[en] The aim of this work is the determination of the twist, writhe, and self-magnetic helicity of penumbral filaments located in an inner sunspot penumbra. For this purpose, we inverted data taken with the spectropolarimeter on board Hinode with the SIR (Stokes Inversion based on Response function) code. For the construction of a three-dimensional geometrical model we applied a genetic algorithm minimizing the divergence of B-vector and the net magnetohydrodynamic force, consequently a force-free solution would be reached if possible. We estimated two proxies to the magnetic helicity frequently used in literature: the force-free parameter α_z and the current helicity term h_cz. We show that both proxies are only qualitative indicators of the local twist as the magnetic field in the area under study significantly departs from a force-free configuration. The local twist shows significant values only at the borders of bright penumbral filaments with opposite signs on each side. These locations are precisely correlated to large electric currents. The average twist (and writhe) of penumbral structures is very small. The spines (dark filaments in the background) show a nearly zero writhe. The writhe per unit length of the intraspines diminishes with increasing length of the tube axes. Thus, the axes of tubes related to intraspines are less wrung when the tubes are more horizontal. As the writhe of the spines is very small, we can conclude that the writhe reaches only significant values when the tube includes the border of an intraspine.

[en] We determine the entire electrical current density vector in a geometrical three-dimensional volume of the inner penumbra of a sunspot from an inversion of spectropolarimetric data obtained with Hinode/SP. Significant currents are seen to wrap around the hotter, more elevated regions with lower and more horizontal magnetic fields that harbor strong upflows and radial outflows (the intraspines). The horizontal component of the current density vector is 3-4 times larger than the vertical; nearly all previous studies only obtain the vertical component J_z , thus strongly underestimating the current density. The current density J-vector and the magnetic field B-vector form an angle of about 20⁰. The plasma β at the 0 km level is larger than 1 in the intraspines and is one order of magnitude lower in the background component of the penumbra (spines). At the 200 km level, the plasma β is below 0.3, nearly everywhere. The plasma β surface as well as the surface optical depth unity is very corrugated. At the borders of intraspines and inside, B-vector is not force-free at deeper layers and nearly force-free at the top layers. The magnetic field of the spines is close to being potential everywhere. The dissipated ohmic energy is five orders of magnitudes smaller than the solar energy flux and thus negligible for the energy balance of the penumbra.

[en] Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.

[en] We report on the discovery of mostly horizontal field channels just outside sunspot penumbrae (in the so-called 'moat' region) that are seen to sustain supersonic flows (line-of-sight component of 6 km s^-1). The spectral signature of these supersonic flows corresponds to circular polarization profiles with an additional, satellite, third lobe of the same sign as the parent sunspot' Stokes V blue lobe, for both downflows and upflows. This is consistent with an outward directed flow that we interpret as the continuation of the magnetized Evershed flow outside sunspots at supersonic speeds. In Stokes Q and U, a clear signature of a transverse field connecting the two flow streams is observed. Such an easily detectable spectral signature should allow for a clear identification of these horizontal field channels in other spectropolarimetric sunspot data. For the spot analyzed in this paper, a total of five channels with this spectral signature have been unambiguously found.

[en] Before using three-dimensional (3D) magnetohydrodynamical (MHD) simulations of the solar photosphere in the determination of elemental abundances, one has to ensure that the correct amount of magnetic flux is present in the simulations. The presence of magnetic flux modifies the thermal structure of the solar photosphere, which affects abundance determinations and the solar spectral irradiance. The amount of magnetic flux in the solar photosphere also constrains any possible heating in the outer solar atmosphere through magnetic reconnection. We compare the polarization signals in disk-center observations of the solar photosphere in quiet-Sun regions with those in Stokes spectra computed on the basis of 3D MHD simulations having average magnetic flux densities of about 20, 56, 112, and 224 G. This approach allows us to find the simulation run that best matches the observations. The observations were taken with the Hinode SpectroPolarimeter (SP), the Tenerife Infrared Polarimeter (TIP), the Polarimetric Littrow Spectrograph (POLIS), and the GREGOR Fabry–Pèrot Interferometer (GFPI), respectively. We determine characteristic quantities of full Stokes profiles in a few photospheric spectral lines in the visible (630 nm) and near-infrared (1083 and 1565 nm). We find that the appearance of abnormal granulation in intensity maps of degraded simulations can be traced back to an initially regular granulation pattern with numerous bright points in the intergranular lanes before the spatial degradation. The linear polarization signals in the simulations are almost exclusively related to canopies of strong magnetic flux concentrations and not to transient events of magnetic flux emergence. We find that the average vertical magnetic flux density in the simulation should be less than 50 G to reproduce the observed polarization signals in the quiet-Sun internetwork. A value of about 35 G gives the best match across the SP, TIP, POLIS, and GFPI observations.