The metal enrichment of passive galaxies in cosmological simulations of
  galaxy formation
  Massive early-type galaxies have higher metallicities and higher ratios of
$\alpha$ elements to iron than their less massive counterparts. Reproducing
these correlations has long been a problem for hierarchical galaxy formation
theory, both in semi-analytic models and cosmological hydrodynamic simulations.
We show that a simulation in which gas cooling in massive dark haloes is
quenched by radio-mode active galactic nuclei (AGNs) feedback naturally
reproduces the observed trend between $\alpha$/Fe and the velocity dispersion
of galaxies, $\sigma$. The quenching occurs earlier for more massive galaxies.
Consequently, these galaxies complete their star formation before $\alpha$/Fe
is diluted by the contribution from type Ia supernovae. For galaxies more
massive than $\sim 10^{11}~M_\odot$ whose $\alpha$/Fe correlates positively
with stellar mass, we find an inversely correlated mass-metallicity relation.
This is a common problem in simulations in which star formation in massive
galaxies is quenched either by quasar- or radio-mode AGN feedback. The early
suppression of gas cooling in progenitors of massive galaxies prevents them
from recapturing enriched gas ejected as winds. Simultaneously reproducing the
[$\alpha$/Fe]-$\sigma$ relation and the mass-metallicity relation is, thus,
difficult in the current framework of galaxy formation.
