2.2 The ISM around the stars

SSP models are state of the art for producing the spectra of stellar populations, yet they are not sufficient alone for reproducing the spectra of galaxies. Stars are the dominant power sources within galaxies (excluding AGN). However, the radiation from stars is absorbed and processed by the gas and dust that lies between the stars, the interstellar medium (ISM). This absorption must be accounted for when comparing SSP models with optical/UV observations and a treatment of the radiative transfer of the stellar light through the ISM and subsequent ISM emission is necessary if the full UV–IR SED is to be understood.

While the gas and dust are in reality intermingled within the ISM, in practice they are often treated as separate components because their absorption properties have a different wavelength dependence.

2.2.1 Interstellar gas

Interstellar gas is predominantly treated as atomic in the modelling of galaxies. While molecular gas is clearly present in many galaxies, it has generally a low volume filling factor, meaning that rarely contributes significantly to the overall opacity in a galaxy. It is only a noticeable opacity source in specific spectral features or in galaxies dominated by nuclear/heavily obscured sources, such as AGN and ultra-luminous IR galaxies (ULIRGs). Molecular gas emission in galaxies is predominantly seen at longer wavelengths (NIR and longer) and is generally treated to arise mostly from “Photodissociation Regions”, where the gas is heated by the diffuse interstellar radiation field of the galaxy. Although it provides insight into the molecular phase of the ISM, molecular emission is not considered to be a significant contributor to the overall SED of a galaxy (for further details see reviews by e.g. Young and Scoville 1991; Hollenbach and Tielens 1997).

Atomic gas however is the dominant opacity source in the extreme-UV ( 13.6 eV). It reprocesses this light into strong emission lines in the UV, optical and IR. It is thus especially important for young, actively star-forming galaxies. Usually, it is assumed that all hydrogen ionizing photons (hν > 13.6 eV) are absorbed locally, within a small volume around the ionizing sources (approximately the Strömgren sphere¹), which is appropriate due to the high opacity in this wavelength regime. This energy is then re-emitted in the hydrogen recombination lines, which correlate directly with the total number of ionizing photons (see e.g. Storey and Hummer 1995; Leitherer et al. 1999). However to determine the emission from other elements, or to take account of both gas and dust absorption, full radiative transfer is needed using photoionization codes such as CLOUDY (Ferland et al. 1998) or Mappings III (Groves et al. 2008). For further details, see reviews by Ferland (2003) and Stasińska (2007).

As both the number density and absorption cross-section of dust is low relative to hydrogen in the EUV, dust is often ignored as an opacity source. However, as hydrogen absorption is limited by the recombination rate, dust absorption becomes relatively more important as the strength of the ionizing radiation field increases, becoming the dominant EUV-opacity source when q(H⁰) > α_B∕κ ~ 5 × 10⁸cm s^-1 assuming typical values for the dust opacity, κ (Dopita et al. 2002). This value of the ionization parameter q is well above the average value measured for star-forming galaxies (see e.g. Kewley et al. 2001), meaning negligible EUV absorption by dust in typical H ii regions (< 5%), but such high values may be reached within compact H ii regions and AGN meaning dust will absorb a significant fraction of EUV photons (Dopita et al. 2002; Draine 2010).

2.2.2 Interstellar dust

Interstellar dust has been a field of constant inquiry since it was first realized that an obscuring material existed between the stars and a large body of research exists on the composition, shape and distribution of dust exists (see Draine 2003, for a detailed review of the field, and some remaining questions about dust).

Most of our understanding of interstellar dust has come locally, from observations within our own Galaxy and the Magellanic clouds, and also through theoretical and experimental laboratory work. It is generally accepted that the grains can be considered to be composed of three different compositions; graphitic/amorphous carbon grains, amorphous silicate grains, and polycyclic aromatic hydrocarbons (PAHs), which may or may not be an extension of the carbonaceous grains. The former two were found to reproduce the observed extinction along different lines-of-sight within our galaxy (Mathis, Rumpl, and Nordsieck 1977), while the latter were added to explain unidentified emission bands in the mid-IR (Leger and Puget 1984). Other forms of dust have been suggested, such as SiC (Treffers and Cohen 1974), and ice is expected to form on grains in the coldest environments such as deep in molecular clouds, but generally only these forms are considered in the SED modelling of galaxies.

The size distribution of interstellar dust grains is thought to be power-law in nature, with a distribution N(a) ∝ a^-3.5 or similar, with the average cross-section dominated by small grains, but mass dominated by large. This slope arises from both theory (Jones, Tielens, and Hollenbach 1996) and matching observations (Mathis, Rumpl, and Nordsieck 1977; Draine and Lee 1984; Weingartner and Draine 2001).

To obtain the optical data used for dust calculations in SED modelling, the size distribution and types are then convolved with absorption/emission cross-sections and scattering cross-sections and phase functions which are determined by both laboratory observations and Mie theory (see Draine and Li 2007a; Zubko, Dwek, and Arendt 2004, and references within). PAHs are treated slightly differently as their composition is not fully understood, and their properties can change significantly with the charge of the grains, and thus have more empirical based treatments (Weingartner and Draine 2001, see e.g.). Altogether these form the dust models which are used most often in SED modelling, such as Draine and Li (2007a) or Zubko, Dwek, and Arendt (2004), that have been successfully compared with determined depletion patterns within the ISM and observations in the UV, optical, and IR. These models are either used as an ensemble of individual grain sizes, or integrated to give the opacity data of dust as a whole. Of course empirically based laws and templates are also often used in SED modelling such as the Milky way extinction law and Calzetti law (see below).

For the purposes of SED modelling and fitting, dust absorption and scattering, and dust emission are often treated as distinct components. As the hottest dust is constrained by sublimation to 2000K (corresponding to ~ 3 - 4μm  peak emission), in practice only the scattering and absorption of light needs to be considered for modelling the optical-UV emission of galaxies. Conversely, as dust opacity strongly decreases with increasing wavelength, in the far-infrared (FIR) only dust emission needs to be considered.

Attenuation by dust The effects of dust on the optical-UV light are often described by two parameters - the reddening and total obscuration. Reddening is the wavelength dependence of dust effects, including features, and takes account of the fact that shorter wavelength photons are more readily scattered and absorbed by dust. This is often parametrized by the color excess E(B -V ) or the Balmer decrement Hα∕Hβ. The total obscuration is a measure of the total light absorbed or scattered out of our -line-of-sight by dust either bolometrically or in a single band and can be considered the normalization of the reddening. This is generally parametrized as A(V ). For relative measures correcting only for reddening is sufficient, however for absolute quantities the total obscuration must also be taken into account. This is especially important when the reddening is close to flat, i.e.  only small visible effects by dust on the spectrum.

For individual stars in the Milky Way, the Large and Small Magellanic clouds, extinction laws have been measured (e.g. Cardelli, Clayton, and Mathis 1989). However, when considering a galaxy as a whole, it must be taken into account that stars reside at different optical depths, depending on whether they lie on the side of the galaxy facing the observer or averted from the observer, and that the stellar light can be scattered into the observer’s line-of-sight as well as out of it. Additionally, stellar populations of different age will have different extinction optical depths, and this extinction might have a different wavelength dependence. These issues lead to the concept of ‘attenuation’, where the complexity of the actual star-gas geometry is wrapped into a single attenuation law, now not applied individually to each star in the galaxy, but applied to the full spectrum of the galaxy.

Using an attenuation law, the dust obscuration of stellar light is expressed through a screen approximation (see Equation 2), as if the dust was lying between us and the stellar population of the galaxy, with a wavelength-dependent reddening law (a_λ). The total amount of attenuation then depends only upon the thickness of the screen (Δτ),

(2)

The attenuation law was derived empirically for starburst galaxies by Calzetti, Kinney, and Storchi-Bergmann (1994); Calzetti (1997) who fit the law with a simple polynomial as a function of 1∕λ. They found a law much greyer than the extinction laws of the Milky Way and LMC demonstrating the effects of geometry and mixing compared to simple extinction. Generally an simple power-law , a_λ ∝ λ^-0.7, is able to reproduce the observed effective attenuation in galaxies (Charlot and Fall 2000).

However, a simple attenuation law cannot account for differential geometries and star formation histories within and between galaxies. This can be seen with the higher optical depths observed for nebular emission lines relative to the underlying stellar continuum, indicating that the stars and gas that give rise to the lines and to the continuum see different amounts of dust (Calzetti, Kinney, and Storchi-Bergmann 1994; Calzetti 1997). These observations led to the improvement over a simple attenuation law in the approaches of Silva et al. (1998) and Charlot and Fall (2000), who created a more physical two-step model in which young stars which emit ionizing photons are likely to be still surrounded by the clouds of gas and dust from which they formed. In this model all stars are attenuated by ‘diffuse’ dust in the same manner as equation 2. However young (< 10Myr) stars undergo an additional ‘birth cloud’ attenuation. In practice this means that the UV light and nebular emission lines associated with the short-lived massive stars are more obscured than the optical light dominated by the longer-lived stars, as observed in real galaxies.

While the empirically calibrated Charlot and Fall (2000) model is an improvement over a simple attenuation law, it still does not take account of the differential dust and star geometries that are clearly visible in resolved galaxies, such as bulges, disks, and dust lanes. The clumpiness of the ISM, both within the diffuse phase (see e.g. Kuchinski et al. 1998; Witt and Gordon 2000) and within the birth clouds (see e.g. Popescu et al. 2000; Dopita et al. 2005), will also affect the resulting attenuation of galaxies. However the greatest difficulty that simple, empirically-based attenuation laws face is the anisotropic scattering of light by dust, as photons are not only scattered out of the line-of-sight, but can also be scattered into it. This can cause bluer integrated spectra than can be accounted for by simple attenuation laws, especially for face on galaxies (see e.g Baes and Dejonghe 2001b; Fischera, Dopita, and Sutherland 2003; Pierini et al. 2004; Inoue et al. 2006).

However, to take account of all these issues, proper radiative transfer (RT) calculations must be done, which require intensive computations. To limit these calculations several treatments exist, which can be broadly grouped into iterative methods and Monte Carlo methods (for a more detailed description for several of the methods used in RT calculations, see Baes and Dejonghe 2001a). In the iterative approach, the light is broken up into emitted and scattered components, with the RT equation solved separately for each component, and the solution from the previous component being used for the subsequent (i.e. directly emitted photons by stars, then photons scattered once by dust, photons scattered twice etc.) and these equations iterated to convergence (see e.g. Kylafis and Bahcall 1987; Xilouris et al. 1998, 1999; Tuffs et al. 2004). Monte Carlo methods use a method closer to reality, where the paths of individual ’photons’ are followed through their interactions (absorption and scattering) through the galaxy. The photons are emitted in a random direction from the sources, such as stars, and interact randomly with the surrounding ISM with a certain probability based on the mean free path length, and are followed through these scattering events until the photons escape or are absorbed. To build up an integrated SED of a galaxy, many photons must then be followed, though many treatments now exist to limit this number, such as only following photons which end up in the observer’s line of sight (see e.g. Witt, Thronson, and Capuano 1992; Bianchi, Ferrara, and Giovanardi 1996; Witt and Gordon 1996, for some early work on Monte Carlo RT in galaxies). Both of these approaches are currently used, with the iterative quicker for given geometries, while Monte Carlo is more able to handle complex distributions of stars and dust (several existing codes are discussed in the following section).

While obviously the most realistic approach, the limitation of the radiative transfer is that it requires complex calculations and thus it is not directly applicable to large sample of galaxies. RT codes have been used to provide template libraries of attenuation for a range of galaxies (Bruzual A., Magris, and Calvet 1988; Ferrara et al. 1999; Pierini et al. 2004), and also analytic functions for the attenuation of the components of galaxies (i.e. bulge, disk, clumps etc., Tuffs et al. 2004), to deal with this issue, yet these introduce several free parameters which may be difficult to determine for unresolved galaxies for which only broad-band SED is available. It is for these reasons that a simple attenuation law is still the most commonly used way to account for the effects of dust on the UV-optical SED.

One final note about the attenuation by dust is the silicate dust features that can appear in absorption at 9.7 and 18 μm . These features require large optical depths to be observed, and thus are generally only seen in galaxies with strong nuclear sources (i.e. nuclear starburst/AGN). As this absorption occurs againstmodeled dust emission, it is usually only modeled with a simple absorbing screen, otherwise it requires self-consistent radiative transfer (discussed in section 2.2.3).

Emission by dust Dust emission in the FIR and sub-mm is most commonly modeled by a single black body (F_FIR ∝ B_λ(T_dust)) or emissivity-modified black body (∝ B_λ(T_dust)λ^-β, also called grey body), or a simple sum over a limited (2–3) number of these. The first form assumes that all dust is in thermal equilibrium at one temperature T_dust. The emissivity of dust grains is generally taken to be a power-law at these long wavelengths, with models and laboratory data suggesting indices ranging from β = 1.0–2.0. Actually the β index is expected to be a function of both grain size, composition and temperature (see e.g. Andriesse 1974; Draine and Lee 1984; Agladze et al. 1996; Mennella et al. 1998, with a nice discussion on the constraints on β in the latter). When introducing more than one black body, one is generally limited by the number of wavelengths observed and the details of the model (see e.g. Dunne and Eales 2001). In general, two modified black-bodies are sufficient to model these wavelengths, encompassing the idea of warm and cold components of the ISM (see e.g. Popescu and Tuffs 2002; Hippelein et al. 2003, and the review by Sauvage, Tuffs, and Popescu 2005).

In the MIR range simple black bodies are not sufficient and more detailed modelling is necessary. This is due to strong dust (PAH) emission features and the stochastic heating processes that become important for smaller dust grains. As the size of a dust grain decreases, the impingement of photons onto the dust grain surface becomes less frequent and more random, thus less statistically representative of the interstellar radiation field, allowing significant cooling between photon impacts (Figure 13 of Draine 2003). Thus, rather than having a single temperature, the dust has a range of temperatures and is parametrized rather by the strength of the radiation field heating it. To model this one can use either Monte Carlo calculations simulating the arrival of photons and subsequent emission, or more simply one assumes and solves for a steady-state distribution of temperatures given the strength and shape of the impinging radiation field and dust size and composition(see e.g. Guhathakurta and Draine 1989; Desert, Boulanger, and Puget 1990; Draine and Li 2007a). Once this temperature distribution is known, it can be convolved with black bodies modified by the dust emissivity in the MIR, including any features.

Polycyclic aromatic hydrocarbons (PAHs) could be either called the largest molecular species or the tiniest dust – emit strong features in the MIR (see e.g. Smith et al. 2007). These features arise from specific bending and stretching modes of the large aromatic molecules (Bauschlicher, Peeters, and Allamandola 2009). As PAH emission bands are so complex they are generally incorporated into the models by either assuming a template form for the MIR emission features (see e.g. Desert, Boulanger, and Puget 1990) or by modelling the physical processes in a way similar to the small dust grains (e.g. Weingartner and Draine 2001; Draine and Li 2007a). On the whole, while aromatic molecules within galaxies are accepted to be the source of the MIR features, the typical shapes, sizes, and ionization-charges of these molecules are an active field of research.

More realistic FIR dust emission models must take into account that the dust within the ISM of galaxies will exhibit a range of temperatures, from the hot dust around young stars and in outflows to the coldest dust in cold molecular cores, driven by the range of radiation fields and dust sizes. Such complex emission models calculate, for a given radiation field, the emission from each grain size and composition and then integrate over these for a given dust distribution to obtain the total dust emission. The largest grains are generally considered to have a single temperature, as they will be in thermal equilibrium, leading to a simple distribution of temperatures dependent upon grain size and composition. In more accurate models, the smallest grains are considered to be stochastically heated and the temperature distribution of the individual grains is calculated (using, e.g., the treatment of Guhathakurta and Draine 1989). To finally calculate the IR emission from a galaxy, the distribution of dust masses over heating radiation field are also needed. Simpler IR emission models assume a functional form of dust mass over heating intensity; dM_d = f(U)dU, with f(U) most often assumed to be a power law (see e.g. Dale et al. 2001; Dale and Helou 2002; Draine et al. 2007b). The most complex IR emission models use radiative transfer to calculate the radiation field distribution over a galaxy, where the distribution of dust and stars are assumed (i.e. parameters of the model), and thus these models directly link the dust absorption and dust emission. These are discussed in Section 2.2.3.

However, as the temperature distributions of the dust in the galactic ISM are dependent upon dust–gas geometry and cannot be determined from optical-UV data alone, empirically-based templates are often used for representing the IR SED of galaxies, especially when IR data is limited due to sensitivity or confusion. These templates take dust models as described above (i.e. multiple modified black bodies, or dust heated by a range of radiation fields) and match these to observed IR SEDs (or IR colors) of groups of galaxies. These templates then tend to have galaxy-wide properties such as IR luminosity or galaxy type as parameters, though intrinsic properties such as average interstellar radiation field intensity are also used. Well known examples of templates include those of Chary and Elbaz (2001), Dale and Helou (2002), Lagache et al. (2004), and, more recently, Rieke et al. (2009). Though these templates tend to be limited by the samples that define them, they provide a good alternative to models when no or very little information is available about the actual IR emission of a galaxy.

2.2.3 Combining stellar and dust emission

The full UV to IR SED of a theoretical galaxy can be created through the combination of the techniques and modelling discussed in the previous sections (2.1–2.2.2). However, the different wavelength regimes need to be consistently connected. The simplest method is to take the energy absorbed in the optical-UV (see Equation 2) and to distribute it across the MIR and FIR, assuming simple emission properties for the dust, such as black bodies. This is the method used by Devriendt, Guiderdoni, and Sadat (1999) and da Cunha, Charlot, and Elbaz (2008). These authors attempt to strike the balance between the capability to model large datasets and the minimum sophistication necessary for a realistic model.

To associate full UV–submm SEDs with their semi-analytic models (discussed in the following section) Devriendt, Guiderdoni, and Sadat (1999) created “STARDUST”. This model assumes that stars and dust are homogeneously-mixed in the galaxy. The light from the stars, i.e. summed from SSPs, is then passed through an ISM with the amount of dust determined from a simple galaxy chemical evolution model. The dust-absorbed radiation is then re-emitted via a series of templates generated from the Desert, Boulanger, and Puget (1990) model and fitted to observed IRAS points, parametrized by the total IR luminosity.

da Cunha, Charlot, and Elbaz (2008) follow a similar idea, but improve upon this by using the Charlot and Fall (2000) recipe for the attenuation. They thus obtain naturally corresponding ‘birth cloud’ and ‘diffuse ISM’ dust emission components over which the absorbed energy is distributed (see Figure 4). The two emission components are both made up of a PAH template and variable grey body contributions, with the birth cloud emission consisting of shorter wavelength (hotter dust) emission. Such a model can simultaneously determine quantities such as stellar mass and dust mass of a galaxy, and provide quantitative uncertainties for all parameters (see section 4.1). While this method is quick, and hence suitable for comparison against large datasets, it is self-consistent across the two emission components only in terms of the total amount of radiation absorbed and re-emitted; physical properties, such as the dust temperature or the shape of the emission within the components, are based on educated assumptions and are not constrained directly by the optical-UV absorption in the model.

A very similar method was followed by (Noll et al. 2009) with the CIGALE code, which uses either the Maraston (2005) or PEGASE codes for the stellar populations and only a Calzetti attenuation law to attenuate the stellar light. The major differences lies in the use of existing empirically calibrated templates, such as from (Dale and Helou 2002). rather than a free IR emission made up of several parameter-controlled components.

To be properly self-consistent, the absorption and emission must occur more ‘simultaneously’, such that the exact temperatures (including stochastic effects) of the dust causing the absorbing can be directly calculated. Such models require radiative transfer calculations to be performed, such that the exact radiation field, or at least the heating intensity, is known at each point in the dusty ISM. This, along with assumptions about the stellar ages and distribution, and the dust distribution and properties can then give the full UV-IR SED of a model galaxy.

The models of Efstathiou, Rowan-Robinson, and Siebenmorgen (2000) and Siebenmorgen and Krügel (2007) do this radiative-transfer calculation using the ray-tracing method for starburst galaxies, which, being dominated by young stars and their birth clouds, are well represented by simple spherical approximations. These models build upon a strong history of dust radiative transfer and emission modelling and star-formation region modelling work to create simple models for the understanding of the UV–submm SEDs of starburst galaxies (Rowan-Robinson 1980; Rowan-Robinson and Crawford 1989; Rowan-Robinson 1992; Siebenmorgen and Kruegel 1992a; Siebenmorgen, Kruegel, and Mathis 1992b; Rowan-Robinson and Efstathiou 1993; Siebenmorgen 1993; Krugel and Siebenmorgen 1994). These works are based on the observation that young stars are both relatively more luminous and more obscured (thanks to the birth clouds) than older stars, and that in strongly star-forming galaxies these young stars will be the dominant IR (and significant bolometric) sources. In particular, Siebenmorgen and Krügel (2007), reduce the results of complex modelling to a series of templates, based upon the physical properties of starbursting galaxies, such as the total luminosity, size and extinction of the star-forming regions and the contribution of the young stars to the total luminosity of the galaxy.

Groves et al. (2008) (building on previous works; Dopita et al. 2005, 2006a,b), take this work a step further by self-consistently calculating the emission of a star-forming region, including the radiative transfer through the surrounding gas and dust simultaneously. Like Efstathiou, Rowan-Robinson, and Siebenmorgen (2000) they allow for the H ii regions to evolve over time, using empirically calibrated models. This model is well suited for modelling starburst (star-formation dominated) galaxies, where young stars and their ’birth clouds’ dominate the emission, determining conditions such as star-formation rate and compactness of the gas and stars. Like da Cunha, Charlot, and Elbaz (2008) and Siebenmorgen and Krügel (2007) it provides physical templates with as few parameters as possible. Yet, while it fits well the SEDs of star-formation dominated galaxies (see Figure 5), this model is not suited for non-starbursting galaxies, where the distribution of the diffuse dust and stars must be accounted for.

By assuming a simple molecular cloud-disk-bulge geometry (as shown in figure 6), the GRASIL model (Silva et al. 1998; Granato et al. 2000) is able to account for the differential extinction suffered by the stars of different ages associated with each of these components in a galaxy. In addition, by varying the contribution of each component, galaxies from spirals to ellipticals can be modeled. Unfortunately, the more general geometry means that some parts (such as the gas-dust connection calculated in Groves et al. 2008) cannot be calculated, and also means more parameters are needed to define the model. As with the Groves et al. (2008) model, the more accurate dust calculations mean a longer calculation time, as compared with simpler models such as da Cunha, Charlot, and Elbaz (2008). The GRASIL team is currently working on speeding up their calculations for semi-analytic models (see following section) by the use of neural networks (Silva et al. 2010).

The main issue with all models discussed above is that, while they take account of absorption (and emission) reasonably well, they do not accurately take account of dust scattering, which, as discussed above, can make some galaxies appear bluer or redder depending upon inclination. This can be even more obvious in spatially resolved SEDs of galaxies, where light from stars which are obscured along our line of sight can be seen in reflection. However, as scattering is an inherently stochastic process, it is difficult to model simply in a galaxy, especially when multiple scatterings can occur.

Tuffs et al. (2004), following on from Popescu et al. (2000) and Misiriotis et al. (2001), use the iterative ray-tracing radiative transfer method of Kylafis and Bahcall (1987) to efficiently calculate the radiation field throughout model galaxies consisting of a stellar bulge, stellar and dusty disks and dusty clumps. Their resulting SEDs are then self-consistent across the UV-IR range. In addition, one of the strong benefits of radiative transfer is that the resulting SEDs can also be spatially resolved, and be compared to multi-wavelength studies of resolved galaxies, which they have done with edge-on galaxies such as NGC 891 (Popescu et al. 2000) and NGC 5097 (Misiriotis et al. 2001).

The other common approaches is to use the Monte-Carlo radiative transfer method to model the UV-IR SED of galaxies. Existing Monte-Carlo codes that have been applied to galaxies include SUNRISE (Jonsson 2006; Jonsson, Groves, and Cox 2010), DIRTY(Gordon et al. 2001; Misselt et al. 2001), TRADING (Bianchi, Ferrara, and Giovanardi 1996; Bianchi, Davies, and Alton 2000; Bianchi 2008), SKIRT (Baes et al. 2003), and RADISHE (Chakrabarti and Whitney 2009). These are able to model arbitrary and complex geometries of dust and gas, including spiral arms, dust lanes, bulges and clumpy ISM. However unlike the ray tracing method, the radiation field within the galaxy is not directly calculated (as only individual photons or photon packets are followed). Thus dust heating and emission must be treated through approximations (discussed in detail within the papers listed above). One treatment is to integrate within set volumes (i.e. a grid) the amount of energy absorbed by dust, and to redistribute this energy over large equilibrium grains. In some cases (Bianchi, Davies, and Alton 2000), small stochastic grains are also considered (using template assumptions). This approach can suffer from stochastic noise if the number of photons used is not sufficient. A similar treatment is to convert the absorbed energy into a radiation field using the dust cross-sections, and thus with the radiation field known the methods described in the Section 2.2.2 can be used (see e.g. Misselt et al. 2001), though this still suffers from issues of stochastic noise. Another treatment is called the “dust temperature update method”. Here, the temperature of the grains is updated with the absorption and emission of each photon (described in detail in Bjorkman and Wood 2001; Baes et al. 2005). All these methods must iterate in the case of self-absorption of dust. A more efficient method iterates on the calculation of the radiation field density by using the previous estimates as a base and only calculating for the difference at each iteration. This method will always converge as each iteration only adds a small amount of dust emission which will provide an even smaller amount of dust emission. The new radiation field is converted to IR emission using models such as Dale and Helou (2002) or Draine and Li (2007a) (see e.g. Juvela 2005; Jonsson, Groves, and Cox 2010). While definitely more accurate in the treatment of dust, Monte Carlo codes require some representation of the ISM as input and are much more expensive computationally, especially in the cases where the dust is optically thick to its own (IR) emission and many iterations may be required. Current models are also, due to resolution effects both within the RT and galaxy models, unable to calculate the absorption on both diffuse (kpc) and local (pc) scales, and thus currently use approximations or sub-resolution models (see e.g. Jonsson, Groves, and Cox 2010). Hence, while reproducing “real” galaxies, they cannot be directly used to fit observations of individual galaxies.

In summary, the modelling of the transfer of stellar light through the ISM is well advanced, yet two significant challenges still exist. The first is simply the computational effort needed to represent the radiative transfer accurately. Many of the above models are limited in their resolution to trace the ISM accurately, and thus need sub-resolution approximations to treat some of the coldest or hottest dust (e.g. SUNRISE uses the starburst templates of Groves et al. 2008) . The second is our general lack of understanding of the dust composition in the ISM. Generally, dust is assumed to consist mainly of carbonaceous and silicate-like grains (such as olivine), in some power-law size distribution, (see e.g. Mathis, Rumpl, and Nordsieck 1977). This form is reasonably well constrained by observations of extinction in the optical-UV and emission features in the IR (see Draine 2003). Yet there are still open questions on shape (how ordered or “fluffy” are the grains, e.g.  Zubko, Dwek, and Arendt 2004), on whether there are other kinds of dust, and on what formation and destruction processes lead to this power-law distribution of sizes (e.g.  Jones, Tielens, and Hollenbach 1996). Conversely there are still spectral features associated with dust that are yet to be properly explained, such as the 2175Å absorption feature, the diffuse interstellar bands in the optical, and the “Extended Red Emission” band observed around 7000Å (see  Draine 2003, for a discussion on these features and other remaining issues).