Preparatory Material for Volker Springel's PiTP Lectures


This series of lectures covers gravitational N-body dynamics in the collisionless limit as it applies to dark matter and the stars in galaxies. The lectures will also cover smoothed particle hydrodynamics (SPH), a Lagrangian approach to continuum hydrodynamics that discretizes the mass of the fluid in terms of tracer particles. Combined, these two numerical techniques are a powerful tool for studying, in particular, problems of cosmic structure formation.

In terms of physics, familiarity with the basics of cosmic structure formation (Friedmann-Lemaitre models, growth of linear perturbations, etc.) will be assumed, as covered for example in Peacock's Cosmological Physics (chapters 3, 15 & 16). Also, you are expected to have some background in the fluid dynamics of an ideal gas and in the basics of collisionless dynamics. A particularly clear exposition of the latter is given in the excellent book Galactic Dynamics by Binney & Tremaine.

More on the numerical side, the book Computer Simulations Using Particles by Hockney & Eastwood provides a useful introduction to N-body techniques, and especially to particle-mesh force solvers. To those unfamiliar with SPH, it is recommened to read the classic review article by Monaghan (1992) on this technique. For those interested in more modern derivations of SPH, you may also look into Springel & Hernquist (2002), or the recent review by Rosswog (2009).

In some of the excercises, we will use the N-body/SPH code GADGET, which is described in the papers Springel, Yoshida & White (2001) and Springel (2005). A public version of this code can be downloaded here. The distribution package includes a set of example simulations, ranging from a simple collisionless galaxy merger to a cosmic structure formation problem with gas and dark matter. In order to get acquainted with this code, I recommend to run the example problems that are included in the code package of GADGET-2.

As a further warm-up excercise, I would suggest to try setting up initial conditions for a simple sod-shock problem in SPH and run this with GADGET-2, similar to what is shown in Figure 9 in the above paper (Springel 2005). This involves writing a script that sets-up the initial conditions, configuring the code appropriatly for running the problem, and plotting up the results. Don't get worried if it doesn't work straight away... We will get back to this SPH problem and more complicated ones during the summer school.