3.1.2. The Infrared-to-Blue Ratio
The infrared-to-blue ratio (IR/B) compares the luminosity reprocessed by dust to that of escaping starlight, and is therefore short-hand for the ratio of total infrared to total emerging photospheric emission, from the near-infrared to the ultra-violet. This ratio ranges broadly, from < 0.01 to ~ 100 in known galaxies (Figure 1), with a weak dependence on parameters such as morphology (Sauvage & Thuan 1994), suggesting that it fluctuates substantially in time for the same galaxy.
Because it is a dust-to-star luminosity ratio, IR/B might be interpreted as a function of the effective optical depth of a simple system of stars and dust, with IR/B [ - (1 - e-)] / (1 - e-). Most normal galaxies however are far from this simplicity: Some of the visible luminosity comes from stars not participating in the heating of dust, especially old stars in the bulge or far from interstellar clouds. On the other hand, some of the infrared luminosity is traceable to stars completely hidden inside dense clouds, and all but invisible from the outside. Still, IR/B could be turned into a measure of effective optical depth using assumptions for the geometry of stars and dust, for the spectral energy distributions of heating stars, and for the dust efficiency of absorption as a function of (e.g. Xu & Helou 1996). Such assumptions may be well bounded in special cases such as specific parts of a disk, or star-burst galaxies, but their uncertainty is harder to estimate for whole galaxies.
While the interpretation above may be a good approximation for IR/B 1, an alternative at lower values is that IR/B characterizes the ratio of current or recent star formation rate to the long-term average rate. In a picture where geometry, heating spectra and dust properties are fixed, the dust luminosity may be interpreted as a measure of stars interacting with the ISM, and thus of the stars recently formed out of that ISM. Unfortunately, the precise time intervals implied by the terms ``recent'' and ``long-term'' are themselves a function of the history of star formation in a given galaxy. This interpretation of IR/B applies to systems whose infrared emission is limited by the amount of heating photons available, whereas the optical depth interpretation applies to systems whose infrared emission is limited by the amount of dust available to heat. A dwarf galaxy like NGC 1569 for instance may be undergoing intense star heating by young stars, but have very little neutral ISM left, resulting in low IR/B. On the other hand, a quiescent galaxy may generate most of its infrared emission in HI clouds heated by the older stellar population, and display a similarly low IR/B. The degeneracy between these two cases can only be broken by use of other observables, such as stellar population and morphology, infrared spectral energy distribution, or spectroscopic diagnostics of the gas.
The large dispersion in the IR/B ratio points to dramatic fluctuations in the star formation activity during the lifetime of a galaxy, hence the notion that much of star formation is episodic. Small irregular galaxies are characterized almost entirely by intense episodes of star formation separated by long quiescent periods. There is abundant evidence that galaxies undergoing a nuclear starburst cannot sustain it for more than a small fraction of their lifetime (Sanders & Mirabel 1987). Large disk galaxies in steady state appear to have several episodes under way at any time within their disk, and observed parameters integrated over the whole galaxy are an ensemble average across all phases of these episodes.