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 occurred 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 fitted by this mechanism, because ionizing photon flux fades much more quickly than broadband 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.