The Influence of Environment on the Chemical Evolution in Low-mass
  Galaxies
  The mean alpha-to-iron abundance ratio ([$\alpha$/Fe]) of galaxies is
sensitive to the chemical evolution processes at early time, and it is an
indicator of star formation timescale ($\tau_{{\rm SF}}$). Although the
physical reason remains ambiguous, there is a tight relation between
[$\alpha$/Fe] and stellar velocity dispersion ($\sigma$) among massive
early-type galaxies (ETGs). However, no work has shown convincing results as to
how this relation behaves at low masses. We assemble 15 data sets from the
literature and build a large sample that includes 192 nearby low-mass
($18<\sigma<80$~\kms) ETGs. We find that the [$\alpha$/Fe]-$\sigma$ relation
generally holds for low-mass ETGs, except in extreme environments.
Specifically, in normal galaxy cluster environments, the [$\alpha$/Fe]-$\sigma$
relation and its intrinsic scatter are, within uncertainties, similar for
low-mass and high-mass ETGs. However, in the most massive relaxed galaxy
cluster in our sample, the zero point of the relation is higher and the
intrinsic scatter is significantly larger. By contrast, in galaxy groups the
zero point of the relation offsets in the opposite direction, again with
substantial intrinsic scatter. The elevated [$\alpha$/Fe] of low-mass ETGs in
the densest environments suggests that their star formation was quenched
earlier than in high-mass ETGs. For the low-mass ETGs in the lowest density
environments, we suggest that their more extended star formation histories
suppressed their average [$\alpha$/Fe]. The large scatter in [$\alpha$/Fe] may
reflect stochasticity in the chemical evolution of low-mass galaxies.
