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Probing the magnetism of the upper solar chromosphere requires measuring andmodeling the scattering polarization produced by anisotropic radiation pumpingin UV spectral lines. Here we apply PORTA (a novel radiative transfer code) toinvestigate the hydrogen Ly$\alpha$ line in a 3D model of the solar atmosphereresulting from a state of the art MHD simulation. At full spatial resolutionthe linear polarization signals are very significant all over the solar disk,with a large fraction of the field of view showing line-center amplitudes wellabove the 1% level. Via the Hanle effect the line-center polarization signalsare sensitive to the magnetic field of the model's transition region, even whenits mean field strength is only 15 G. The breaking of the axial symmetry of theradiation field produces significant forward-scattering polarization inLy$\alpha$, without the need of an inclined magnetic field. Interestingly, theHanle effect tends to decrease such forward-scattering polarization signals inmost of the points of the field of view. When the spatial resolution isdegraded, the line-center polarization of Ly$\alpha$ drops below the 1% level,reaching values similar to those previously found in 1D semi-empirical models(i.e., up to about 0.5%). The center to limb variation of thespatially-averaged polarization signals is qualitatively similar to that foundin 1D models, with the largest line-center amplitudes at $\mu=\cos\theta\approx0.4$ ($\theta$ being the heliocentric angle). These results are important, bothfor designing the needed space-based instrumentation and for a reliableinterpretation of future observations of the Ly$\alpha$ polarization.

astrophysical journal/the astrophysical journal

Three-dimensional radiative transfer simulations of the scattering  polarization of the hydrogen Ly$\alpha$ line in a MHD model of the  chromosphere-corona transition region