New analytical model for turbulence pressure in galaxy clusters

Mass determinations of galaxy clusters based on observations of the hot intracluster gas often neglect non-thermal processes, most importantly intracluster turbulence. This introduces a systematic error in the estimate. A group of scientists at MPA has therefore developed an analytical, one-dimensional model for the non-thermal pressure contribution, which combines the growth of galaxy clusters in a cosmological context and the physics of turbulence. If further tests against both observations and simulations confirm the initial positive results, this new model could improve the determination of cluster masses and thus make galaxy clusters a more accurate cosmological tool.

Fig. 1: The galaxy cluster Abell 1689, one of the biggest and most massive galaxy clusters known. Most of the mass is in the form of dark matter, so astronomers need to use indirect methods such as gravitational lensing, the SZ-effect or X-ray observations of the hot intracluster gas to determine the mass of a galaxy cluster.
Credit: X-ray: NASA/CXC/MIT/E.-H Peng et al; Optical: NASA/STScI

Fig. 2: This analytical equation is at the heart of the new method: it describes the evolution of pressure due to turbulence in galaxy clusters.

Fig. 3: The predicted total (dash-dotted) and thermal (solid) pressure profiles calculated with the new model. The calculations were performed for a group of clusters at a mean redshift z=0.1 with a average mass of 300 trillion solar masses. The thick dashed line shows the profile derived from X-ray and SZ observations.

The expansion of the present-day Universe is accelerating, and the origin of this acceleration is unknown. It indicates either the presence of “Dark Energy” - a mysterious energy component in the Universe with negative pressure, or a breakdown of Einstein’s General Relativity - how gravity works on cosmological scales. In order to distinguish between these two explanations, we must measure how structures in the Universe evolve over time.

Galaxy clusters (see Fig. 1) grow in mass by accreting material from their surroundings over cosmic history. They are the largest known gravitationally bound objects in the Universe and therefore are an excellent probe of the growth of large-scale structures – and thus of the origin of the cosmic acceleration. If we want to use galaxy clusters as a probe of the acceleration, we need to accurately determine their masses. Although these giants are dominated by invisible “dark matter”, we can infer their total mass from observations of the intracluster gas under the assumption of a hydrostatic equilibrium between the gravitational pull and the gas pressure, or more accurately the gradient of the gas pressure.

Observations of the intracluster gas, however, typically measure only the thermal pressure of the gas. Non-thermal pressure, especially from turbulent gas motion, has been recognized to provide an additional pressure gradient and therefore has to be taken into account as well. Neglecting this contribution would result in a deviation of the inferred cluster mass from the true mass and in consequence this would influence the study of cosmic acceleration.

So far, the amplitude of the turbulence pressure has mainly been estimated with large-scale hydrodynamical numerical simulations. These state-of-the-art simulations, however, yield quantitatively different results when using different numerical methods. Moreover, they are computationally expensive and do not lead to a direct physical understanding of what is happening in the galaxy clusters.

Therefore, we took a different approach to this problem by gathering physical insights about how turbulence arises and dissipates in the intracluster gas. From this input, we formed a one-dimensional analytical model of the non-thermal pressure contribution, which describes the velocity dispersion due to turbulence at each radius as the galaxy cluster grows in mass (Fig.2).

This new analytical model predicts that the non-thermal fraction of the gas pressure increases towards cluster outskirts as it takes significantly longer for turbulence to dissipate at larger distances from the cluster centre. Another prediction is that the non-thermal fraction is larger in clusters with higher masses and in clusters observed at higher redshift (i.e. at earlier cosmic times), since they grow faster which triggers more turbulence.

With the help of an existing model of the total pressure, the new model also gives the thermal pressure as well as the biased mass estimate derived from this thermal pressure gradient. If we compare our results with observations of a population of galaxy clusters, the predicted thermal pressure profile is in excellent agreement with the data (Fig.3).

Thus, our model has passed an important observational test; in addition we found qualitative agreement with simulation data. More specific tests on the predicted mass and redshift dependence will be performed both against observations and numerical simulations. If all the tests are passed successfully, the physical understanding provided by the new model will lead to a better determination of the cluster masses. We can then use galaxy clusters as a competitive probe of the origin of cosmic acceleration.

Xun Shi and Eiichiro Komatsu

Original publication:

Xun Shi, Eiichiro Komatsu, "Analytical model for non-thermal pressure in galaxy clusters", submitted to MNRAS linkPfeilExtern.gifarXiv:1401.7657