Fast rotating and low-turbulence discs at <i>z</i> ? 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 convert their gas very quickly into stars, possibly leading a rapid quenching star formation. For these reasons, they considered progenitors massive early-type (ETGs). In this paper, we study two high-$z$ starbursts, AzTEC/C159 ($z\simeq 4.57$) J1000+0234 4.54$), observed with ALMA [CII] 158-$\mu$m emission line. These observations reveal regularly rotating gaseous discs. A 3D modelling discs returns rotation velocities about $500$ km/s velocity dispersions as low $\approx 20$ km/s, high ratios between regular random motion ($V/\sigma {\lower.7ex\hbox{$\;\stackrel{\textstyle>}{\sim}\;$}} 20$), at least AzTEC/C159. The mass decompositions curves show that both highly baryon-dominated masses 10^{11}M_{\odot}$, which, for J1000+0234, is significantly higher than previous estimates. We overlap $z=0$ ETGs ETG analogue stellar-mass Tully-Fisher relation once converted stars. This provides dynamical evidence connection starbursts ETGs, although transformation mechanism from fast nearly pressure-supported systems remains unclear.