  Several studies have suggested that the observed size evolution of massive
early-type galaxies (ETGs) can be explained as a combination of dry mergers and
progenitor bias, at least since z\sim1. In this paper we carry out a new test
of the dry-merger scenario based on recent lensing measurements of the
evolution of the mass density profile of ETGs. We construct a theoretical model
for the joint evolution of the size and mass density profile slope \gamma'
driven by dry mergers occurring at rates given by cosmological simulations.
Such dry-merger model predicts a strong decrease of \gamma' with cosmic time,
inconsistent with the almost constant \gamma' inferred from observations in the
redshift range 0<z<1. We then show with a simple toy model that a modest amount
of cold gas in the mergers -- consistent with the upper limits on recent star
formation in ETGs -- is sufficient to reconcile the model with measurements of
\gamma'. By fitting for the amount of gas accreted during mergers, we find that
models with dissipation are consistent with observations of the evolution in
both size and density slope, if \sim4% of the total final stellar mass arises
from the gas accreted since z\sim1. Purely dry merger models are ruled out at >
99% CL. We thus suggest a scenario where the outer regions of massive ETGs grow
by accretion of stars and dark matter, while small amounts of dissipation and
nuclear star formation conspire to keep the mass density profile constant and
approximately isothermal.
