This section is intended to provide a quick introduction on the realization of initial conditions for N body simulations of isolated galaxies. It includes a few standard methods as well as some specific pieces of software.

The main aim is to generate a set of positions (x,y,z) and velocities (Vx, Vy, Vz) for N particles, consistently with either a given gravitational potential (and some a priori knowledge of the internal dynamics) or the full distribution function. The easiest part is usually to set up the positions of the particles for them to follow a certain mass density distribution. The use of cumulative functions is generally the most efficient way of doing so, but other techniques such as the rejection method are also used.

We will start with simple examples, and then follow on with more refined techniques. We will first start with two simple ways of generating a set of N bodies which reproduce an a priori fixed gravitational potential (or density distribution): an algorithm using the cumulative mass density, and one using a rejection technique. We will then review two ways of associating velocities to these points: the first via simple Jeans Equations, and the second via the distribution function itself.

• . Initial conditions for isolated galaxies
• Density distributions using cumulative functions
• From distribution functions
• From Jeans Equations