2015A&A...573A.110G

This paper aims at understanding whether the normalization of the stellar initial mass function (IMF) of massive galaxies varies with cosmic time and/or with mean stellar mass density Σ=M_*/(2πR_e²). We have tackled this question by taking advantage of a spectroscopic sample of 18 dense (Σ>2500M_☉/pc2) massive early-type galaxies (ETGs) that we collected at 1.2≲z≲1.6. Each galaxy in the sample was selected in order to have available: i) a high-resolution deep HST-F160W image to visually classify it as an ETG; ii) an accurate velocity dispersion estimate; iii) stellar mass derived through the fit of multiband photometry; and iv) structural parameters (i.e. effective radius R_e and Sersic index n) derived in the F160W-band. We have constrained the mass-normalization of the IMF of dense high-z ETGs by comparing the true stellar masses of the ETGs in the sample (M_true) derived through virial theorem, hence IMF independent, with those inferred through the fit of the photometry which assume a reference IMF (M_ref). Adopting the virial estimator as proxy of the true stellar mass, we have implicitly assumed that these systems have zero dark matter. However, recent dynamical analysis of massive local ETGs have shown that the dark matter fraction within R_e in dense ETGs is negligible (<5-10%) and simulations of dissipationless mergers of spheroidal galaxies have shown that this fraction decreases going back with time. Accurate dynamical models of local ETGs performed by the ATLAS^3D team have shown that the virial estimator is prone to underestimating or overestimating the total masses. We have considered this, and based on the results of ATLAS^3D we have shown that for dense ETGs the mean value of total masses derived through the virial estimator with a non-homologous virial coefficient and Sersic-R_e are perfectly in agreement with the mean value of those derived through more sophisticated dynamical models, although, of course, the estimates show higher uncertainties. Tracing the variation of the parameter Γ=M_true/M_ref with velocity dispersion σ_e, we have found that, on average, dense ETGs at <z> =1.4 follow the same IMF-σ_e trend of typical local ETGs, but with a lower mass-normalization. The observed lower normalization could be evidence of i) an evolution of the IMF with time or ii) a correlation with Σ. To discriminate between the two possibilities, we have compared the IMF-σ_e trend that we have found for high-z dense ETGs with that of local ETGs with similar mean stellar mass density and velocity dispersion and we have found that the IMF of massive dense ETGs does not depend on redshift. The similarity between the IMF-σ_e trends observed both in dense high-z and low-z ETGs over 9Gyr of evolution and their lower mass-normalization with respect to the mean value of local ETGs suggests that, independently of formation redshift, the physical conditions which characterized the formation of a dense spheroid on average lead to a mass spectrum of newly formed stars with a higher ratio of high- to low-mass stars with respect to the IMF of normal local ETGs. In the direction of our findings, recent hydrodynamical simulations show that the higher star-formation rate that should have characterized the early stage of star formation of dense ETGs is expected to inhibit the formation of low-mass stars. Hence, compact ETGs should have higher ratio of high- to low-mass stars than normal spheroids, as we observe.