We present a SINFONI integral field kinematical study of 33 galaxies at z \sim 3 from the AMAZE and LSD projects which are aimed at studying metallicity and dynamics of high-redshift galaxies .
The number of galaxies analyzed in this paper constitutes a significant improvement compared to existing data in the literature and this is the first time that a dynamical analysis is obtained for a relatively large sample of galaxies at z \sim 3 .
11 galaxies show ordered rotational motions ( \sim 30 \% of the sample ) , in these cases we estimate dynamical masses by modeling the gas kinematics with rotating disks and exponential mass distributions .
We find dynamical masses in the range 2 \times 10 ^ { 9 } M _ { \sun } -2 \times 10 ^ { 11 } M _ { \sun } with a mean value of \sim 2 \times 10 ^ { 10 } M _ { \sun } .
By comparing observed gas velocity dispersion with that expected from models , we find that most rotating objects are dynamically “ hot ” , with intrinsic velocity dispersions of the order of \sim 90 km s ^ { -1 } .
The median value of the ratio between the maximum disk rotational velocity and the intrinsic velocity dispersion for the rotating objects is 1.6 , much lower than observed in local galaxies value ( \sim 10 ) and slightly lower than the z \sim 2 value ( 2 - 4 ) .
Finally we use the maximum rotational velocity from our modeling to build a baryonic Tully-Fisher relation at z \sim 3 .
Our measurements indicate that z \sim 3 galaxies have lower stellar masses ( by a factor of ten on average ) compared to local galaxies with the same dynamical mass .
However , the large observed scatter suggests that the Tully-Fisher relation is not yet “ in place ” at these early cosmic ages , possibly due to the young age of galaxies .
A smaller dispersion of the Tuly-Fisher relation is obtained by taking into account the velocity dispersion with the use of the S _ { 0.5 } indicator , suggesting that turbulent motions might have an important dynamical role .