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.
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).
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.
Authors
Zhang, Congyao
Postdoc
Phone: 2299
Email: cyzhang@mpa-garching.mpg.de
Churazov, Eugene
Scientific Staff
Phone: 2219
Email: echurazov@mpa-garching.mpg.de
Links: personal homepage (the institute is not responsible for the contents of personal homepages)
Original Publication
1. Congyao Zhang, Eugene Churazov, Alexander A. Schekochihin
Generation of Internal Waves by Buoyant Bubbles in Galaxy Clusters and Heating of Intracluster Medium
submitted to MNRAS. Source
