Together, the SSP and ISM radiative transfer models of the previous sections are able to reproduce the full UV–sub-mm SED of galaxies with a reasonably high degree of accuracy (see e.g. da Cunha, Charlot, and Elbaz 2008; Groves et al. 2008). Yet, by themselves, these models are inherently static. Only limited model assumptions about the past evolution of the galaxy can be introduced through the star formation history. In particular, the ISM is rarely evolved along with the stars, and is presumed to be the same metallicity as the latest generation of stars in the SSP models. It is common form to assume that the dust in the ISM is a constant fraction of the metals within the gas, distributed in a form similar to that found in our Milky Way.
These assumptions are sufficient to reproduce the observed SEDs of real galaxies using empirically based priors (e.g. Section 4.5), or multiple components (e.g. Section 4.4, and see Section 4 for full discussion). However to produce fully-theoretical SED models that are at least conceptually similar to local galaxies, one needs to fall back on galaxy evolution codes. There are three levels of these. At the innermost level are galactic chemical evolution codes, which, given some star-formation history and/or some “pristine” inter-galactic medium (IGM) infall rate, trace the evolution of the ISM metallicity, allowing for outflows, infalls, and pollution by stars (see reviews by Hensler 2008; Matteucci 2008). The more recent of these codes also evolve the dust along with the gas, taking into account the different pollution rates of different elements, and the evolving temperature/phases of the ISM (e.g. Calura, Pipino, and Matteucci 2008). Once these codes have given the corresponding ISM evolution with the star-formation history (input or calculated), these can be associated with SSP and ISM codes to give a more self-consistent instantaneous spectrum of a galaxy (e.g. Schurer et al. 2009; Conroy, White, and Gunn 2010a). Some of the main issues with these are the limited knowledge of the external gas losses and infalls, meaning that exact evolution cannot be obtained, and the computational time needed to calculate this evolution and associate it with a spectrum, meaning that only specific sets of SFH or infall can be calculated at a time.
The next scale above the chemical evolution models are models that evolve the whole galaxy. These models are based upon hydrodynamic and N-body codes that follow the evolution of the ISM and stars within a dark matter halo representing a galaxy (e.g. Springel 2005). These codes use empirically based relations to follow the detailed evolution, such as the formation of stars from gas, and the feedback from stars to the gas (see e.g. Tormen 1996; Cox et al. 2006). Containing both the stars (or “stellar particles”) and the ISM (with known metallicity), these galaxy simulation/evolution codes are perfectly suited for linking with the Monte-Carlo radiative transfer codes such as SUNRISE (Jonsson 2006) or RADISHE (Chakrabarti and Whitney 2009) which have been purposely built to create spectra and broad-band images of these simulated galaxies.
The outermost layer are the cosmological models. These trace the formation of structure in the Universe from the original perturbations in the cosmic microwave background to redshift zero, using N-Body codes to simulate dark matter and its gravitational interaction (see Dolag et al. 2008, for a review). While some of these models trace baryonic matter as well as the dark matter, most trace only the dark matter due to the more complex interactions of baryonic matter. Thus to trace the formation of galaxies within the forming dark matter halos semi-analytic models (SAMs) are used (e.g. Cole et al. 2000; Kauffmann and Haehnelt 2000; Hatton et al. 2003; De Lucia, Kauffmann, and White 2004; Somerville et al. 2008). These models use the outputs from the dark matter simulations and approximate the physics of galaxy formation within the dark matter halos by empirical relations (e.g. for gas cooling, star formation, AGN fueling, feedback).
The SAMs return (and trace) the star formation history of each galaxy that is created, including the effects of mergers, as well as the gas content and metallicity of the gas (and stars). These results can be used in association with SSP models (as discussed in section 2.1) to determine the stellar spectra of each galaxy. As little geometrical information is returned by the SAMs, associating the ISM effects on the stellar spectra is more difficult, especially so for the IR emission. For the gas, most tend to use the associated emission lines added to the SSP models (see e.g. Leitherer et al. 1999; Charlot and Longhetti 2001). For dust attenuation, a simple treatment taken by many is to determine the extinction assuming a uniform mixing of the stars and gas in a galaxy, a fixed ‘template’ attenuation curve, and basing the optical depth on either empirical relations between galaxy luminosity (e.g. Kauffmann et al. 1999; De Lucia, Kauffmann, and White 2004), or amount of dust in the galaxy (e.g. Guiderdoni and Rocca-Volmerange 1987; Devriendt and Guiderdoni 2000). More advanced treatments include the use of the Charlot and Fall (2000) model (e.g. De Lucia and Blaizot 2007) or attenuation libraries like that of Ferrara et al. (1999), made for such purposes (e.g. Bell et al. 2003b).
For the dust emission, the situation is more challenging. The simplest treatments assume that all of the radiation attenuated in the optical (by the above treatments) are re-emitted in the IR. This radiation is either distributed through modified Planck functions with empirically-calibrated temperatures (e.g. Kaviani, Haehnelt, and Kauffmann 2003) or empirically-based templates (e.g. Guiderdoni et al. 1998; Devriendt and Guiderdoni 2000). Yet such models do not take into account the strong geometrical dependence of dust heating or the strong variations in the spectral shape and they are clearly not self-consistent with the extinction in the optical–UV (see Section 2.2.3).
For self-consistent SED models, the SAMs need to be coupled with radiative transfer (RT) calculations such as GRASIL, which has been done only for a few models (e.g. Granato et al. 2000; Lacey et al. 2008). However one of the main strengths of SAMs is their computational efficiency and speed which allows the calculation of the physical parameters of the many galaxies in large cosmological volumes and over large redshift intervals for many different implementations of the galaxy formation physics. Yet RT is computationally intensive, and severely slows the SAMs, meaning only relatively small volumes were investigated in the SAM-RT models. In addition some of the details necessary for the RT calculations are generally poorly modeled within the SAMs. Thus currently there is a choice between poorly representative but fast, or better modelling and slow (see Fontanot et al. 2009, for an overview). The currently most advanced models choose to compromise by using a RT-based library, empirically linked with the SAMs (Fontanot et al. 2009) or even linked through artificial neural networks to account for the large and complex variations in galactic UV–IR SEDs (Silva et al., in prep).
Models of galaxy SEDs thus exist of varying resolution and complexity, adapted to model everything from individual galaxies or to large catalogs of galaxies on cosmological scales. While at each level of the SED models our knowledge of the important physical processes could be improved, SED modelling today is much more accurate across the wavelength range than it was even a decade ago.