Time series of high resolution photospheric spectra in a quiet region of the Sun

From the inversion of a time series of high resolution slit spectrograms obtained from the quiet sun, the spatial and temporal distribution of the thermodynamical quantities and the vertical flow velocity is derived as a function of optical depth ($\log\tau$) and geometrical height (z). Spatial coherence and phase shift analyses between temperature and vertical velocity depict the height variation of these physical quantities for structures of different size. An average granular cell model is presented, showing the granule-intergranular lane stratification of temperature, vertical velocity, gas pressure and density as a function of $\log\tau$ and z. Studies of a specific small and a specific large granular cell complement these results. A strong decay of the temperature fluctuations with increasing height together with a less efficient penetration of smaller cells is revealed. The $T-T$ coherence at all granular scales is broken already at $\log\tau$ = -1 or z ~ 170 km. At the layers beyond, an inversion of the temperature contrast at granular scales >1$\farcs$5 is revealed, both in $\log\tau$ and z. At deeper layers the temperature sensitivity of the H- opacity leeds to much smaller temperature fluctuations at equal $\log\tau$ than at equal z, in concordance with Stein & Nordlund (1998, ApJ, 499, 914). Vertical velocities are in phase throughout the photosphere and penetrate into the highest layers under study. Velocities at the largest granular scales (~ 4´´) are still found even at $\log\tau$ ~ -2.8 or z ~ 370 km. Again a less efficient height penetration of smaller cells concerning convective velocities is revealed, although still at $\log\tau$ ~ -2 or z ~ 280 km structures >1$\farcs$4 are detected. A similar size distribution of velocity and temperature structures with height provides observational evidence for substantial overshoot into the photosphere. At deep photospheric layers, the behaviour of the vertical velocities reflected in simulations is for the first time qualitatively reproduced by observations: intergranular velocities are larger than the granular ones and, both reach extrema, where the granular one is shifted towards higher layers.