Los Alamos - Fermilab SDSS Collaboration      

The Sloan Digital Sky Survey (SDSS) is the largest astronomical survey project ever conceived. It is producing a wealth of data on the clustering of mass in the Universe. This dataset represents a defining challenge to theoretical cosmology: The aim of the LANL/FNAL collaboration is to study gravitational lensing, Lyman-alpha systems, redshift distortions, peculiar velocity fields, and cluster mass distributions using advanced methods of particle simulation, computational hydrodynamics, and analysis of large data sets.

Kev Abazajian (FNAL), Scott Dodelson (FNAL), Josh Frieman (FNAL), Salman Habib (T-8, PI), Katrin Heitmann (T-8), Lam Hui (FNAL), Gerard Jungman (T-6), Paul Ricker (UIUC), Ryan Scranton (CMU), Luis Teodoro (T-8), and Idit Zehavi (Chicago).

Over the last decade, a powerful and diverse suite of observations has led to remarkable discoveries in astrophysics and cosmology. Taken together, results from cosmic microwave background (CMB) observations, studies of the large-scale distribution of matter in the Universe, the temperature of X-ray gas in clusters, observations of quasar spectra, and of the redshift distribution of supernovae, yield an impressively consistent picture of the fundamental make-up of the Universe. The density is critical, i.e., Omega=1, with a dominant contribution Omega_Lambda of approximately 0.65 arising from a mysterious `dark energy.' The baryonic matter contribution of Omega_B = 0.05 to the total mass contribution Omega_M is dwarfed by the nonbaryonic `dark matter' component: Omega_DM of approximately 0.35. These observations also strongly support the picture that structure forms in the Universe via the gravitational amplification of primordial fluctuations.

Fundamental questions regarding the evolved mass distribution in the Universe are (a) what constitutes the mass and (b) how is it distributed? The Sloan Digital Sky Survey (SDSS), the most ambitious astronomical survey project yet undertaken, is targeted at answering precisely these questions. The survey will map in detail one-quarter of the entire sky, determining the position and absolute brightness of more than 100 million celestial objects. It will also measure the redshifts of more than a million galaxies and quasars. The SDSS uses a dedicated 2.5 meter survey telescope located at the Apache Point Observatory in New Mexico. The SDSS data-stream is expected to dominate observational cosmology in the near future. The SDSS is much more than just a redshift survey: Early results include observations of high redshift quasars, weak gravitational lensing, mapping of the dark matter distribution within the Galaxy, and determination of galaxy clustering.

The core of the joint LANL/FNAL effort consists of two interlocking parts: first to characterize the mass distribution of the Universe as sampled by the multiple probes offered by SDSS. Second, we wish to understand the dynamical processes that underlie structure formation. This requires a very significant high-performance computing (HPC) effort both in numerical simulations and data analysis. To focus the computational program, we have nucleated the Sloan Computational Cosmology Project (SCCP). The SCCP research targets include: weak and strong gravitational lensing, determination of the cluster mass function, the three-dimensional power spectrum characterizing the distribution of galaxies, the distribution of Lyman-alpha clouds, and studies of redshift space distortions. These topics are all in the `Key Project' list identified by the main SDSS collaboration.

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.

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.

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 weak gravitational lensing, redshift space distortions, peculiar velocities, and Lyman-alpha clouds.

Among the data products expected from SDSS is a large dataset on gravitational lenses. 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. The depth-enhanced southern component of the SDSS survey promises to provide a new measurement of Omega_M using this technique. The success of this measurement depends on calibration against simulations which will be provided as part of this project. A successful simulation of this type requires a dynamic range of 10 Mpc - 1 Gpc which can be achieved with the MC^2 code described below.

The lensing of background galaxies by clusters is a very useful probe of cosmology, providing constraints on the amplitude of the power spectrum and the values of Omega_M and Omega_Lambda. This lensing provides an essentially unbiased method of locating clusters. Dynamical simulations of structure formation are necessary to interpret the data and provide constraints on cosmological parameters. As discussed above for cosmic shear detection, simulations with a similar dynamic range will be performed early in the project. Determining the distribution of cluster masses over a wide range of cluster masses will require higher resolution simulations (10 kpc - 100 Mpc) which will be attempted later in the project. The dynamic range of simulations will be extended using multiple-sampling techniques and adaptive mesh methods.

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. These simulations cover the range of 100 kpc - 300 Mpc but are made somewhat easier since very large scale coverage is less important. The full dynamic range will be covered by our codes during the latter half of the project.

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 range of scales that needs to be handled is 0.5 Mpc - 200 Mpc, the target resolution of the MC^2/HPM code described immediately below.

The cosmological Vlasov-Poisson code MC^2 has been developed from work initially carried out by Habib and collaborators under a DOE Grand Challenge for both beam physics and cosmology applications. The code utilizes a PIC method, where particles represent the sampled phase-space density function and the self-consistent potential is calculated on a grid. Particle time-stepping is accomplished using a symplectic method with the option of second or fourth-order accuracy. This scheme has proven to be remarkably accurate and efficient: relatively large time-steps are possible with exceptional energy conservation being achieved. The code has excellent mass resolution and has proven its efficiency on multiple HPC platforms. As part of this proposal, the capabilities of this code will first be extended by the addition of hydrodynamics using the Hydro-Particle-Mesh (HPM) method of Gnedin and Hui. HPM follows the motion of two sets of particles, the dark matter and gas, computing in addition to the usual gravitational potential, a new effective potential due to the presence of gas pressure. HPM provides a completely adequate treatment of the hydrodynamics needed for the study of Lyman-alpha systems.

As part of the ASCI Flash Center at the University of Chicago, Ricker has played a major role in developing FLASH, an adaptive-mesh hydrodynamics code originally designed to study thermonuclear flashes on white dwarfs and neutron stars. Ricker and Dodelson earlier collaborated in developing COSMOS, a cosmological hydrodynamics plus particle-mesh code, and using this experience Ricker and collaborators have succeeded in adding self-gravity and particle-mesh capabilities to FLASH. Once fully developed, the capabilities of MC^2 and FLASH allow for complete coverage of the computational requirements of this proposal.

Sloan Digital Sky Survey main website.

Sloan Computational Cosmology Project (SCCP) homepage.

Salman Habib / LANL / habib@lanl.gov / revised December 2002