Annu. Rev. Astron. Astrophys. 1998. 36: 189-231
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2. DIAGNOSTIC METHODS

Individual young stars are unresolved in all but the closest galaxies, even with the Hubble Space Telescope (HST), so most information on the star formation properties of galaxies comes from integrated light measurements in the ultraviolet (UV), far-infrared (FIR), or nebular recombination lines. These direct tracers of the young stellar population have largely supplanted earlier SFR measures based on synthesis modeling of broadband colors, though the latter are still applied to multicolor observations of faint galaxies. This section begins with a brief discussion of synthesis models, which form the basis of all of the methods, followed by more detailed discussions of the direct SFR tracers.

2.1. Integrated Colors and Spectra, Synthesis Modeling

The basic trends in galaxy spectra with Hubble type are illustrated in Figure 1, which shows examples of integrated spectra for E, Sa, Sc, and Magellanic irregular galaxies (Kennicutt 1992b). When progressing along this sequence, several changes in the spectrum are apparent: a broad rise in the blue continuum, a gradual change in the composite stellar absorption spectrum from K-giant dominated to A-star dominated, and a dramatic increase in the strengths of the nebular emission lines, especially Halpha.

Figure 1

Figure 1. Integrated spectra of elliptical, spiral, and irregular galaxies, from Kennicutt (1992b). The fluxes have been normalized to unity at 5500 Å.

Although the integrated spectra contain contributions from the full range of stellar spectral types and luminosities, it is easy to show that the dominant contributors at visible wavelengths are intermediate-type main sequence stars (A to early F) and G-K giants. As a result, the integrated colors and spectra of normal galaxies fall on a relatively tight sequence, with the spectrum of any given object dictated by the ratio of early- to late-type stars or, alternatively, by the ratio of young (< 1 Gyr) to old (3-15 Gyr) stars. This makes it possible to use the observed colors to estimate the fraction of young stars and the mean SFR over the past 108 - 109 years.

The simplest application of this method would assume a linear scaling between the SFR and the continuum luminosity integrated over a fixed bandpass in the blue or near-ultraviolet. Although this may be a valid approximation in starburst galaxies, where young stars dominate the integrated light across the visible spectrum, the approximation breaks down in most normal galaxies, where a considerable fraction of the continuum is produced by old stars, even in the blue (Figure 1). However, the scaling of the SFR to continuum luminosity is a smooth function of the color of the population, and this can be calibrated using an evolutionary synthesis model.

Synthesis models are used in all of the methods described here, so it is useful to summarize the main steps in the construction of a model. A grid of stellar evolution tracks is used to derive the effective temperatures and bolometric luminosities for various stellar masses as a function of time, and these are converted into broadband luminosities (or spectra) using stellar atmosphere models or spectral libraries. The individual stellar templates are then summed together, weighted by an initial mass function (IMF), to synthesize the luminosities, colors, or spectra of single-age populations as functions of age. These isochrones can then be added in linear combination to synthesize the spectrum or colors of a galaxy with an arbitrary star formation history, usually parametrized as an exponential function of time. Although a single model contains at least four free parameters (the star formation history, galaxy age, metal abundance, and IMF), the colors of normal galaxies are well represented by a one-parameter sequence with fixed age, composition, and IMF, varying only in the time dependence of the SFR (Searle et al 1973, Larson & Tinsley 1978, Charlot & Bruzual 1991).

Synthesis models have been published by several authors and are often available in digital form. An extensive library of models has been compiled by Leitherer et al (1996a), and the models are described in a companion conference volume (Leitherer et al 1996b). Widely used models for star forming galaxies include those of Bruzual & Charlot (1993), Bertelli et al (1994), Fioc & Rocca-Volmerange (1997). Leitherer & Heckman (1995) have published an extensive grid of models that is optimized for applications to starburst galaxies.

The synthesis models provide relations between the SFR per unit mass or luminosity and the integrated color of the population. An example is given in Figure 2, which plots the SFR per unit of U, B, and V luminosity as functions of U - V color, based on the models of Kennicutt et al (1994). Figure 2 confirms that the broadband luminosity by itself is a poor tracer of the SFR; even the SFR / LU ratio varies by more than an order of magnitude over the relevant range of galaxy colors. However, the integrated color provides a reasonable estimate of the SFR per unit of luminosity, especially for the bluer galaxies.

Figure 2

Figure 2. Relationship between star formation rate (SFR) per unit broadband luminosity in the UBV passbands and integrated color, from the evolutionary synthesis models of Kennicutt et al (1994). The models are for 10-billion-year-old disks, a Salpeter IMF, and exponential star formation histories. The U, B, and V luminosities are normalized to those of the Sun in the respective bandpasses.

The SFRs derived in this way are relatively imprecise and are prone to systematic errors from reddening or from an incorrect IMF, age, or metallicity of star formation history (Larson & Tinsley 1978). Nevertheless, the method offers a useful means of comparing the average SFR properties of large samples of galaxies when absolute accuracy is not required. The method should be avoided in applications where the dust content, abundances, or IMFs are likely to change systematically across a population.

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