3.4. The ``Two-Component Model''

A ``two-component model'' is any representation of the spread of properties of a system as the result of the superposition of two components whose properties define the extremes of that spread. Such a model was invoked to explain the IRAS color-color diagram, describing normal galaxies as a linear combination of a quiescent component and a star-forming component, whose mixing ratio determines the colors of a given system (Helou 1986). The FIR-cold, ``cirrus-like'' component is supposed to arise primarily from low density, low radiation intensity quiescent regions heated primarily though not exclusively by older stars. The FIR-warm ``active'' component corresponds to dust heated in the vicinity of star-forming regions. Each of these components has its own luminosity and effective optical depth, and one could in principle solve for at least some of these quantities in any given galaxy with sufficient data. The infrared luminosity and optical depth of the active component combine to yield the heating luminosity in star forming regions, and therefore the star formation rate. This type of decomposition is mostly morphological, and particularly useful for nearby, well resolved galaxies such as M31 (Xu & Helou 1996). Note the similar but lower dynamic range decomposition proposed by Larson & Tinsley (1978) using the visible colors U-B and B-V.

A more physical and useful decomposition would be to represent the infrared luminosity as L_ION(IR) + L_NON(IR), where the first term reflects heating by ionizing stars, and the second heating by non-ionizing stars. The very existence of L_NON(IR) has been challenged by Devereux & Young (1990, 1992, and subsequent papers). Their arguments however are critically dependent on very uncertain assumptions about the upper mass cut-off of the stellar mass function in galaxies, and can therefore be easily dismissed. Furthermore, detailed studies of nearby galaxies prove that L_NON(IR) can contribute more than half L(IR) (Walterbos et al. 1987; Rice et al. 1990; Rand et al. 1992; Xu & Helou 1996). Smith et al. (1991) show in NGC 4736 a striking example of the infrared emission from the nuclear region being dominated by L_NON(IR), and surrounded by a star forming ring whose emission is dominated by L_ION(IR).

How can the mixing ratio of the two components in this physical decomposition be estimated? Given its definition, the best indicator would be a measure of the hydrogen recombination rate and thus of the total ionizing flux in the system, preferably obtained from a long-wavelength transition such as Br to avoid extinction effects. That would determine the amount of ionizing flux and the total stellar luminosity, from which the dust heating could be estimated, yielding L_ION(IR). Another approach to estimating the mixing ratio is offered by the infrared-radio correlation. Because of the close coincidence between the lower mass limit for ionizing stars ~ 6 M, and the lower mass limit for supernova-capable stars ~ 8 M, one could associate L_ION(IR) with the radio-loud component and thus use Q = L(IR) / L(radio) as an index to L_ION(IR)/L_NON(IR).

In any case, galaxies at the extremes of the L_ION(IR) / L_NON(IR) can be readily identified since parameters such as IR/B, L(FIR)/L(HI), IRAS colors or Q also approach their extreme values in such galaxies. More detailed modeling as in papers mentioned earlier might be needed to estimate the mixing ratio in specific galaxies. On the other hand, infrared luminosity and morphology would be poor indicators of a galaxy's position on that mixing ratio scale.

The two-component model proposes a simple picture where the infrared properties of a galaxy are determined by the mixing ratio L_ION(IR)/L_NON(IR), and where each of these infrared components results from a heating luminosity and a corresponding optical depth. While the mixing ratio in a given galaxy may be quite uncertain, one can select samples of galaxies for statistical analysis where this ratio is biased towards L_ION(IR) or L_NON(IR). Studies of the star formation rate in galaxies should use samples biased towards high mixing ratios of ionizing to non-ionizing luminosities, to support the simple assumption that L(IR) is a good measure of the star formation rate. Infrared selected samples such as the IRAS Bright Galaxy Sample (Soifer et al. 1989) are ~ 80% populated by galaxies dominated by L_ION(IR), and comprise 10% objects dominated by L_NON(IR). Objects with high mixing ratios also tend to have high IR/B ratios, since the optical depth associated with star formation naturally tends to be quite elevated. On the other hand, studies aimed at the structure of stars and the ISM in galaxies should use broader samples, such as optically selected or volume-limited samples. Optically selected samples such as one derived from the Uppsala Galaxy Catalogue (Bothun et al. 1989) have 40 to 50% of galaxies dominated by L_ION(IR) and 20 to 25% dominated by L_NON(IR). Volume-limited or cluster samples may be even richer in quiescent galaxies. In galaxies with low mixing ratios, the optical depths are harder to estimate, but remain smaller than unity in general.