2. A "RECIPE" FOR REDDENING

Despite the complications discussed in the previous section, dust reddening at UV and optical wavelengths can be "treated", at least in galaxies and galaxy regions where massive stars dominate the radiation output [8, 23, 24, 9, 7]. This includes a wide range of extragalactic objects, from the centrally concentrated starbursts in spirals to the Blue Compact Dwarfs. In regions of SF, the massive star population responsible for the nebular line emission is also responsible for most of the UV radiation. The spectral shape of the UV emission (> 1200 Å) is relatively constant over a relatively large range of ages, because we are observing the Rayleigh-Jeans part of the massive stars' spectrum; the non-ionizing photons which make the UV spectrum are less age-sensitive than the ionizing photons (i.e., nebular line emission); the latter disappear before appreciable changes in the UV spectral shape can be observed. If the UV spectrum is fit as F() , the UV index has values between -2.5 and -2 for a reddening-free, ionizing star population [22]. The relation between UV stellar continuum and ionized gas emission has proven crucial for pinning down the selective effects of dust obscuration in star-forming galaxies. Various diagnostics have been constructed from multiwavelength data (Figure 1a and 1b; [8, 7]), extending the relation between stellar continuum and nebular emission from the UV to the K band.

Figure 1. a) (left panel). The ratio of H to UV emission, observed in a sample of star-forming galaxies, is shown as a function of the color excess of the ionized gas E(B-V)g (measured from the Balmer line ratio H / H). The UV is centered at 1600 Å. If both nebular lines and UV continuum radiation are due to massive stars, the correlation is explainable as an effect of selective reddening at different wavelengths. b) (right panel) The UV index is plotted as a function of E(B - V)g for the same sample of galaxies. The best linear fit is shown as a continuous line. In a stellar population, the values of are relatively constant for the range of ages where the nebular hydrogen lines (H, H, etc.) are detectable; therefore, the observed correlation between and E(B - V) is attributable to dust reddening, and not aging, with the UV spectrum becoming redder for increasing values of the color excess.

The selective attenuation is shown in Figure 2a in comparison with two extinction curves, the Milky Way and the SMC. The comparison is purely illustrative and should not be taken at face value, because the dust attenuation of galaxies is conceptually different from the dust extinction of stars. The latter measures strictly the dimming effect of the dust between the observer and the star, while the former folds in one expression (equation 2) a variety of effects: extinction, scattering, and the geometrical distribution of the dust relative to the emitters. One comparison is, however, licit: the 2175 Å bump, which is a prominent feature of the Milky Way extinction curve, is absent in the attenuation curve. Gordon et al. (1997, see also, this Conference) have proven that the absence of the feature cannot be explained either with scattering or dust geometry, and must be intrinsic to the extinction curve of the ISM in the star-forming galaxies.

Expressions (1) and (2) can be used to derive the intrinsic spectral energy distribution F₀() of the star-forming region, once the effective color excess E(B - V)_s of the stellar continuum is known. Because of the geometrical information folded into the expression of k(), E(B - V)_s is not a straightforward measure of the total amount of dust between the observer and the source (as in the case of individual stars). The relation between E(B - V)_s and the color excess E(B - V)_g of the ionized gas is:

(3)

Here, the color excess of the ionized gas is derived from the Balmer decrement (or any suitable set of atomic hydrogen emission lines) and the application of a 'standard' extinction curve. The selective extinction of the Milky Way, LMC or SMC curves has similar values at optical wavelengths [15], so any of these curves can be used for the ionized gas. In addition, a foreground dust distribution appears to work well for the gas when moderate extinctions, E(B - V)_g 0.1-1, are present.

Regions of active SF may be inhospitable to dust; supernovae explosions and massive star winds generate shock waves and, possibly, mass outflows [20]. Shocks and outflows likely destroy or remove the dust from inside the region; only the external (foreground) dust survives [9], accounting for the observed gas reddening geometry. This simple interpretation does not account, however, for Equation (3): stars are on average a factor 2 less reddened than the ionized gas [14, 8]. The factor 2 difference in reddening implies that the covering factor of the dust is larger for the gas than for the stars [7]. Indeed, while the nebular emission requires the presence of the ionizing stars, the UV and optical stellar continuum is contributed also by non-ionizing stars. Ionizing stars are short-lived and remain relatively close to their (dusty) place of birth during their entire lifetime, while the long-lived non-ionizing stars have time to 'diffuse' into regions of lower dust density. If this is the case, stars and gas will not occupy the same regions [10], and stellar continuum and nebular emission should be largely uncorrelated. Why then does the reddening of the stellar continuum correlate with the reddening of the ionized gas, as implied by Figure 1? For both the correlation and Equation (3) to be valid, the aging and diffusion of the stars must be compensated by the production of new massive stars. In other words, the SF event must have a finite duration and cannot be instantaneous. A lower limit to the SF duration can be placed by remembering that the crossing time of a region of ~ 500 pc is about 50 Myr for a star with v = 10 km/s.

Whichever the interpretation, expressions (2) and (3) are purely empirical results, and are independent of any assumption on the geometry of the dust distribution and on the details of the dust extinction curve. They yield probably the most appropriate reddening corrections for the integrated light of extended star-forming regions (or galaxies, see Figure 2b).

Figure 2. a) (left panel). The attenuation curve of Eq.(2) (continuous line) is compared with the diffuse ISM extinction curves of the Milky Way and the SMC (dashed and dotted line, respectively). The attenuation is normalized to k(B) - k(V) = 1. The most prominent feature of the Milky Way curve, the 2175 Å bump, is absent in the attenuation curve. b) (right panel) The H / UV emission for the same galaxies of Figure 1a is shown after correcting the UV emission for dust attenuation using Eqs.(2) and (3) and E(B - V)g from the Balmer decrement. The H emission is corrected using the Balmer decrement and the Milky Way extinction curve. The two horizontal lines represent the range of expected values for H / UV for stellar populations undergoing continuous star formation in the two extreme cases of 0.1-100 M and 0.1-30 M Salpeter Initial Mass Function (top and bottom line, respectively). Eq. (2) does recover the UV emission expected for the observed H emission.