Predicting the Sunyaev-Zeldovich signal from cosmological, hydro-dynamical simulations

July 01, 2016

Using recent, extensive cosmological simulations, researchers at the Max Planck Institute for Astrophysics have shown that the expected signal from the Sunyaev-Zeldovich (SZ) effect of galaxy clusters on the Cosmic Microwave Background agrees remarkably well with observations by the Planck satellite. However, only a small fraction of this predicted signal is currently observable. The scientists developed a simple analytical model to understand the SZ probability distribution function, which is also helpful in interpreting the observed distribution of galaxy clusters masses.

Sky map of the SZ signal from the simulation, with darker colours indicating a stronger signal. The zoomed image on the right shows a region containing several rich galaxy clusters.

Three-dimensional, cosmological, and hydro-dynamical simulations of structures in the universe have become precise enough to allow for direct comparison with observations. These simulations close the gap between the gravitationally-driven evolution of dark matter and the formation of visible structures, such as galaxies and galaxy clusters. While dark matter - together with the imprint of dark energy - dominates the large-scale evolution of structures and forms the backbone for visible structure to form, various additional physical processes are at play for shaping the appearance of galaxies and galaxy clusters. State-of-the-art cosmological hydro-dynamical simulations include not only gravity but many other, relevant physical processes as well. Therefore they significantly contribute to making our current models of the universe more precise and predictive.

Observations of the cosmic microwave background (CMB) by satellite missions, such as the WMAP and Planck, as well as by a host of ground-based experiments, like the ACT or SPT, currently deliver the most precise measurements of density fluctuations in the early universe. In addition, they constrain the values of the parameters describing our cosmological model – but they are far more powerful than that. They also encode the imprint of cosmological structures growing over the course of 13.8 billion years, ever since the time of the last-scattering of CMB photons, i.e. when the primordial fog lifted and the Universe became transparent. Specifically, the black body spectrum of the CMB is distorted due to Compton scattering of CMB photons within the hot gas in galaxy clusters. This intra cluster medium (ICM) can be detected from multi-wavelength data in microwave bands, an effect known as the Sunyaev-Zeldovich (SZ) effect after a seminal paper by MPA director Rashid Sunyaev in 1972.

Multi-wavelength data are necessary for separating the SZ signal from the CMB itself and various other sources of microwaves in the sky. Over the past years, this SZ signal was measured by the Planck satellite and its interpretation attracted the attention of cosmologists world-wide, as it seemed to imply values of the cosmological parameters which were inconsistent with measurements of the CMB at the last-scattering surface. In other words, the parameters inferred from the early universe (the CMB) were at odds with those inferred from the late universe (the SZ effect). If true, this could be interpreted as hinting at additional processes in our universe, for example neutrino masses slowing down structure formation.

Probability distribution function of the predicted SZ signal in the simulated sky map. The horizontal axis shows the Compton y-parameter, which can be understood as the cummulative energy gain of the CMB photons due to repeated scattering in the hot intracluster gas of galaxy clusters. The predicted SZ signal observable with the Planck satellite (incl. resolution observational noise) is shown as red line, which agrees well with the actually observed Planck data (red diamonds). The simple analytical model is shown as the blue line.

In this study, scientists at MPA and the University Observatory Munich investigated the SZ signal predicted by large, cosmological, hydro-dynamical simulations of the growth of structures in the universe, which are a part of the Magneticum Pathfinder (LINK: www.magneticum.org) project. For the first time, such simulations sample a volume of the universe large enough to have a good statistical representation of the overall structure and incorporate a variety of physical processes in the calculations to realistically reproduce details of smaller structures. Three of these processes are considered particularly important for the development of the visible universe: the condensation of matter into stars; their further evolution when the surrounding matter is heated by stellar winds and supernova explosions which also enrich the inter-galactic medium (IGM) with chemical elements; and the feedback of super-massive black holes that eject enormous amounts of energy into the IGM.

Outputs of this simulation at various time steps — which cover the evolution of structures from the early days of the universe until now – are then stacked to construct a large “sky map”, about 8x8 degrees (almost 20 times larger than the moon) of the predicted SZ imprint onto the CMB. Figure 1 shows this map, including a close up revealing the incredible amount of detail resolved by these modern simulations.

The probability distribution function (PDF) of the SZ signal found in this simulated sky map shows a clear power-law tail towards large values caused by galaxy clusters (figure 2). Due to the limited sensitivity and spacial resolution of the Planck satellite, only a small fraction of this predicted signal is currently observable, but in the range accessible by Planck, the predicted and observed signals agree remarkably well.

Power spectrum of the SZ signal. The parameter l is inversely proportional to the spacial scale, i.e. large l means small structures on the sky. The estimated SZ power spectrum from Planck data is shown as red diamonds, while the red triangles show the power spectrum from SPT data. Note that due to the limited wavelength range covered by the SPT observations these measurements are a sum of the SZ signal and various other sources of microwaves in the sky, i.e. these data points should be seen as a upper limit. The black solid line shows the SZ signal predicted from the simulations; the blue line shows the analytical model.

A simple analytical model can help to qualitatively understand the SZ probability distribution function. To develop such an analytical model, however, the scientists needed the precise number counts of expected galaxy clusters with a given mass. Here as well, the increased precision and large cosmological volume covered by the simulation allows the researchers to precisely obtain this so-called “mass function” for the relevant range of masses and cosmic times.

It turns out that the analytical model is quite important for interpreting the observed mass function properly. Instead of counting galaxy clusters, one can analyse the fluctuation of the SZ signal across the sky. Namely, instead of just counting peaks in the SZ map, the researchers did a full statistical analysis of the fluctuations. The easiest statistic to obtain and interpret is the so-called power spectrum, which shows how much structure is present at a given scale (figure 3). The Planck data are in excellent agreement with both the simulation and the analytical model, which were both computed for the best-fit cosmological parameters of the Planck CMB data. As there is no discrepancy between the predicted signals and the Planck SZ data, the tension between early and late Universe is resolved.

This work demonstrates that state-of-the-art cosmological hydro-dynamical simulations have reached the precision to yield detailed predictions of the appearance of the visible universe. They significantly contribute to making our current models of the universe more precise, predictive, and helpful to better calibrate analytical models. Moreover, they are also essential for the proper interpretation of observational data being obtained by current and future experiments.

Klaus Dolag

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