| Summary: | We present dynamical measurements for 586 Hα-detected star-forming galaxies from the KMOS (K-band Multi-Object Spectrograph) Redshift One Spectroscopic Survey (KROSS). The sample represents typical star-forming galaxies at this redshift (z = 0.6-1.0), with a median star formation rate of ≈7 M ⊙ yr -1 and a stellar mass range of log (M * [M ⊙ ]) ≈ 9-11. We find that the rotation velocity-stellar mass relationship (the inverse of the Tully- Fisher relationship) for our rotationally dominated sources (v C /σ 0 > 1) has a consistent slope and normalization as that observed for z = 0 discs. In contrast, the specific angular momentum (j * angular momentum divided by stellar mass) is ≈0.2-0.3 dex lower on average compared to z = 0 discs. The specific angular momentum scales as j s ∝ M * 0.6±0.2 , consistent with that expected for dark matter (i.e. j DM ∝ M DM 2/3 ). We find that z≈ 0.9 star-forming galaxies have decreasing specific angular momentum with increasing Sérsic index. Visually, the sources with the highest specific angular momentum, for a given mass, have the most disc-dominated morphologies. This implies that an angular momentum-mass-morphology relationship, similar to that observed in local massive galaxies, is already in place by z ≈ 1.
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