Evolution of the optical Tully-Fisher relation up to

Context. The study of the evolution of the Tully-Fisher relation has been controversial in the past years. The main difficulty is in determining the required parameters for intermediate and high redshift galaxies, given the cosmological corrections and biases involved. Aims. This work aims to identify the main problems of the study of the Tully-Fisher relation at high redshift using optical emission lines, in order to draw conclusions about the possible evolution of this relation in the B, R, and I-bands. Methods. With this aim, the rotational velocities obtained from the widths of different optical lines using DEEP2 spectra are compared. This method allows reaching higher redshifts against the rotation curve one, due to spatial resolution limitations. Morphology has been determined via HST images, using and comparing different methodologies. Instrumental magnitudes are then corrected for K and extinction and the absolute magnitudes derived for the concordance cosmological model. Finally, the optical Tully-Fisher relations in B, R, and I-bands at different redshifts up to $z = 1.3$ are derived. Results. Although most studies (this one included) find evidence of evolution, the results are not conclusive enough, since the possible luminosity evolution is within the scattering of the relation, and the evolution in slope is difficult to determine because at high redshift only the brightest galaxies can be measured. Nevertheless, our study shows a clear tendency, which is the same for all bands studied, that favours a luminosity evolution where galaxies were brighter in the past for the same rotation velocity. This result also implies that the colour of the Tully-Fisher relation does not change with redshift, supporting the collapse model versus the accretion model of disc galaxy formation