We report on two regularly rotating galaxies at redshift z \approx 2 , using high resolution spectra of the bright [ CII ] 158 \mu m emission line from the HIFI instrument on the Herschel Space Observatory .
Both SDSS090122.37+181432.3 ( “ S0901 ” ) and SDSS J120602.09+514229.5 ( “ the Clone ” ) are strongly lensed and show the double-horned line profile that is typical of rotating gas disks .
Using a parametric disk model to fit the emission line profiles , we find that S0901 has a rotation speed v \sin ( i ) \approx 120 \pm 7 \hbox { km s$ { } ^ { -1 } $ } and gas velocity dispersion \sigma _ { g } < 23 \hbox { km s$ { } ^ { -1 } $ } ( 1 \sigma ) .
The best fitting model for the Clone is a rotationally supported disk having v \sin ( i ) \approx 79 \pm 11 \hbox { km s$ { } ^ { -1 } $ } and \sigma _ { g } \lesssim 4 \hbox { km s$ { } ^ { -1 } $ } ( 1 \sigma ) .
However the Clone is also consistent with a family of dispersion-dominated models having \sigma _ { g } = 92 \pm 20 \hbox { km s$ { } ^ { -1 } $ } .
Our results showcase the potential of the [ CII ] line as a kinematic probe of high redshift galaxy dynamics : [ CII ] is bright ; accessible to heterodyne receivers with exquisite velocity resolution ; and traces dense star-forming interstellar gas .
Future [ CII ] line observations with ALMA would offer the further advantage of spatial resolution , allowing a clearer separation between rotation and velocity dispersion .