Formation and Evolution of Cosmological Structure
António C. da Silva
One of the most challenging and exciting problems of Astronomy is to understand how structure forms and evolves in the Universe. The challenge is to understand how small density fluctuations present in a highly uniform primordial universe give rise to the complex pattern of structures we observe today. In this series of four modules we will address the problem of formation and evolution of cosmological structure. The course was prepared at the level of final year of graduation and post-graduate students. In the first two modules we will overview the standard model of Cosmology and the main features of today’s most popular model of structure formation. In this first part of the course we will give emphasis to the analytical description of density field and the fundamental equations describing the linear growth of density fluctuations.
Session 1: Large Scale Structure: The Fabric of the Universe
12 November 2008
One of the most challenging and exciting problems of Astronomy is to understand how structure forms and evolves in the Universe. The observable Universe presents itself to the human eye structured with different classes of celestial bodies and matter distributed on different length scales. On small scales the Universe looks heterogeneous with planets, stars, and interstellar gas appearing spatially distributed on preferred directions of the sky. On progressively larger scales, the Universe appears progressively less heterogeneous, with galaxies, groups of galaxies and galaxy clusters being spatially distributed in a structured pattern, expressively called the cosmic web, without apparent preferred directions. Why is the Universe structured in such a way? What’s the origin and physical mechanism responsible for such structure?
Session 2: Growth of Cosmological Structure: Linear versus Non-Linear evolution
19 November 2008
Presently, the most popular mechanism of structure formation is based on fundamental discoveries, on both theoretical and observational fronts, during the first half of the twentieth century. Structure is believed to have grown via gravitational instability from passive density perturbations produced in a primordial phase of the Universe. In 1902 Jeans was the first to demonstrate that small density perturbations can grow with time in a homogeneous and isotropic self-gravitating fluid. The theory of gravitational instability was applied to an expanding universe by Lifshitz in 1946, which presented the first general analysis on the evolution of inhomogeneities in Friedman-Lemaitre-Robertson-Walker background models using linear perturbation theory. As long as the perturbations are small they are indeed well described in linear theory. However the accuracy of the theory starts to degrade as perturbations grow larger and higher-order terms need to be considered at later times. Eventually the perturbation theory itself breaks down at the point when complex non-linear structures form. At this stage other methods need to be used to follow the evolution of structure.
Session 3: The Dark Matter component: Collisionaless N-body simulations
28 November 2008
Over the past two decades, numerical N-body simulations have become the most powerful technique to investigate the evolution of cosmological structure. Complex non-linear physics, acting over a wide range of scales, makes the structure formation process hard or impossible to describe without the use of numerical computation methods. These methods follow the growth of structure in time by integrating the equations of motion of billions of individual particles that evolve under the action of gravity and other physical forces involved. Numerical simulations which only account for the effects of gravity are appropriate to describe the evolution of colissionaless systems such as the cold dark matter component of the Universe. These are usually referred to as N-body simulations. To describe the evolution of collisinal systems such as those including baryonic matter (gas), simulations need also to account for the dynamics of the gas and to include the appropriate gas physics for the range of mass and time scales probed by the simulations. These are known as hydrodynamic N-body simulations.
Session 4: The Role of Baryon Physics: Hydrodynamic N-body simulations
3 December 2008
A description of structure formation exclusively based on the behaviour of collissionaless matter under its self-gravity is obviously insufficient. Gas dynamics, shocks, non-gravitational heating and pressure gradients become progressively important as structures evolve. Hydrodynamic effects are clearly important to describe the evolution of the baryonic component of the Universe, and play a central role in determining how collapsing structures, such as galaxy groups and clusters, reach virial equilibrium.