Dynamical properties of AMAZE and LSD galaxies from gas kinematics and the Tully-Fisher relation at z ∼ 3

We present a SINFONI integral-field kinematical study of 33 galaxies at z similar to 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 over 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 similar to 3. Eleven galaxies show ordered rotational motions (similar to 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 x 10(9) M-circle dot-2 x 10(11) M-circle dot with a mean value of similar to 2 x 10(10) M-circle dot. By comparing observed gas velocity dispersion with what is expected from models, we find that most rotating objects are dynamically hot, with intrinsic velocity dispersions of similar to 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 (similar to 10) and slightly lower than the z similar to 2 value (2-4). Finally we use the maximum rotational velocity from our modeling to build a baryonic Tully-Fisher relation at z similar to 3. Our measurements indicate that z similar to 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 owing to the young age of galaxies. A smaller dispersion of the Tully-Fisher relation is obtained by taking the velocity dispersion into account with the use of the S-0.5 indicator, suggesting that turbulent motions might play an important dynamical role.