How to fit the Local Universe into a Supercomputer?
In 1965 Arno Penzias and Robert Wilson detected the cosmic microwave background radiation (CMB). More than 13 billion years ago this radiation was imprinted on the sky, only a few 100,000 years after the Big Bang. In 1992 the COBE satellite detected anisotropies in the temperature of the CMB radiation. Meanwhile these temperature fluctuations are measured with very high precision by satellites (WMAP, Planck) as well as many ground based observations. The measured temperature fluctuations tell us that shortly after the Big Bang the Universe was almost homogeneous with tiny density fluctuations of the order of 10-5. Comparing the power spectrum of measured temperature fluctuations with theoretical models, cosmologists conclude that the Universe is spatially flat and consists at present of about 68 % of some unknown Dark Energy, 27 % of also unknown Dark Matter and 5 % of baryons.
In the evolved universe one can directly observe the distribution of baryons and indirectly deduce (gravitational lensing, velocity measurements) the distribution of Dark Matter. We see huge clusters of galaxies with masses up to a few 1015 solar masses in the knots of the cosmic web which comprises galaxies in a wide range of masses from tiny dwarf galaxies (109 solar masses) to massive elliptical galaxies (1013 solar masses). All these structures have evolved from tiny fluctuations generated during the early inflationary phase and measured in the CMB background.
The formation of structure on large scales is well understood within the concordance model of cosmology. The initial small perturbations grow by gravitational instability and form bound objects called halos which decouple from the expansion of the universe. These bound objects grow further hierarchically by accretion of matter and merging with smaller halos. The gravitational clustering becomes increasingly non-linear. Dark Matter is more abundant and hence most important for formation of large scale structures where gravity dominates. On smaller (galactic) scales baryons play an important role. They interact not only gravitationally but form a gas with a certain pressure and temperature. In the gravitational potential wells of the Dark Matter halos the originally hot gas cools via radiative cooling and finally stars are formed of the cooled gas. Almost all chemical elements above helium are formed in stars and then redistributed into the cosmic medium. Star formation and the feedback of the stars on the gas are the most important processes in galaxy formation. Nevertheless due to the domination of gravity at early times galaxies are closely associated with the Dark Matter halos.
|Figure 1: A slice of thickness 110 million light years through the simulation box. Some very prominent structures lie within that plane such as the galaxy clusters indicated with name. The simulated and observed positions of the clusters match very well.
The vastness of scales and the non-linearity of gravitational clustering are the reasons why numerical simulations and the intensive use of the largest supercomputers are the only methods suited to study the gravitationally driven growth of structures down to local over-densities in halos and the formation of galaxies therein. Cosmological simulations follow the clustering of matter by numerically solving the gravitational interaction based on an N-body approach. Additionally one needs to model hydrodynamical processes, radiative cooling, star formation and the feedback of stars, in order to simulate in detail the formation of galaxies in their different environments. To this end very high mass- and spatial-resolution are necessary which imposes a strong challenge for present day computational algorithms. One important limitation of state of the art galaxy formation simulations is that galaxies are usually selected to be relatively isolated systems, to avoid extra computational costs. However it has been shown that the environment of galaxies plays an important role in their evolution. Therefore simulations of isolated galaxies can only offer limited insights into the more complex process of galaxy evolution.
One way to overcome this selection bias and to draw general conclusions about galaxy evolution is to simulate and observe galaxies in all possible environments and compare ensemble averaged observables. However this marginalization approach would require a computationally infeasible number of high-resolution simulations. An alternative way to investigate galaxy evolution is to compare simulated and observed galaxies that reside in a similar environment. This has been the scope of the CLUES (Constrained Local UniversE Simulations) project (http://www.clues-project.org), and it is also the goal of our work - to provide initial conditions that reproduce the local environment of the Milky Way and its neighbours. The Local Universe is naturally the best observed region of the Universe where even the tiniest dwarf galaxies can be observed. Therefore, it is best suited to study the formation of structures in controlled computer experiments. To this end we need to fit the observed Local Universe into a (super)computer. In the next section we describe our way of doing this.
Recovering and Simulating Structures of the Local Universe
The initial conditions for cosmological simulations are formulated in agreement with the observed CMB power spectrum. Running the simulation over more than 13 billion years one obtains a realisation of the universe which represents the observed Universe in a statistical way, but it has nothing to do with the observed nearby universe. To simulate the formation of the observed nearby universe one has to recover the initial phase distribution of density perturbations which is responsible for the formation of the local structures. To this end observations of the nearby universe must be imposed as constraints on the initial conditions of the simulations. The resulting constrained simulations serve as a numerical laboratory of the nearby universe.
Recovering the initial phase distribution of density perturbations is challenging for several reasons. First, today's large scale structures are usually observed with galaxy surveys. Galaxies however are biased tracers of the underlying density field - like the tips of icebergs. Furthermore their receding velocities due to the expansion of the universe and their peculiar velocities (the velocity with respect to the local rest frame) are difficult to disentangle observationally. Second, the present day density field is connected to the initial density field by non-linear structure formation. Especially on small scales this makes it extremely difficult to trace it back in time.
Hence we apply an iterative Markov Chain Monte Carlo approach that approximates the evolution of the universe forward in time every iteration step. Using a combined approach consisting of this iterative reconstruction based on non-linear Lagrangian Perturbation Theory and a fully non-linear N-body simulation we are able to reconstruct the initial conditions and simulate the dark matter density in the Local Universe. The aim is to derive the density field that resembles the Local Universe as it is being observed by the 2MRS galaxy survey (www.cfa.harvard.edu/~dfabricant/huchra/2mass/) up to distances of 418 million light-years.
To this end we used a new algorithm called Augmented Lagrangian Perturbation Theory (ALPT) to model structure formation in each iteration step. ALPT complements the accuracy of Lagrangian perturbation theory on large scales with the local spherical collapse model which is more precise on small scales. This approach allows to reconstruct the initial density perturbations 13 billion years ago which are responsible for the formation of the large scale structures that are observed today. The quality of the recovered initial density field which contains the seeds of today observed structures can be assessed by direct comparison of the simulated and observed structures. To this end also the line-of-sight distortions are modelled that are inherent to modern galaxy surveys. Then the simulated structures can be directly compared to the observed positions of the 31,017 galaxies of the 2MRS that lie within the desired volume. With this comparison the sampling of the initial Gaussian density field for the next iteration step can be refined. Therefore we iteratively recover an initial density field that seeds structures as observed by the 2MRS survey. This iterative reconstruction algorithm is fast and accurate.
We then use the reconstructed initial field of density perturbations to simulate the full non-linear formation of structure using the N-body code Gadget3 (by V. Springel, http://www.mpa-garching.mpg.de/gadget/). This code follows the gravitational clustering of matter. Halos reside in the highest density peaks of the dark matter distribution and they host galaxies. Now we have a numerical realisation of the Local Universe in our computer and we can directly compare it with the real one. We have chosen a medium mass resolution of 453 million particles in the simulation box so that we achieve a mass resolution of 10 billion solar masses, i.e. a Milky Way sized galaxy is represented in the simulation by 100 particles. With this resolution we can identify galaxies in the simulation box down to the faintest ones of the observational sample in a reliable way. Our simulations resembles the Local Universe very well as we demonstrate in the two figures.
|Figure 2: The top panel shows the sky projection of all galaxies in the 2MRS catalog at distances of 170 to 280 million light-years. The bottom panel shows the matter density in the same shell of the N-body simulations. Very prominent structures are in the left the Perseus-Pisces Supercluster connected to the lower left with the Cetus Wall and near the equator slightly to the right the Norma cluster and the Great Attractor.
In the first figures we show the resulting density distribution in a slice of 110 million light years thickness through the center of the simulation box. This slice corresponds to the Super-galactic plane. The color coding follows the logarithm of the density field. The largest halos (with bound masses of more than 1014 solar masses) which presumable host galaxy clusters are marked by circles. Crosses mark the position of some nearby galaxy clusters which have been extracted from the NED database (http://ned.ipac.caltech.edu/). Our own galaxy - the Milky Way - is in the center of the box in a distance of about 50 million light years to the Virgo cluster. The second figure shows an all-sky projection of all galaxies observed in a distance of 170 to 280 million light-years from the Milky Way taken from the 2MRS survey compared to the matter density in the same shell of our simulation.
The constrained simulations of the Local Universe serve as laboratory for studying the evolution of the local density distribution, the non-linear gravitational potential and the velocity field. We can study the formation of the local cosmic web as well as the formation histories of the simulated counterparts of observed local galaxy clusters. Based on our reconstructed initial density field we are also able to re-simulate specific selected regions with higher resolution. In these so called zoomed simulations we can then re-simulate galaxies like the ones of our Local Group resolved with millions of particles including hydrodynamics and models for gas cooling, formation of stars and feedback. Being able to do so we can search for traces of the evolution in the simulated and observed galaxies and the influence of the environment on their evolution.
The authors acknowledge the support by the Deutsche Forschungsgemeinschaft under the grant GO563/21-1. The simulations have been performed at JSC.
 Heß, S., Kitaura, F.-S., Gottlöber, S.
Simulating Structure Formation of the Local Universe, ArXiv 1304.6565
 Kitaura, F.-S.
The initial conditions of the Universe from constrained simulations, ArXiv 1203.4184
 Kitaura, F.-S., Heß, S.
Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory, ArXiv 1212.3514
• Steffen Heß
• Francisco Kitaura
• Stefan Gottlöber
Leibniz-Institut für Astrophysik Potsdam