Merger-driven evolution of the effective stellar initial mass function
  of massive early-type galaxies
  The stellar initial mass function (IMF) of early-type galaxies is the
combination of the IMF of the stellar population formed in-situ and that of
accreted stellar populations. Using as an observable the effective IMF
$\alpha_{IMF}$, defined as the ratio between the true stellar mass of a galaxy
and the stellar mass inferred assuming a Salpeter IMF, we present a theoretical
model for its evolution as a result of dry mergers. We use a simple dry merger
evolution model, based on cosmological $N$-body simulations, together with
empirically motivated prescriptions for the IMF to make predictions for how the
effective IMF of massive early-type galaxies changes from $z=2$ to $z=0$. We
find that the IMF normalization of individual galaxies becomes lighter with
time. At fixed velocity dispersion, $\alpha_{IMF}$ is predicted to be constant
with redshift. Current constraints on the evolution of the IMF are in slight
tension with this prediction, even though systematic uncertainties prevent a
conclusive statement. The correlation of $\alpha_{IMF}$ with stellar mass
becomes shallower with time, while the correlation between $\alpha_{IMF}$ and
velocity dispersion is mostly preserved by dry mergers. We also find that dry
mergers can mix the dependence of the IMF on stellar mass and velocity
dispersion, making it challenging to infer, from $z=0$ observations of global
galactic properties, what is the quantity that is originally coupled with the
IMF.
