Observations of the baryon to dark matter fraction in galaxies through cosmic time are a fundamental test for galaxy formation models .
Recent observational studies have suggested that some disk galaxies at z > 1 host declining rotation curves , in contrast with observations of low redshift disk galaxies where stellar or HI rotation curves flatten at large radii .
We present an observational counterexample , a galaxy named DSFG850.95 at z = 1.555 ( 4.1 Gyr after the big bang ) that hosts a flat rotation curve between radii of \sim 6–14 kpc ( 1.2–2.8 disk scale lengths ) and has a dark matter fraction of 0.44 \raisebox { 0.86 pt } { $ \scriptstyle \pm$ } 0.08 at the H-band half light radius , similar to the Milky Way .
We create position-velocity and position-dispersion diagrams using Keck/MOSFIRE spectroscopic observations of H \alpha and [ NII ] emission features , which reveal a flat rotation velocity of V _ { flat } = 285 \raisebox { 0.86 pt } { $ \scriptstyle \pm$ } 12 km s ^ { -1 } and an ionized gas velocity dispersion of \sigma _ { 0 } = 48 \raisebox { 0.86 pt } { $ \scriptstyle \pm$ } 4 km s ^ { -1 } .
This galaxy has a rotation-dominated velocity field with V _ { flat } / \sigma _ { 0 } \sim 6 .
Ground-based H-band imaging reveals a disk with Sérsic index of 1.29 \raisebox { 0.86 pt } { $ \scriptstyle \pm$ } 0.03 , an edge-on inclination angle of 87 \raisebox { 0.86 pt } { $ \scriptstyle \pm$ } 2 ^ { \circ } , and an H-band half light radius of 8.4 \raisebox { 0.86 pt } { $ \scriptstyle \pm$ } 0.1 kpc .
Our results point to DSFG850.95 being a massive , rotationally-supported disk galaxy with a high dark-matter-to-baryon fraction in the outer galaxy , similar to disk galaxies at low redshift .