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Measuring gas velocities in galaxy clusters with X-ray images

X-ray observations provide us with detailed information on the density and temperature of the hot gas inside galaxy clusters. The other major gas characteristic that still needs to be measured is the gas velocity. While current generation X-ray observatories lack the required energy resolution to measure velocities directly, future observatories such as ASTRO-H and ATHENA will address this limitation. An international team including MPA scientists has shown that the power spectrum of the velocity field can inferred indirectly from existing X-ray images of relaxed clusters. Numerical simulations confirm this simple theoretical idea, opening a way of probing gas velocities using already existing X-ray data.

Fig 1: Schematic illustration of gas density distribution in a spherically symmetric cluster in perfect hydrostatic equilibrium (v=0, top) and in a slightly disturbed cluster (v ≠ 0, middle). Slow large-scale perturbations in a stratified cluster atmosphere can be interpreted as internal waves (as illustrated in the bottom panel), similar to waves in the ocean, where the velocity of water and the amplitude of waves are linked. In clusters, similar perturbations are caused by a variety of reasons, including minor mergers or the activity of the central supermassive black holes.

Fig 2: X-ray image of the Coma cluster as seen with Chandra observatory. The substructure seen in the image implies that the X-ray emitting gas is not at rest.

Galaxy clusters are the largest gravitationally bound structures in the present Universe. Hot gas (with temperatures of 10 to 100 million Kelvin) fills their gravitational potential wells and shines in the X-ray band, making the clusters an easy target for orbital X-ray observatories. Both the density and the temperature of the gas in clusters is routinely measured using X-ray data, while it is notoriously difficult to directly measure the turbulent motion of the gas via the Doppler shift of X-ray lines. Since the information on the turbulent gas velocities would have profound implications for the mass determination of clusters and for determining the plasma microphysics, new approaches have been developed to indirectly measure the gas velocities using existing X-ray data. One of these approaches is based on the analysis of small-scale fluctuations in X-ray images as described below.

In relaxed clusters the gas approaches the state of hydrostatic equilibrium, when all thermodynamic properties are aligned along surfaces with equal gravitational potential, making X-ray images smooth and round (see Fig.1). These stratified and stable atmospheres of cluster gas bear much similarity to the Earth's atmosphere or to water in the oceans where cold and dense material tends to be below hotter and lighter material due to the combined action of gravity and buoyancy. Slow subsonic perturbations of such atmospheres can be represented as a combination of internal (gravity) waves, very much like waves in the ocean (bottom panel of Fig.1). In oceans there is a simple relation: the larger the amplitude of the waves, the higher the velocity of water. Is the same true for gas in galaxy clusters? Both theoretical analysis and numerical simulations have shown that this is indeed the case.

The main idea is that gas is disturbed on large scales and that this results in a cascade of waves. In clusters these waves are creating perturbations in the gas density that are visible in X-ray images as small-scale fluctuations of the surface brightness relative to a smooth global model. Our analysis shows that there is a simple linear relation between the gas velocities and density perturbations. Moreover, this relation holds for a broad range of scales: on large scales, where buoyancy effects dominate (internal waves), as well as on small scales where the isotropic turbulent cascade usually develops. At these small scales, the entropy of the gas acts as a passive scalar advected by the velocity field and makes the gas displacement visible in X-rays.

Based on these arguments one can expect that in relaxed clusters (i.e. clusters which are only slightly disturbed) the power spectrum of the velocity field can simply be recovered from the power spectrum of density fluctuations. The latter can be straightforwardly estimated from X-ray images.

Numerical simulations (cosmological simulations of cluster formation and pure hydrodynamic simulations with turbulence) confirm this conclusion and open an interesting possibility to use gas density power spectra as a proxy for the velocity power spectra in relaxed clusters.

Once the gas velocities can be measured directly with future X-ray observatories, it will be possible to push this analysis further and search for differences between the density and velocity power spectra. Strong departures of the two power spectra from the universal behavior described above can then be used to constrain physical effects such as conductivity or viscosity in the gas.

Eugene Churazov (MPA), Massimo Gaspari (MPA), Irina Zhuravleva (Stanford), Alex Schekochihin (Oxford), Rashid Sunyaev (MPA)


Zhuravleva I., Churazov E., Schekochihin A. A., Lau E. T., Nagai D., Gaspari  M., Allen S. W., Nelson K., Parrish I. J., The Relation between Gas Density and Velocity Power Spectra in Galaxy Clusters: Qualitative Treatment and Cosmological Simulations, linkPfeilExtern.gif2014, ApJL, 788, 13

Gaspari M., Churazov E., Nagai D., Lau E. T., Zhuravleva, I., The relation between gas density and velocity power spectra in galaxy clusters: high-resolution hydrodynamic simulations and the role of conduction,linkPfeilExtern.gif2014, A&A, 569A, 67

Gaspari M., Churazov E., Constraining turbulence and conduction in the hot ICM through density perturbations, linkPfeilExtern.gif2013, A&A, 559A, 78

Churazov E.; Vikhlinin A.; Zhuravleva I.; Schekochihin A.; Parrish I.; Sunyaev R.; Forman W.; Böhringer H.; Randall S., X-ray surface brightness and gas density fluctuations in the Coma cluster,linkPfeilExtern.gif2012, MNRAS, 421,1123

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