretion of collisional gas with radiative cooling

We describe similarity solutions that characterize the collapse of collisional gas on to scale-free perturbations in an Einstein–de Sitter universe. We consider the effects of radiative cooling and derive self-similar solutions under the assumption that the cooling function is a power law of density and temperature, Λ( T , ρ )∝ ρ ^3/2 T . We use these results to test the ability of smooth particle hydrodynamics (SPH) techniques to follow the collapse and accretion of shocked, rapidly cooling gas in a cosmological context. Our SPH code reproduces the analytical results very well in cases that include or exclude radiative cooling. No substantial deviations from the predicted central mass accretion rates or from the temperature, density and velocity profiles are observed in well-resolved regions inside the shock radius. This test problem lends support to the reliability of SPH techniques to model the complex process of galaxy formation.     

Stochastic heating of cooling flows

It is generally accepted that the heating of gas in clusters of galaxies by active galactic nuclei is a form of feedback. Feedback is required to ensure a long-term, sustainable balance between heating and cooling. This work investigates the impact of proportional stochastic feedback on the energy balance in the intracluster medium. Using a generalized analytical model for a cluster atmosphere, it is shown that an energy equilibrium can be reached exponentially quickly. Applying the tools of stochastic calculus, it is demonstrated that the result is robust with regard to the model parameters, even though they affect the amount of variability in the system.     

Exciting molecular hydrogen in the central galaxies of cooling flows

The origin of rovibrational H₂ emission in the central galaxies of cooling flow clusters is poorly understood. Here we address this issue using data from our near-infrared spectroscopic survey of 32 of the most line-luminous such systems, presented in the companion paper by Edge et al.
We consider excitation by X-rays from the surrounding intracluster medium (ICM), ultra-violet (UV) radiation from young stars, and shocks. The   v = 1–0  K -band lines with upper levels within  10⁴ K  of the ground state appear to be mostly thermalized (implying gas densities  ≳10⁵ cm⁻³  ), with the excitation temperature typically exceeding 2000 K, as found earlier by Jaffe, Bremer & van der Werf. Together with the lack of strong   v = 2–0  lines in the H -band, this rules out UV radiative fluorescence.
Using the cloudy photoionization code, we deduce that the H₂ lines can originate in a population of dense clouds, exposed to the same hot  ( T ∼ 50 000 K)  stellar continuum as the lower density gas which produces the bulk of the forbidden optical line emission in the Hα-luminous systems. This dense gas may be in the form of self-gravitating clouds deposited directly by the cooling flow, or may instead be produced in the high-pressure zones behind strong shocks. Furthermore, the shocked gas is likely to be gravitationally unstable, so collisions between the larger clouds may lead to the formation of globular clusters.     

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 missing soft X-ray luminosity in cluster cooling flows

The gas temperature in the cores of many clusters of galaxies drops inward by about a factor of 3 or more within the central 100-kpc radius. The radiative cooling time drops over the same region from 5 or more Gyr down to below a few 10⁸ yr. Although this indicates that cooling flows are taking place, XMM-Newton spectra show no evidence for strong mass cooling rates of gas below  1–2 keV  . The soft X-ray luminosity expected from steady cooling flows is missing. Here we outline and test the energetics of a cold mixing model in which gas below  1–2 keV  falls from the flow and is rapidly cooled by mixing with cold gas. The missing X-ray luminosity can emerge in the ultraviolet, optical and infrared bands, where strong emission nebulosities are commonly seen. We explore further the requirements for any heat sources that balance the radiative cooling in cluster cores.