Fast rotating and low-turbulence discs at z ≃ 4.5: Dynamical evidence of their evolution into local early-type galaxies

Massive starburst galaxies in the early Universe are estimated to have depletion times of $\sim 100$ Myr and thus be able to convert their gas very quickly into stars, possibly leading to a rapid quenching of their star formation. For these reasons they are considered progenitors of massive early-type galaxies (ETGs). In this paper, we study two high-$z$ starbursts, AzTEC/C159 ($z\simeq 4.57$) and J1000+0234 ($z\simeq 4.54$), observed with ALMA in the ${\rm [C}\,{\rm II}{\rm ]}$ emission line. These observations reveal two massive and regularly rotating gaseous discs. A 3D modelling of these discs returns rotation velocities of about $500\, {\rm km}\, {\rm s}^{-1} $ and gas velocity dispersions as low as $\approx 20\, {\rm km}\, {\rm s}^{-1}$, at least in AzTEC/C159, leading to very high ratios between regular and random motion ($V/\sigma \lower.7ex\hbox{$\;\stackrel{\textstyle>}{\sim}\;$} 20$). The mass decompositions of the rotation curves show that both galaxies are highly baryon-dominated with gas masses of $\approx 10^{11}\,{M}_{\odot}$, which, for J1000+0234, is significantly higher than previous estimates. We show that these high-$z$ galaxies overlap with $z=0$ massive ETGs in the ETG-analogue of the Tully-Fisher relation once their gas is converted into stars. This provides a dynamical evidence of the connection between massive high-$z$ starbursts and ETGs, although the transformation mechanism from fast-rotating to nearly pressure-supported systems remains unclear.