Penumbral structure and kinematics from high-spatial-resolution observations of

High-spatial-resolution spectra of the $\ion{Ca}{ii}$ K line obtained with the Swedish Vacuum Solar Telescope (SVST) on La Palma are used to study the penumbra of a sunspot. The observed radiation temperatures in the $\ion{Ca}{ii}$ K wing are used to derive the temperature stratification of fine-structure elements in the penumbra. It is found that in general, over the observed atmospheric depth range, penumbral structures keep their relative brightness identity with respect to their local surroundings, i.e., bright (dark) structures in the lower photosphere remain bright (dark) in the upper photosphere. Hot structures have a larger temperature difference between the bottom and the top of the photosphere than cool structures. Three semi-empirical atmosphere models, a cool, hot and mean model, are presented as being representative for the temperature stratification of penumbral fine structure. The mean temperature distribution of the centre-side penumbra is found to be up to 50 K hotter in the higher photosphere as compared to the limb-side penumbra. Hot structures being more numerous in the centre-side penumbra can account for this difference. These are primarily found near the outer penumbral boundary. It is suggested that the asymmetry can be explained by a differential line-of-sight effect that is caused by isotherms in bright structures having in the higher photosphere a tilt angle of approximately 7° with the horizontal, pointing downward towards the outer boundary. Line blends in the extended $\ion{Ca}{ii}$ K wing are selected to study the Evershed effect and its height dependence. At a number of locations, the Evershed effect is found to be concentrated in channels which have a tendency to coincide with dark filaments. A weak correlation between brightness and velocity signal is found but also a number of bright structures with a significant Evershed signal. Simple numerical tests of flow channels in the penumbral atmosphere are performed to confront existing theoretical models with the observations. From these experiments it is found that the bulk of the flow must be concentrated in the lower atmospheric layers, i.e., below 200 km, and must have a velocity not higher than 6 km s-1. A channel width of 200 km is found to give the best reproduction of the observed velocities, so that the flow is either concentrated in a single channel or in a bundle of narrower channels. No direct indication is found of the Evershed channels being elevated above the continuum, and it is estimated that the flow channels reach down to at least 50 km above the continuum