Context. The study of high redshift Tully-Fisher relations (TFRs) is limited by the use of long slit spectrographs, rest frame B band and star formation selected galaxies. Aims. We try to circumvent these issues by using integral field spectroscopy (
SINFONI), by studying the rest frame K band and stellar mass TFR, and by selecting targets without a bias to strongly star forming galaxies. In this paper, we demonstrate our methods on our best case. This galaxy, F257, at z=2.03, was selecte from a sample of candidate high redshift large disk galaxies in the Hubble Deep Field South that were selected with photometric and morphological criteria. Methods. We used SINFONI at the VLT to obtain an integral field spectrum of the Halpha line and hence a velocity field and rotation curve. We also use UBVIJHK+IRAC band photometry to determine a stellar photometric mass. Results. We find that F257 is indistinguishable from local late type galaxies in many respects: it has a regular velocity field, increasing velocity disperion towards its center, its rotation curve flattens at 1-2 disk scale lengths, it has the same specific angular momentum as local disks, its properties are consistent with the local K band TFR. Although mainly rotationally supported, its gas component is dynamically heated with respect to local galaxies (V/sigma_z ~ 4) and it is offset from the local stellar mass TFR at the 2sigma level. But, this offset depends on the SED modeling parameters. In particular, for a 2-component star formation history (SFH), F257 is in agreement with the local stellar mass TFR. F257 is then a nearly (~75%) maximum disk. The dynamical properties of F257 are more like those of local galaxies than those of any other galaxy at similar redshift observed to date. However, the gas-to-stellar mass ratio is unusally large: 2.5.
