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There are two main causes for a red UV stellar continuum: 1) ageing of the stellar population; 2) presence of dust (variations of the intrisic IMF will not be discussed here).

An ageing stellar population loses the high-mass, hot stars first, and then, progressively, lower-mass and colder stars. In the process, the UV stellar continuum becomes redder and redder and, also, the 4,000 Å break increases in strenght. This break spans a small wavelength range, thus is unaffected by dust reddening. The strenght of the 4,000 Å break is therefore a powerful constraint on the age of the stellar population. The Local starbursts can have very red UV continua (beta > 0), while still showing rather small 4,000 Å breaks, telltales of the presence of a young stellar population ( < 107 yr) or of constant star formation (over timescales ~ 109 yr, see [4]. Ageing of the stellar population is not the main reason for the presence of a red UV SED in Local starbursts. Broad-band J, H, and K observations provide limited information on the strenght of the 4,000 Å break in high-z galaxies, still accurate enough to exclude ageing as a general cause for the red UV spectra in this case as well (Dickinson 1997, priv. communication).

Dust reddening is then the likely cause for red UV spectra, as demonstrated by the correlation between beta and color excess (Figure 1, right panel). Dust reddening is generally a close-to-unsolvable problem for unresolved stellar populations (e.g., distant galaxies), because the effective obscuration will be a combination of dust distribution relative to the emitters, scattering, and environment-dependence of the extinction ([33], [6]). The situation gets better in the case of starbursts because the high energy environment is generally inhospitable to dust. Shocks from supernovae can destroy dust grains, while gas outflows can eject significant amounts of interstellar gas and dust from the site of star formation. If little diffuse dust is present within the star-forming region, the main source of opacity will come from the dust surrounding the region. Parametrizing the ``net'' obscuration of the stellar continuum as: Fobs(lambda) = F0(lambda) 10-0.4 Es(B-V) k(lambda), with Fobs(lambda) and F0(lambda) the observed and intrinsic fluxes, respectively, obscuration in starbursts is expressed as:

k(lambda) = 2.656 (-2.310 + 1.315/lambda) + 4.88 0.63 µm leq lambda leq 1.60 µm
= 2.656 (-2.156 + 1.509/lambda - 0.198/lambda2 + 0.011/lambda3) + 4.88
0.12 µm leq lambda < 0.63 µm. (1)

The connection between the color excess Es(B - V) and the measured spectral slope beta is given by the correlation in Figure 1 (right panel).

It is worth stressing that, although dust reddening corrections for starbursts are parametrized above as a foreground dust screen, Equation 1 has been derived with NO assumptions on the geometrical distribution of the dust within the galaxies. Equation 1 is a purely empirical result ([6], [4]), which includes into a single expression any effect of dust geometry, scattering, and environment-dependence of the dust composition.

Equation 1 provides a recipe for correcting the observed SEDs for the effects of dust reddening. Does it fully account for the dust obscuration as well? In other words, does Equation 1 completely recover the light from the region of star formation or does it misses the flux from dust-enshrouded regions? The answer to these questions is a positive one: Equation 1 is able to recover, within a factor ~ 2, the UV-optical light from the entire star-forming region of UV-bright, i.e. moderately obscured, starbursts.

We can prove the above statement by studying the FIR emission of the local starbursts. Dust emits in the Far-IR the stellar energy absorbed in the UV-optical. However, the Far-IR emission is not, by itself, an unambiguous measure of the opacity of the galaxy, as the intensity of the dust emission is also a function of the SFR in the galaxy. A good measure of the total opacity of the galaxy is instead provided by the ratio FIR/F(UV) ([25]). The Far-IR flux, FIR, and the UV flux, F(UV), are both proportional to the SFR, but their sensitivity to dust has opposite trends: roughly, FIR increases while F(UV) decreases for increasing amounts of dust, although the details of the trends are dictated by the geometrical distribution of the dust. In the assumption that the foreground dust screen parametrization is valid, the FIR/F(UV) ratio is related to the UV attenuation in magnitudes, A(UV), via ([25]):

FIR/F(UV) = 1.19 [ 100.4 A(UV) - 1], (2)

where the constant value 1.19 is the combination of the ratio of the bolometric stellar luminosity to the UV luminosity and the ratio of the bolometric dust emission to the FIR emission. Since F(UV) and FIR (e.g., from IRAS) are measurable in galaxies, as is beta, the UV attenuation can be related to the UV spectral slope via Equation 2 ([25]). Figure 2 shows A(UV) measured at 1,600 Å as a function of beta for a sample of Local starbursts. Overplot on the data is the trend predicted by Equation 1, with beta related to Es(B - V) using Figure 1 and the limiting case beta0 = -2.1 for Es(B - V) = 0 ([4]). Equation 1 and Figure 1 have no adjustable parameters. The agreement between the data and the predicted trend is therefore impressive, especially if we take into account that the latter is a recipe for reddening, and could in principle not account for the entire dust obscuration. Discrepancies at the low end of the locus of data points in Figure 2 are understandable in terms of sample incompletenesses.

Figure 2

Figure 2. The attenuation in magnitudes at 1,600 Å, A(1600), as a function of the UV spectral index beta. The data points (empty and filled circles) are from the same sample of UV-bright, local starbursts of Figure 1 ([18]). A(1,600) is proportional to log[FIR/F(UV)] where FIR and F(UV) are the Far-IR and UV observed luminosities, respectively (see text). The filled and empty circles correspond to two different choices of the bolometric-to-FIR correction for the dust emission. This is the most uncertain parameter in the derivation of Equation 2; yet, its effect on the data is fairly small. The straight line across the data, marked C97, is the location of the reddening curve of Equation 1, with beta0 = -2.1 for Es(B - V) = 0 ([4]). There are no adjustable parameters in the positioning of the C97 line. The agreement between the data points and the predicted attenuations from the reddening curve (Equation 1) demonstrates that reddening corrections can fully recover the intrinsic UV emission from these galaxies and the amount of star formation buried in dust is relatively small.

How does all this apply to Lyman-break galaxies? The entire purpose of obtaining dust obscuration corrections for the high-z galaxy sample is to recover the intrinsic UV emission of the galaxies, therefore deriving a more meaningful UV luminosity function, a more accurate value of the SFR for each object (which can bear into the understanding of the nature of these objects), and, finally, the intrinsic cosmic SFR density ([22]). Figure 1 (right panel) shows the observed UV spectral slopes of the z ~ 3 galaxies. Those slopes can be ``translated'' into a value of the effective color excess, which is calculated to have mean value Es(B - V) appeq 0.15 for the z ~ 3 galaxies, or an attenuation A(1600) appeq 1.6 mag ([31], see also [3]). Incidentally, this mean value of Es(B - V) is similar to that observed in the local starburst sample ([3]); this is purely coincidental, and is borne of the fact that the two samples of galaxies cover similar ranges of beta. A similar mean value of the effective color excess has been obtained by Pettini et al. ([27]) from the analysis of the nebular emission lines in the NIR spectra of a small sample of Lyman-break galaxies. Correcting the observed UV spectra for dust attenuation increases the median SFR of approx x5 in the z > 2 galaxies and of approx x3 in the z leq 1 galaxies (Figure 3). The difference in the correction factors at low and high-z is entirely due to the different wavelengths at which the two redshift regimes are probed: ~ 1,600 Å the high-z galaxies and ~ 2,800 Å the lower-z galaxies. The dust correction factors have been ``measured'' only for the high-z sample and have been assumed to hold unchanged for the z leq 1 sample, modulo the change in wavelength (see discussion in [31]).

Figure 3

Figure 3. The SFR density, in Msmsun yr-1 Mpc-3, as a function of redshift z. The data points are derived from the UV luminosity density of galaxies, converted to SFR using a Salpeter IMF in the range 0.35-100 Msmsun and continuous SF. The triangles are the observed values at 2,800 Å of Lilly et al. ([20]) and Connolly et al. ([7]). The squares are the observed values at ~ 1,600 Å as reported in Madau et al. ([23]), while the crosses are the new values from the Lyman-break galaxies by Steidel et al. ([31]). The circles represent the intrinsic SFR densities from the data of Lilly et al., Connolly et al., and Steidel et al., corrected for dust obscuration using Es(B - V) = 0.15 (see [31]). The curves marked A and B bracket the range of solutions for the intrinsic SFR density from the evolution model described in Section 4. Curve B agrees well with the obscuration-corrected data points (circles).

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