Stellar velocity dispersion and initial mass function gradients in dissipationless galaxy mergers

The stellar initial mass function (IMF) is believed to be non-universal among early-type galaxies (ETGs). Parametrizing the IMF with the so-called IMF mismatch parameter alpha(IMF), which is a measure of the stellar mass-to-light ratio of an ensemble of stars and thus of the 'heaviness' of its IMF, one finds that for ETGs alpha(e) (i.e. alpha(IMF) integrated within the effective radius R-e) increases with se (the line-of-sight velocity dispersion sigma(los) integrated within R-e) and that, within the same ETG, alpha(IMF) tends to decrease outwards. We study the effect of dissipationless (dry) mergers on the distribution of the IMF mismatch parameter aIMF in ETGs using the results of binary major and minor merging simulations. We find that dry mergers tend to make the alpha(IMF) profiles of ETGs shallower, but do not alter significantly the shape of the distributions in the spatially resolved sigma(los)-alpha(IMF) space. Individual galaxies undergoing dry mergers tend to decrease their alpha(e), due to erosion of alpha(IMF) gradients and mixing with stellar populations with lighter IMF. Their sigma(e) can either decrease or increase, depending on the merging orbital parameters and mass ratio, but tends to decrease for cosmologically motivated merging histories. The alpha(e)-sigma(e) relation can vary with redshift as a consequence of the evolution of individual ETGs: based on a simple dry-merging model, ETGs of given sigma(e) are expected to have higher alpha(e) at higher redshift, unless the accreted satellites are so diffuse that they contribute negligibly to the inner stellar distribution of the merger remnant.