Advanced Particle Simulation for Computational Cosmology and Beam Physics: Cosmology

The first era of the `golden age' of cosmology - the era that finally made cosmology a true science - is now drawing to a close. Defined by the observational landmarks provided by COBE and the CfA redshift survey, this stage of progress has resulted in a `standard model' of cosmology based on the hot big bang and general relativity. The parameters of this standard model are now known, or will soon be known, to better than 10%. Despite its astonishing achievements, the standard model is at best only a phenomenological success. Far from mere consolidation, cosmology is now moving into a second and even more exciting era where unresolved basic questions are being confronted.

What are these fundamental questions? Dark energy, dark matter, the primordial fluctuation spectrum, the clustering of matter and galaxy formation, and the ionization history of the Universe are the frontiers of the new cosmological era. We have strong evidence that approximately two-thirds of the energy budget of the Universe is composed of dark energy, and the remaining one-third is dominated by an unseen form of matter, observed only indirectly. However, the essential nature of the `dark' Universe remains mysterious. We have a good characterization of the initial fluctuations in the primordial fireball as adiabatic, Gaussian, and close to scale-invariant. But how did they arise? Inflation is a possible answer, but we do not know for certain. We have solid evidence that gravitational instability underlies structure formation but we have not yet located most of the baryons that must exist. The detailed mechanism of star and galaxy formation remains to be elucidated; neither does there exist a fully satisfactory understanding of galaxy groups and clusters. We know that the Universe was reionized by a certain redshift but we do not know its ionization history nor do we know for sure the sources of ionization.

As is clear from the list above, cosmology is inherently inter-disciplinary and presents a fascinating melange of puzzles that involves physics across all of its enormous range and scale of applications. The major sources of cosmological information are: probes of the cosmic microwave background (CMB) radiation; optical, IR, radio, UV, and X-ray astronomical observations and surveys and direct dark matter search experiments.

This project is aimed at understanding the process of structure formation in the Universe via large scale simulations closely connected to observations of galaxy distributions (two- and three-dimensional), the Lyman-Alpha forest, weak and strong gravitational lensing, cluster surveys, cross-correlation of large scale structure with the microwave background and radio sources, and the galactic velocity distribution. A major component of our connection to observations is the Sloan Digital Sky Survey (SDSS).

Theoretical modeling of structure formation has two essential aspects. The first is the confrontation of predictions from different cosmological models with SDSS observations, and the second, via the testing of SDSS observational strategies on mock catalogs, is the validation and verification of the observational strategies themselves. There are several different computational approaches to model structure formation in the dark matter component. These include tree-based N-body, particle-in-cell (PIC), and hybrid methods. Fundamentally, each of these methods attempts to solve the Vlasov-Poisson equations for a collisionless gas of gravitating particles. As mentioned above, the structure of galaxy clusters and galactic halos depends on baryon hydrodynamics, and therefore, at these scales, a complete simulation must incorporate this physics.

In order to address the formation of structure, several astrophysical issues must be understood. These include how galaxies formed, the role of mechanisms aside from gravity, and the processes that determine the luminosity, size, color, and morphology of galaxies. The visible structure of galaxies and the density structure of their cores depend on baryonic cooling and collapse processes which remain a profound challenge for theoretical and computational modeling. Finally, there is the central issue of the relation between the distribution of galaxies and the underlying distribution of mass which consists mainly of dark matter.

The SDSS database is a uniquely powerful tool for investigating the large-scale structure of the Universe. The number of galaxies in the redshift sample represents a nearly two-order-of-magnitude increase over the largest existing surveys. Great care has been taken to ensure that the quality and uniformity of the photometric data will dramatically reduce systematic effects that might otherwise limit the accuracy of clustering analyses on large scales. In addition to the redshift survey, SDSS incorporates a deeper, multi-color, photometric survey as well as a spectroscopic survey of quasars and their absorption systems. Together these features of the SDSS bring unprecedented precision, dynamic range, and detail to the study of structure in the Universe.

The wealth of precision information available from SDSS requires a coupling of advanced theoretical modeling of the dynamics of structure formation with equally sophisticated methods of data analysis. Results from HPC modeling tools such as N-body and hydrodynamic simulations have to be interpreted within the context of the survey by the construction of artificial, or mock, catalogs which reproduce the sky coverage and depth of the survey. At the same time, the size and complexity of the database requires HPC-based analysis methods to efficiently extract mass and galaxy clustering information, such as multiple-point correlation functions and topological measures of structure.

The primary objective of our research program is to understand the mass distribution at different epochs of the Universe as probed by SDSS. A unique aspect is the very tight coupling of theory and observations. Our effort focuses on gravitational lensing, galaxy clusters, peculiar velocities, and Lyman-Alpha clouds. Below, some of the activities carried out in the first year are described in more detail.

Weak gravitational lensing occurs when the distortion of individual light paths is very small, but many objects are observed, leading to a statistical detection. Intervening clusters of galaxies can be studied by observing the distortions in the shapes of distant background galaxies; the shapes of background galaxies are also distorted by the large scale mass distribution itself. This last effect is called the cosmic shear. Weak lensing measurements are the focus of several observational efforts worldwide; the SNAP mission promises a 1% measurement of the shear power spectrum. The success of Omega_M and other measurements from weak lensing depends on calibration against simulations which are presently being carried out as part of this project using the MC^2 code. The figure on the right is a two-dimensional map of the convergence from a test MC^2 simulation. The convergence measures the ratio of the observed surface density to the critical surface density (multiple imaging condition). Twenty, 130 million particle MC^2 simulations are now being analyzed for weak lensing studies.

The mass and redshift distribution of clusters is a very useful probe of cosmology. SDSS has found several thousand optical clusters by using three different observational strategies. Direct redshifts are not available for most of them since they are at relatively high redshifts (z > 0.5). Dynamical simulations of structure formation are necessary to interpret the data and provide constraints on cosmological parameters (preliminary results from SDSS have been published though much better constraints will be available in a year or so). Determining the cluster mass distribution over a wide range of cluster masses requires high resolution simulations, and these are being carried out with the HOT code. Data from the code is being used to provide mock cluster catalogs for the SDSS cluster team. Comparison of cluster masses from multiple techniques -- dynamics of cluster galaxies, gravitational lensing, X-ray measurements of cluster gas temperature -- requires physics-rich, high-resolution simulations to control systematic and statistical errors. The figure on the right shows the dark matter distribution of a single cluster, the `Santa Barbara' cluster, named after a particular set of initial conditions used for comparing results from a large variety of simulation codes. This test simulation was run using MC^2 with 17 million particles. High-resolution simulations run on bigger volumes will be valuable for understanding the dynamics of cluster formation.

The figure on the right shows how the number of dark matter halos are distributed as a function of the halo mass. The HOT simulations shown here (colored lines) are three sets of 130 million particle simulations at a fixed physical volume but with varying force resolution. A low resolution simulation (green curve) does not form small structures, while the upper mass end is sensitive to the simulation volume. The solid line is an analytic fit to numerical data; overall we reproduce the accepted form of the mass function over four orders of magnitude in mass to within 10%. Dark matter halos consisting of tens to many thousands of individual particles are extracted from an N-body simulation with a sophisticated halo finding algorithm. The halo masses over most of the mass range shown here cover the range of typical cluster masses, the precise behavior of the curve being a sensitive function of the particular values of cosmological parameters chosen for the simulation. To construct mock catalogs, the dark matter halos are statistically populated by `galaxies' using a halo occupation model with the a known galaxy two-point function already measured by SDSS. This is followed the creation of a mock SDSS sky by incorporating survey geometry and selection effects. Cluster finding techniques used by observers are then tested on these simulated catalogs.

Historically, the measurement of velocity dispersion has been an important part of large-scale structure observations, in contrast to direct mass determinations. Redshift distortions due to peculiar velocities along the line of sight occur up to redshifts of z ~ 0.1 and provide powerful constraints on theoretical models, especially in estimating the bias parameter which describes the relative amplitudes of the galaxy and mass distributions. This effect provides an important probe of the gravitational potential and, indirectly, information on the value of Omega_M. It is also critical to the correct interpretation of the power spectrum on these scales; for example, it suppresses oscillations in the spectrum due to baryons. Simulations that incorporate the effect of redshift distortions are crucial in interpreting observations made by the SDSS redshift survey. Another important measurement is that of the distribution of relative pairwise peculiar velocities of galaxies as a function of galaxy separation, v_12(r). Measurements of this quantity provide an independent probe of Omega_M and the normalization of the power spectrum sigma_8. Simulations are necesssary to properly evaluate systematic and statistical errors, an absolutely key issue for the success of this technique. Both HOT and MC^2 are being used here.

Lyman-Alpha systems are tenuous gas clouds at intermediate redshifts. They are detected via their absorption spectrum when lit from behind by distant quasars. Since they are formed by gas falling into gravitational potential wells due to the total amount of matter, they provide another tracer of dark matter. Structure of the absorption spectrum as a function of redshift gives a direct measurement of a one-dimensional projected power spectrum. In order to extract the three-dimensional spectrum from this data, it is necessary to match simulations to the data. In particular, it is important to correctly include the resolution of the Sloan spectrographs. The impressive size of the SDSS quasar catalog guarantees accurate determination of correlation functions, including higher-order quantities such as the skewness. This probe of nongaussianity in the power spectrum at z ~ 3-4 is one of the unique aspects of SDSS. Since Lyman-Alpha clouds formed at an early enough epoch, reliable computer simulations can be performed without the need for high-resolution treatment of hydrodynamics. The MC^2 code has been augmented with a Hydro-Particle-Mesh (HPM) treatment of baryons and is now being used for this analysis. The figure on the right shows a simulated QSO line of sight from a simulation with MC^2. The top panel shows the flux field, the middle the density, and the bottom, the peculiar velocity field. The red curve are measurements from the baryons directly, while the blue curves are extrapolations using only the dark matter distribution, the agreement between the two is very good.

Sloan Digital Sky Survey main website.

SNAP Homepage.

Back to Cosmology/Beams Main Page.

Back to ICP Main Page.

Salman Habib / LANL / revised November 03