The Dust Opacity of Star‐forming Galaxies

A pointlike source (a star or an active galactic nucleus [AGN]) behind a screen of dust is the simplest source/dust geometry, and equation (1) has the solution

where I_a(λ) and I_o(λ) are the attenuated (observed) and intrinsic radiation intensity, and τ(λ) = ∫κ_λds = 0.921A^o_λ is the optical depth of the dust screen.¹ The total‐to‐selective extinction, i.e., the part of the optical depth that depends only on the physics of the dust grains and, therefore, only on the wavelength, is often expressed as k(λ) = A^o_λ/E(B−V). The color excess E(B−V) is defined as A^o(B) - A^o(V), hence k(B) - k(V) = 1.

Although many studies traditionally employ a "mean Galactic extinction curve" to correct Galactic and extragalactic sources for the effects of dust obscuration, the well‐studied Milky Way interstellar extinction has been shown to be spatially variable and highly dependent on the dust grain environment along the line of sight (see reviews of Mathis 1990 and Fitzpatrick 1999). Cardelli, Clayton, & Mathis (1989) demonstrated that the variations can be effectively parameterized by the total‐to‐selective extinction at V, R(V) = A^o_V/E(B−V). Both the steepness of the far‐UV (λ≲0.3 μm) rise of the extinction curve and the strength of the 0.2175 μm absorption feature decrease for increasing R(V), as schematically shown in Figure 1 (Cardelli et al. 1989). Most sight lines have R(V) ≈ 2–6, with the low values corresponding to the diffuse ISM [for which R(V) = 3.1 is a reasonable average value; e.g., Rieke & Lebofsky 1985] and the high values pertaining to dense clouds. The large values of R(V) in dense clouds, usually accompanied by a gray extinction curve, are consistent with dust grains having systematically larger sizes than in the diffuse medium (Cardelli et al. 1989).

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The only galaxies external to the Milky Way for which some measurements of the UV extinction curves exist are the Magellanic Clouds (Fig. 1; Koornneef & Code 1981; Nandy et al. 1981; Bouchet et al. 1985; Fitzpatrick 1986; Gordon & Clayton 1998; Misselt, Clayton, & Gordon 1999), although tentative measurements in M31 have been made (Bianchi et al. 1996). Despite the large variation of extinction properties found within each of the Magellanic Clouds (e.g., Fitzpatrick 1986; Lequeux et al. 1982; Misselt et al. 1999), the average curves of the Clouds appear to have some intrinsic differences from the average Milky Way curve, including a smaller R(V) [R(V)≃2.4–2.9; Gordon & Clayton 1998; Misselt et al. 1999]. This has been interpreted as an effect of the lower metallicity in the Clouds, which causes the molecular clouds to be more diffuse (Pak et al. 1998) and, possibly, to produce on average smaller dust grains (Misselt et al. 1999). The weak or absent UV absorption "bump" at 0.2175 μm in the extinction curves of the LMC 30 Doradus region and of the SMC bar, respectively (Fig. 1), could be related to local processes in these regions, possibly to the ongoing star formation activity (Fitzpatrick 1986; Gordon & Clayton 1998; Misselt et al. 1999; Reach et al. 2000). Although the bump carriers have not been positively identified yet (e.g., Reach et al. 2000), mid‐ and far‐infrared studies of star‐forming regions in the Milky Way have provided evidence that the environmental UV energy density level affects the dust properties, such as the grain size distribution, via destruction or coagulation, and/or the dust physical characteristics, via ionization state changes (Boulanger et al. 1988; Cesarsky et al. 1996). Thus, the environmental UV energy density appears to play as important a role as the metallicity in shaping the extinction curve. If confirmed by further observations, this hypothesis may explain the general absence of a 0.2175 μm absorption bump in the extinction curve of starburst galaxies (§ 4.1) and may partially account for its weakness in QSOs (e.g., Jura 1977; Sprayberry & Foltz 1992; Yamamoto & Vansevicius 1999).

In addition to absorbing stellar light, dust manifests itself through emission and absorption features and continuum emission at λ>1 μm. Features in the near/mid‐IR include, among others, the silicate absorption at 9.7 and 18 μm, H₂O and CO₂ ice absorption at 3.0 and 4.3 μm (see Lutz et al. 1996 and Schutte et al. 1998) for a list of other absorption features), and the emission bands at 3.3, 6.2, 7.7, 8.6, and 11.3 μm (Sellgren 1994, 2001). The continuum emission beyond a few microns and up to ∼40–70 μm is considered to be mainly due to discrete photon heating of very small dust grains, the smallest among which are transiently heated up to ≈1000 K (e.g., Sellgren 1984; Draine & Anderson 1985; Li & Draine 2001); dust heated by massive stars to temperatures greater than 70 K also contributes to the flux in the wavelength region below ∼50 μm, albeit with decreasing filling factor for increasing temperature (Natta & Panagia 1976). Beyond 40–70 μm, the emission is mainly due to dust grains in nearly steady balance with the average heating by starlight; the transition wavelength between predominance of discrete photon heating versus that of nearly steady state depends on the average color temperature of the dust and, thus, on the mean UV energy density level of the galaxy (Mezger, Mathis, & Panagia 1982; Mathis, Mezger, & Panagia 1983; Helou 1986; Chini, Krügel, & Kreysa 1986; Lonsdale‐Persson & Helou 1987; Rowan‐Robinson & Crawford 1989; Désert et al. 1990).

The original dust model of bare graphite and silicate grains (Mathis, Rumpl, & Nordsieck 1977; Draine & Lee 1984) has evolved over time by including more complex grain compositions and extended grain size distributions, to accommodate all the details of the absorption and emission, and the variability of the environment, while at the same time accounting for the constraints imposed by the heavy elements' overall abundance (e.g., Mathis 1996). Polycyclic aromatic hydrocarbons (PAHs; Léger & Puget 1984; Désert et al. 1990; Weingartner & Draine 2001; Sellgren 2001), hydrogenated amorphous carbons (Duley, Jones, & Williams 1989; Furton, Laiho, & Witt 1999), icy and organic refractory mantles (Greenberg 1984, 1989; Tielens 1989; Jenniskens 1993; Greenberg et al. 2000), and composite and/or porous grains (Mathis & Whiffen 1989; Mathis 1996; Wolff, Clayton, & Gibson 1998; Voshchinnikov & Mathis 1999), as well as grain size distributions that significantly depart from the original power‐law model (Kim, Martin, & Hendry 1994; Weingartner & Draine 2001), have all been suggested as possible alternatives/complements to the graphite/silicate model.

In the late 1980s, Disney, Davies, & Phillips (1989) and Valentijn (1990) revived the decade‐long debate on whether galaxy disks are mainly transparent or opaque to dust. Using multiwavelength information and surface brightness versus inclination tests, respectively, the two groups of authors reached the similar conclusion that the disks of galaxies are fairly opaque, with total face‐on extinctions in the B band A_B,f≳1 mag.² These results countered earlier findings, also based on the surface brightness versus inclination tests, that galaxy disks are mostly transparent with face‐on extinctions at B of less than 1 mag (Holmberg 1958; de Vaucouleurs 1959a).

The reason why similar approaches can produce very different results can be found in the complexity of the absolute and relative distribution of stars and dust inside galaxies. When there is a significant departure from the simplest geometry of a point source (a star) behind a homogeneous screen of dust, the dust distribution, rather than the optical depth of the dust layer, becomes the dominant factor in determining the obscuration suffered by the stellar radiation (Natta & Panagia 1984; Witt, Thronson, & Capuano 1992; Calzetti, Kinney, & Storchi‐Bergmann 1994). In particular, differential optical depth effects come into play. If, for instance, the stars are homogeneously mixed with the dust, the shorter the wavelength of the radiation, the smaller the optical depth of the dust layer from which it can emerge; thus, an observer will detect blue light only from the closest outer "skin" of the mixed distribution, while redder light will come from deeper layers. An extreme case is that of infinitely optically thick clumps in front of an extended light distribution: the stellar emission will come only from those lines of sight that do not intersect clumps, and the net result will be an unreddened, albeit dimmer than the original, SED. The scattering component of the extinction curve will also modify the general characteristics of the dust obscuration, as light will be scattered into the line of sight as well as out of it. The net result of all these effects is a general blueing of the emerging SED relative to the foreground homogeneous dust screen case, or, in other words, an often much grayer "effective extinction," even in the presence of large dust optical depths³ (Bruzual, Magris, & Calvet 1988; Witt et al. 1992).

For illustrative purposes, Figures 2 and 3 show how photometric and spectroscopic quantities are affected by the dust geometry for five "toy models." The models represent plane‐parallel geometries of dust and stars (details are given in Natta & Panagia 1984; Calzetti et al. 1994; Wang & Heckman 1996) for (1) the simple case of a homogeneous, nonscattering dust screen foreground to the light source; (2) a homogeneous, scattering dust screen foreground to the light source (e.g., a screen in close proximity to the source, so that scattering into the line of sight becomes an important effect); (3) a Poissonian distribution of clumps in front of the light source, with average number = 10; (4) a homogeneous mixture of dust and emitters; and (5) a homogeneous dust/emitter distribution averaged over all inclination angles, with the UV and ionized gas emission having the same scale height of the dust while the scale height of the optical light gradually increases to twice that of the dust at V and beyond. Models 2–5 include scattering in the calculations.⁴ In all cases, the light source is assumed to be extended and to be represented by a 300 Myr old stellar population undergoing constant star formation, with solar metallicity and a Salpeter IMF in the mass range 0.1–100 M_⊙ (Leitherer et al. 1999).

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The "blueing" effect of geometries more complex than a foreground dust screen is evident from the comparison of the five models. At fixed optical depth τ_V (fixed amount of dust), the reddening of the V−I color of a stellar population induced by a generic geometry of stars and dust will be less, and the effective extinction A_V lower, than that induced by a foreground screen (Figs. 2a and 2b). The same will be true for colors at other wavelengths (Fig. 2), where, again, the foreground nonscattering screen will provide the maximum reddening. For mixtures of dust and stars (models 4 and 5), reddening of colors and effective extinction reach asymptotic values; beyond certain values of the optical depth, an increase in τ_V corresponds to small or negligible changes in colors and A_V. This is due to the fact that the shortest wavelength emission is contributed only by the dust layers closest to the observer. One common consequence of the grayer "effective extinction" caused by complex dust/emitter geometries is that a limited number of diagnostics over a small wavelength range will lead to underestimates of the true galaxy opacity, especially if the actual dust geometry is not known and is a priori assumed to be foreground (Witt et al. 1992).

To aid the comparison with data on local starbursts and high‐redshift star‐forming galaxies (§§ 4 and 5), the models shown in Figure 3 are a function of the ratio of the attenuated‐to‐intrinsic Balmer line ratio

and of the UV spectral slope⁵ β. The luminosity ratios of nebular hydrogen lines, such as Hβ, Hα, Paβ, Brγ, etc., are rather insensitive to the details of the underlying stellar population and of the IMF, being affected at the ∼5%–10% level by variations of the gas physical conditions (e.g., Osterbrock 1989); they represent, therefore, accurate probes of dust reddening and geometry. Table 2 lists the commonly used hydrogen emission line ratios and the differential extinction between each pair. When multiple line ratios widely separated in wavelength are available, they can constrain the dust geometry in the sampled wavelength range. The two drawbacks of using nebular lines are that (1) they are produced by ionizing photons; therefore, an ionizing stellar population needs to be present in the galaxy; and (2) they probe the attenuation of only the ionized gas, and such attenuation may or may not be directly related to that of the stellar population (§ 4). The explicit expression of R_αβ depends on the dust geometry; in the simple case of a foreground, nonscattering screen,

where the values of k(Hα) and k(Hβ) are given in Table 2.

Degeneracies between the reddening induced by dust and that induced by variations in the age, metallicity, and IMF of the stellar populations play a nonnegligible role in opacity determinations of galaxies. These effects are especially important when only broadband colors or low‐resolution spectroscopy are available and age‐sensitive or IMF‐sensitive stellar features are not identifiable (e.g., discussion in Papovich, Dickinson, & Ferguson 2001). For the age‐dust degeneracy, an example is given in Figure 4; here, the broadband colors and magnitudes of a dust‐free, aging stellar population produced by an instantaneous burst of star formation are compared with the analogous quantities of an increasingly extincted 6 Myr old stellar population. A clumpy dust distribution with τ_V∼2 in front of the young population reddens and attenuates it enough that its broadband UV, optical, and near‐IR colors closely resemble those of a 20 Myr old, dust‐free population (corresponding to the color V−I∼0.6 in Fig. 4). Thus, the dusty, young population can be mistaken for a dust‐free population a factor of ∼3 older. This example is just one of a large range of possibilities in the multidimensional dust/age/IMF/metallicity parameter space.

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In summary, the gray effective extinction produced by dust geometry and scattering and the age‐IMF‐metallicity‐dust degeneracy, together with uncertainties on the appropriate extinction curve to be applied to different galaxies (§ 2.1) and the absence of strong emission and absorption features below ∼1 μm (apart from the ∼0.22 Å absorption bump that is not universal), all contribute to make dust obscuration measurements very difficult in galaxies.

Efforts to determine the dust opacity of local galaxies have spawned the development of a number of independent techniques that have been applied to a large array of samples. The most widely used methods in the case of galaxy disks are tests of the dependence of the surface brightness on inclination, multiwavelength comparisons, and statistical analysis of the color and number count variations induced by a foreground galaxy onto background sources. Each method has its strengths and weaknesses, as briefly detailed below.

As Burstein, Haynes, & Faber (1991), Choloniewski (1991), and Davies et al. (1993) pointed out, probing galaxy dust opacity by measuring the surface brightness dependence of galaxy disks on inclination can suffer from drastic selection biases. For increasing inclination, an apparent magnitude–limited catalog will mimic the condition for transparent galaxies, with mildly increasing surface brightnesses, increasing diameters, and constant total luminosities. Conversely, an apparent diameter–limited catalog will mimic the conditions for opaque disks, with roughly constant surface brightnesses, increasing magnitudes, and constant diameters as a function of increasing inclination (Burstein et al. 1991). Selection effects can, however, be controlled by combining different samples and by using galaxy redshifts/distances to discriminate among the different biases, and analysis of large samples of late‐type (mainly Sbc and Sc) spirals (Huizinga & van Albada 1992; Peletier & Willner 1992; Giovanelli et al. 1994, 1995; Jones, Davies, & Trewhella 1996; Moriondo, Giovanelli, & Haynes 1998) has shown that the central regions of disk galaxies are opaque while the external regions beyond 2–3 scale lengths are almost completely transparent; there is also a trend for luminous galaxies to be more opaque than less luminous galaxies (Giovanelli et al. 1995). In bright, M_I< -21 disk galaxies, the observed magnitude correction from edge‐on to face‐on, Δm_I∼1 mag, corresponds to a face‐on central optical depth⁶ τ_V(0)≳5; this implies effective face‐on extinctions A_B,f∼0.4–0.5 mag, A_I,f∼0.2 mag, and A_H,f∼0.1 mag (Peletier & Willner 1992) for a double exponential distribution of dust and stars and for practically transparent external galaxy regions (Byun, Freeman, & Kylafis 1994). Less luminous galaxies are progressively less opaque in their central regions, with an edge‐on to face‐on correction of Δm_I∼0.5 mag at M_I> -18, corresponding to effective face‐on extinctions A_B,f<0.1 mag (Giovanelli et al. 1995).

Qualitative results similar to those above have been obtained by Bosma et al. (1992) and Byun (1993) for a small number of edge‐on late‐type spirals using multiwavelength kinematic information. The method, proposed by Goad & Roberts (1981), consists of comparing rotation curves of an edge‐on galaxy at widely different wavelengths. If the edge‐on galaxy is optically thick at a given wavelength, say, Hα, the rotation curve measured at this wavelength shows apparent solid‐body rotation throughout the entire disk because the Hα emission is coming only from the external regions of the galaxy. A comparison with a mostly unextincted rotation curve measured at a longer wavelength, such as H i, can then establish whether optical thickness at Hα exists. This method, although fairly direct in principle, may suffer from two limitations: first, dust in galaxies tends to be patchy and the Hα emission may be detected along the least extincted sight lines even in the presence of considerable opacity; second, the method implicitly assumes that Hα‐emitting regions are uniformly distributed across the disk.

The multiwavelength comparison method provides an independent approach to the problem of determining the dust opacity of galaxies. In broad terms, the technique consists of using multiwavelength data to solve simultaneously for the intrinsic colors of the stellar populations and for the reddening/attenuation induced by the dust. Generally, broadband images covering as large as possible a wavelength baseline, often from B to K band, are used to determine the opacity of the disks by exploiting the differential extinction property of dust (Rix & Rieke 1993; Block et al. 1994; Peletier et al. 1995; Emsellem 1995; Beckman et al. 1996; Kuchinski et al. 1998; Xilouris et al. 1999). Indeed, in face‐on quiescent galaxies, K‐band emission appears negligibly affected by dust obscuration, with ≲10% of the light lost to dust absorption and scattering (Rix & Rieke 1993). The multiwavelength technique is the most widely adopted for measuring dust opacity in galaxies because it employs easily accessible information on diverse galaxy types and enables detailed modeling of optical depths as a function of galactic region. There are, however, three main weaknesses to the method: first, this technique needs as wide a wavelength coverage as possible, often difficult to obtain, to yield unambiguous results; second, if the dust optical depth exceeds unity at some wavelength, different volumes of the galaxy will be sampled at different wavelengths; third, the need for large data sets and detailed modeling makes obtaining results on large samples relatively cumbersome. Results vary from author to author because of the different sample selections, galaxy and dust distribution models, and measurement techniques applied. Optical and near‐IR image analysis gives typical central optical depths τ_V(0) in the range 0.3–2.5 for types Sab–Sc (Peletier et al. 1995; Kuchinski et al. 1998; Xilouris et al. 1999), although higher values have been obtained by Block et al. (1994). For exponential stellar and dust profiles, these values of τ_V(0) result in optical depths 〈τ_V〉≲1 averaged over the inner 2–3 scale lengths (Rix & Rieke 1993; Beckman et al. 1996; Kuchinski et al. 1998) and A_B,f∼0.3–0.4 mag and A_I,f≲0.15 mag over the same area. Much lower values of the optical depth are found for late‐type, low surface brightness galaxies, with face‐on, central values τ_V (0)∼0.15 (Matthews & Wood 2001). In galaxy disks, arm regions tend to be opaque, with τ_V∼1.4–5.5 (A_I,f∼0.2–0.7 mag) and peak values at τ_V∼10–12, while interarm regions are generally transparent, with τ_V∼0.3–1.1 (A_I,f∼0.05–0.15 mag; Elmegreen 1980; Rix & Rieke 1993; Beckman et al. 1996; but see the higher interarm extinction values found by Trewhella 1998).

Energy balance estimates between dust absorption and emission can also be classified as a "multiwavelength technique," but it is conceptually different from the one above. This technique employs direct measurements of the dust emission in the infrared to derive an estimate of the total stellar energy absorbed by dust and then derive opacities at shorter wavelengths; whenever possible, the wavelength baseline is extended to the UV to probe the direct light from massive stellar populations and constrain bolometric quantities (Xu & Buat 1995; Xu & Helou 1996; Buat & Xu 1996; Wang & Heckman 1996; Trewhella et al. 1997; Trewhella 1998). By combining UV and infrared (IRAS) data, Xu & Buat (1995), Wang & Heckman (1996), and Buat & Xu (1996) find typically lower 〈τ_V〉 values than those derived from optical/near‐IR images. This is not incompatible with those results, since the models of Xu & Buat (1995) and Wang & Heckman (1996) assume plane‐parallel dust and stars, instead of exponential profiles, and thus the opaque inner regions are averaged with the nearly transparent outer regions (Peletier et al. 1995; Kuchinski et al. 1998). Still, the UV selection of the samples may bias the conclusions toward lower optical depths, and the use of IRAS data leaves some uncertainty as to the bolometric correction of the dust emission. The use of ISO data, which extend the infrared wavelength coverage out to 200 μm, appears indeed to favor higher values of the effective extinction (Trewhella 1998). Wang & Heckman (1996) find that opacity in disk galaxies is a function of luminosity (Fig. 5), in agreement with Giovanelli et al. (1995). These authors parameterize the opacity as 〈τ_V〉 = 〈τ_V,*〉(L_V/L_V,*)^0.5, with 〈τ_V,*〉 = 0.6 and L_V,* the visible luminosity of an L^* galaxy in the local universe. Similarly, Buat & Xu (1996) note that Sb–Scd galaxies have 〈τ_V〉∼0.8 and are on average 1.5 times more opaque than Sa–Sab and ∼3 times more opaque than Sd–Irr galaxies, with effective face‐on extinctions A_B,f∼0.3 mag, A_B,f∼0.15 mag, and A_B,f<0.1 mag for Sb–Scd, Sa–Sab, and Sd–Irr, respectively.

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All methods described so far use the stellar radiation of the galaxy itself as the light source for the dust, with the complication that intrinsic colors, age and metallicity gradients of the stellar populations, and the relative distributions of dust and stars need to be disentangled from the extinction proper. A technique that overcomes these problems is the one that uses background sources as "light bulbs" for the dust in foreground galaxies. In this case, the dust opacity is measured across the full thickness of the foreground galaxy. There are basically two approaches to the technique. In the first approach the foreground galaxy is partially projected onto a nearby background galaxy (Keel 1983; White & Keel 1992; White, Keel, & Conselice 2000; Keel & White 2001a, 2001b; Berlind et al. 1997; Pizagno & Rix 1998). In general, the background galaxy needs to present a smooth light profile; thus, early types and preferably elliptical galaxies are required (see, however, Keel & White 2001b); the dimming and color changes induced by the foreground galaxy dust onto the isophotes of the background source provide a measurement of dust opacity. The drawbacks of this approach are twofold: (1) there are very few known pairs of galaxies that fulfill all the requirements and (2) the method is limited by the degree of symmetry of both galaxies (White, Keel, & Conselice 2000). The second approach uses distant galaxies as background light sources. Statistical variations in number counts and colors of the background galaxies relative to control fields provide a handle on the total dust optical depth of the foreground galaxy (González et al. 1998). This method overcomes most of the limitations of the first one, but it presents some of its own: (1) high angular resolution images (e.g., from the Hubble Space Telescope [HST]) are needed in order to identify background galaxies; (2) even with such images it is often difficult to discriminate background sources from extended regions within the foreground galaxy (e.g., H ii regions), especially in crowded areas. Because of these limitations, the second method may also tend to avoid crowded and/or heavily extincted areas, thus biasing the results toward less dusty galactic regions. Results from various authors indicate that the spiral arms of galaxies tend to be opaque with A^o_B∼0.5–2 mag and A^o_I∼0.3–1.5 mag at any radius, while the opacity of interarm regions decreases with increasing distance from the galaxy center, starting at A^o_I ≈ 0.7 mag within 0.3R₂₅ and decreasing to practically zero at R₂₅ (González et al. 1998; White et al. 2000; Keel & White 2001b). The dust masses inferred from these extinction measures agree within a factor of ∼2 with masses derived from the infrared/submillimeter (ISO and Submillimeter Common User Bolometer Array [SCUBA]) dust emission (Domingue et al. 1999). One common trend generally found is the grayer than Galactic reddening in the arm regions (see, however, Keel & White 2001b). The clumpiness of the dust within each resolution bin has been suggested to be responsible for the gray reddening (Berlind et al. 1997; González et al. 1998; White et al. 2000; Keel & White 2001a). Less agreement exists on the shape of the reddening curve in the interarm regions, because of the larger uncertainties resulting from the lower extinction values. The measured extinctions are front to back, i.e., represent the optical depth of the intervening dust between the observer and the background sources. To relate these numbers to those derived from the inclination and multiwavelength tests, one has to make assumptions as to the distribution of stars relative to the dust in the foreground galaxy; for a mixed geometry of stars and small dusty clumps, the measured optical depths correspond to effective I extinctions of A_I,f∼0.3–0.4 mag and A_I,f≲0.2 mag for the arms and the interarm regions, respectively.

Multiwavelength optical and near‐IR imaging of edge‐on or nearly edge‐on systems indicates that the scale length of the dust is about 40% larger than the scale length of the stars (Xilouris et al. 1999), while the dust/stars scale height ratio is in the range 0.25–0.75, with a mean value of 0.5 (Kylafis & Bahcall 1987; Xilouris et al. 1997, 1999), for late‐type spirals (Sb and later) and appears to have a ratio of ∼1 in early‐type spirals (Wainscoat, Hyland, & Freeman 1990). IRAS 100 μm (Nelson, Zaritsky, & Cutri 1998) and ISO long‐wavelength maps (Alton et al. 1998; Davies et al. 1999; Trewhella et al. 2000; Radovich, Kahanpää, & Lemke 2001) confirm that cold dust emission extends beyond the limits of the optical disks along the radial direction, with scales that are ∼40% larger than those of the B‐band–emitting stars, but still well within the H i disks (e.g., Martin 1998). Using statistical measurements of color variations between background galaxies and control fields, Zaritsky (1994) gives a ≳2 σ detection of A^o_I ≈ 0.04 in galaxy halos, at a distance of about 60 kpc from the galaxy centers, along the optical major axis.

Spiral and irregular galaxies follow a global metallicity‐luminosity (and metallicity‐mass) relation, where the oxygen abundance increases by a factor of ∼100 for an increase of ∼10⁴ in absolute blue luminosity (Skillman, Kennicutt, & Hodge 1989; Zaritsky, Kennicutt, & Huchra 1994). Irregulars occupy the low‐metallicity locus of the relation, with ≈10 times on average lower oxygen abundance than spirals. Since the H i masses per unit L_B in irregulars are a factor of ≈3 larger than in spirals (Roberts & Haynes 1994; Zaritsky et al. 1994), the mass in interstellar metals per unit L_B is ≈3 times smaller. Adding the H₂ gas into the balance does not change this conclusion, since the H₂/H i mass ratio in irregulars appears to be no larger than that in spirals, even accounting for the uncertainties in the CO‐to‐H₂ conversion factor (Verter & Hodge 1995; Arimoto, Sofue, & Tsujimoto 1996; Wilson, Walker, & Thornley 1997). Measurements give the H₂ mass as 25%–50% of the H i mass in late spirals and as ≈20% of the H i mass in irregulars (Young & Scoville 1991; Hunter & Sage 1993; Hunter & Thronson 1996; Hunter 1997; Meier et al. 2001). Smaller metal masses for the irregulars translate into smaller dust masses per unit L_B, for standard values of the metal‐to‐dust ratio (van den Bergh 1974; Lequeux et al. 1984), and into the expectation that irregular galaxies are at least 3 times more transparent at B than spiral galaxies, for similar dust/star geometries.

The analysis of the blue, Hα, and IRAS‐detected infrared emission confirms that irregular galaxies are relatively transparent systems (Hunter et al. 1986, 1989). In a study of the Magellanic Clouds using background galaxies, Dutra et al. (2001) find that the central regions have A^o_B≳0.25 in the LMC and A^o_B≳0.16 in the SMC. In their UV‐selected samples, Wang & Heckman (1996) find that a 0.1 L^* galaxy has a mean optical depth about 1/3 of the optical depth of an L^* galaxy, and Buat & Xu (1996) reach a similar conclusion by comparing Sb–Scd galaxies with Sd–Irr. Thus, if the typical face‐on effective extinction for an Sc galaxy is A_B,f∼0.4–0.5 mag, the analogous quantities for an irregular are A_B,f∼0.15 and A_I,f∼0.05–0.10.

Although early Hubble type galaxies (elliptical galaxies and S0s) do not generally fall under the category of "star‐forming" galaxies, they occupy a niche in terms of dust opacity properties that is at the same time opposite and complementary to that of other galaxies. Elliptical galaxies and S0s are at the opposite end of the Hubble classification relative to irregulars, but they appear to be no more opaque than those late systems.

Early‐type galaxies cover a metallicity range similar to that of late‐type spirals (Brodie & Huchra 1991; Zaritsky et al. 1994) but have total (Hi + H₂) gas fractions per unit optical luminosity that are ∼3 times or more smaller (Young & Scoville 1991; Roberts & Haynes 1994). Thus, for standard interstellar metal‐to‐dust ratios, early‐type galaxies are expected to be more transparent than disk galaxies.

The IRAS survey has shown that between 10% and 50% of all nearby early‐type systems (45% of elliptical galaxies and 68% of S0s) contain dust (Jura et al. 1987; Knapp et al. 1989; Bregman et al. 1998), although the involved masses are generally modest, typically in the range 10⁵–10⁶ M_⊙ or M_dust/L_B ≈ 10^-5–10^-4 M_⊙ L^-1_⊙ (Roberts et al. 1991; Goudfrooij & de Jong 1995; Wise & Silva 1996; Bregman et al. 1998). The exact fraction of dusty systems appears to depend on the adopted detection threshold (Bregman et al. 1998), but it is likely a lower bound to the actual value, given the limits in the IRAS sensitivity. The 50% figure seems in agreement with the results of optical surveys: at least 40% of the local elliptical galaxies and S0s show the presence of disks, lanes, and/or patchy distributions of dust in visual images (Ebneter & Balick 1985; Sadler & Gerhard 1985; Ebneter, Djorgovski, & Davis 1988; Goudfrooij et al. 1994). About 40%–50%, and possibly as many as 80%, of elliptical galaxies also show evidence for circumnuclear dust on scales less than 100 pc, as seen in HST images; the small‐scale dust is mostly associated with nuclear radio activity (van Dokkum & Franx 1995; Lauer et al. 1995; Forbes, Franx, & Illingworth 1995; Carollo et al. 1997; Tran et al. 2001).

Despite the abundance of evidence for dust, optical extinction determinations of dust features in elliptical galaxies generally account for only ∼1/10–∼1/5 of the dust mass measured from the infrared (IRAS) emission; the remaining 80%–90% of the dust mass is probably associated with a component smoothly distributed across the galaxy and thus difficult to detect with standard techniques (Goudfrooij & de Jong 1995; Wise & Silva 1996; Bregman et al. 1998; Merluzzi 1998). Limited data from ISO in the wavelength range 120–200 μm confirm these findings (Haas 1998). Using the elliptical galaxy model of Witt et al. (1992), Goudfrooij & de Jong (1995) determine that the observed infrared luminosities are compatible with central optical depths of the diffuse component τ_V(0)≲0.7, with a typical value τ_V(0)∼0.2–0.3 (see, however, the somewhat larger values predicted by the models of Wise & Silva 1996). The corresponding effective extinction is A_B≲0.05–0.10 mag and A_I≲0.02–0.04 mag.

The giant elliptical galaxies found at the centers of cooling flow clusters are often surrounded by extended, ≈10–100 kpc, filamentary, and dusty emission‐line nebulae, with a higher frequency in those clusters with cooling times shorter than a Hubble time (Heckman et al. 1989; Sparks, Macchetto, & Golombek 1989; Hu 1992; Voit & Donahue 1997; Donahue et al. 2000). Dust lanes in the central galaxies have, indeed, been directly observed (Pinkney et al. 1996). Optical and UV emission‐line studies give extinction values in the range A_V∼0.3–2 mag for the dust associated with the nebula (Sparks et al. 1989; Hu 1992; Allen 1995; Voit & Donahue 1997; Donahue et al. 2000); infrared and submillimeter measurements give dust masses of the order of 10⁷–10⁸ M_⊙, or M_dust/L_B ≈ 10^-4–10^-3 M_⊙ L^-1_⊙, for these systems (Cox, Bregman, & Schombert 1995; Edge et al. 1999). The existing controversy on the origin of the dust associated with the central galaxies of cooling flow clusters will be briefly reviewed in § 6. Such galaxies are, however, not a statistically significant component of elliptical galaxies in general; thus, their contribution to the dust mass budget of early‐type galaxies is small.

The galaxies discussed so far tend to be mostly "quiescent"—i.e., their bolometric output is not dominated by a single region of active star formation or by nuclear nonthermal activity—and have modest infrared outputs. Their infrared luminosities in the 3–1000 μm band are typically ≈10⁹ L_⊙ and less than ∼(4–6) × 10¹⁰ L_⊙, with infrared‐to‐blue luminosity ratios L_IR/L_B∼0.4–0.5 (de Jong et al. 1984; Soifer et al. 1987; Devereux & Young 1991; Soifer & Neugebauer 1991; Hunter & Thronson 1996), and ≈1/2 or less of the stellar bolometric luminosity converted into infrared emission via dust reprocessing⁷ (see Table 3).

Galaxies with L_IR>6 × 10¹⁰ L_⊙ and L_IR/L_B>1 are progressively associated with dustier and more active systems for increasing values of the infrared luminosity (Rieke & Lebofsky 1986). The brightest infrared sources are not necessarily associated with the most massive galaxies, despite the existence of a relation between a galaxy's luminosity (mass) and its dust content (Wang & Heckman 1996). Infrared luminosity is a combination of dust content and activity: brighter sources have larger amounts of star formation and/or nonthermal activity embedded in dust. Most of the luminosity from galaxies with L_IR ≈ L_bol≳10¹¹ L_⊙∼(3–4)L^* seems to be associated with sources heavily obscured by dust (Sanders & Mirabel 1996). At the bright end of the infrared luminosity function (Soifer et al. 1987; Soifer & Neugebauer 1991; Kim & Sanders 1998) are the ultraluminous infrared galaxies (ULIRGs), with luminosities from L_IR∼10¹² L_⊙ up to ∼8 × 10¹² L_⊙ (Soifer et al. 1987; Kim & Sanders 1998), infrared‐to‐blue ratios around 30–400 (Sanders & Mirabel 1996; Clements et al. 1996), and optical extinctions in excess of 10–40 mag (Genzel et al. 1998; Murphy et al. 2001). These sources show a continuum of properties as a function of increasing luminosity, with the fraction of starburst‐dominated ULIRGs ranging from ∼80%–85% at the low‐luminosity end to ∼50% for L_IR>2 × 10¹² L_⊙ and the remaining fraction being AGN dominated (Genzel et al. 1998; Lutz et al. 1998; Veilleux, Kim, & Sanders 1999). Comprehensive reviews of the properties of ULIRGs are given in Sanders & Mirabel (1996) and Genzel & Cesarsky (2000).

Despite their large luminosities, bright infrared sources do not represent a major contributor to the energy budget of galaxies in the present‐day universe. Such objects are relatively rare within the local 100–200 Mpc: galaxies with L_IR≥10¹¹ L_⊙ and with L_IR≥10¹² L_⊙ represent ∼6% and less than 1%, respectively, of the total infrared emission in the local universe (Soifer et al. 1987; Sanders & Mirabel 1996; Kim & Sanders 1998; Yun, Reddy, & Condon 2001). However, the contribution of infrared‐bright sources to the galaxy energy budget increases with redshift (see § 5.2), as does their relevance in the framework of galaxy evolution.

Although the issue of dust opacity of galaxies is far from settled, an overall picture is apparent: galaxies in the local universe are only moderately opaque, and extreme values of the opacity are found only in the statistically nondominant, more active systems.

Table 3 summarizes the main conclusions of this section by listing the effective extinction values for local galaxies according to morphological type. For disk and irregular galaxies, both the face‐on and the inclination‐averaged extinctions are given. For instance, in Sb–Scd galaxies, the typical inclination‐averaged extinctions are 0.6–0.65 mag larger than face‐on at 0.15 μm, ∼0.4 mag at B, ∼0.25 mag at I, and 0.1 mag at K for a stellar‐to‐dust scale height ratio that varies between 1 in the UV and 2 in the I and K bands (model 5 of § 2.2).

Among the nonactive galaxies, luminous Sb–Scd galaxies contain the largest amounts of dust, which absorb ≈1/2 of their bolometric light. For comparison, dust emission represents between 35% and 40% of the bolometric luminosity of the Milky Way (Cox, Krügel, & Mezger 1986; Sodroski et al. 1994). The dust content generally decreases in less luminous galaxies and for earlier and later type galaxies; dust absorbs less than ∼15% of the bolometric light in E/S0 galaxies, and the fraction rises to ≈30% in irregulars (Table 3).

Interpolating from Table 3, the inclination‐averaged effective extinction of the stellar emission in late spiral galaxies at the rest‐frame wavelength of Hα is A_0.6563≲0.60 mag. This value should be compared with the effective extinction measured for the Hα line emission, A_Hα∼0.8–1.1 mag, from the ratio of the line to the reddening‐free thermal radio emission (Kennicutt 1983, 1998; Niklas, Klein, & Wielebinski 1997; Bell & Kennicutt 2001). Although there are relatively large uncertainties associated with both numbers, the two extinction values suggest that the nebular emission is more reddened than the stellar continuum, with A_Hα ≈ 1.5A_0.6563. Studies of controlled samples indicate a value of 2 as more typical for the ratio between the dust attenuation of the ionized gas and that of the stellar continuum, both in the case of spirals and irregulars (E. F. Bell 2001, private communication) and in the case of moderate‐intensity starbursts (§ 4).

Although the UV‐selected starbursts form a heterogeneous set, their dust reddening and obscuration properties are remarkably uniform. Higher dust optical depths produce redder UV–to–near‐IR SEDs and nebular emission‐line ratios (Fig. 6), almost independent of the details of the dust distribution and of the intrinsic stellar population (Calzetti et al. 1994; Calzetti 1997a).

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The geometry of the dust that best describes the reddening of the ionized gas emission in these systems, in the wavelength range 0.48–2.2 μm, is that of a foreground‐like distribution. Figure 6b shows the comparison between observations and the models of § 2.2 for the attenuated‐to‐intrinsic hydrogen line ratios Hα/Hβ and Hβ/Brγ. Internal dust does not appear to be a major component in the starburst region(s), and the little present is likely to be in compact clumps (Calzetti et al. 1995b). The main source of opacity appears to be given by dust that is external, or mostly external, to the starburst region (although still internal to the host galaxy), similar to a (clumpy) dust shell surrounding a central starburst. This is, of course, verified only in the B–K wavelength range where the reddening of the nebular emission lines has been measured; measurements at longer wavelengths could easily reveal more complex geometries. From a practical point of view, the data in Figure 6b are well described by a simple foreground, nonscattering dust distribution, with Milky Way (MW) diffuse ISM extinction curve and R(V) = 3.1; the reddening of the ionized gas is thus parameterized by the color excess E(B−V)_gas (eq. [4]).

The stellar continuum colors show the trend to become redder for increasing reddening of the hydrogen emission line ratios (Figs. 6a, 6c, and 6d). The implications are twofold: (1) variations of the intrinsic SED from galaxy to galaxy are secondary relative to the trend induced by dust obscuration, and (2) within each starburst, the same foreground‐like dust geometry holds for both the ionized gas and the nonionizing stellar continuum.

The first implication is not surprising, at least at UV wavelengths. Since we are observing the Rayleigh‐Jeans part of the massive stars spectrum, the intrinsic UV spectral slope⁸ β_26,0 is relatively constant over a fairly large range of ages, with values −2.7≳β_26,0≳ -2.2 for constant star formation over 10⁶ yr≲age≲10⁹ yr (see Leitherer & Heckman 1995 and Table 6 in Appendix B). In the same conditions, the production of ionizing photons is also constant. In an instantaneous burst of star formation, the ionizing photons are more age sensitive than the nonionizing photons that produce the stellar continuum and disappear before appreciable changes in the UV spectral shape can be observed. The observed UV spectral slope β₂₆ of the UV‐selected starbursts spans the range −2.5≲β₂₆≲ +0.4, much larger than what is expected from stellar population variations alone, and increases for increasing values of the attenuated‐to‐intrinsic hydrogen line ratios (i.e., color excess; Fig. 6).

In addition to correlating with the reddening of the ionized gas, the reddening of the UV stellar continuum, as measured by β₂₆, correlates with the infrared‐to‐blue and the infrared‐to‐UV luminosity ratios, L_IR/L_B and L_IR/L_0.16 (Fig. 7 and Calzetti et al. 1995b; Meurer, Heckman, & Calzetti 1999). These ratios are a measure of the total dust opacity in the starburst region because the bulk of the starburst's energy is coming out in the UV‐B. In addition, dust absorption is the main process that removes light from the line of sight (Calzetti et al. 1995b); when large galactic regions are observed, light scattered by dust out of the line of sight compensates, on average, that scattered into the line of sight. The opacity‐reddening correlation means that measurements of reddening can be used to infer the total dust absorption in UV‐selected starbursts (Meurer et al. 1999) with an uncertainty, ΔA_0.16∼0.6 mag for individual objects and ∼20% when averaged over large samples (Calzetti et al. 2000), that is dominated by variations in the starburst populations and in the details of the dust geometry from galaxy to galaxy. Such a correlation is expected for a foreground‐like dust geometry (Fig. 3d; see discussion in Gordon et al. 2000).

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The slopes of the correlations in Figure 6 identify the reddening suffered by the stellar continuum, A_λ1,star - A_λ2,star = [k^e(λ₁) - k^e(λ₂)]E(B−V)_gas, with k^e(λ) the obscuration curve, while the total obscuration measurements of Figure 7 provide the zero point for k^e(λ) (see also Calzetti et al. 2000). The intrinsic starburst flux density f_i(λ) is thus recovered from the observed flux density f_o(λ) via

where the obscuration curve for the stellar continuum, k^e(λ), is given by Calzetti et al. (2000):

Equations (8a) and (8b) fold into a single functional form a variety of effects: extinction proper, scattering, and the geometrical distribution of the dust relative to the emitters. It is derived from the spatially integrated colors of the entire stellar population in the starburst and represents the "net" obscuration of the population itself. As mentioned above, the obscuration curve has mainly an absorption component because the effects of scattering are averaged out. Thus, it should not be confused with the extinction curve k(λ) defined in § 2.1. Equations (8a) and (8b) imply that 1 mag of reddening between B and V for the ionized gas, A_B,gas - A_V,gas = 1 mag, corresponds to A_B,star - A_V,star = 0.44 mag of reddening for the stellar continuum. This fact can be alternatively expressed as

In other words, the stellar continuum suffers roughly one‐half of the reddening suffered by the ionized gas (Calzetti et al. 1994; Fanelli, O'Connell & Thuan 1988; Mas‐Hesse, Arnault, & Kunth 1989; see also Figs. 3e and 3f). Although E(B−V)_star parameterizes the amount of reddening of the stellar continuum, it is not a color excess proper as in the case of individual stars, because of the dust geometry effects folded in the expression of k^e(λ). One obvious characteristic of the obscuration curve is the absence of the 0.2175 μm bump, which is a prominent feature of the MW extinction curve (Fig. 1). Dust/emitter geometries that can dilute the bump include mixed distributions with large optical depths (Natta & Panagia 1984; Granato et al. 2000; Gordon et al. 2000). However, mixed geometries do not account for the full range of observational data (Fig. 3) because the sources that contribute to the emerging SED are located at progressively lower optical depths τ_V for decreasing wavelength. In particular, the reddest UV slope produced by mixed geometries is β₂₆∼ -0.7 (Charlot & Fall 2000), to be compared with β₂₆∼0 observed in starburst galaxies (Fig. 6a). Thus, the lack of the feature is probably intrinsic to the extinction curve of the starbursts (Gordon, Calzetti, & Witt 1997) and may be due to the high UV energy densities that characterize these regions (§§ 2.1 and 4.2).

This section describes a dust model that attempts to reconcile two apparently contradictory facts: (1) stars in starbursts are on average a factor of ≈2 less reddened than the ionized gas (eq. [9]), and (2) both stars and ionized gas are affected by the same foreground‐like dust distribution (Fig. 6). A schematic representation of a dust/star/gas configuration that can at the same time account for both effects is shown in Figure 8. Stars are born within optically thick molecular clouds, and the short‐lived, most massive stars remain closely associated with their parental cloud and the gas they ionize for their entire lifetime (e.g., Walborn et al. 1999). These stars and their surrounding gas will be generally highly attenuated. As the starburst population evolves, the inside of the region of star formation becomes depleted of dust (Calzetti, Kinney, & Storchi‐Bergmann 1996). With energy densities ≫100 times higher than in the local ISM, starburst environments are rather inhospitable to dust. Shocks from supernovae destroy dust grains, via grain‐grain collisions and sputtering (Draine & Salpeter 1979; Jones et al. 1994). The average lifetime of a refractory grain is ∼8 × 10⁶ yr, for a supernova rate of 0.05 yr⁻¹ and an ISM mass of 5 × 10⁸ M_⊙ (e.g., McKee 1989), about 1 order of magnitude or more shorter than the typical lifetimes of starbursts (Calzetti 1997a; Calzetti et al. 1997; Greggio et al. 1998; Aloisi, Tosi, & Greggio 1999). In addition, hot star wind– and supernova‐driven outflows evacuate both interstellar gas and dust from the region (Heckman, Armus, & Miley 1990; De Young & Heckman 1994; Mac Low & Ferrara 1999; Ferrara & Tolstoy 2000; Heckman et al. 2000). R136, the central cluster in 30 Doradus, is an example of a few million years old cluster surrounded by an evacuating region (Scowen et al. 1998). Ionized gas separated, in projection, from the hot stars has also been observed in nearby starbursts (Hunter & Gallagher 1997; Wang, Heckman, & Lehnert 1998; Calzetti et al. 1999; Maíz‐Apellániz & Walborn 2000).

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The evacuated (clumpy) dust will act as a foreground‐like distribution for both the gas (also at the edges of the region) and the central stars (Fig. 8; Calzetti et al. 1996; Witt & Gordon 2000; Gordon et al. 2000); however, the ionized gas will be more obscured than the stars, because of its spatial location and closer association with the dust (Calzetti 1997a). This gas is more likely to contribute to the nebular emission observed at UV‐optical wavelengths than the gas in molecular clouds, because of its milder obscuration. In the presence of multiple generations of starburst populations, the long‐lived, nonionizing stars have time to "diffuse" into regions of lower dust density (Calzetti et al. 1994; Charlot & Fall 2000; Granato et al. 2000), as their native clusters are disrupted by evaporation or by the host galaxy's gravitational field (Leisawitz & Hauser 1988; Kim, Morris, & Lee 1999; Tremonti et al. 2001). Cool stellar populations in the LMC have, for instance, been observed to be less embedded in dust than hotter stellar populations (Zaritsky 1999). A similar trend is observed in the young (<20 Myr) open clusters of the MW (Yadav & Sagar 2001). Massive, nonionizing stars can still produce significant UV emission. Hence, the integrated UV‐optical stellar continuum from the combination of the aging, diffusing populations and the starburst‐embedded young populations will be less obscured than the emission from the nebular gas (Calzetti et al. 1994; Gasda & Leitherer 1996). For the stellar continuum and the ionized gas to have correlated obscuration values (eq. [9]), multiple starburst generations or long‐lasting star formation events (rather than "instantaneous" events) are needed to attain an equilibrium between the number of stars drifting out of molecular clouds/starburst regions and the number of newly born, dusty stars. Starbursts hosted in dwarf galaxies are observed to have ongoing star formation over ≳200 Myr (Calzetti et al. 1997; Greggio et al. 1998; Aloisi, Tosi, & Greggio 1999), and durations could be as long in more massive starburst galaxies (Calzetti 1997a).

Although the obscuration curve can be widely applied to UV‐selected starbursts, it is not necessarily applicable to systems with different stellar population or ISM characteristics. In the case of nonstarburst galaxies there is no obvious mechanism for creating a foreground‐dust–like geometry. In extreme starbursts such as the ULIRGs, the nonapplicability of the obscuration curve has been demonstrated observationally (Goldader et al. 2001 and Fig. 7a). In these galaxies, the high central concentration of gas and dust is likely to induce more extreme geometries than in UV‐selected galaxies and to produce combinations of clumpy mixed and foreground distributions. Galaxies whose infrared properties are intermediate between the ULIRGs and the UV‐selected galaxies will progressively deviate from the dust geometry of the latter (Alonso‐Herrero et al. 2001; Förster Schreiber et al. 2001). Dust in subsonic H ii regions is likely to be mixed with the stars rather than having been pushed away or destroyed as in starbursts, and scattering of stellar light into the line of sight may be an important component in the attenuation budget (Caplan & Deharveng 1986; Bell et al. 2001). Because of the differences in the physical environment between the two types of objects, the foreground‐dust–like approximation no longer holds for subsonic H ii regions and equations (8a) and (8b) do not apply. Differences in the star formation history can also contribute to the difference between subsonic H ii regions and starbursts, with instantaneous bursts being a better description for the former and extended star formation for the latter; thus, differential attenuation between ionized gas and stars is not necessarily expected in the H ii regions. Supersonic H ii regions could be at the boundary between the two extremes just discussed; one example is 30 Doradus, which has evolved to the point of resembling a ministarburst (Walborn 1991).

To conclude, the starburst obscuration curve is a purely empirical result, and its derivation is independent of any assumption about the starburst's population, the dust geometry, or the details of the extinction curve. It provides statistical estimates of the reddening and obscuration of local UV‐selected starbursts, and deviations as large as ∼0.6 mag from the mean obscuration at 0.16 μm are to be expected on an case‐by‐case basis. The physics of the starburst environment provides an explanation of the "foreground‐dust–like" behavior of the curve, of the correlation between the reddening of the ionized gas and that of the stellar continuum, and of the correlation between reddening and total obscuration. As a sample, local UV‐selected starbursts are characterized by modest amounts of reddening and obscuration, which are correlated with the star formation activity (eq. [6]). The median color excess is E(B−V)_gas∼0.35 (Calzetti 1997b), corresponding to UV continuum attenuations of A_UV,star∼1.6, 1.4, and 1.1 mag at 0.15, 0.20, and 0.30 μm, respectively (Table 4 and Buat & Burgarella 1998; Meurer et al. 1999).

Observables such as the UV slope, the colors, and the luminosities and equivalent widths of the hydrogen lines can be readily related to the dust‐induced color excess of the ionized gas and, through equation (9), of the stellar continuum. The UV slope is correlated with E(B−V)_gas (Fig. 6a), and equations (8a) and (8b) give

where a list of β_26,0 values is given in Table 6 in Appendix B. The slope of the correlation between β₂₆ and E(B−V)_gas is somewhat steeper than that measured by Calzetti et al. (1994) directly from the data (1.88 ± 0.28), but the two are within 1 σ of each other. It should also be noted that equation (10) becomes a lower envelope to the data points in Figure 6a, for β_26,0< -2.25, a value appropriate for dust‐free, star‐forming populations. This indicates that variations of the dust/stars/gas geometry from the schematic model of Figure 8 and/or of the stellar population from the theoretical extreme β_26,0≤ -2.25 have the effect of reddening the UV slope even for E(B−V)_gas∼0. The vertical scatter in Figure 6a should thus be interpreted as due to such variations from galaxy to galaxy.

Reddening expressions for optical colors can be directly derived from equations (8a) and (8b) (see also Figs. 6c and 6d). A mixed UV‐optical color, 0.28−V, could be useful to infer the reddening of intermediate‐redshift (〈z〉∼0.6) starburst galaxies observed in B and I, and the reddening of one relative to the other is given by

Under the assumption that the rest‐frame UV emission and the nebular lines are both due to massive stars, the reddening of the UV continuum relative to the nebular hydrogen emission is given by

Figure 6e shows the comparison between data of local galaxies and equation (13) (Calzetti 1997b). While the agreement between the data in the first four panels of Figure 6 and equations (8a) and (8b) is a direct consequence of the fact that those data were used to derive the starburst obscuration curve, the match between data and expected trend in the bottom two panels of the figure is a consistency check, since it was not imposed a priori.

One immediate consequence of the differential reddening between gas and stars is that the equivalent widths of the nebular lines depend on the amount of gas obscuration; for the Hα and Hβ emission lines the relations are (Calzetti et al. 1994)

where the attenuated and intrinsic EWs are directly compared. Comparison of these trends with the data points is shown in Figure 6f; the trend given by the obscuration curve marks an upper envelope to the ensemble of observed EWs because the presence of older stellar populations underlying the starbursts dilutes the contrast between the emission lines and the stellar continuum in the data.

Statistically speaking, the UV slope is a good estimator of the total obscuration affecting the starburst (Meurer et al. 1999 and Fig. 7); in particular, the ratio of the dust infrared luminosity, L_IR, to the stellar UV or blue luminosity, L_0.16 or L_B, is related to β₂₆ via

The two constant values on the left‐hand side of equations (17) and (18), 1.68 and 3.85, represent the bolometric corrections of the stellar emission relative to the UV or B. The correction for the B band is larger and subject to more uncertainties than that for the UV, hence the larger scatter in the data point of Figure 7b. Equation (17) can be rewritten as

where the equation above represents a lower envelope to the data (Fig. 7 d and Calzetti et al. 2000) and has a scatter comparable to that of Figure 6a. The nature of the scatter in the β₂₆ versus E(B−V)_gas and in the L_IR/L_0.16 versus E(B−V)_gas relations is the same: it is due to variations from galaxy to galaxy of the starburst populations and of the dust/star/gas geometry.

The very first evidence for the presence of dust in high‐redshift systems came from studies of damped Lyα systems (DLAs; Meyer & York 1987; Fall, Pei, & McMahon 1989; Meyer & Roth 1990; Pettini, Boksenberg, & Hunstead 1990; Pei, Fall, & Bechtold 1991; Pettini et al. 1994, 1997a, 2000a; Zuo et al. 1997; Vladilo 1998; Ge, Bechtold, & Kulkarni 2001). DLAs are the largest H i column density absorption systems seen in the spectra of background quasars, with N(Hi)≥10^20.3 cm⁻². Their metallicities cover the range ∼1/100–1/10 solar for z∼0.5–4, with a mean value of ∼1/13 solar at z∼0.5–3 and little evidence for evolution with redshift (Prochaska & Wolfe 2000; Pettini et al. 1999, 1997b; Lu et al. 1996). Selection biases against the dustiest and most metal‐rich DLAs and problems with dust depletion corrections have been advocated as possible reasons for the observed weak metallicity evolution (Fall & Pei 1993; Boissé et al. 1998; Savaglio, Panagia, & Stiavelli 2000; see, however, Ellison et al. 2001). The dust fraction in DLAs is measured by comparing the abundance of dust‐depleted metals such as Cr ii, Fe ii, and Si ii against that of a metallicity tracer such as Zn ii, all of them producing rest‐frame UV absorption lines (Meyer & York 1987). The dust‐to‐metals ratio in DLAs is in the range 50%–60% of the MW value; this, combined with the generally low metallicities, indicates that DLAs are relatively transparent systems, with dust‐to‐gas ratios between 2% and 25% of the MW value (Fall, Pei, & McMahon 1989; Pei, Fall, & Bechtold 1991; Pettini et al. 1997a; Vladilo 1998). The absence of the 0.2175 μm dust absorption associated with DLAs led Pei et al. (1991) to conclude that the extinction curve in these systems is probably similar to the one observed in the Magellanic Clouds. More recently, though, Malhotra (1997) reported a ∼3 σ detection of the dust absorption feature in the composite spectra of Mg ii absorbers. Although the presence of modest quantities of dust is well established in DLAs, the weak or absent evolution of the metal content and of the cosmological mass density with redshift (Rao & Turnshek 2000) questions their relationship to luminous galaxies and favors the interpretation that DLAs preferentially trace galaxies with extended gas distributions and low metal and dust contents (Le Brun et al. 1997; Turnshek, Rao, & Nestor 2001) and the unevolved outskirts of galaxies (Ferguson, Gallagher, & Wyse 1998).

In recent years, facilities/instruments such as ISO and SCUBA at the James Clerk Maxwell Telescope have achieved high enough sensitivities in the mid‐ and far‐infrared to detect dust emission beyond a few microns from statistically significant samples of galaxies at cosmological distances. Studies on the ISO and SCUBA surveys, especially the identification of the optical/near‐IR counterparts to the infrared sources and the redshift measurements, are still ongoing, and the results described below should be considered in many instances preliminary.

ISO surveys have yielded ≈1500 sources in the redshift range 0≲z≲1.5, down to a sensitivity limit of ≈0.1 mJy in the mid‐IR (6.75, 12, and 15 μm) and ≈0.1 Jy in the far‐IR (90 and 175 μm; Rowan‐Robinson et al. 1997; Oliver et al. 1997; Taniguchi et al. 1997; Kawara et al. 1998; Clements et al. 1999; Altieri et al. 1999; Aussel et al. 1999; Flores et al. 1999a, 1999b; Puget et al. 1999; Serjeant et al. 2000; Scott et al. 2000; Efstathiou et al. 2000; Dole et al. 2001). Full lists of all surveys are given in Rowan‐Robinson et al. (1999) and Elbaz (1999). The number counts at 175 μm account for ∼10% of the CIB (Puget et al. 1999; Dole et al. 2001), showing that the bulk of the background has not been resolved yet at these wavelengths. Nevertheless, the number counts at mid‐ and far‐IR wavelengths are about 3–10 times above the no‐evolution extrapolation of the local IRAS counts (Elbaz et al. 1999; Aussel et al. 1999; Puget et al. 1999; Serjeant et al. 2000; Efstathiou, Rowan‐Robinson, & Siebenmorgen 2000). The implication is a strong luminosity evolution, L_IR∝(1 + z)^4.5, or a combination of luminosity and density evolution of the infrared sources out to z∼1 (Clements et al. 1999; Xu 2000; Chary & Elbaz 2001; Franceschini et al. 1994; Guiderdoni et al. 1998) that is comparable to or stronger than the luminosity evolution observed at rest‐frame UV wavelengths out to the same redshift (Lilly et al. 1996; Cowie et al. 1999; Sullivan et al. 2000). The ISO counts are thus dominated by luminous infrared galaxies at z≲1, with L_bol∼L_IR≳10¹¹ h^-2₆₅ L_⊙ (Rowan‐Robinson et al. 1997; Elbaz 1999; Xu 2000). Although this conclusion is based on the highly uncertain conversion of the 15 μm emission⁹ to a total infrared luminosity, it is qualitatively supported by the optical counterparts of the ISO sources. Close to 100 mid‐IR sources, with median redshift 〈z〉∼0.7–0.8, have so far been identified at optical/near‐IR wavelengths (Aussel et al. 1999; Flores et al. 1999b; Rigopoulou et al. 2000) (〈z〉∼0.1–0.2 for the 12 μm sample; Clements, Désert, & Franceschini 2001). Many of the rest‐frame optical spectra show characteristics of dusty luminous starbursts, with current bursts of star formation superposed on a prominent population of A stars and with attenuation values A_V≳0.5–1.8 mag (Flores et al. 1999b; Rigopoulou et al. 2000; Poggianti & Wu 2000).

At the time of writing, SCUBA surveys at 850 μm of "blank" fields and targeted lensed objects have detected a total of ≈100 sources with flux densities in the range ∼0.5–≳10 mJy and redshifts between z∼1 and 3, although sources as far away as z ≈ 5 may be present (Smail, Ivison, & Blain 1997; Hughes et al. 1998; Barger et al. 1998, 1999b, 2000; Smail et al. 1998, 1999, 2000; Eales et al. 1999, 2000; Lilly et al. 1999; Chapman et al. 2001; Fox et al. 2001; Scott et al. 2001). The number counts down to 2 mJy and to 0.5 mJy account for ∼20%–30% and more than 90%, respectively, of the CIB (Hughes et al. 1998; Barger et al. 1998; Eales et al. 1999, 2000; Barger, Cowie, & Sanders 1999a; Blain et al. 1999c). However, the latter fraction is potentially affected by small number statistics: so far only a few sources have flux densities below 2 mJy, the SCUBA confusion limit in blank fields, all of them from the survey of lensed galaxies (Blain et al. 1999a). Observations at 850 μm probe the Rayleigh‐Jeans tail of the thermal dust emission of galaxies at least to redshift ≈5–7. A source at z≥1 and with an 850 μm flux density of 2 mJy corresponds to a luminosity L_IR∼2 × 10¹² h^-2₆₅ L_⊙, for typical SEDs of local infrared‐selected galaxies (Lisenfeld, Isaak, & Hills 2000; Dunne et al. 2000; Dunne & Eales 2001); this is roughly the luminosity of a ULIRG like Arp 220. The few optical/near‐IR counterparts that have been identified are faint, often with I>24 and K≳20–21 (Smail et al. 1998, 1999; Barger et al. 1999b; Lilly et al. 1999; Ivison et al. 2000); in most cases the ratio L_IR/L_R<0.05, where L_R is the luminosity in the observer‐frame R band, and the infrared emission accounts for more than 95%–99% of the bolometric luminosity. It is indeed widely accepted, also on the basis of the few available multiwavelength SEDs, that the SCUBA sources are "cosmological ULIRGs" (Hughes et al. 1998; Barger et al. 1998; Lilly et al. 1999; Smail et al. 1998; Ivison et al. 2000), although this generalization has been recently questioned (Eales et al. 2000). The median redshift of the surveys is 〈z〉≃2.5 (Lilly et al. 1999; Smail et al. 1999, 2000; Barger et al. 1999b, 2000; Eales et al. 2000; Chapman et al. 2001; Fox et al. 2001); however, less than 10% of all the sources have reliable redshift determinations from optical/near‐IR counterparts, and a total of ≈50% of the sample have photometric redshifts, most often derived from the radio/submillimeter spectral index relation of Carilli & Yun (1999). The comoving number density of SCUBA sources in the redshift range z = 1–3 brighter than 6 mJy is ∼(3–5) × 10^-5 h³₆₅ Mpc⁻³ in our cosmology (Barger et al. 2000; Scott et al. 2001), about 2 orders of magnitude larger than the corresponding number density of local ULIRGs brighter than 10¹² L_⊙ (Kim & Sanders 1998). A strong luminosity evolution, possibly as strong as L_IR∝(1 + z)³ to z∼2, is also implied by the number counts (e.g., Scott et al. 2001). Although the statistical properties of the sources are often inferred using the star‐forming Arp 220 as a template, a fraction of AGNs is present in the sample (Ivison et al. 1998; Barger et al. 1999b). Current best estimates, based on the X‐ray luminosity of the sources, favor an AGN fraction of ∼20% (Severgnini et al. 2000; Hornschemeier et al. 2000; Fabian et al. 2000; Barger et al. 2001); this value will generally depend on the source luminosity range, as it does in the local universe (Genzel et al. 1998; Lutz et al. 1998; Veilleux et al. 1999).

Multiwavelength observations of optically selected samples of intermediate‐ and high‐redshift galaxies are generally limited to the rest‐frame UV and optical windows, with few exceptions (e.g., Flores et al. 1999b; Chapman et al. 2000). Such surveys suffer the same limitations of local UV‐optical samples, with the added complication of the often incomplete wavelength coverage. By probing only the differential attenuation, the UV‐optical data provide, in principle, lower limits to the actual dust opacity of the galaxy (§ 2.2, but see also § 4). In order to differentiate an aging stellar population from dust as the cause of the SED reddening, a variety of approaches have been adopted by different authors. Common diagnostics include the Balmer line decrement Hα/Hβ, line‐to‐continuum ratios, e.g., Hα/UV and Hβ/UV, and multicolor SED fitting. Limitations to each of these diagnostics are discussed in § 2.2 and in the sections below, as appropriate.

5.3.1. Galaxies at Redshift z≲2

For a UV‐selected sample of star‐forming galaxies at z ≈ 0.2, Sullivan et al. (2000, 2001) derive an average attenuation A_Hα∼0.8 mag and find tentative evidence that those systems follow an obscuration‐SFR correlation similar to that observed in more local galaxies (Wang & Heckman 1996; Heckman et al. 1998; Hopkins et al. 2001). The authors use a combination of UV (0.20 μm), optical (Hα and Hβ), and radio (1.4 GHz) data to analyze their sample, although their reddening estimates are mostly based on the subsample for which they can measure Hα/Hβ ratios. If the starburst obscuration curve (§ 4) applies to z ≈ 0.2 star‐forming galaxies, an attenuation A_Hα∼0.8 mag for the nebular line corresponds to A_0.20∼1.3 and A_0.16∼1.4 for the UV stellar continuum. Although these figures agree with local measurements of the extinction at UV and Hα in star‐forming galaxies (§ 3.6 and Table 3), the UV selection of the sample potentially biases the reddening measures toward low values by excluding more heavily extincted galaxies.

The z∼1 Balmer break sample of Adelberger & Steidel (2000) is also a rest‐frame–UV/blue‐selected one. Exploiting the presence of the Balmer discontinuity at ∼0.365 μm in galaxy SEDs to select z∼1 candidates (a derivative of the Lyman break technique; see next section), these authors have obtained spectroscopic confirmation for ≈700 galaxies. The sample contains a large variety of galaxies, from active starbursts to quiescent star forming to poststarbursts. If the z∼1 galaxies with blue (β₂₆≲ -0.3) SEDs are analogs of local starbursts and follow the same IR/UV versus β relation, they also follow an obscuration‐SFR relation similar to the local one, with a comparable range of attenuations (Fig. 9a). However, for fixed opacity, the z∼1 galaxies tend to have on average brighter UV + IR luminosities (larger SFRs) than the z∼0 galaxies. Thus, even taking selection effects into account, the distant galaxies are, on average, more actively star forming for the same amount of obscuration than the local starbursts (Adelberger & Steidel 2000).

Glazebrook et al. (1999), Yan et al. (1999), and Moorwood et al. (2000) use rest‐frame Hα observations and Hα/UV comparisons to infer dust reddening in star‐forming galaxies at redshift z∼1–2.2. The I‐band–selected sample of Glazebrook et al. (1999) corresponds to rest frame ∼V for a z = 1 galaxy: the longer wavelength selection of the samples mitigates, although does not remove completely, the bias against dust‐obscured galaxies introduced by UV selections (for the Canada‐France Redshift Survey employed by Glazebrook et al. 1999, see Lilly et al. 1995, and for the sample used by Yan et al. 1999, see McCarthy et al. 1999). The presence of dust reddening in the z∼1–2.2 samples is derived from the discrepancy between the measured L_Hα/L_0.28 luminosity ratio and the ratio predicted by dust‐free models.¹⁰ Figure 10 compares the range of attenuated‐to‐intrinsic values (L_Hα/L_0.28)_a/(L_Hα/L_0.28)_o derived from data by the three groups of authors¹¹ with predictions from the dust models of § 2.2. Geometries where dust and stars are homogeneously mixed, in either spheroidal or flattened distributions, appear less effective in reproducing the observed Hα/UV ratios than foreground geometries (Fig. 10). If the foreground and starburst distributions bracket the possible range of dust/emitter morphologies for the z∼1–2 Hα galaxies, the front‐to‐back optical depths are τ_V∼0.6–4.9 mag (Fig. 10, bottom panel), and the effective attenuations are A_Hα∼0.6–4.3 mag, A_0.28∼1.5–5 mag, and A_0.16∼3–7 mag for SMC extinction. MW‐like and SMC‐like extinction curves give results that are less than 0.1 mag apart at λ≥0.28 μm but ∼1.2 mag different at λ = 0.16 μm, with larger obscurations given by the SMC extinction curve. Uncertainties in the metallicity, IMF, and star formation history of the galaxy stellar populations introduce a factor ≳2 additional scatter on the inferred opacities (Table 3 in Glazebrook et al. 1999). The major limitation is, however, that dust opacities measured from the current Hα surveys of galaxies are probably not representative of the z∼1–2 population as a whole. By number, the samples of Glazebrook et al. (1999) and Moorwood et al. (2000) are small (13 galaxies and five galaxies, respectively); the sample of Yan et al. (1999), albeit 2.5 times larger than that of Glazebrook et al. (1999), does not measure the Hα emission on the same galaxies for which UV is available. For such small samples, sensitivity limits induce a strong selection effect: the observed galaxies will be among the brightest in Hα, and, in addition, contamination from AGN/Seyfert nuclei is not excluded (Whittle 1992). Therefore, such surveys sample the high end of the activity and dust obscuration ranges for optically detectable systems at z∼1–2 (Glazebrook et al. 1999; Sullivan et al. 2000; and eq. [6]).

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In summary, the limited information available on galaxies at z ≈ 1 suggests that dust opacities cover a range similar to that of local star‐forming and starburst galaxies; they may follow a similar relation A_λ∝log (SFR)^α (see eq. [6]), with the proportionality constant revised downward relative to the local sample.

5.3.2. Galaxies at Redshift z>2

To date, the surveys that have most efficiently secured large populations of galaxies beyond z∼2 are those that exploit the Lyman discontinuity at rest frame 0.0912 μm to identify high‐redshift candidates; these are the so‐called Lyman break galaxies (LBGs; Guhathakurta, Tyson, & Majewski 1990; Steidel & Hamilton 1992; Steidel et al. 1996a, 1996b, 1999; Giavalisco, Steidel, & Macchetto 1996b; Lowenthal et al. 1997; Giavalisco et al. 1998; Adelberger et al. 1998; Adelberger & Steidel 2000). So far, there are ∼1000 spectroscopically confirmed LBGs at z∼3 and ∼70 at z∼4. The LBG population is a substantial component of the high‐redshift "zoo": their comoving number density at z = 3 is n(z = 3)∼3 × 10^-2 h³₆₅ Mpc⁻³ (Steidel et al. 1999), comparable to the density of local galaxies (Marzke, Huchra, & Geller 1994). By selection, i.e., because of the need of presenting a relatively blue continuum longward of Lyα, this high‐redshift population tends to be biased against systems with predominantly old populations, or systems with large amounts of dust extinction. Indeed, most LBGs show evidence for ongoing or recent star formation activity (Steidel et al. 1996b; Pettini et al. 2000b, 2001; Papovich et al. 2001). From a purely phenomenological point of view, LBGs resemble local UV‐selected starburst galaxies (§ 4). The obscuration‐corrected SFRs per unit galactic area are ∼0.2–25 M_⊙ yr⁻¹ kpc⁻², for a 0.1–100 M_⊙ Salpeter IMF (Steidel et al. 1996b, 1999; Papovich et al. 2001; Shapley et al. 2001), corresponding to ∼0.5%–50% the maximum SFR per unit galactic area measured in the local universe (Lehnert & Heckman 1996; Meurer et al. 1997); this is similar to the observed range in nearby UV‐selected starbursts. Rest‐frame UV spectra show a wealth of absorption features, and often P Cygni profiles in the C iv (1550 Å) line (Steidel et al. 1996b), which indicates the predominance of young, massive stars. Nebular emission lines observed in the brightest LBGs (Pettini et al. 1998, 2001; Teplitz et al. 2000a) have intensities comparable to those of local starbursts (Meurer et al. 1999). The observed blueshifts in the UV interstellar absorption lines relative to the systemic redshifts of LBGs have been interpreted as bulk gas outflows with velocities v∼200–500 km s⁻¹ (Pettini et al. 1998, 2000b), again very similar to what is observed in nearby starbursts (Heckman et al. 2000). Finally, more luminous LBGs tend to be dustier (Fig. 9b and eq. [6]; Adelberger & Steidel 2000; Shapley et al. 2001). However, dissimilarities also exist between the two classes of galaxies. Star formation extends over a large fraction of the galactic body in LBGs, typically 5–30 h^-2₆₅ kpc² (Giavalisco et al. 1996b, 1998), while it is confined within the inner ∼1 kpc² in local starbursts. As a result, LBGs are, on average, more rapidly star forming than either z∼0 or z∼1 galaxies (Fig. 9; Adelberger & Steidel 2000; Shapley et al. 2001). The bulk outflows in LBGs have velocities that are similar to those of local infrared‐bright starbursts like NGC 6240 and a few times larger than those of H ii galaxies (Heckman et al. 2000; Heckman & Leitherer 1997; Kunth et al. 1998; Gonzalez Delgado et al. 1998). The implications of such differences are not fully understood yet.

Establishing how much dust LBGs contain is the subject of ongoing debate. Metals are definitely present in these systems. Although the exact value of the metallicity has not been constrained, it most likely lies between 0.1 and 0.7 Z_⊙ (Pettini et al. 2000b, 2001; Leitherer et al. 2001). The UV spectral slopes of LBGs have median value β₂₆∼ -1.5 (Adelberger & Steidel 2000), significantly redder than the value β_26,0∼ -2.2 to −2.7 expected for a dust‐free star‐forming population (Appendix B). If interpreted in the same fashion as the UV slope of nearby UV‐selected starbursts, LBGs suffer from dust obscuration at the level of A_0.16∼1–2 mag (Calzetti 1997b; Pettini et al. 1998; Dickinson 1998; Meurer et al. 1999; Steidel et al. 1999; Adelberger & Steidel 2000) and, possibly, more (Meurer et al. 1997; Sawicki & Yee 1998). However, a number of uncertainties and systematics limit the usefulness of UV data alone to derive obscuration estimates. First and foremost, the high‐redshift galaxy for which reddening corrections are sought needs to possess active, ongoing star formation (i.e., not to be a poststarburst); this appears to be true for the LBGs as a population but may not be true on a individual basis (Papovich et al. 2001). Second, for most LBGs the UV slope is derived from photometry alone; the conversion of G− colors¹² to β₂₆ suffers from uncertainties due to the presence of both intrinsic (stellar lines and Lyman break) and intervening (Lyα forest) absorption in the photometric filters (Adelberger & Steidel 2000; Pettini et al. 2001). Finally, because of the age‐dust degeneracy, the intrinsic UV slope is a free parameter that can lead to greater than 1 mag difference in the derived obscuration value at 0.16 μm (cf. Sawicki & Yee 1998; Steidel et al. 1999).

Supplementing the UV with rest‐frame optical data provides further leverage for determining the level of dust reddening in LBGs. The negligible correlation between L_Hβ/L_0.16 and the UV slope found for a sample of ≲15 luminous LBGs¹³ supports the notion that LBGs are subject to modest reddening (Pettini et al. 1998, 2001; Teplitz et al. 2000a). Although this result is still dominated by the large scatter induced by both observational and model uncertainties (Pettini et al. 2001), it is consistent with what is observed in local UV‐selected starbursts,¹⁴ for which an obscuration of 1–2 mag at 0.16 μm corresponds to the modest reddening A_0.16 - A_Hβ∼0.15–0.3 (§ 4.3).

Although the age‐dust degeneracy cannot be easily broken even with the addition of long‐wavelength data, extending the wavelength coverage of LBGs to the rest‐frame optical has helped delimit the locus of allowed combinations in the age‐dust plane (Papovich et al. 2001; Shapley et al. 2001). Using complementary data sets of LBGs in terms of luminosity range, Papovich et al. (2001) and Shapley et al. (2001) have established that there is an inverse correlation between the age of the stellar populations in a galaxy and the amount of dust reddening it suffers: the older the galaxy, the lower its reddening. In agreement with previous results (Sawicki & Yee 1998), LBGs whose SEDs are compatible with young (≲10⁸ yr) stellar populations are also dusty. Whatever dust is present, it is not preferentially obscuring selected regions of the galaxies, because of the similarity between the rest‐frame UV and optical morphologies (Bunker 1999; Dickinson 2000). A typical LBG obscuration of A_0.16∼1–2 mag, with a median of ∼1.5 mag and a high‐end tail around 4.5–5 mag (Steidel et al. 1999; Papovich et al. 2001; Shapley et al. 2001), is currently the most broadly accepted value.

Despite all the uncertainties in estimating dust obscuration in LBGs, the inferred opacity values are modest enough that the high‐redshift galaxies are expected to be faint submillimeter emitters, with 850 μm flux densities at or below the SCUBA detection limit of ∼1–2 mJy (Adelberger & Steidel 2000; Peacock et al. 2000). Out of ≳10 LBGs targeted with SCUBA, only a couple have been detected (Chapman et al. 2000; van der Werf et al. 2001). Table 5 gives three examples (two LBGs and one SCUBA source) of highly reddened z∼3 galaxies, plus the average values of a typical LBG. The three examples are meant to show some of the most attenuated cases that are also detected at rest‐frame UV. Table 5 demonstrates that the exact prediction of the flux density at rest frame ≈200 μm is heavily dependent on the adopted dust temperature(s) and emissivity, because long infrared wavelengths probe only the Rayleigh‐Jeans tail of the thermal dust emission in galaxies (Fig. 11). Local galaxies, although extensively used as analogs of high‐redshift galaxies, are of limited help in this respect, given the wide range of properties they show. If the flux density of a local galaxy beyond 60–70 μm is parameterized by a modified blackbody with dust emissivity ∝ν,

ULIRGs and bright IR‐selected galaxies tend to be well described either by a single‐temperature component with T∼40 K and ∼1.5 (Lisenfeld et al. 2000; Blain et al. 1999a) or by a warm/cool two‐temperature model with = 2 (Dunne & Eales 2001); however, there is tentative indication that UV‐bright, metal‐poor starbursts have hotter dust SEDs, with T∼50 K and = 2 (Tol 1924−416; Calzetti et al. 2000). Equation (20), which is used for purely illustrative purposes, is clearly an oversimplification of the dust SED in local galaxies, which is characterized by a range of temperatures and, at rest frame λ≲40–70 μm, by the emission from nonequilibrium dust grains (Sellgren 1984; Draine & Anderson 1985; Li & Draine 2001; see also § 2.1). In starbursts, the latter component represents ∼25% of the total infrared emission. Given the uncertainty of the submillimeter measures and the current poor understanding of the detailed physics of dust emission in both local and high‐redshift galaxies, the opacity of LBGs is still relatively unconstrained by submillimeter observations (Ouchi et al. 1999; Sawicki 2001; and Table 5). Further complications (and uncertainties) arise when the comparison between predictions and observations of infrared flux densities is made for individual objects (van der Werf et al. 2001; Sawicki 2001; Baker et al. 2001); reddening/obscuration corrections at UV‐optical wavelengths are accurate only in a statistical sense and, generally, do not apply on a one‐to‐one basis to individual objects. For instance, if the dust geometry in a particular system is such that the scattering out of the line of sight is larger than that into the line of sight, the infrared energy, which is due to the absorption part of the extinction only, will be overestimated when derived from UV data.

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There is so far limited overlap between infrared and optical surveys at intermediate and high redshift (e.g., Aussel et al. 1999; Flores et al. 1999b; Barger et al. 1999b; Rigopoulou et al. 2000; Chapman et al. 2000). Consequently, multiwavelength coverage from the rest‐frame ∼UV‐optical to the infrared is available only for a small number of galaxies. To make matters worse, observational limitations lead to vastly different selection criteria for the optical surveys in different redshift bins (Glazebrook et al. 1999; Yan et al. 1999; Moorwood et al. 2000; Steidel et al. 1996b). Thus, conclusions about the dust opacity of galaxy populations as a whole and as a function of redshift are at the moment based on "reasonable" extrapolations of existing data rather than hard evidence.

Available infrared and optical data support the scenario that z ≈ 1 star‐forming galaxies cover at least the same range of dust opacities as local galaxies. The luminosity (or combined luminosity and density) evolution implied by the ISO counts suggests that luminous infrared galaxies, with L_bol∼L_IR≳10¹¹ h^-2₆₅ L_⊙, were common at z≲1. The range of dust attenuation values at UV wavelengths inferred for optically selected z∼1 galaxies is comparable to those of local disk galaxies and UV‐selected starbursts (Fig. 9), although the distant galaxies tend to be more luminous (more active) on average. Larger samples with more extended wavelength coverage are needed before a more complete picture can be drawn in this redshift range.

The ISM of z∼3 galaxies has been observed to be metal polluted to at least ≈0.1 Z_⊙, implying that nonnegligible amounts of dust must be present in the galaxy population at large by z = 3 and, in many cases, earlier (Shapley et al. 2001). The observed properties of the z>1 SCUBA sources and of the LBGs suggest that both objects are the high‐redshift analogs of local actively star‐forming galaxies, where dust content and level of activity determines a continuum of characteristics. The SCUBA sources are at the high end of such a continuum, with powerful activity, both thermal and nonthermal, and large dust contents that make them similar to local ULIRGs; more than 95% of their bolometric light is absorbed by dust. LBGs appear to span a larger range of the continuum of dust content and activity level, although they tend to have, on average, lower values than the SCUBA sources. Typical UV attenuations are A_0.16∼1–2 mag, corresponding to 35%–95% of the bolometric light being absorbed by dust.

Assuming that the local infrared luminosity function can be applied to high‐redshift sources as well, the comoving number density of z ≈ 3 SCUBA galaxies with 850 μm flux densities brighter than 2 and 0.5 mJy (corresponding to ∼2 × 10¹² and ∼5 × 10¹¹ L_⊙ for an Arp 220–like SED) would be ≈4 × 10^-4 h³₆₅ Mpc⁻³ and ≈10^-2 h³₆₅ Mpc⁻³, respectively. High‐redshift infrared galaxies as bright as Arp 220 are almost 100 times less numerous than LBGs; for comparison, in the local universe ULIRGs are more than 4 orders of magnitude less numerous than optically selected galaxies. At lower 850 μm luminosities, z∼3 SCUBA sources are about as numerous as LBGs at the same redshift, but there could be large overlap between the two samples at the millijansky level. LBGs are, in fact, predicted to occupy the faint end of the SCUBA 850 μm source counts, with flux densities of a few millijanskys or less (Adelberger & Steidel 2000). Thus, although SCUBA sources down to 0.5 mJy at all redshifts already account for more than 90% of the CIB, a nonnegligible fraction of this, at least 25%, could be due to LBGs (Peacock et al. 2000; Adelberger & Steidel 2000; van der Werf et al. 2001).

The author is grateful to Mark Dickinson, Megan Donahue, Paul Goudfrooij, Claus Leitherer, and Mark Voit for insightful comments on specific sections of this review. She thanks Kurt Adelberger for data on the Lyman break and Balmer break galaxies and Max Pettini and Chuck Steidel for the UV spectrum of MS 1512‐cB58. She is also indebted with Veronique Buat, Bruce Draine, Tim Heckman, Nino Panagia, Marcia Rieke, and Max Pettini for a critical reading of the manuscript, which has greatly improved its content and presentation.