First Stokes inversions with magnetohydrostatic constraints

Figure 1: Top panel: continuum intensity at a wavelength of 630 nm (Ic) normalized to the average value in the quiet Sun (Ic;qs) in a region around sunspot NOAA AR 10923 (observed by Hinode/SP satellite on November 14th, 2006). Below we show the physical parameters inferred with our newly developed Stokes inversion code on a vertical slice (XZ-plane) along a constant y cutting through the middle of the uppermost panel. From top to bottom: vertical component of the magnetic field Βz, radial component of the magnetic field Br =√B2x + B2y, temperature Τ, and logarithm of the gas pressure Ρg. The solid black line indicates the location of theWilson depression (z(τc = 1)-level) which is the region where most of the photons at the continuum wavelength of 630 nm (i.e. continuum image on the uppermost panel) are emitted.

Stokes inversion codes allow us to infer the physical properties of the solar atmosphere (temperature, magnetic field, etc.) from observations of the polarization signals in spectral lines. Until now, all inversion codes available provide those physical parameters as a function of the vertical optical depth (τc). Converting from τc to the more useful z-coordinate depends upon physical parameters such as density and pressure, that are obtained under the assumption of hydrostatic equilibrium. Pressure and density thus obtained are highly inaccurate in and around sunspots and active regions because the magnetic field breaks the assumption of hydrostatic equilibrium. Our newly developed inversion code is the first one that determines the gas pressure and density by considering the effects of the magnetic field (magnetic pressure and tension) thus providing a much more accurate conversion to z. Because of this our code can be used to determine electric currents in the solar atmosphere and thus improve our ability to detect configurations of the magnetic field (i.e. non-potential) that are likely to produce flares, coronal mass ejections, etc.
Reference: Borrero, J.M., Pastor Yabar, A. & Ruiz Cobo, B. (2021), A&A forthcoming.