The bulge-halo conspiracy in massive elliptical galaxies: implications for the stellar initial mass function and halo response to baryonic processes

Recent studies have shown that massive elliptical galaxies have total mass density profiles within an effective radius that can be approximated as rho(tot) proportional to r(-gamma)', with mean slope <> = 2.08 +/- 0.03 and scatter sigma(gamma') = 0.16 +/- 0.02. The small scatter of the slope (known as the bulge-halo conspiracy) is not generic in Lambda cold dark matter (Lambda CDM) based models and therefore contains information about the galaxy formation process. We compute the distribution of gamma(') for Lambda CDM-based models that reproduce the observed correlations between stellar mass, velocity dispersion, and effective radius of early-type galaxies in the Sloan Digital Sky Survey. The models have a range of stellar initial mass functions (IMFs) and dark halo responses to galaxy formation. The observed distribution of gamma(') is well reproduced by a model with cosmologically motivated but uncontracted dark matter haloes, and a Salpeter-type IMF. Other models are on average ruled out by the data, even though they may happen in individual cases. Models with adiabatic halo contraction (and lighter IMFs) predict too small values of gamma('). Models with halo expansion, or mass-follows-light predict too high values of gamma('). Our study shows that the non-homologous structure of massive early-type galaxies can be precisely reproduced by Lambda CDM models if the IMF is not universal and if mechanisms, such as feedback from active galactic nuclei, or dynamical friction, effectively on average counterbalance the contraction of the halo expected as a result of baryonic cooling.