3.3. The Infrared-Radio Connection
The tightest and most universal correlation known among galaxy fluxes connects the FIR emission from dust heated by stars with the non-thermal radio emission in the range from 2 to 50 cm, which is known to be synchrotron radiation from CR e- trapped in the interstellar magnetic field. This tightest of correlations is also the most puzzling. First, because of the indirect connection between the two mechanisms and populations of emitters, and the many parameters involved in producing the luminosities at the two wavelengths, such as current stellar population properties, dust optical depth, magnetic field strength, and CR e- acceleration and escape mechanisms. Secondly, surprising because of the large difference between the two luminosities; the ratio between the two bands is about 5 x 105, with a dispersion of about 50%. See reviews by Helou (1991) and Condon (1992).
The first mention of a close relation between far infrared and radio emission appeared as soon as the relevant data became available. Rickard and Harvey (1984) pointed out a strong correlation in a sample of 30 late type galaxies between the central emission at 20 cm and the emission in the 40 to 160 µm spectral range. They related the correlation to star formation activity, and assumed the non-thermal radio emission to be dominated by supernova remnants, as predicted by Harwit and Pacini (1975). Rickard and Harvey (1984) were puzzled however by indications that the same correlation applied to the disk emission, because that would imply cooperation between the magnetic field B, the interstellar gas density n, and the density of CR e-. Since 1984, the vastly superior data returned by the VLA and IRAS have placed the correlation on a far more solid empirical footing without changing the basic facts. The situation on the side of interpretation however has improved more slowly, and a consensus has yet to emerge as to the physical significance of this correlation.
The global correlation was noticed early on in the IRAS data by Dickey and Salpeter (1984), then independently established by de Jong et al. (1985) using a sample of IRAS sources selected from the early mission returns, and by Helou, Soifer and Rowan-Robinson (1985) using an optically selected list of galaxies in the Virgo cluster and in the field. Regardless of the sample selection criteria, the ratio Q of infrared to radio in samples of star forming galaxies displays an intrinsic population dispersion of 50% or less (Helou, Soifer and Rowan-Robinson 1985; Sanders and Mirabel 1985; Condon and Broderick 1988; Wunderlich and Klein 1988; Unger et al. 1989) over four decades in luminosity, though non-linearities have been claimed, with the radio increasing faster than the infrared power (Cox et al. 1988; Menon 1991). The correlation has been shown to hold at high redshifts (e.g. Karoji, Dennefeld and Ukita (1985), Hacking et al. 1989) and has become an accepted property of all star forming galaxies (Condon 1992).
A definitive empirical treatment of the correlation was published by Condon, Anderson & Helou (1991), showing that it is asymptotically linear as the ratio of radio-to-visible, or equivalently of infrared-to-visible, increases, so that the ``true'' correlation is evident when the system is powered by young stars (Figure 3; see also Xu 1990). This happens consistently for galaxies with infrared-to-visible luminosity ratios greater than ~ 0.3, which are still relatively optically thin galaxies. For galaxies less active in star formation, Q rises slowly above the standard correlation value. Within galaxy disks, the infrared emission is clearly more centrally peaked than the radio emission (Marsh & Helou 1998; Marsh & Helou 1995; Bicay & Helou 1990; Rice et al. 1990; Beck & Golla 1988; Wainscoat et al. 1987).
Figure 3. The strong relation between infrared and radio is best shown in this figure from Condon, Anderson & Helou (1991), clearly illustrating the low dispersion in the ratio Q in the more active galaxies. The left-hand-side frame shows data from the IRAS Bright Galaxy Sample (Soifer et al. 1986), an infrared-selected sample with a preponderance of galaxies dominated by on-going star formation. The right-hand-side frame shows data for a sample drawn from the Revised Shapley-Ames catalog, whose visible-light selection gives a more quiescent galaxy population.
The theoretical understanding of this correlation is still imperfect. The physical explanation needs to invoke a two-part argument, namely a luminosity balance to explain optically thick systems, and a filtering match to explain optically thin systems. In an optically thick galaxy, all dust-heating radiation is re-radiated in the infrared on the one hand, and all CR e- created are trapped by the magnetic fields long enough for their available energy to dissipate as synchrotron luminosity. In this case, linking the dust-heating luminosity and the CR e- luminosity is sufficient to produce the observed correlation. This linkage is achieved because stars more massive than ~ 8 M dominate the dust heating and produce Type II supernovae whose shocks accelerate cosmic rays including CR e- (Völk 1989). Condon (1992) has shown that the ratio of heating to CR e- luminosities is not very sensitive to upper mass cut-off of the Initial Mass Function (IMF), nor to age of starburst. See for historical interest also Lequeux (1971), Klein (1982) and Kennicutt (1983).
For optically thin galaxies, the effective dust optical depth of the galaxy to heating radiation must match its efficiency at extracting synchrotron radiation from CR e-. Helou & Bicay (1993) presented a model which achieves that match by assuming simple connections among physical parameters in the ISM, most importantly between the density of the medium and the magnetic field intensity. The model takes into consideration geometry of dust and stars and magnetic field, diffusion, radiative decay and escape of CR e-, and develops a picture where the radio disk is a smeared version of the infrared disk, the smearing being greater for more transparent disks. This model was found subsequently to be consistent with the observed details of the infrared-radio correlation within disks of galaxies (Marsh & Helou 1998). However, models for the physics underlying the correlation remain sufficiently complex that other mechanisms for the radio emission have been proposed because they provide closer connection to the infrared (e.g. Harwit in this volume).