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 phi(L)-propto- L^(-1.8). This form is exactly what is expected if the luminosities of these objects fade with time as L-propto-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 H-alpha 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.