Buoyant bubbles in galaxy clusters and heating of the intracluster medium

March 01, 2018

Buoyant bubbles of relativistic plasma in galaxy cluster cores plausibly play a key role in conveying the energy from a supermassive black hole to the intracluster medium (ICM). While the amount of energy supplied by the bubbles to the ICM is set by energy conservation, the physical mechanisms involved in coupling the bubbles and the ICM are still being debated. A team of researchers from the Max Planck Institute for Astrophysics (MPA) and the University of Oxford argues that internal waves might be efficient in extracting energy from the bubbles and distributing it over large masses of the ICM.

Galaxy clusters are the most massive gravitational bound structures in the Universe. The temperature of the gas filling the deep potential wells of clusters reaches 10 – 100 million Kelvin, leading to powerful X-ray emission from these objects. While the gas cooling timescales in the cluster cores are much shorter than the Hubble time, there is no evidence that the gas cools below X-ray temperatures. This implies the existence of a powerful heating source that offsets cooling losses of the gas. Supermassive black holes in cluster cores have been widely accepted as a prime candidate for such a heating source.

Figure 1. Chandra X-ray image of the Perseus cluster. The bubbles appear as dark (X-ray dim) regions in this image. “Active” bubbles (radius ∼ 7 kpc) are marked with black dashed circles. They are surrounded by quasi-spherical weak shocks (radius ∼ 14 kpc), shown by yellow circles. The outer bubble, to the north-west from the centre, has the “horizontal” and “vertical” (radial) sizes L ∼ 25 kpc and h ∼ 7 kpc, respectively.

Observations of clusters provide us with a unique opportunity to study the impact of supermassive black holes on the ambient gas – the process known as active galactic nuclei (AGN) feedback, and in particular its flavour, called radio-mode feedback. In the cluster centre, bubbles of relativistic plasma are inflated by bipolar jets from a supermassive black hole, and subsequently expand until the expansion velocity becomes comparable to their rise velocity driven by the buoyancy force. The bubbles then detach from the jet and buoyantly rise upwards. They finally reach their terminal velocity when the drag force balances the buoyancy force. X-ray and radio observations of nearby clusters show clear signs of the intracluster medium (ICM) interacting with these bubbles (see Fig. 1). Estimates of the power needed to inflate the bubbles based on comparing the inflation and buoyancy time scales show that this power is comparable to the gas cooling losses.

For a bubble rising with terminal velocity, energy conservation arguments imply that much of the energy used by the supermassive black hole to inflate it will be transferred to the ICM once the bubble crosses several pressure scale heights. While this argument guarantees a high coupling efficiency of the bubble-heating process, the particular channels responsible for the energy transfer to the ICM have long been debated. In other words, the nature of the drag force that balances the buoyancy of the bubble is largely unknown. Processes contributing to the drag could be the excitation of sound and internal waves, turbulence in the wake of the bubble, the potential energy of the uplifted gas or others (see Fig. 2).

Figure 2. Sketch showing a bubble rising in a stratified medium. The bubble rises at the terminal velocity (Uterm) when the buoyancy force is balanced by the drag force. The grey, black and orange lines schematically show sound waves, turbulence, and internal waves excited by the moving bubble, which can all contribute to the total drag.

Astrophysicists have long attempted to explore bubble dynamics and the relevant heating process through numerical simulations. However, these attempts are hindered by uncertainties in the properties of the ICM and the bubbles, especially in the topology and strength of the magnetic field. For instance, ideal hydrodynamic models often lead to a rapid destruction of rising bubbles. However, observations show that some clusters (e.g. Perseus, M87/Virgo) have X-ray cavities with relatively regular shapes even far from the cluster centre (see Fig. 1). As can be seen in this figure, the bubbles are initially almost spherical, but become flattened once they rise buoyantly. Phenomenologically, this can be interpreted as if an effective surface tension acts on the bubble surface and keeps the bubble stable. The flattened bubble shape could result from the combined action of pressure gradients of the flow that squeeze the bubble along the direction of its motion, and surface tension, which prevents the bubble surface from shredding. However, the detailed physical description of this effective surface tension, presumably magnetic, is difficult. To circumvent this difficulty, a team of researchers from MPA and Oxford modelled the bubbles as rigid bodies buoyantly rising in the stratified cluster gas and studied the perturbation induced by such bodies in the gas – a problem that has many applications in atmospheric sciences and oceanology.

It was found that the degree of flattening has dramatic effects on the nature of the drag force generated by rising bubbles. For spherical bubbles, the turbulence in the wake of the bubble dominates the drag, similarly to the case of a homogeneous fluid, while for strongly flattened bubbles, the stratification leads to pronounced changes in the flow. Flattened bubbles move slower and, in particular, clear signs of internal waves are seen in the simulations. Such waves are conceptually similar to the surface waves exited by ships moving in the water. The movie (below) shows how internal waves are excited and propagate horizontally and downwards from the rising bubble, spreading their energy over large volumes of the ICM (see Fig. 3). Attractive features of internal waves, as one of the possible bubble-heating channels, are that: (1) internal waves are trapped in the central region of a cluster, because the Brunt-Väisälä frequency (a.k.a., buoyancy frequency) is a decreasing function of radius, implying that the energy will not leak outside the cluster core; (2) these waves can travel in the tangential direction (azimuthal) and spread energy throughout the cluster core. Another interesting feature is a complex pattern in the wake of the bubble, which reflects the interplay between buoyancy and eddies shed by the flattened bubble.

According to simulations, the expected terminal velocity of the north-west bubble in the Perseus cluster (marked with a white ellipse in Fig. 1) is ∼200 km/s, which broadly agrees with the sole measurements of the gas velocity by the Hitomi satellite. This estimate also agrees with constraints on the velocity from the analysis of the morphology and size of the cool gas filaments trailing the bubble. These results are very encouraging, but of course they only represent the first step towards a comprehensive modelling of bubbles in galaxy clusters and a complete census of all relevant gas heating channels.

Flattened bubble in stratified cluster atmosphere

Figure 3. Specific kinetic energy of the gas in the simulation with a flattened bubble moving in a stratified cluster atmosphere. Internal waves are excited, revealed by a characteristic “Christmas tree” pattern.

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