Data Guide | Semi Analytic Model Basics

There are a number of ways to model the evolution of a galaxy inside a dark matter halo. For the higher-level science modules, TAO requires the galaxies in its database to have a minimum set of properties. Each galaxy record in the TAO database should contain information about its position, merger history, and star formation history. So, at a minimum, the methodology used to generate the galaxy population must produce this information. The best-suited methodology for this purpose is that of semi-analytics (White & Frenk 1991). Semi-analytic models not only calculate all the required properties for galaxies but also link their evolution over time using the halo merger trees to follow the growth histories. Note that any other method that produces the minimum set of properties is also acceptable; we focus on semi-analytics here as it is the most common and nicely illustrates the requirements of the TAO system.

Semi-analytic models of galaxy evolution take advantage of the relative computational efficiency of N-body simulations by adding the bound baryons to a simulation in post-processing. By using information about the gravitationally bound halos, such as their mass, size, spin, substructure, and merger history, the properties orders of galaxies hosted within these structures can be inferred through differential equations that describe the relevant physics macroscopically. The runtime of such a model is orders of magnitudes less than the N-body simulation itself. Hence after that initial investment, one can explore large regions of the parameter space that underlies the baryonic physics by running the model many times.

A semi-analytic galaxy model takes as input a dark matter halo merger tree and evolves its baryonic content with time using prescriptions that describe the phenomenology of each key galaxy formation process.

1. As a dark matter halo grows its potential well gets deeper and hence attracts baryons in the form of diffuse gas from the surrounding medium.
2. This gas cools, conserving angular momentum as it falls to the centre of the halo and forms a rotationally supported disk.
3. Within this flattened disk stars begin to form. A galaxy is born.
4. Each episode of star formation results in a distribution of stellar masses sampled from the initial mass function.
5. The most massive stars are short-lived and explode as supernovae, injecting metals and energy back into the interstellar and intergalactic medium.
6. Galaxies merge as hierarchical growth proceeds, resulting in morphological evolution and the birth of supermassive black holes.
7. Supernova and super-massive black hole feedback can heat and/or remove gas from the disk and halo, gas that would otherwise contribute to the formation of the next generation of stars.
8. Thus, an equilibrium state is established as the galaxy goes through cycles of stellar birth, feedback, gas heating/removal and star formation suppression.

The above processes provide us with a history of galaxy properties. The simulations and models used in TAO are often large, tracking many tens of millions of halos and hence galaxies. It is from the properties contained in such large catalogues that the output of TAO is derived. To introduce the semi-analytic method we use the Semi-Analytic Galaxy Evolution (SAGE; Croton et al. 2016) model as a template, which nicely introduces many of the key features typical for all models of this type. For a more detailed description of semi-analytic modelling please refer to Baugh (2006) and Croton et al. (2016).