Depth-dependent global properties of a sunspot observed by Hinode using the Solar Optical Telescope/Spectropolarimeter

Context. For the past two decades, the three-dimensional structure of sunspots has been studied extensively. A recent improvement in the Stokes inversion technique prompts us to revisit the depth-dependent properties of sunspots.
Aims: In the present work, we aim to investigate the global depth-dependent thermal, velocity, and magnetic properties of a sunspot, as well as the interconnection between various local properties.
Methods: We analysed high-quality Stokes profiles of the disk-centred, regular, leading sunspot of NOAA AR 10933, acquired by the Solar Optical Telescope/Spectropolarimeter (SOT/SP) on board the Hinode spacecraft. To obtain depth-dependent stratification of the physical parameters, we used the recently developed, spatially coupled version of the SPINOR inversion code.
Results: First, we study the azimuthally averaged physical parameters of the sunspot. We find that the vertical temperature gradient in the lower- to mid-photosphere is at its weakest in the umbra, while it is considerably stronger in the penumbra, and stronger still in the spot's surroundings. The azimuthally averaged field becomes more horizontal with radial distance from the centre of the spot, but more vertical with height. At continuum optical depth unity, the line-of-sight velocity shows an average upflow of ~300 ms^-1 in the inner penumbra and an average downflow of ~1300 ms^-1 in the outer penumbra. The downflow continues outside the visible penumbral boundary. The sunspot shows, at most, a moderate negative twist of <5° at log (τ) = 0, which increases with height. The sunspot umbra and the spines of the penumbra show considerable similarity with regard to their physical properties, albeit with some quantitative differences (weaker, somewhat more horizontal fields in spines, commensurate with their location being further away from the sunspot's core). The temperature shows a general anti-correlation with the field strength, with the exception of the heads of penumbral filaments, where a weak positive correlation is found. The dependence of the physical parameters on each other over the full sunspot shows a qualitative similarity to that of a standard penumbral filament and its surrounding spines.
Conclusions: The large-scale variation in the physical parameters of a sunspot at various optical depths is presented. Our results suggest that the spines in the penumbra are basically the outward extension of the umbra. The spines and the penumbral filaments, together, are the basic elements that form a sunspot penumbra.