Annu. Rev. Astron. Astrophys. 2005. 43: 727-768 Copyright © 2005 by Annual Reviews. All rights reserved

APPENDIX: THE PHENOMENOLOGICAL MODEL OF LAGACHE ET AL. (2004)

In this paper, we make extensive use of the Lagache et al. (2004) phenomenological model to illustrate our points. This model constrains in a simple way the evolution of the infrared luminosity function with redshift. It fits all the existing source counts consistent with the redshift distribution, the CIB intensity, and, for the first time, the CIB fluctuation observations, from the mid-infrared to the submillimeter range. In this model, Lagache et al. (2004) assume that infrared galaxies are mostly powered by star formation and hence they use SEDs typical of star-forming galaxies. Although some of the galaxies will have AGN-dominated SEDs, they are a small enough fraction that they do not affect the results significantly. They therefore construct "normal" and starburst galaxy template SEDs: a single form of SED is associated with each activity type and luminosity. They assume that the luminosity function is represented by these two activity types and that they evolve independently. They search for the form of evolution that best reproduces the existing data. An example of two cosmological implications of this model is (a) the PAH features remain prominent in the redshift band 0.5-2.5 (as observationally shown by e.g., Caputi et al. 2005), and (b) the infrared energy output has to be dominated by ~ 3 ~ 10¹¹ L to ~ 3 × 10¹² L galaxies from redshift 0.5 to 2.5.

The excellent agreement between the model and all the available observational constraints makes this model a likely good representation of the average luminosity function as a function of redshift and a useful tool to discuss observations and models. Its rather simple assumptions such as the single parameter sequence of SEDs for starburst galaxies is certainly not accounting for some of the detailed recent observations but probably do not affect seriously the redshift evolution of the averaged properties which are what is modeled.