Annu. Rev. Astron. Astrophys. 1998. 36: 189-231 Copyright © 1998 by Annual Reviews. All rights reserved

2.5. Far-Infrared Continuum

A significant fraction of the bolometric luminosity of a galaxy is absorbed by interstellar dust and re-emitted in the thermal IR, at wavelengths of roughly 10-300 µm. The absorption cross section of the dust is strongly peaked in the ultraviolet, so in principle the FIR emission can be a sensitive tracer of the young stellar population and SFR. The IRAS survey provides FIR fluxes for over 30,000 galaxies (Moshir et al 1992), offering a rich reward to those who can calibrate an accurate SFR scale from the 10- to 100-µm FIR emission.

The efficacy of the FIR luminosity as an SFR tracer depends on the contribution of young stars to heating of the dust and on the optical depth of the dust in the star forming regions. The simplest physical situation is one in which young stars dominate the radiation field throughout the UV-visible and the dust opacity is high everywhere, in which case the FIR luminosity measures the bolometric luminosity of the starburst. In such a limiting case the FIR luminosity is the ultimate SFR tracer, providing what is essentially a calorimetric measure of the SFR. Such conditions roughly hold in the dense circumnuclear starbursts that power many IR-luminous galaxies.

The physical situation is more complex in the disks of normal galaxies, however (e.g. Lonsdale & Helou 1987, Cox & Mezger 1989, Rowan-Robinson & Crawford 1989). The FIR spectra of galaxies contain both a "warm" component associated with dust around young star-forming regions ( ~ 60 µm) and a cooler "infrared cirrus" component ( 100 µm), which is associated with more extended dust heated by the interstellar radiation field. In blue galaxies, both spectral components may be dominated by young stars, but in red galaxies, where the composite stellar continuum drops off steeply in the blue, dust heating from the visible spectra of older stars may be very important.

The relation of the global FIR emission of galaxies to the SFR has been a controversial subject. In late-type star-forming galaxies, where dust heating from young stars is expected to dominate the 40- to 120-µm emission, the FIR luminosity correlates with other SFR tracers such as the UV continuum and H luminosities (e.g. Lonsdale & Helou 1987, Sauvage & Thuan 1992, Buat & Xu 1996). However, early-type (S0-Sab) galaxies often exhibit high FIR luminosities but much cooler, cirrus-dominated emission. This emission has usually been attributed to dust heating from the general stellar radiation field, including the visible radiation from older stars (Lonsdale & Helou 1987, Buat & Deharveng 1988, Rowan-Robinson & Crawford 1989, Sauvage & Thuan 1992, 1994, Walterbos & Greenawalt 1996). This interpretation is supported by anomalously low UV and H emission (relative to the FIR luminosity) in these galaxies. However, Devereux & Young (1990), Devereux & Hameed (1997) have argued that young stars dominate the 40- to 120-µm emission in all of these galaxies, so that the FIR emission directly traces the SFR. They have provided convincing evidence that young stars are an important source of FIR luminosity in at least some early-type galaxies, including barred galaxies with strong nuclear starbursts and some unusually blue objects (Section 4). On the other hand, many early-type galaxies show no independent evidence of high SFRs, suggesting that the older stars or active galactic nuclei (AGNs) are responsible for much of the FIR emission. The Space Infrared Telescope Facility, scheduled for launch early in the next decade, should provide high-resolution FIR images of nearby galaxies and clarify the relationship between the SFR and IR emission in these galaxies.

The ambiguities discussed above affect the calibration of SFRs in terms of FIR luminosity, and there probably is no single calibration that applies to all galaxy types. However, the FIR emission should provide an excellent measure of the SFR in dusty circumnuclear starbursts. The SFR vs L_FIR conversion is derived using synthesis models as described above. In the optically thick limit, it is only necessary to model the bolometric luminosity of the stellar population. The greatest uncertainty in this case is adoption of an appropriate age for the stellar population; this may be dictated by the time scale of the starburst itself or by the time scale for the dispersal of the dust (so the >> 1 approximation no longer holds). Calibrations have been published by several authors under different assumptions about the star formation time scale (e.g. Hunter et al 1986, Lehnert & Heckman 1996, Meurer et al 1997, Kennicutt 1998). Applying the models of Leitherer & Heckman (1995) for continuous bursts of age 10-100 Myr and adopting the IMF in this paper yields the following relation (Kennicutt 1998):

(4)

where L_FIR refers to the IR luminosity integrated over the full-, mid-, and far-IR spectrum (8-1000 µm), though for starbursts most of this emission will fall in the 10- to 120-µm region (readers should beware that the definition of L_FIR varies in the literature). Most of the other published calibrations lie within ± 30% of Equation 4. Strictly speaking, the relation given above applies only to starbursts with ages less than 10⁸ years, where the approximations applied are valid. In more quiescent, normal star-forming galaxies, the relation will be more complicated; the contribution of dust heating from old stars will tend to lower the effective coefficient in Equation 4, whereas the lower optical depth of the dust will tend to increase the coefficient. In such cases, it is probably better to rely on an empirical calibration of SFR / L_FIR that is based on other methods. For example, Buat & Xu (1996) derived a coefficient of 8⁺⁸_-3 × 10^-44, valid for galaxies of type Sb and later only, based on IRAS and UV flux measurements of 152 disk galaxies. The FIR luminosities share the same IMF sensitivity as the other direct star formation tracers, and it is important to be consistent when comparing results from different sources.