We study the origin of the wide distribution of angles between the angular momenta of the stellar and gas components, $alpha_{rm G,S}$, in early-type galaxies (ETGs). We use the GALFORM model of galaxy formation, set in the $Lambda$ cold dark matter
framework, and coupled it with a Monte-Carlo simulation to follow the angular momenta flips driven by matter accretion onto haloes and galaxies. We consider a gas disk to be misaligned with respect to the stellar body if $alpha_{rm G,S}>30$~degrees. By assuming that the only sources of misaligments in galaxies are galaxy mergers, we place a lower limit of $2-5$ per cent on the fraction of ETGs with misaligned gas/stellar components. These low fractions are inconsistent with the observed value of $approx 42pm 6$ per cent in ATLAS$^{rm 3D}$. In the more general case, in which smooth gas accretion in addition to galaxy mergers can drive misalignments, our calculation predicts that $approx 46$ per cent of ETGs have $alpha_{rm G,S}>30$~degrees. In this calculation, we find correlations between $alpha_{rm G,S}$ and stellar mass, cold gas fraction and star formation rate, such that ETGs with high masses, low cold gas fractions and low star formation rates are more likely to display aligned cold gas and stellar components. We confirm these trends observationally for the first time using ATLAS$^{rm 3D}$ data. We argue that the high fraction of misaligned gas discs observed in ETGs is mostly due to smooth gas accretion (e.g. cooling from the hot halo of galaxies) which takes place after most of the stellar mass of the galaxy is in place and comes misaligned with respect to the stellar component. Galaxies that have accreted most of their cold gas content prior to the time where most of the stellar mass was in place show aligned components.
We make use of a semi-analytical model of galaxy formation to investigate the origin of the observed correlation between [a/Fe] abundance ratios and stellar mass in elliptical galaxies. We implement a new galaxy-wide stellar initial mass function (To
p Heavy Integrated Galaxy Initial Mass Function, TH-IGIMF) in the semi-analytic model SAG and evaluate its impact on the chemical evolution of galaxies. The SFR-dependence of the slope of the TH-IGIMF is found to be key to reproducing the correct [a/Fe]-stellar mass relation. Massive galaxies reach higher [a/Fe] abundance ratios because they are characterized by more top-heavy IMFs as a result of their higher SFR. As a consequence of our analysis, the value of the minimum embedded star cluster mass and of the slope of the embedded cluster mass function, which are free parameters involved in the TH-IGIMF theory, are found to be as low as 5 solar masses and 2, respectively. A mild downsizing trend is present for galaxies generated assuming either a universal IMF or a variable TH-IGIMF. We find that, regardless of galaxy mass, older galaxies (with formation redshifts > 2) are formed in shorter time-scales (< 2 Gyr), thus achieving larger [a/Fe] values. Hence, the time-scale of galaxy formation alone cannot explain the slope of the [a/Fe]-galaxy mass relation, but is responsible for the big dispersion of [a/Fe] abundance ratios at fixed stellar mass.We further test the hyphothesis of a TH-IGIMF in elliptical galaxies by looking into mass-to-light ratios, and luminosity functions. Models with a TH-IGIMF are also favoured by these constraints. In particular, mass-to-light ratios agree with observed values for massive galaxies while being overpredicted for less massive ones; this overprediction is present regardless of the IMF considered.
