We present an analysis of the evolution of the central mass-density profile of massive elliptical galaxies from the SLACS and BELLS strong gravitational lens samples over the redshift interval z ~ 0.1-0.6, based on the combination of strong-lensing aperture mass and stellar velocity-dispersion constraints. We find a significant trend towards steeper mass profiles (parameterized by the power-law density model with rho ~ r^[-gamma]) at later cosmic times, with magnitude d<gamma>/dz = -0.60 +/- 0.15. We show that the combined lens-galaxy sample is consistent with a non-evolving distribution of stellar velocity dispersions. Considering possible additional dependence of <gamma> on lens-galaxy stellar mass, effective radius, and Sersic index, we find marginal evidence for shallower mass profiles at higher masses and larger sizes, but with a significance that is sub-dominant to the redshift dependence. Using the results of published Monte Carlo simulations of spectroscopic lens surveys, we verify that our mass-profile evolution result cannot be explained by lensing selection biases as a function of redshift. Interpreted as a true evolutionary signal, our result suggests that major dry mergers involving off-axis trajectories play a significant role in the evolution of the average mass-density structure of massive early-type galaxies over the past 6 Gyr. We also consider an alternative non-evolutionary hypothesis based on variations in the strong-lensing measurement aperture with redshift, which would imply the detection of an inflection zone marking the transition between the baryon-dominated and dark-matter halo-dominated regions of the lens galaxies. Further observations of the combined SLACS+BELLS sample can constrain this picture more precisely, and enable a more detailed investigation of the multivariate dependences of galaxy mass structure across cosmic time.
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