Origin of a bottom-heavy stellar initial mass function in elliptical
  galaxies
  We investigate the origin of a bottom-heavy stellar initial mass function
(IMF) recently observed in elliptical galaxies by using chemical evolution
models with a non-universal IMF. We adopt the Kroupa IMF with the three slopes
(alpha_1, alpha_2, and alpha_3) dependent on metallicities ([Fe/H]) and
densities (rho_g) of star-forming gas clouds and thereby search for the best
IMF model that can reproduce (i) the observed steep IMF slope (alpha_2 ~ 3,
i.e., bottom-heavy) for low stellar masses (m < 1 M_sun) and (ii) the
correlation of alpha_2 with chemical properties of elliptical galaxies in a
self-consistent manner. We find that if the IMF slope alpha_2 depends both on
[Fe/H] and rho_g, then elliptical galaxies with higher [Mg/Fe] can have steeper
alpha_2 (~3) in our models. We also find that the observed positive correlation
of stellar mass-to-light ratios (M/L) with [Mg/Fe] in elliptical galaxies can
be quantitatively reproduced in our models with alpha_2 = beta[Fe/H]}+gamma log
rho_g, where beta ~ 0.5 and gamma ~ 2. We discuss whether the IMF slopes for
low-mass (alpha_2) and high-mass stars (alpha_3) need to vary independently
from each other to explain a number of IMF-related observational results
self-consistently. We also briefly discuss why alpha_2 depends differently on
[Fe/H] in dwarf and giant elliptical galaxies.
