We present spatially resolved ALMA observations of the CO J = 3 - 2 emission line in two massive galaxies at z = 2.5 on the star-forming main sequence .
Both galaxies have compact dusty star-forming cores with effective radii of R _ { \mathrm { e } } = 1.3 \pm 0.1 kpc and R _ { \mathrm { e } } = 1.2 \pm 0.1 kpc in the 870 \mu m continuum emission .
The spatial extent of star-forming molecular gas is also compact with R _ { \mathrm { e } } = 1.9 \pm 0.4 kpc and R _ { \mathrm { e } } = 2.3 \pm 0.4 kpc , but more extended than the dust emission .
Interpreting the observed position-velocity diagrams with dynamical models , we find the starburst cores to be rotation-dominated with the ratio of the maximum rotation velocity to the local velocity dispersion of v _ { \mathrm { max } } / \sigma _ { 0 } = 7.0 ^ { +2.5 } _ { -2.8 } ( v _ { \mathrm { max } } = 386 ^ { +36 } _ { -32 } km s ^ { -1 } ) and v _ { \mathrm { max } } / \sigma _ { 0 } = 4.1 ^ { +1.7 } _ { -1.5 } ( v _ { \mathrm { max } } = 391 ^ { +54 } _ { -41 } km s ^ { -1 } ) .
Given that the descendants of these massive galaxies in the local universe are likely ellipticals with v / \sigma nearly an order of magnitude lower , the rapidly rotating galaxies would lose significant net angular momentum in the intervening time .
The comparisons among dynamical , stellar , gas , and dust mass suggest that the starburst CO-to-H _ { 2 } conversion factor of \alpha _ { \mathrm { CO } } = 0.8 ~ { } M _ { \odot } ( K km s ^ { -1 } pc ^ { -2 } ) ^ { -1 } is appropriate in the spatially resolved cores .
The dense cores are likely to be formed in extreme environments similar to the central regions of local ultraluminous infrared galaxies .
Our work also demonstrates that a combination of medium-resolution CO and high-resolution dust continuum observations is a powerful tool for characterizing the dynamical state of molecular gas in distant galaxies .