6.2 Dust

Dust cannot be ignored when fitting a galaxy’s SED, as shown by the cosmic infrared background, which has comparable power to the distinct peak of the cosmic UV-optical background (Hauser and Dwek 2001). The relative strength of the cosmic background in the infrared suggests a significant processing of the galactic stellar light over the age of the universe. This processing must have also been more significant with increasing redshift as the percentage of stellar light re-radiated by dust is only ~ 30% locally (Popescu and Tuffs 2002), as supported by the increasing number density of luminous IR galaxies up to z ~ 1.3 (Magnelli et al. 2009).

As discussed in section 2, the absorption and emission of light by dust are generally treated as separate processes in modelling, and this is similarly true in SED fitting.

6.2.1 Attenuation by Dust

Dust between the observer and the individual stars of a galaxy acts to extinguish and redden the light from those stars. When the stars in our own Galaxy were examined it was found that a simple relation with wavelength was able to describe the extinction and reddening by dust for a wide range of galactic environments, with the only strong feature occurring at ~2175Å (Cardelli, Clayton, and Mathis 1989). A similar but steeper extinction law was found for the Magellanic Clouds, with weaker or non-existent feature at 2175Å (Gordon and Clayton 1998; Misselt, Clayton, and Gordon 1999). It is these extinction laws that have given rise to the contemporary model of dust in the ISM (i.e. Mathis, Rumpl, and Nordsieck 1977), and the understanding that the dust composition between the Milky Way and Magellanic clouds is different.

Yet when integrated over the whole of a galaxy the situation becomes complex, with the geometry of the stars and dust strongly affecting the resulting spectrum. The effects of varying amounts of extinction of the different stellar populations due to the spatial distribution of stars and clumpy dust, and the scattering of blue stellar light into our line of sight act to flatten the effects of dust on the spectrum, creating an attenuation law, where the amount of reddening with extinction is less (or ‘greyer’) than we observe locally (Witt, Thronson, and Capuano 1992). This was exactly what was found in starburst galaxies by Calzetti, Kinney, and Storchi-Bergmann (1994), and Charlot and Fall (2000) found that a simple screen effective attenuation (i.e. a screen of dust between the galaxy and observer) with a power-law relation, τ_ISM ∝ λ^-0.7, was able to account reasonably well for the diffuse ISM attenuation in galaxy observations. It is this complexity that makes disentangling the effects of geometry and differing dust difficult, and thus the extraction of physical dust properties from galaxy SEDs problematic. There are two areas where some progress has been made.

The 2175Å feature The 2175Å feature has been associated with small carbonaceous grains in the ISM (Mathis, Rumpl, and Nordsieck 1977), and is observed in both the Milky way, M33 (Gordon et al. 1999), and (weakly) in the LMC, but is almost non-existent in the SMC. This feature is not observed in the attenuation law of starburst galaxies (Calzetti, Kinney, and Storchi-Bergmann 1994). Whether this lack is due to the clumpy geometry of dust and stars (Fischera, Dopita, and Sutherland 2003) or is actually indicative of SMC-like dust in starburst galaxies (Gordon et al. 1999) is still under debate, yet this feature is generally not needed to fit the attenuation of galaxies. In QSOs, which, being dominated by a nuclear source, are closer to the galactic extinction situation, an average attenuation curve does not show this feature, suggesting processing of the ISM in these active objects (Czerny et al. 2004). However, in a few non-local galaxies where direct extinction lines of sight are available, this feature has been observed, suggesting it may be more common than the attenuation curves of local galaxies suggest (Wang et al. 2004; Elíasdóttir et al. 2009). At higher redshifts, where UV spectra are more commonly observed, recent studies find evidence for the existence of the 2175Å bump (e.g.  Noll et al. 2007; Noterdaeme et al. 2009).

Young versus old attenuation One important progress made in the treatment of galaxy attenuation is the realisation that the effective attenuation of a galaxy is dependent upon its star formation history. Calzetti (1997) found that in starburst galaxies the effective attenuation of the stellar continuum was less than that suffered by the nebula emission, as measured through emission lines. This clear indication of the clumpiness of the dust in galaxies has been interpreted as an indication of differential attenuation of different stellar populations, with young stars, and their associated ionized nebula, strongly attenuated by the clouds from which the stars formed, while older stars have evolved out of their ‘birth clouds’ either through cloud or stellar dispersion, and are only attenuated by the diffuse ISM dust, which acts on both the young and old stars (see e.g. Charlot and Fall 2000). Exactly what is the clearing time of these clouds and the differential attenuation is still uncertain, and may be galaxy specific, but this forms a basis for current galaxy SED models as discussed in section 2.

6.2.2 Dust Emission

Extracting physical properties from dust emission in the IR is difficult for both theoretical and observational reasons: excluding the mid-IR, there are no observed dust features, most being washed out due to the broad shape of the blackbody emission; the IR suffers from strong observational constraints, with most data coming from space- and balloon-based observations; associated with this is the, until recently, limited sensitivity and spatial resolution and in the far-IR, at wavelengths > 100μm, the sparsity of data.

With ISO and, especially, Spitzer space telescopes this situation has recently improved, and will improve more so in the near future with the recent launch of Herschel and ALMA beginning to take form. So we touch upon here some of the galaxy physical properties that have been determined from the dust IR emission.

PAH emission in the Mid-IR As mentioned in section 2, the 5-20μm mid-infrared spectrum of galaxies is generally dominated by broad emission features arising from large molecules, polycyclic aromatic hydrocarbons (see e.g. Smith et al. 2007). Underlying these features is the stellar continuum at short wavelengths and hot dust emission. Confusing the interpretation of the emission features are strong ionic emission lines arising from species such as Ne⁺ and Ne⁺⁺ and strong, broad absorption features from silicate grains at 9.8μm  and 18μm.

A recent tool, PAHFIT, has been developed to decompose the mid-infrared spectra into its stellar, PAH, dust continuum, and line emission constituents, using functional forms and templates for the features in this wavelength range (Smith et al. 2007). An example of this can be seen in figure 25. The PAH feature luminosity has been used as star formation rate tracers (see section 6.2.4), and the relative strength of these features to the continuum have been found to be strongly linked to the presence of AGN (see e.g. Spoon et al. 2007, and below), and to the gas phase metallicity (see e.g. Smith et al. 2007). The relative strengths of these features can also be used to diagnose the mean size and ionization state of the PAHs, which is related to the average radiation field and dust size distribution (Draine and Li 2007a).

Diagnosing the energy source in ULIRGs Due to the high obscuration by dust in IR bright galaxies, especially ultra luminous IR galaxies (ULIRGs), diagnosing the dominant heating source is problematic. The diagram put forward by Spoon et al. (2007) helps resolve this issue by using the strength of the strong silicate absorption feature that is determined from fitting the mid-IR SED (as discussed above in Section 6.2.2) in association with the equivalent width of the PAH features. This diagram cleanly separates different classes of ULIRGs, from obvious Seyfert galaxies, strongly starbursting galaxies, and to deeply buried AGN ULIRGs and represents one of the strengths of IR SED fitting, extracting information from objects which are heavily obscured at shorter wavelengths.

Dust masses One of the more important properties obtained by fitting the IR SED is the dust mass. Through fitting of the far-IR SED the temperature(s) and the relative contributions of the different dust components that make up the SED can be constrained. Then, using knowledge of the emissivity per unit mass of dust, the total dust mass (M_d ) can be determined, using an equation such as (based on Dunne and Eales 2001);

(5)

with L₈₅₀ the 850μm luminosity, and N_k and T_k the relative contribution and temperature of dust component k. The sum of dust components is usually limited (≤ 3) by the sparse observational points at long wavelengths, but can also be represented by an integral of temperatures, parametrized by the strength of the heating radiation field (such as used by, e.g. Dale and Helou 2002; Draine and Li 2007a). κ_d (850) is the dust mass opacity coefficient, taken to be 0.077 m²kg^-1 by Dunne et al. (2000); Dunne and Eales (2001), an intermediate value between graphite and silicate. It is generally with this parameter that most of the uncertainties in determining dust masses remain.

Longer wavelength fluxes (> 300μm, such as 850μm) are preferable to shorter wavelengths when determining dust masses as these sample the Rayleigh-Jeans part of the Planck curve, where the flux is least sensitive to temperature. Longer wavelengths are also more sensitive to the mass of the emitting material, as they are sensitive to cold dust as well as warm.

Clear examples of fitting the far IR SED using simple, emissivity-modified black-bodies and determining the total dust masses can be found in Dunne et al. (2000),Dunne and Eales (2001) and more recently in Clements, Dunne, and Eales (2009) (see also da Cunha et al. 2010, Section 6.3 below). These works detail nicely the pertinent issues with both the data and fitting the far-IR SEDs. One of the best examples of determining the total dust mass, as well as other parameters, using the full IR SED was done by Draine et al. (2007b). Their physically based SED models (described in detail in Draine et al. 2007b) were fitted to the far-IR SEDs of galaxies from the SINGS sample, and gave determinations of the total dust mass, PAH fraction and information on the interstellar radiation field heating the dust. They found that dust in spiral galaxies resembled that found in the local Milky Way ISM, with similar dust-to-gas ratios, and that generally it is the diffuse ISM that dominates the total IR power, excluding strong starbursting systems. These results thus confirmed the earlier ISO discoveries (see the review by Sauvage, Tuffs, and Popescu 2005). Note also that even earlier detailed radiative transfer modelling of individual galaxies had pointed to the dominance of the diffuse component (Popescu et al. 2000).

Sub-mm excess emission SED fitting can not only return physical properties, but can also indicate where our current knowledge is failing. As mentioned above, the long wavelength dust emission is a good handle for the total dust mass. However, when fitting the IR SED of several dwarf galaxies it has been found that the sub-mm flux is in excess to a standard cool dust-body emission, requiring additional dust components at a unreasonably low temperatures ( 7 K) to fit the SED (Lisenfeld et al. 2002; Israel et al. 2010, e.g.). While very cold large grains could be one possible cause, other suggestions have included small stochastic grains that spend most of their time at cold temperatures (Lisenfeld et al. 2002), rotating dust grains (Israel et al. 2010), or some modification of the dust emissivity at these wavelengths or temperatures (Draine and Lee 1984; Weingartner and Draine 2001). Either way until this issue is resolved on the cause of this excess, the dust mass of these dwarf galaxies such as NGC 1569 will have large uncertainties. It is hoped that telescopes such as Herschel and ALMA may find more of these objects in the near future and help find the cause of this excess emission.

6.2.3 Dust in the UV to IR

The infrared-to-ultraviolet ratio is a coarse measure of dust extinction in the ultraviolet, and thus should be related to the amount of reddening in ultraviolet spectra. Indeed, starbursting galaxies follow a tight correlation between the ratio of infrared-to-ultraviolet emission and the ultraviolet spectral slope (e.g. Calzetti 1997; Meurer, Heckman, and Calzetti 1999). Compared to the relation defined by starbursts, normal star-forming galaxies are offset to redder ultraviolet spectral slopes, exhibit lower infrared-to-ultraviolet ratios, and show significantly larger scatter (Kong et al. 2004; Buat et al. 2005; Burgarella, Buat, and Iglesias-Páramo 2005; Seibert et al. 2005; Cortese et al. 2006; Boissier et al. 2007; Gil de Paz et al. 2007; Dale et al. 2007). Offsets from the locus formed by starbursting and normal star-forming galaxies can be particularly pronounced for systems lacking significant current star formation, such as elliptical galaxies, systems for which the luminosity is more dominated by a passively evolving older, redder stellar population.

Using a sample of 1000 galaxies with spectroscopy from the SDSS and homogeneous photometric coverage from the UV to 24μm from SDSS and the Galex and Spitzer satellites, Johnson et al. (2007a) found that the sample galaxies span a plane in the three-dimensional space of NUV-3.6μm colour, D_n(4000) index (as defined by Balogh et al. 1999), and infrared excess, IRX (=L_IR/L_FUV ). The three-dimensional relation can be expressed in terms of empirical functions, where IRX is a function of NUV-3.6μm (or more weakly with other colours) and D_n (4000). They suggest that this relation can be explained primarily through SFH and dust attenuation, with both acting to steepen the optical-UV slope (as measured by the NUV-3.6μm color), but only attenuation increasing the IR flux and hence IRX (Johnson et al. 2006).

A similar analysis was presented at the workshop by D. Dale using the LVL survey (see Section 3.3.1), which consists of a statistically complete set of star-forming galaxies, nearly two-thirds of which are dwarf/irregular systems. Figure 26 shows the ratio of far-ultraviolet-to-near-infrared luminosity as a function of the (perpendicular) distance from the starburst curve (e.g. Calzetti 1997; Meurer, Heckman, and Calzetti 1999) for the LVL galaxies, with the far-ultraviolet emission is corrected for attenuation using the infrared-to-ultraviolet-based recipe formulated in Buat et al. (2005). By correcting for dust, the FUV/3.6 μm ratio measures only the ratio of past-to-present star formation, sometimes referred to as the birthrate parameter (see also, for example, Boselli et al. 2001; Cortese et al. 2006). This ratio represents the birthrate parameter since the far-ultraviolet traces star formation over 100 Myr timescales whereas the near-infrared probes the total stellar mass built up over much longer timescales. This plot is as such a compression of the plane discussed by Johnson et al. (2007a), and shows a clear trend, with lower birthrate systems exhibiting larger distances from the starburst trend, consistent with the study of Kong et al. (2004). To further quantify this, theoretical models with solar metallicity, 1 M_⊙ yr^-1 continuous star formation curves assuming a double power law initial mass function, with α_1,IMF = 1.3 for 0.1 < m∕M_⊙ < 0.5 and α_2,IMF = 2.3 for 0.5 < m∕M_⊙ < 100 were run (Vázquez and Leitherer 2005) and were matched with their determined FUV/3.6 μm ratio on the right axis, demonstrating that those with the oldest SFH (i.e. lowest birthrate parameters) lie furthest from the theoretical starburst curve.

6.2.4 Star Formation Rate from the IR

One of the most commonly extracted galaxy properties from the IR is the star formation rate. As discussed above, recently formed stellar populations tend to be more obscured than older stellar populations. They are also more luminous and emit more in the ultraviolet where dust opacity peaks, and thus dust emission is in principle a good tracer of recent star formation, assuming a simple calorimetric situation. It is these assumptions that lead to the widely-used Kennicutt (1998) relation between total IR luminosity (8–1000μm) and star formation rate.

Of course the situation is more complex than this, as discussed in the same work. A range of ages contribute to dust heating (Kennicutt et al. 2009), and star forming regions in galaxies suffer a range of obscurations, from totally obscured (ULIRGs) to unobscured (blue compact dwarfs). It is for this reason that this relation has been re-examined and empirically calibrated with new data from Spitzer. In general, all recent studies have found that the IR can be used as a SFR indicator, albeit without a direct one-to-one connection. Complications arise due to the correlation of SFR, luminosity, and galaxy gas and dust masses, and possible non-linearities due to metallicity effects (Wu et al. 2005).

More specifically, Calzetti et al. (2007) using spatially resolved observations, found strong correlations between the 24μm  and Pα luminosity densities (a proxy for SFR, assuming little attenuation in the near-IR), and a correlation between the 8μm and Pα luminosity densities, though this failed at low metallicities. Using these, they were able to create new calibrations for SFR versus 24 μm  luminosity, and SFR versus 24 μm and observed Hα luminosities, with the latter relation accounting better for the escaping radiation not accounted for by the dust emission. Rieke et al. (2009) took this further, showing that for higher IR luminosity objects, Pα was no longer a good tracer for SFR as even it was obscured, and gave their own calibrations for SFR with the IR luminosities.

On galactic scales, Zhu et al. (2008) showed with a larger galaxy sample from SWIRE that the Calzetti et al. (2007) relations between 24μm luminosity and extinction corrected Hα luminosity hold, and thus L(24μm ) is a good SFR indicator. In addition they also showed that 24μm is well correlated with 70μm and total IR luminosities, indicating that these too can be used as SFR indicators, albeit with larger scatter.

The 8μm  (and other PAH bands) and longer wavelength observations, such as the Spitzer 160 μm band, are observed to be correlated with each other (Bendo et al. 2008), and are thought to be more associated with the cooler diffuse ISM. While the diffuse ISM is heated by the radiation from star forming regions, it is also heated by the diffuse radiation field from older stars, meaning that these bands are not as strong SFR traces, especially at low SFRs.