The MASSIVE SURVEY XVI. The Stellar Initial Mass Function in the Center
  of MASSIVE Early-Type Galaxies
  The stellar initial mass function (IMF) is a fundamental property in the
measurement of stellar masses and galaxy star formation histories. In this work
we focus on the most massive galaxies in the nearby universe
$\log(M_{\star}/M_{\odot})>11.2$. We obtain high quality Magellan/LDSS-3 long
slit spectroscopy with a wide wavelength coverage of $0.4\mu{\rm m}-1.01\mu{\rm
m}$ for 41 early-type galaxies (ETGs) in the MASSIVE survey, and derive high
S/N spectra within an aperture of $R_{\rm e}/8$. Using detailed stellar
synthesis models, we constrain the elemental abundances and stellar IMF of each
galaxy through full spectral modeling. All the ETGs in our sample have an IMF
that is steeper than a Milky Way (Kroupa) IMF. The best-fit IMF mismatch
parameter, $\alpha_{\rm IMF}=(M/L)/(M/L)_{\rm MW}$, ranges from 1.12 to 3.05,
with an average of $\langle \alpha_{\rm IMF} \rangle=1.84$, suggesting that on
average, the IMF is more bottom-heavy than Salpeter. Comparing the estimated
stellar mass with the dynamical mass, we find that most galaxies have stellar
masses smaller than their dynamical masses within the $1\sigma$ uncertainty. We
complement our sample with lower-mass galaxies from the literature, and confirm
that $\log(\alpha_{\rm IMF})$ is positively correlated with $\log(\sigma)$,
$\log(M_{\star})$, and $\log(M_{\rm dyn})$. The IMF in the centers of more
massive ETGs is more bottom-heavy. In addition, we find that $\log(\alpha_{\rm
IMF})$ is positively correlated with both [Mg/Fe] and the estimated total
metallicity [Z/H]. We find suggestive evidence that the effective stellar
surface density $\Sigma_{\rm Kroupa}$ might be responsible for the variation of
$\alpha_{\rm IMF}$. We conclude that $\sigma$, [Mg/Fe] and [Z/H] are the
primary drivers of the global stellar IMF variation.
