The Mystery of the Dark Side

During the last three decades cosmology became a very important part of astronomy. An increasing number of large ground based telescopes and very sensitive satellite-based telescopes delivered many data which lead to new insights about the properties of the present universe and its evolution. Meanwhile such parameters like the mean density or the expansion velocity are already known with high precision. According to the current paradigm the total mean energy density of the universe is equal to the critical density in Friedmann´s equation and, therefore, the three-dimensional space is flat. However, baryons, i.e. the normal observed matter, contribute only about 5% to this density. The remaining 95% are made of some still unknown Dark Matter and Dark Energy, often called the Dark Side of the Universe. One of the main aims of modern cosmology is to unravel the mystery of the dark components in our Universe.

Dark Matter means a kind of particles which interact only gravitationally. These still undetected particles are a necessary ingredient without which one could not understand and explain both the formation of large scale structure and the inner structure of galaxies as measured from their rotation curves. But, according to observations, these particles only contribute about 21% of the measured total energy density of the universe. The remaining 74% are made of Dark Energy, an even more mysterious ingredient of our universe. As opposed to matter, Dark Energy is assumed to be homogeneously distributed in the universe. It has a constant energy density and a negative pressure that - according to General Relativity - accelerates the cosmic expansion. Thus, the cosmic pie consists of about 5% normal matter (which includes also the negligible contribution of radiation and neutrinos at present), 21% of Dark Matter and 74% of Dark Energy.

We observe that the universe expands with a velocity of about 72 km/s/Mpc, the Hubble constant. Thus temperature and matter density decrease with time while the dark energy stays constant. Looking backwards in time the density becomes infinite at about 13.7 billion years ago - the Big Bang. According to theory, during an inflationary stage, shortly after Big Bang, the universe expanded exponentially and quantum fluctuations became scale free classical density fluctuations. Later-on the density fluctuations in the dark matter component started to grow whereas the baryons were tightly coupled to the radiation field until the temperature decreased below a critical value and free electrons and nuclei combined into atoms. This occurred some 370,000 years after the Big Bang. At this moment the universe became transparent to radiation that is being observed today as a cosmic microwave background radiation (Nobel prize 1978 for its first detection).

Tiny fluctuations in the temperature of this radiation (Nobel prize 2006 for the detection of the fluctuations) give us insight into the properties of the early universe when the density fluctuations were small and could be described analytically by linear theory. During the following more than 13 billion years the fluctuations grew due to gravitational instability and formed the observed nonlinear structures in the universe. Since most of the particles are dark matter particles which interact only gravitationally they constitute the backbone of the large scale structure within which galaxies formed. This process of nonlinear gravitational clustering is extremely complex and can be described only by means of sophisticated numerical simulations that challenge the most powerful supercomputers in the world. These simulations take into account the expansion of the universe according to General Relativity. As we said before, the expansion depends on the properties of the Dark Energy. The matter density field within a simulated volume is represented by point particles. The interaction between these particles is described according to Newton´s gravitational law. Therefore, the non-linear evolution of the initial density field is equivalent to compute the gravitational forces among a set of N-body particles. The larger the number of particles used, the better the resolution of the simulation will be. At present, high resolution simulations contain typically billions of N-body particles. Depending on the desired resolution, several 100,000 CPU hours are necessary for such simulations on the most powerful parallel computers, thanks to the development of efficient parallel algorithms. The situation becomes even more complicated if baryons are also taken into account. Unlike Dark Matter, baryons do not only interact gravitationally, but also through other fundamental interactions (electromagnetic and nuclear as well). Such gas-dynamical simulations which include also radiative cooling processes, star formation and the feedback of stars on the gas are much more complex and, therefore, numerically much more expensive. In most cases only the evolution of relatively small volumes can be simulated.

Figure 1: A Milky-way sized halo is simulated in the Cold Dark Matter cosmology. The dark matter distribution is shown color coded to the logarithm of the projected density. Besides the massive satellite, close to the center, more than hundred smaller ones are clearly visible in the figure.

Within the DEISA Extreme Computing Initiative we were granted with 2 million CPU hours during the past two years. We used this computational time on supercomputers in Barcelona, Munich and Jülich to study the problems of small scale structure formation. A substantial part of these simulations has been performed at MareNostrum in Barcelona whereas most of the analysis has been done on the shared memory machines at Jülich and Munich. Most of these simulations were done with 10243 particles, although the initial conditions were generated with 64 times more (40963) particles. This allows us to resimulate some specific objects in the simulation boxes with higher resolution (up to 64 times more than the rest of the box). The galactic object shown in the pictures is one such example.

Figure 2: The same halo as shown in Figure 1 but this time simulated with Warm Dark Matter particles. Their projected distribution is shown at about the same time moment than in the previous case.

At least three co-ordinates and three velocities must be stored for 10243 particles. Thus, in single precision and for dark matter only simulations at least 24 GB of data have to be stored for each time step. Since we are interested in the evolution of structures we store typically 135 time steps (every 100 mega-years). Thus terabytes of data have been generated. These data had to be transferred between the different supercomputers for permanent storage and to perform many different data analyzes. During this data transfer we have benefited from the DEISA high capacity dedicated network among the different computer centers. We used the Globus software for parallel data transfer with sustained transfer rates of several tens of Mbytes/s.

The inflationary paradigm predicts a scale free initial spectrum of density perturbations which has widely been confirmed on large scales by measurements of the cosmic microwave temperature fluctuations. Thus, massive objects like galaxy clusters with hundreds of galaxies are expected to look similar to galactic size dark matter halos. However real galaxies do not have hundreds of satellites, as it is shown in simulations, but only a few tens, in the best case. There are two possible explanations for the absence of satellites in simulations: Either the satellites do not exist at all or they are invisible because they do not contain stars. In the first case, this would be related to the nature of the dark matter particles, while in the other case, it would require a proper modeling of the baryonic physics. In order to disentangle between these two situations, we have been doing large scale N-body simulations with different dark matter candidates: a massive (more than Giga electron Volt mass) weakly interacting particle named as Cold Dark Matter (CDM) and another candidate with lighter mass (of the order of kilo electron Volt) called Warm Dark Matter (WDM).

Comparing Figure 1 and Figure 2 we can appreciate the strong difference in the number of satellites orbiting around a galactic size dark matter halo depending on the kind of dark matter particles assumed. We show the projected dark matter density around one halo color-coded according to the logarithm of the density in each pixel. Within this dark matter halo resides a Milky Way sized galaxy (in the center of the plot) with one very massive satellite in the upper part. All the other satellites have much less mass. Figure 1 corresponds to the CDM simulation, while Figure 2 is for the WDM simulation. As can be clearly seen, the number of low mass satellites in Figure 2 is considerably smaller: If we assume that the dark matter particles have a relatively light mass, i.e. Warm Dark Matter, the small scale fluctuations are washed out and during further evolution only a very few low mass satellites formed. This would explain why we observe only a few satellites within our Local Group.

Another open problem is the nature of Dark Energy. The simplest assumption is a constant vacuum energy which acts like a cosmological constant in Einstein´s equations. A straightforward generalization is dark energy with a time-independent equation of state. Such a generalization leads to a slightly modified expansion history of the universe and, therefore, to a slightly different evolution of objects. Within the German astrogrid we were running a set of simulations assuming different equations of state of the Dark Energy. The number of objects above a certain mass per volume element (the mass function) changes with time and depends on the expansion speed. The tiny oscillations in the power spectrum are another characteristics. Besides a model with a cosmological constant (constant vacuum energy) we simulated also the evolution of structures in Dark Energy models with negative pressure as a function of energy density. The predicted mass functions and power spectra at different redshifts can be compared with future observations to constrain the parameters of the equation of state of Dark Energy.

References

• Stefan Gottlöber¹
• Gustavo Yepes²

Astrophysikalisches Institut Potsdam¹
Universidad Autónoma de Madrid, Grupo de Astrofísica²

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