This paper revisits the classical Kennicutt method for inferring the stellar initial mass function ( IMF ) from the integrated light properties of galaxies .
The large size , uniform high quality data set from the Sloan Digital Sky Survey DR4 is combined with more in depth modeling and quantitative statistical analysis to search for systematic IMF variations as a function of galaxy luminosity .
Galaxy H \alpha equivalent widths are compared to a broadband color index to constrain the IMF .
This parameter space is useful for breaking degeneracies which are traditionally problematic .
Age and dust corrections are largely orthogonal to IMF variations .
In addition the effects of metallicity and smooth star formation history e-folding times are small compared to IMF variations .
We find that for the sample as a whole the best fitting IMF slope above 0.5 { M } _ { \odot } is \Gamma = 1.4535 with a negligible random error of \pm 0.0004 and a systematic error of \pm 0.1 .
Galaxies brighter than around { M } _ { r, 0.1 } = -20 ( including galaxies like the Milky Way which has { M } _ { r, 0.1 } \sim - 21 ) are well fit by a universal \Gamma \sim 1.4 IMF , similar to Salpeter , and smooth , exponential star formation histories ( SFH ) .
Fainter galaxies prefer steeper IMFs and the quality of the fits reveal that for these galaxies a universal IMF with smooth SFHs is actually a poor assumption .
Several sources of sample bias are ruled out as the cause of these luminosity dependent IMF variations .
Analysis of bursting SFH models shows that an implausible coordination of burst times is required to fit a universal IMF to the { M } _ { r, 0.1 } = -17 galaxies .
This leads to the conclusions that the IMF in low luminosity galaxies has fewer massive stars , either by steeper slope or lower upper mass cutoff , and is not universal .