We investigate the time evolution and spatial variation of the stellar initial mass function ( IMF ) in star-forming disk galaxies by using chemodynamical simulations with an IMF model depending both on local densities and metallicities ( [ Fe/H ] ) of the interstellar medium ( ISM ) .
We find that the slope ( \alpha ) of a power-law IMF ( N ( m ) \propto m ^ { - \alpha } ) for stellar masses larger than 1 M _ { \odot } evolves from the canonical Salpeter IMF ( \alpha \approx 2.35 ) to be moderately top-heavy one ( \alpha \approx 1.9 ) in the simulated disk galaxies with starbursts triggered by galaxy interaction .
We also find that \alpha in star-forming regions correlates with star formation rate densities ( \Sigma _ { SFR } in units of M _ { \odot } yr ^ { -1 } kpc ^ { -2 } ) .
Feedback effects of Type Ia and II supernovae are found to prevent IMFs from being too top-heavy ( \alpha < 1.5 ) .
The simulation predicts \alpha \approx 0.23 \log \Sigma _ { SFR } +1.7 for \log \Sigma _ { SFR } \geq - 2 ( i.e. , more top-heavy in higher \Sigma _ { SFR } ) , which is reasonably consistent well with corresponding recent observational results .
The present study also predicts that inner regions of starburst disk galaxies have smaller \alpha thus are more top-heavy ( d \alpha / dR \sim 0.07 kpc ^ { -1 } for R \leq 5 kpc ) .
The predicted radial \alpha gradient can be tested against future observational studies of the \alpha variation in star-forming galaxies .