Solving the hydrostatic mass bias problem in cosmology with galaxy clusters

October 01, 2015

Booming observations of galaxy clusters provide great opportunities for exploring the nature of Dark Energy. At the same time, they post great challenges to scientists. The "hydrostatic mass bias" problem, which leads to a systematic error in estimating the mass of galaxy clusters, is one big limitation when doing precision cosmology with galaxy clusters. Now researchers at MPA have developed a method to correct for it.

Dark Energy is the most dominant energy component in the present-day universe, but its physical nature remains unknown. Dark Energy leaves unique signatures in the universe: it accelerates the expansion of the universe and slows down the growth of structure. As the largest gravitationally-bound structures in the universe, galaxy clusters are a sensitive tracer to these signatures. Thus, researchers can constrain the properties of Dark Energy by counting the numbers of clusters as a function of their masses at various cosmic times.

An accurate measurement of the masses of galaxy clusters is crucial for the success of this method. Although galaxy clusters get their name from observations of galaxies in optical light, the most precise way to estimate their masses - the so-called "hydrostatic mass estimation method" - comes from observations at X-ray wavelengths. X-ray images of galaxy clusters reveal the diffuse hot gas in galaxy clusters that accounts for 90% of their ordinary matter (see mock X-ray images in Fig. 1). In spite of its high temperature - which means high thermal velocities - this hot gas is trapped deep inside the galaxy cluster. This is because of the enormous gravitational attraction from the dark matter component, which makes up about 85% of the total mass of a cluster. (Ordinary matter accounts for only about 15% of the mass.)

The hydrostatic mass estimation method assumes that the hot gas is in hydrostatic equilibrium, i.e. its thermal pressure balances the gravitational pull. However, the hot gas in a galaxy cluster is never fully thermalized because it is continuously fed by mass accretion. The residue motions of the infalling gas leads to a non-thermal pressure support, together with possible contributions from magnetic fields and cosmic rays. This breaks the assumption of hydrostatic equilibrium and causes a bias of typically 5-30% to the mass estimation.

This hydrostatic mass bias problem calls for a better description of the underlying physics in galaxy clusters. Researchers at MPA have therefore developed a new analytical model for the non-thermal pressure, which captures the growth and dissipation of the random motions in the hot gas. Adding this contribution to the hydrostatic balance, they were able to correct for the mass estimations when testing with state-of-the-art cosmological hydrodynamics simulations (see Fig. 2), where the random motions are the dominating contribution to the hydrostatic mass bias. Remarkably, this correction method works for samples of galaxy clusters with various dynamical states (horizontal axis of Fig. 2).

Aided by this correction, the application of the precise hydrostatic mass estimation method can be extended to dynamically disturbed galaxy clusters as long as spatially well-resolved observations are available. With advances in the observation of the Sunyaev-Zeldovich (SZ) effect which directly probes the thermal pressure of the hot gas, spatially well-resolved data will be much easier to obtain, as researchers will no longer rely on the time-consuming X-ray temperature measurements. Already in the last few years, the Planck satellite, the South Pole Telescope and the Atacama Cosmology Telescope have detected more than a thousand galaxy clusters, most of them dynamically disturbed, via their SZ signal. Some of the data already have good spatial resolution.

Still, much more galaxy clusters will be detected without immediate spatially-resolved data. However the newly developed method is also useful for them. For example, the eROSITA survey will measure the X-ray emission of more than 50,000 galaxy clusters and their progenitors. Most of them will not be spatially well-resolved. Masses for these objects will be obtained by scaling relations between the mass and spatially-averaged observables, such as the mean X-ray luminosity, temperature, or their combination. Correcting the hydrostatic mass bias will lead to a more accurate calibration of the scaling relations, and thus allow researchers to better exploit the huge number of galaxy clusters to explore the nature of Dark Energy.

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