Cluster and field elliptical galaxies at z~1.3. The marginal role of the environment and the relevance of the galaxy central regions

We compared the properties of 56 elliptical galaxies selected from three clusters at $1.2<z<1.4$ with those of field galaxies in the GOODS-S (~30), COSMOS (~180) and CANDELS (~220) fields. We studied the relationships among effective radius, surface brightness, stellar mass, stellar mass density $\Sigma_{Re}$ and central mass density $\Sigma_{1kpc}$ within 1 kpc radius. We find that cluster ellipticals do not differ from field ellipticals: they share the same structural parameters at fixed mass and the same scaling relations. On the other hand, the population of field ellipticals at $z\sim1.3$ shows a significant lack of massive ($M_*> 2\times 10^{11}$ M$_\odot$) and large (R$_e > 4-5$ kpc) ellipticals with respect to the cluster. Nonetheless, at $M*<2\times 10^{11}$ M$_\odot$, the two populations are similar. The size-mass relation of ellipticals at z~1.3 defines two different regimes, above and below a transition mass $m_t\sim 2-3\times10^{10}$ M$_\odot$: at lower masses the relation is nearly flat (R$_e\propto M_*^{-0.1\pm 0.2}$), the mean radius is constant at ~1 kpc and $\Sigma_{Re}\sim \Sigma_{1kpc}$ while, at larger masses, the relation is R$_e\propto M*^{0.64\pm0.09}$. The transition mass marks the mass at which galaxies reach the maximum $\Sigma_{Re}$. Also the $\Sigma_{1kpc}$-mass relation follows two different regimes, $\Sigma_{1kpc}\propto M*^{0.64\ >m_t}_{1.07\ <m_t}$, defining a transition mass density $\Sigma_{1kpc}\sim 2-3\times10^3$ M$_\odot$ pc$^{-2}$. The mass density $\Sigma_{Re}$ does not correlate with mass, dense/compact galaxies can be assembled over a wide mass regime, independently of the environment. The central mass density, $\Sigma_{1kpc}$, besides to be correlated with the mass, is correlated to the age of the stellar population: the higher the central stellar mass density, the higher the mass, the older the age of the stellar population. [Abridged]