Annu. Rev. Astron. Astrophys. 1998. 36: 189-231
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2.3. Recombination Lines

Figure 1 shows that the most dramatic change in the integrated spectrum with galaxy type is a rapid increase in the strengths of the nebular emission lines. The nebular lines effectively re-emit the integrated stellar luminosity of galaxies shortward of the Lyman limit, so they provide a direct, sensitive probe of the young massive stellar population. Most applications of this method have been based on measurements of the Halpha line, but other recombination lines, including Hbeta, Palpha, Pbeta, Bralpha, and Br gamma, have been used as well.

The conversion factor between ionizing flux and the SFR is usually computed using an evolutionary synthesis model. Only stars with masses of > 10 Modot and lifetimes of < 20 Myr contribute significantly to the integrated ionizing flux, so the emission lines provide a nearly instantaneous measure of the SFR, independent of the previous star formation history. Calibrations have been published by numerous authors, including Kennicutt (1983a), Gallagher et al (1984), Kennicutt et al (1994), Leitherer & Heckman (1995), Madau et al (1998). For solar abundances and the same Salpeter IMF (0.1-100 Modot) as was used in deriving Equation 1, the calibrations of Kennicutt et al (1994), Madau et al (1998) yield

Equation 2 (2)

where Q (H0) is the ionizing photon luminosity and the Halpha calibration is computed for Case B recombination at Te = 10,000 K. The corresponding conversion factor for L(Brgamma) is 8.2 × 10-40 in the same units, and it is straightforward to derive conversions for other recombination lines. Equation 2 yields SFRs that are 7% lower than the widely used calibration of Kennicutt (1983a), with the difference reflecting a combination of updated stellar models and a slightly different IMF (Kennicutt et al 1994). As with other methods, there is a significant variation among published calibrations (~ 30%), with most of the dispersion reflecting differences in the stellar evolution and atmosphere models.

Large Halpha surveys of normal galaxies have been published by Cohen (1976), Kennicutt & Kent (1983), Romanishin (1990), Gavazzi et al (1991), Ryder & Dopita (1994), Gallego et al (1995), Young et al (1996). Imaging surveys have been published by numerous other authors, with some of the largest including Hodge & Kennicutt (1983), Hunter & Gallagher (1985), Ryder & Dopita (1993), Phillips (1993), Evans et al (1996), González Delgado et al (1997), Feinstein (1997). Gallego et al (1995) have observed a complete emission-line selected sample, in order to measure the volume-averaged SFR in the local universe, and this work has been applied extensively to studies of the evolution in the SFR density of the universe (Madau et al 1996).

The primary advantages of this method are its high sensitivity and the direct coupling between the nebular emission and the massive SFR. The star formation in nearby galaxies can be mapped at high resolution even with small telescopes, and the Halpha line can be detected in the redshifted spectra of starburst galaxies to z >> 2 (e.g. Bechtold et al 1997). The chief limitations of the method are its sensitivity to uncertainties in extinction and the IMF and the assumption that all of the massive star formation is traced by the ionized gas. The escape fraction of ionizing radiation from individual HII regions has been measured both directly (Oey & Kennicutt 1997) and from observations of the diffuse Halpha emission in nearby galaxies (e.g. Hunter et al 1993, Walterbos & Braun 1994, Kennicutt et al 1995, Ferguson et al 1996, Martin 1997), with fractions of 15-50% derived in both sets of studies. Thus it is important when using this method to include the diffuse Halpha emission in the SFR measurement (Ferguson et al 1996). However, the escape fraction from a galaxy as a whole should be much lower. Leitherer et al (1995a) directly measured the redshifted Lyman continuum region in four starburst galaxies, and they derived an upper limit of 3% on the escape fraction of ionizing photons. Much higher global escape fractions of 50-94% and local escape fractions as high as 99% have been estimated by Patel & Wilson (1995a, b), based on a comparison of O-star densities and Halpha luminosities in M33 and NGC 6822, but those results are subject to large uncertainties because the O-star properties and SFRs were derived from UBV photometry, without spectroscopic identifications. If the direct limit of < 3% from Leitherer et al (1995a) is representative, then density bounding effects are a negligible source of error in this method. However, it is very important to test this conclusion by extending these types of measurements to a more diverse sample of galaxies.

Extinction is probably the most important source of systematic error in Halpha-derived SFRs. The extinction can be measured by comparing Halpha fluxes with those of IR recombination lines or the thermal radio continuum. Kennicutt (1983a), Niklas et al (1997) have used integrated Halpha and radio fluxes of galaxies to derive a mean extinction A(Halpha) = 0.8-1.1 mag. Studies of large samples of individual HII regions in nearby galaxies yield similar results, with mean A(Halpha) = 0.5-1.8 mag (e.g. Caplan & Deharveng 1986, Kaufman et al 1987, van der Hulst et al 1988, Caplan et al 1996).

Much higher extinction is encountered in localized regions, especially in the the dense HII regions in circumnuclear starbursts, and there the near-IR Paschen or Brackett recombination lines are required to reliably measure the SFR. Compilations of these data include those by Puxley et al (1990), Ho et al (1990), Calzetti et al (1996), Goldader et al (1995, 1997), Engelbracht (1997), and references therein. The Paschen and Brackett lines are typically 1-2 orders of magnitude weaker than Halpha, so most measurements to date have been restricted to high surface brightness nuclear HII regions, but it is gradually becoming feasible to extend this approach to galaxies as a whole. The same method can be applied to higher-order recombination lines or the thermal continuum emission at submillimeter and radio wavelengths. Examples of such applications include H53alpha measurements of M82 by Puxley et al (1989) and radio continuum measurements of disk galaxies and starbursts by Israel & van der Hulst (1983), Klein & Grave (1986), Turner & Ho (1994), Niklas et al (1995).

The ionizing flux is produced almost exclusively by stars with M > 10 Modot, so SFRs derived from this method are especially sensitive to the form of the IMF. Adopting the Scalo (1986) IMF, for example, yields SFRs that are approximately three times higher than that derived with a Salpeter IMF. Fortunately, the Halpha equivalent widths and broadband colors of galaxies are very sensitive to the slope of the IMF over the mass range 1-30 Modot, and these can be used to constrain the IMF slope (Kennicutt 1983a, Kennicutt et al 1994). The properties of normal disks are well fitted by a Salpeter IMF (or by a Scalo function with Salpeter slope above 1 Modot), consistent with observations of resolved stellar populations in nearby galaxies (e.g. Massey 1998). As with the UV continuum method, it is important when applying published SFRs to take proper account of the IMF that was assumed.

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