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We use state-of-the-art, three-dimensional non-local thermodynamicequilibrium (non-LTE) radiative magnetohydrodynamic simulations of the quietsolar atmosphere to carry out detailed tests of chromospheric magnetic fielddiagnostics from free-free radiation at millimeter and submillimeterwavelengths (mm/submm). The vertical component of the magnetic field wasdeduced from the mm/submm brightness spectra and the degree of circularpolarization synthesized at millimeter frequencies. We used the frequency bandsobserved by the Atacama Large Millimeter/Submillimeter Array (ALMA) as aconvenient reference. The magnetic field maps obtained describe thelongitudinal magnetic field at the effective formation heights of the relevantwavelengths in the solar chromosphere. The comparison of the deduced and modelchromospheric magnetic fields at the spatial resolution of both the model andcurrent observations demonstrates a good correlation, but has a tendency tounderestimate the model field. The systematic discrepancy of about 10 percentis probably due to averaging of the restored field over the heightscontributing to the radiation, weighted by the strength of the contribution. Onthe whole, the method of probing the longitudinal component of the magneticfield with free-free emission at mm/submm wavelengths is found to be applicableto measurements of the weak quiet-Sun magnetic fields. However, successfulexploitation of this technique requires very accurate measurements of thepolarization properties (primary beam and receiver polarization response) ofthe antennas, which will be the principal factor that determines the level towhich chromospheric magnetic fields can be measured. Consequently,high-resolution and high-precision observations of circularly polarizedradiation at millimeter wavelengths can be a powerful tool for producingchromospheric longitudinal magnetograms.

Millimeter radiation from a 3D model of the solar atmosphere II. Chromospheric magnetic field