We present a first combined analysis of the morphological and dynamical properties for the Intermediate MAss Galaxy Evolution Sequence (IMAGES) sample. It is a representative sample of 52 z~0.6 galaxies with Mstell from 1.5 to 15 10^10Msun and possessing 3D resolved kinematics and HST deep imaging in at least two broad band filters. We aim at evaluate robustly the evolution of rotating spirals since z~0.6, as well as to test the different schemes for classifying galaxies morphologically. We used all the information provided by multi-band images, color maps and 2 dimensional light fitting to assign to each object a morphological class. We divided our sample between spiral disks, peculiar objects, compact objects and mergers. Using our morphological classification scheme, 4/5 of identified spirals are rotating disks and more than 4/5 of identified peculiar galaxies show complex kinematics, while automatic classification methods such as Concentration-Asymmetry and GINI-M20 severely overestimate the fraction of relaxed disk galaxies. Using this methodology, we find that the fraction of rotating spirals has increased by a factor ~ 2 during the last 6 Gyrs, a much higher fraction that found previously based on morphologies alone. These rotating spiral disks are forming stars very rapidly, doubling their stellar masses over the last 6 Gyrs, while most of their stars have been formed few Gyrs earlier, which reveals the presence of a large gas supply. Because they are likely the progenitors of local spirals, we can conjecture how their properties are evolving. Their disks show some evidence for an inside-out growth and the gas supply/accretion is not made randomly as the disk need to be stable in order to match the local disk properties.
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