Global VLBI observations at 5 GHz have been performed to study the source morphology in 10 compact steep-spectrum (CSS) sources selected from the Peacock & Wall catalogue with the aim of finding asymmetric structures produced by the interaction with the ambient medium. The combination of these data and earlier 1.7-GHz observations allows the study of the spectral index distribution across the source structure and the unambiguous determination of the nature of each component. In seven sources we detected the core component with a flat or inverted spectrum. In six sources the radio emission has a two-sided morphology and comes mainly from steep-spectrum extended structures, like lobes, jets, and hotspots. Only one source, 0319+121, has a one-sided core-jet structure. In three out of the six sources with a two-sided structure the flux density arising from the lobes is asymmetric, and the brightest lobe is the one closest to the core, suggesting that the jets are expanding in an inhomogeneous ambient medium which may influence the source growth. The interaction between the jet and the environment may slow down the source expansion and enhance the luminosity due to severe radiative losses, likely producing an excess of CSS radio sources in flux density limited samples. The lobes of the other three asymmetric sources have a brighter-when-farther behaviour, in agreement with what is expected by projection and relativistic effects. Simultaneous VLA observations carried out to investigate the polarization properties of the targets detected significant polarized emission (~5.5%) only from the quasar 0319+121.
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