KAOSS: turbulent, but disc-like kinematics in dust-obscured star-forming galaxies at z ∼ 1.3-2.6

We present spatially resolved kinematics of 27 ALMA-identified dust-obscured star-forming galaxies (DSFGs) at z similar to 1.3-2.6, as traced by H alpha emission using VLT/KMOS near-infrared integral field spectroscopy from the 'KMOS-ALMA Observations of Submillimetre Sources' (KAOSS) Large Programme. We derive H alpha rotation curves and velocity dispersion profiles for the DSFGs, and find that among the 27 sources with bright, spatially extended H alpha emission, 24 display evidence for disc-like kinematics. We measure a median inclination-corrected velocity at 2.2 R-d of v(rot) = 190 +/- 40 km s(-1) and intrinsic velocity dispersion of sigma(0) = 87 +/- 6 km s(-1) for these disc-like sources. The kinematics yield median circular velocities of v(circ) = 230 +/- 20 km s(-1) and dynamical masses within 2R(e) (similar to 7 kpc radius) of M-dyn = (1.1 +/- 0.2) x 10(11) M-circle dot. Compared to less actively star-forming galaxies, KAOSS DSFGs are both faster rotating with higher intrinsic velocity dispersions, but have similar v(rot)/sigma(0) ratios, median v/sigma(0) = 2.5 +/- 0.5. We suggest that the kinematics of the DSFGs are primarily rotation supported but with a non-negligible contribution from pressure support, which may be driven by star formation or mergers/interactions. We estimate the normalization of the stellar mass Tully-Fisher relation (sTFR) for the disc-like DSFGs and compare it with local studies, finding no evolution at fixed slope between z similar to 2 and z similar to 0. Finally, we show that the kinematic properties of the DSFG population are consistent with them evolving into massive early-type galaxies, the dominant z similar to 0 population at these masses.