The luminosity function in the far infra-red has been derived from IRAS data by Hacking and Houck (1987). The visibility function and the possibility of evolution in this luminosity function are discussed by Hacking, Condon and Houck (1987). Ratio functions of radio-infrared luminosity and radio-optical luminosity are presented by Hummel et al. (1988). The far IR-radio luminosity ratio is remarkably constant among spiral galaxies (Helou et al. 1985, DeJong et al. 1985, Beck and Golla 1988). The dispersion in this ratio is only about 0.2 (Wunderlich and Klein 1988), which means that f(R) is almost a delta function (although Seyferts and blue compact dwarfs show higher values than normal spirals). Thus the radio luminosity is a good predictor of the FIR luminosity for spirals.
Both the radio and FIR luminosity functions show a variation between cluster and field, which is most easily seen in the ratio functions (Gavazzi and Jaffe 1986, Bicay and Giovanelli 1987). The effect is that spiral galaxies in rich clusters which show evidence for HI deficiency tend to have lower radio continuum luminosity and cooler FIR colors (S60 µm / S100 µm) than similar field galaxies. This is often explained as a quenching of the star formation rate by stripping of the galaxy's interstellar gas. On the other hand, a few spirals in rich clusters show significantly enhanced radio emission, which suggests a burst of star formation during the first passage of a spiral through the intra cluster medium.