ARlogo Annu. Rev. Astron. Astrophys. 2013. 51:393-455
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6.1. Total Dust Attenuation

There exist four primary techniques for measuring dust attenuation in galaxies. (1) As the obscuring effects of dust increase with decreasing wavelength, multi-wavelength analysis (including moderate-resolution spectra) of the UV-NIR SED can yield constraints on the total dust attenuation. (2) One can exploit the fact that the Balmer line ratio Hα/Hβ (sometimes referred to as the Balmer decrement) in the absence of dust can be computed from first principles and depends only weakly on the temperature of the gas (Osterbrock 1989). Comparison of the observed to the intrinsic ratio provides a measurement of the attenuation toward H ii regions. (3) Energy conservation demands that whatever photons are absorbed in the UV/optical must be re-radiated in the IR. The ratio of IR to UV luminosity (often referred to as `IRX') therefore provides a measure of the total dust absorption. (4) A sufficiently luminous background source with a known intrinsic spectrum can provide a constraint on the attenuation in the foreground galaxy. This last technique will not be discussed herein, as it falls outside the scope of what one can learn from the SEDs of galaxies.

Techniques (1)-(3) provide complementary constraints on the dust within galaxies. This was most clearly demonstrated in the work of Calzetti, Kinney & Storchi-Bergmann (1994), who analyzed the reddening in a sample of 39 starburst and blue compact galaxies from both the Balmer line ratio Hα/Hβ and the slope of the UV continuum. Calzetti and collaborators found that the dust optical depth measured from the Balmer lines was nearly twice that estimated from the continuum (sometimes referred to as the `1:2' rule). They speculated that this could occur if young hot stars are embedded in dusty natal clouds while older stars are subject to attenuation only from the diffuse ISM. Charlot & Fall (2000) later provided a detailed model for dust absorption which adopted this physical picture wherein young stars are embedded in their natal dusty clouds and, in addition, all stars experience dust attenuation due to the diffuse ISM. In this two-component model one must specify a transition time, after which the natal cloud is dispersed (typically taken to be 107 yr), and attenuation curves for both the natal cloud and the diffuse ISM. In the standard implementation, both curves are taken to be power-laws with the same exponent (τd ∝ λ-0.7) and the normalization of the natal cloud attenuation curve is taken to be twice that of the diffuse ISM. The Charlot & Fall dust model is widely employed when modeling dusty SEDs.

In subsequent work, Meurer, Heckman & Calzetti (1999) compared the UV continuum slope, β, to the ratio between FIR and UV flux, log(LIR / LUV) ≡ IRX, and concluded that the starburst galaxies formed a well-defined sequence in the IRX-β plane (see Figure 12). With additional assumptions about the underlying stellar populations and dust attenuation curve, these authors were able to relate IRX (and hence β) to the total FUV dust attenuation. The resulting `Meurer relation' has experienced widespread use for estimating the dust attenuation in distant galaxies for which only measurements of β are available. However, many subsequent studies have cast doubt on the practice of using β to estimate UV dust attenuation. Bell et al. (2002) noted that the relationship between β and UV attenuation measured in H ii regions in the LMC differed from the Meurer relation. Kong et al. (2004) demonstrated that, while dust content was the main variable responsible for the Meurer relation, other stellar population parameters, particularly the recent SFH, drive galaxies to other locations in the IRX-β plane (see also Boquien et al. 2012). The underlying extinction curve and star-dust geometry also play an important role in determining where galaxies lie in this plane (Charlot & Fall 2000, Kong et al. 2004, Panuzzo et al. 2007, Conroy, Schiminovich & Blanton 2010).

Figure 12

Figure 12. The IRX-β relation at z = 0 from the Local Volume Legacy Survey (LVL; Dale et al. 2009, left panel) and at z ~ 2 from Reddy et al. (2010) (right panel). The starburst (Meurer) relation is shown as a dotted (solid) line in the left (right) panel. In the left panel, symbols indicate starburst and star-forming galaxies, along with galaxies split by morphological type. In the right panel, symbols indicate galaxies selected in several different ways, either as having a young light-weighted age, high bolometric luminosity, or on the basis of x-ray or 24 μm fluxes. There is an overall trend that redder UV slopes correspond to higher IRX values. However, the more striking impression is the tremendous scatter in IRX at fixed β, especially in the region of the diagram where most galaxies reside, at -2 < β < -1.

Based on UV-IR photometry of 1000 galaxies, Johnson et al. (2007) cast further doubt on the utility of the IRX-β relation for estimating dust content. Their conclusion rested partly on the observation that the relation defined by normal star-forming galaxies is so steep that even small errors in β will translate into large errors on IRX. Figure 12 shows the IRX-β relation for galaxies from the Local Volume Legacy Survey (Dale et al. 2009), and the IRX-β relation for z ~ 2 galaxies from Reddy et al. (2010). It is clear that, while galaxies of a particular type define their own IRX-β relations, the overall galaxy population presents a complicated picture. Fortunately, as multi-wavelength datasets become increasingly common, the estimation of dust content from crude measures such as the IRX-β relation will give way to more robust techniques.

SED fitting of UV-NIR data has become remarkably common in the past decade. In nearly all cases the dust content is a parameter included in the fit, although the derived dust opacities are rarely discussed. The reason for this seems to be the fact that the dust opacity is a relatively poorly constrained quantity when data only reach the NIR. As an example of the difficulty in constraining the dust opacity from broadband data, Salim et al. (2007) fit UV-NIR photometry to models and were able to recover V-band dust opacities with an uncertainty of ~ 0.4 mag. Furthermore, there was only a weak correlation between the dust opacity derived from broadband data and the opacity derived from emission lines via Brinchmann et al. (2004). Some of the difference can be attributed to aperture effects and real differences in the opacity measured from emission lines and stellar continua, but overall the weak correlation confirms that dust content measured from broadband data is quite uncertain. Poorly constrained dust opacities appears to be a generic result of the modeling of UV-NIR broadband SEDs (e.g., Papovich, Dickinson & Ferguson 2001, Shapley et al. 2006, Kriek et al. 2008, Taylor et al. 2011).

Broadband UV-NIR data do not provide strong constraints on dust attenuation because of the well-known degeneracy between age and dust (e.g., Papovich, Dickinson & Ferguson 2001). This degeneracy can be broken, and stronger constraints on the dust opacity can be obtained, when either spectroscopic or FIR data are available. Spectroscopic data offer an estimate of the mean stellar age and metallicity independent of dust content because narrow spectroscopic features are relatively immune to overall changes in the continuum shape. Kauffmann et al. (2003) exploited this technique to measure mean ages of ~ 105 SDSS galaxies from Hδ and the 4000 Å break. With the ages thus constrained, an estimate of the dust attenuation could be obtained by comparing the model colors to the observed ones. This study was limited primarily by the fact that the SDSS spectra sample a modest fraction of the total galaxy, and so a correction must be made for this aperture effect (ongoing and future planned IFU surveys such as CALIFA and MaNGA will remedy this limitation). Narrowband photometric surveys also offer the promise of separately constraining age and dust attenuation, primarily because of the strongly age-sensitive Dn4000 spectral feature, which is so strong that it can be probed with low resolution data (e.g., Whitaker et al. 2010, Perez-Gonzalez et al. 2012). FIR data can also provide a robust measurement of the total dust attenuation because they significantly reduce the degeneracy between age and dust (e.g., Burgarella, Buat & Iglesias-Páramo 2005, Noll et al. 2009a).

Wuyts et al. (2007) and Williams et al. (2009) pioneered the use of restframe optical-NIR color-color diagrams (specifically U - V vs. V - J; commonly referred to as the UVJ diagram) to efficiently separate quiescent and star-forming galaxies. The UVJ diagram has since become a popular tool for separating these two galaxy types, especially at high-redshift where data are limited. In a broad sense, the UVJ diagram allows one to break the age-dust degeneracy, but only in the sense of separating quiescent and dusty star-forming galaxies. Within the star-forming sequence, the age-dust degeneracy is still manifest when only broadband information is available.

Extremely blue UV continua can place strong constraints on the amount of dust in the system. Bouwens et al. (2012) and Finkelstein et al. (2012) measured the UV continuum slopes of high-redshift galaxies and found that β systematically decreases toward higher redshift and fainter galaxy luminosities. At the highest redshifts and faintest luminosities they find -2.0 < β < -2.5, which not only suggests that these galaxies are dust-free but also begins to place interesting constraints on their stellar populations. The models of Schaerer (2003) reach such blue slopes only at very young ages ( ~ 106 yr) and/or very low metallicities (< 10-3 Z), and the inclusion of nebular continuum emission, which presumably must be present whenever stars of these young ages are still alive, sets a lower limit to the UV continuum slope of -2.5 < β < -3.0, depending on the details of the SFH. Clearly more data probing the restframe UV at very high redshifts would be valuable.

6.2. Constraints on the Attenuation Curve

Calzetti, Kinney & Storchi-Bergmann (1994) estimated a mean attenuation curve from 39 starburst and blue compact galaxies based on UV-optical spectra. By assuming that their sample was comprised of galaxies with the same underlying stellar populations, they were able to construct average attenuation curves by comparing galaxies with high and low Balmer line ratios, i.e., by comparing dusty to dust-free galaxies. The resulting average attenuation curve, measured over ≈ 1200 Å -8000 Å, was greyer (shallower) than either the MW or LMC extinction curve and lacked the broad 2175 Å dust feature visible in the MW and LMC. The derived curve is now referred to as the "Calzetti attenuation law" and is widely used when modeling the broadband SEDs of galaxies.

The Calzetti law was estimated from a relatively small sample of unusual (i.e., starburst and blue compact) galaxies at z = 0 and so one may wonder to what extent it is applicable to other systems. As noted in the previous section, the IRX-β relation is sensitive to the attenuation curve. The large range in β at a fixed IRX, evident in Figure 12, suggests considerable variation in the attenuation curve, but interpretation of the IRX-β plane is complicated by the additional variables affecting IRX and β.

Progress can be made by estimating stellar population parameters such as the SFH and metallicity independently of the dust content (e.g., via narrow spectral features). With such quantities in hand, one can exploit the technique pioneered by Calzetti and collaborators by computing ratios of SEDs of more to less dusty galaxies with the same underlying stellar populations. Johnson et al. (2007) estimated mean attenuation curves in this way for galaxies as a function of the 4000 Å break strength and stellar mass. The curves were constrained from broadband FUV-NIR photometry and were consistent both with a simple power-law, τd ∝ λ-0.7, and with the Calzetti law. Wild et al. (2011) exploited a similar technique using pairs of galaxies with similar gas-phase metallicities, specific star formation rates, and inclinations, and significantly different Balmer decrements to construct attenuation curves from broadband FUV-NIR data. These authors found significant variation in the mean attenuation curve as a function of specific SFR, inclination, and stellar mass surface density, based on a sample of 20,000 z ~ 0 star-forming galaxies. They also found variation in the ratio between dust opacity in the stellar continuum and in the nebular line emission, implying that the `1/2' rule of Calzetti, Kinney & Storchi-Bergmann (1994a) — one unit of continuum opacity for ever two units of line opacity — is not universal. Buat et al. (2012) modeled the UV-FIR SEDs of galaxies at 1 < z < 2, allowing for variation in the dust attenuation curve. They found evidence for a steeper attenuation curve (i.e., faster rise in the UV) than the Calzetti law in 20-40% of their sample.

6.2.1. The 2175 Å dust feature The absence of the 2175 Å dust feature from the Calzetti attenuation law is striking given its ubiquity in the MW and LMCWitt & Gordon (2000) were able to reproduce the Calzetti law in their radiative transfer models only by assuming SMC-type dust, i.e., by adopting an underlying extinction curve that lacked the 2175 Å dust feature. In contrast, Granato et al. (2000) were able to reproduce the Calzetti law in their radiative transfer models with MW-type dust. In their model the star-dust geometry plays a central role in shaping the starburst attenuation curve. Their molecular clouds are optically thick and so the attenuation curve is determined primarily by the fraction of stars inside molecular clouds as a function of age (see also Panuzzo et al. 2007). Fischera & Dopita (2011) were able to reproduce a Calzetti-like attenuation curve if the carrier responsible for the 2175 Å feature (e.g., PAHs) was destroyed at high column density.

In all radiative transfer dust models the expectation is that normal star-forming galaxies should show evidence for the 2175 Å dust feature provided that the underlying grain population is similar to the MW or LMC. Owing to a paucity of restframe UV spectra of star-forming galaxies, it has proven difficult to verify this expectation. Burgarella, Buat & Iglesias-Páramo (2005) analyzed the UV-FIR SEDs of 180 star-forming galaxies and concluded that the data required an attenuation curve with a 2175 Å dust feature that was on average weaker than observed in the MW extinction curve. Noll et al. (2009b) presented stacked restframe UV spectra of z ~ 2 star-forming galaxies and found strong evidence for the presence of the 2175 Å dust feature in a subsample of their objects. Conroy, Schiminovich & Blanton (2010) analyzed UV-NIR photometry of z ~ 0 star-forming galaxies as a function of inclination and found evidence for a 2175 Å dust feature with a strength slightly weaker than observed in the MW extinction curve. Hoversten et al. (2011) analyzed medium band UV photometry from the Swift UV/Optical Telescope, and found evidence for a prominent 2175 Å bump in M81. Wild et al. (2011) found evidence in their derived attenuation curves for the presence of the 2175 Å dust feature, with a slight tendency for galaxies with higher specific SFRs to have lower bump strengths. Wijesinghe et al. (2011) compared dust-corrected SFRs estimated from Hα and the UV and found agreement only when the 2175 Å feature was removed from the attenuation curve, but these authors did not consider variation in the shape of the attenuation curve. Buat et al. (2012) found evidence that the 2175 Å dust feature is present in 20% of their sample, with an amplitude that is half the strength found in the MW extinction curve. Similar to Wild et al., they found an anti-correlation between bump strength and specific SFR. The emerging consensus appears to be that the 2175 Å dust feature is present in the typical star-forming galaxy over the redshift range 0 < z < 2, with a strength that is generally lower than in the MW extinction curve, and that increases with increasing inclination and decreasing specific SFR. The absence of the dust feature in the Calzetti law may then simply be a reflection of the fact that the galaxies in the Calzetti sample have unusually high specific SFRs. An outstanding question is whether these trends are due to varying star-dust geometries or changes in the underlying grain population. As emphasized in Conroy, Schiminovich & Blanton (2010) and elsewhere, these results have consequences for interpreting the IRX-β relation, since β is frequently measured over a wavelength range that includes the 2175 Å feature.

6.3. Physical Dust Properties

The IR emission by dust grains provides strong constraints on a variety of physical properties of a galaxy including the bolometric luminosity, dust temperature(s), dust mass, and relative abundance of PAH molecules (or, more generally, the grain size distribution). A constraint on the bolometric luminosity helps to break the age-dust degeneracy in the UV-NIR, as discussed in the previous section. The other parameters provide clues to the nature of dust in galaxies and its spatial relation to the stars and gas.

It has long been recognized that constraints on the dust mass and dust temperatures required data beyond the peak in the thermal dust emission spectrum at ~ 100 μm . The SCUBA bolometer array at the James Clerk Maxwell Telescope, operating at 450 μm and 850 μm , has been extremely influential in this field, and now the SPIRE instrument onboard the Herschel Space Observatory, operating at 250-500 μm , promises to revolutionize the field by dramatically increasing sample sizes over a wide range in redshifts. With data obtained for the SCUBA Local Universe Galaxy Survey, Dunne et al. (2000) and Dunne & Eales (2001) constrained dust masses and temperatures for 104 nearby galaxies. The data favored models that contained both cold and warm dust components (at ~ 20K and ~ 40K, respectively). They also found that dust masses estimated with single-temperature models were on average lower by a factor of ~ 2 compared to two-temperature models, and the two-temperature dust masses yielded dust-to-gas ratios in agreement with measurements in the Galaxy.

Draine et al. (2007) presented a thorough analysis of the IR SEDs of galaxies from the SINGS survey of 65 nearby galaxies. These authors analyzed data from Spitzer, IRAS, and SCUBA with the physical dust models of Draine & Li (2007). The model considers grain populations exposed to a variety of starlight intensities and includes both thermal emission and single photon heating of dust particles. In addition, the fraction of dust mass contained in PAH molecules is a free variable. Draine et al. confirmed the results of previous work that the sub-mm data, provided by SCUBA, were essential for deriving dust masses with an uncertainty of < 50%. They also derived strong constraints on the fraction of dust mass in PAHs, the interstellar radiation field strength in the diffuse ISM, and the flux-weighted mean radiation field strength averaged over the galaxy. The well-sampled spectral coverage from the mid-IR through the sub-mm was essential in order to separately constrain each of these components.

Dale et al. (2012) analyzed FIR and sub-mm photometry for SINGS galaxies from Herschel in conjunction with previously available 2MASS, Spitzer, IRAS, ISO, and SCUBA data. These authors modeled the SEDs with the Draine & Li (2007) dust model, both with and without the Herschel data. They found modest differences (factors of ≈ 1.6 on average) in the best-fit dust masses, PAH mass fractions, and fraction of dust emission arising from the diffuse ISM when the FIR and sub-mm data were either included or excluded. They also demonstrated that dust masses estimated via simple modified blackbody fits significantly underestimated the dust masses (by factors of ≈ 3 in the worst cases), with the underestimation becoming more severe as bluer wavelengths were included in the fits. The Herschel data are of such high quality that simplistic, modified blackbody dust models are no longer capable of providing adequate fits to the data.

da Cunha, Charlot & Elbaz (2008) developed a phenomenological model for the UV-FIR SEDs of galaxies that is based on the Bruzual & Charlot (2003) SPS models for the starlight, the Charlot & Fall (2000) dust attenuation model, and dust emission comprised of multiple components including an empirical spectrum for the PAH emission, warm and cold thermal dust emission, and emission from stochastically heated grains (see Figure 13). Based on tests with mock galaxies, they concluded that a variety of parameters could be constrained within the context of their model, including the temperature of the cold dust component, the fractional contribution of the cold dust to the total FIR emission, and the total dust mass. They analyzed the same SINGS galaxies as in Draine et al. and derived dust masses that agreed to within 50%, demonstrating that dust masses can be reliably measured with reasonably well-sampled mid-IR, FIR, and sub-mm data.

Figure 13

Figure 13. Model fit to the FUV through FIR SED of NGC 337, from da Cunha, Charlot & Elbaz (2008). The black line is the best-fit model. Also shown is the unattenuated model starlight (blue line) and the dust emission separated into dust in the diffuse ISM (solid green line) and dust in birth clouds (dotted green line). Figure courtesy of E. da Cunha.

Galliano, Dwek & Chanial (2008) employed the dust model of Zubko, Dwek & Arendt (2004) to constrain a variety of parameters including the total dust mass, fraction of dust mass in PAHs, fraction of dust luminosity originating from photodissociation regions (PDRs), and the gas-phase metallicity. These authors measured these and other parameters for 35 galaxies with optical, IR, and sub-mm photometry and mid-IR spectroscopy. Although no direct comparison was made with the results from Draine et al. (2007), there appears to be a quantitative difference in the derived PAH mass fractions. As discussed extensively in Draine & Li (2007), the optical properties of the PAH molecules are uncertain and have in many cases been tuned to fit extragalactic data. It would therefore be valuable to compare the results obtained from dust models that assume different treatments of the uncertain PAH properties.

6.4. Cosmic Evolution of IR SEDs

Measuring the cosmic evolution of IR SEDs is important not only for constraining models of galaxy evolution but also because local IR SED templates are frequently employed to interpret high-redshift data. For example, the local templates are often used to convert 24 μm observations of high-redshift galaxies into SFRs. If IR SEDs at fixed Lbol evolve with time then it would considerably complicate the interpretation of higher redshift data.

Pope et al. (2006) presented evidence that the SEDs of ULIRGs at z ~ 2 peak at longer wavelengths than local ULIRGs, implying that the dust temperature in high-redshift ULIRGs is on average ~ 5K cooler than local ULIRGs. Muzzin et al. (2010) analyzed high-quality data for two z ~ 2 ULIRGs and found that these galaxies contained colder dust than local ULIRGs, in agreement with Pope et al. (2006). Muzzin et al. showed that the SED shapes of their ULIRGs were well-fit by the z = 0 (Chary & Elbaz 2001) templates that were an order of magnitude less luminous than their z ~ 2 galaxies. In other words, the z ~ 2 ULIRGs had SED shapes that were similar to local LIRGs. Exploiting the power of Herschel data, Hwang et al. (2010) estimated dust temperatures by fitting modified blackbodies to the data, and found evidence for slightly cooler dust temperatures at z ~ 1, by 2-5 K on average, for galaxies with LIR > 1011L. Daddi et al. (2007) compared restframe 8 μm luminosities of z ~ 2 galaxies to local templates and found evidence for excess mid-IR emission for galaxies with L8 μm > 1011L. This mid-IR excess problem was confirmed by Papovich et al. (2007) and later by Elbaz et al. (2010) with Herschel data. It is noteworthy that the problem only appears at z>1.5. Bolometrically luminous high-redshift galaxies thus have colder dust and more flux in the mid-IR compared to galaxies at the same Lbol at z = 0. The mid-IR excess problem has important implications for the common practice of estimating SFRs for galaxies at z > 2 with Spitzer 24 μm observations (i.e., restframe ~ 8 μm ). The sign of the excess is such that SFRs estimated by extrapolating observed 24 μm flux with local templates will tend to overestimate the true SFRs, by factors of several in the most extreme cases (e.g., Papovich et al. 2007).

Elbaz et al. (2011) investigated the origin of the differences between high and low redshift IR SEDs with very deep Herschel observations. They argued that it is the distribution of SED types that is changing at high luminosity as a function of redshift. At low redshift, high luminosity systems (i.e., ULIRGs) are predominantly star-bursting and compact, while at higher redshift ULIRGs are mostly the high-luminosity extension of normal star-forming galaxies. Local ULIRGs therefore have hotter dust temperatures and a depressed emission component from PAHs in the mid-IR compared to distant ULIRGs because the former are compact starbursts while the latter are normal, extended star-forming galaxies (see also Rujopakarn et al. 2012 who reached similar conclusions). The physical origin of this result is not yet fully understood, but a plausible explanation is that compact starbursts have harder and more intense radiation fields. The radiation field obviously has a direct influence on the dust temperature, and it may also modulate the dust mass fraction in PAHs and therefore the mid-IR luminosity (Voit 1992, Madden et al. 2006, Draine et al. 2007).

6.5. Summary

The Calzetti attenuation curve works remarkably well at describing the mean attenuation properties of star-forming galaxies over most of cosmic history. However, closer scrutiny of the data reveals variation in the attenuation curve of galaxies as a function of galaxy properties, as expected on theoretical grounds. In contrast to the Calzetti attenuation curve for starburst galaxies, the 2175 Å dust feature is apparently common in normal star-forming galaxies, with a strength that is weaker than observed in the MW extinction curve. The IRX-β relation should be used with caution, as there is evidently no universal relation for all galaxies. In addition, the relation is so steep over the range in β where most galaxies reside that estimating dust opacity in this way is highly unreliable. Dust masses can be measured to an accuracy of ~ 50% when FIR and sub-mm data are available. Physical dust models, such as the model of Draine & Li (2007), are capable of extracting a variety of parameters from the global SEDs of galaxies, including the fraction of dust mass in PAHs, the fraction of dust emission due to PDRs vs. the diffuse ISM, and the typical interstellar radiation field strength heating the dust grains (or, alternatively, the typical dust temperature). Further work appears to be needed to sort out which derived parameters are robust, and which are dependent on uncertain components of the model. Below Lbol ~ 1011 L, the IR SEDs of galaxies evolve little over the interval 0 < z < 2. At higher luminosities there is a marked shift such that high redshift ULIRGs have more mid-IR flux and a colder dust component that peaks at longer wavelengths. A plausible explanation for this trend is that ULIRGs at high-redshift are at the massive end of the normal star-forming galaxy sequence, while ULIRGs in the local universe are unusual, compact, star-bursting systems.

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