Annu. Rev. Astron. Astrophys. 1998. 36: 189-231
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2.2. Ultraviolet Continuum

The limitations described above can be avoided if observations are made at wavelengths where the integrated spectrum is dominated by young stars, so that the SFR scales linearly with luminosity. The optimal wavelength range is 1250-2500 Å, longward of the Lyalpha forest but short enough to minimize spectral contamination from older stellar populations. These wavelengths are inaccessible from the ground for local galaxies (z < 0.5), but the region can be observed in the redshifted spectra of galaxies at z ~ 1-5. The recent detection of the redshifted UV continua of large numbers of z > 3 galaxies with the Keck telescope has demonstrated the enormous potential of this technique (Steidel et al 1996).

The most complete UV studies of nearby galaxies are based on dedicated balloon, rocket, and space experiments (Smith & Cornett 1982, Donas & Deharveng 1984, Donas et al 1987, 1995, Buat 1992, Deharveng et al 1994). The database of high-resolution UV imaging of galaxies is improving rapidly, mainly from HST (Meurer et al 1995, Maoz et al 1996) and the Ultraviolet Imaging Telescope (Smith et al 1996, Fanelli et al 1998). An atlas of UV spectra of galaxies from the International Ultraviolet Explorer has been published by Kinney et al (1993). A recent conference volume by Waller et al (1997) highlights recent UV observations of galaxies.

The conversion between the UV flux over a given wavelength interval and the SFR can be derived using the synthesis models described earlier. Calibrations have been published by Buat et al (1989), Deharveng et al (1994), Leitherer et al (1995b), Meurer et al (1995), Cowie et al (1997), Madau et al (1998) for wavelengths in the range 1500-2800 Å. The calibrations differ over a full range of ~ 0.3 dex, when converted to a common reference wavelength and IMF, with most of the difference reflecting the use of different stellar libraries or different assumptions about the star formation time scale. For integrated measurements of galaxies, it is usually appropriate to assume that the SFR has remained constant over time scales that are long compared with the lifetimes of the dominant UV emitting population (< 108 year), in the "continuous star formation" approximation. Converting the calibration of Madau et al (1998) to Salpeter's (1955) IMF with mass limits 0.1 and 100 Modot yields

Equation 1 (1)

For a Salpeter IMF, the composite UV spectrum happens to be nearly flat in Lnu, over the wavelength range 1500-2800 Å, and this allows us to express the conversion in Equation 1 in such simple form. The corresponding conversion in terms of Llambda will scale as lambda-2. Equation 1 applies to galaxies with continuous star formation over time scales of 108 years or longer; the SFR / Lnu ratio will be significantly lower in younger populations such as young starburst galaxies. For example, continuous burst models for a 9-million-year-old population yield SFRs that are 57% higher than those given in Equation 1 (Leitherer et al 1995b). It is important when using this method to apply an SFR calibration that is appropriate to the population of interest.

The main advantages of this technique are that it is directly tied to the photospheric emission of the young stellar population and it can be applied to star-forming galaxies over a wide range of redshifts. As a result, it is currently the most powerful probe of the cosmological evolution in the SFR (Madau et al 1996, Ellis 1997). The chief drawbacks of the method are its sensitivity to extinction and the form of the IMF. Typical extinction corrections in the integrated UV magnitudes are 0-3 magnitudes (mag) (Buat 1992, Buat & Xu 1996). The spatial distribution of the extinction is very patchy, with the emergent UV emission dominated by regions of relatively low obscuration (Calzetti et al 1994), so calibrating the extinction correction is problematic. The best determinations are based on two-component radiative transfer models, which take into account the clumpy distribution of dust and make use of reddening information from the Balmer decrement or IR recombination lines (e.g. Buat 1992, Calzetti et al 1994, Buat & Xu 1996, Calzetti 1997).

The other main limitation, which is shared by all of the direct methods, is the dependence of the derived SFRs on the assumed form of the IMF. The integrated spectrum in the 1500- to 2500-Å range is dominated by stars with masses above ~ 5 Modot, so the SFR determination involves a large extrapolation to lower stellar masses. Fortunately, there is little evidence for large systematic variations in the IMF among star-forming galaxies (Scalo 1986, Gilmore et al 1998), with the possible exception of IR-luminous starbursts, where the UV emission is of little use anyway.

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