Context :

Aims : Galaxy scaling relations such as the Tully-Fisher relation ( between maximum rotation velocity V _ { max } and luminosity ) and the velocity-size relation ( between V _ { max } and disk scale length ) are powerful tools to quantify the evolution of disk galaxies with cosmic time .

Methods : We took spatially resolved slit spectra of 261 field disk galaxies at redshifts up to z \approx 1 using the FORS instruments of the ESO Very Large Telescope .
The targets were selected from the FORS Deep Field and William Herschel Deep Field .
Our spectroscopy was complemented with HST/ACS imaging in the F814W filter .
We analyzed the ionized gas kinematics by extracting rotation curves from the 2-D spectra .
Taking into account all geometrical , observational and instrumental effects , these rotation curves were used to derive the intrinsic V _ { max } .

Results : Neglecting galaxies with disturbed kinematics or insufficient spatial rotation curve extent , V _ { max } could be robustly determined for 124 galaxies covering redshifts 0.05 < z < 0.97 .
This is one of the largest kinematic samples of distant disk galaxies to date .
We compared this data set to the local B -band Tully-Fisher relation and the local velocity-size relation .
The scatter in both scaling relations is a factor of \sim 2 larger at z \approx 0.5 than at z \approx 0 .
The deviations of individual distant galaxies from the local Tully-Fisher relation are systematic in the sense that the galaxies are increasingly overluminous towards higher redshifts , corresponding to an over-luminosity \Delta M _ { B } = - ( 1.2 \pm 0.5 ) mag at z = 1 .
This luminosity evolution at given V _ { max } is probably driven by younger stellar populations of distant galaxies with respect to their local counterparts , potentially combined with modest changes in dark matter mass fractions .
The analysis of the velocity-size relation reveals that disk galaxies of a given V _ { max } have grown in size by a factor of \sim 1.5 over the past \sim 8 Gyr , likely via accretion of cold gas and/or small satellites .
Scrutinizing the combined evolution in luminosity and size , we find that the galaxies which show the strongest evolution towards smaller sizes at z \approx 1 are not those which feature the strongest evolution in luminosity , and vice versa .

Conclusions :