The fading of young stellar populations and the luminosity functions of dwarf, irregular and starburst galaxies

Dwarf, irregular and infrared-luminous starburst galaxies are all known to have “steep” luminosity functions with faint-end behavior roughly φ(L) ∝ L−1.8. This form is exactly what is expected if the luminosities of these objects fade with time as L ∝ t−1.3, because the objects spend more time at low luminosities than high, even if they form with a wide range of initial masses. Models of young stellar populations show this fading behavior when the star formation has occured in a single, short, recent burst. Steep luminosity functions therefore do not require steep mass functions if the galaxies are powered by fading bursts. The local-galaxy Hα luminosity function—which is less steep than L−1.8—is also well-fit by this mechanism, because ionizing photon flux fades much more quickly than broad-band optical luminosity. An age-luminosity relation and a wavelength-dependence of the luminosity function are both predicted. In the context of this mechanism, the slope of the luminosity function provides a constraint on the stellar initial mass function in the bursts. Subject headings: infrared: galaxies — galaxies: luminosity function, mass function — galaxies: starburst — galaxies: stellar content — stars: luminosity function, mass function