The 60- and far-infrared luminosity functions of IRAS galaxies

The 60-μm luminosity function for galaxies detected by IRAS is determined from a compilation of samples with highly complete redshift information totalling 2818 galaxies, including the new QMC–Cambridge–Durham survey and samples including many nearby, low-luminosity galaxies. We use clustering-independent maximum likelihood methods throughout. A non-parametric estimator is used to determine the shape of the luminosity function, and the best parameter set found for a suitable analytic form. We find the luminosity function to be well described by a Gaussian dependence on log(luminosity), changing over to a very flat power law at low luminosities: this latter feature is in strong contrast to previous results. We find our results to be very insensitive to various models for deviations from the Hubble flow and to different values of the Hubble constant. We present a generalization of the non-parametric estimator for determination of the bivariate luminosity function of samples defined by two flux limits. We apply this to two optically + 60-μm limited samples containing relatively large numbers of low-luminosity galaxies and confirm the flatness of the luminosity function at this end. The joint luminosity function suggests simple forms for the distribution of 60-μm luminosity versus blue luminosity and linear diameter, and we determine the maximum likelihood solutions for these forms. In addition, we determine the 40–120 μ luminosity function, and derive separate 60-μm luminosity functions for the normal and starburst populations, as classified by far-infrared temperature. We also present a new method for finding the run of density against distance for any flux and/or magnitude limited sample, independent of any assumptions on the shape of the luminosity function. Large local overdensities are found, confirming the existence of bias in previous work. This method forms an excellent indicator for evolution, and strong evolution $$[\text{luminosity} \propto (1+z)^{3\pm 1} \,\text{or}\,\text{density} \propto (1+z)^{7\pm 2}]$$ is seen in the QCD survey. The combination of luminosity function and density estimator allows us to investigate the internal consistency of our results, and we find no evidence that systematic errors outweigh the statistical uncertainties.